Use \par instead of \details for section.
add a Contributors Section and a Reference Section.
Remove (some) verbatim section when not needed.
Those changes have been done by hand so I am not sure I manage to catch them all.
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY)
*
* COMPLEX CX(*),CY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CAXPY constant times a vector plus a vector.
+*> \verbatim
*>
-*>\endverbatim
+*> CAXPY constant times a vector plus a vector.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCOPY(N,CX,INCX,CY,INCY)
*
* COMPLEX CX(*),CY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCOPY copies a vector x to a vector y.
+*> \verbatim
*>
-*>\endverbatim
+*> CCOPY copies a vector x to a vector y.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY)
*
* COMPLEX CX(*),CY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> forms the dot product of two vectors, conjugating the first
*> vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY)
*
* COMPLEX CX(*),CY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDOTU forms the dot product of two vectors.
+*> \verbatim
*>
-*>\endverbatim
+*> CDOTU forms the dot product of two vectors.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEMM performs one of the matrix-matrix operations
*>
*>
*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGERC performs the rank 1 operation
*>
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGERU performs the rank 1 operation
*>
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n hermitian band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEMM performs one of the matrix-matrix operations
*>
*>
*> where alpha and beta are scalars, A is an hermitian matrix and B and
*> C are m by n matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*
* COMPLEX A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHER performs the hermitian rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHER2 performs the hermitian rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an n
*> by n hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHER2K performs one of the hermitian rank 2k operations
*>
*> where alpha and beta are scalars with beta real, C is an n by n
*> hermitian matrix and A and B are n by k matrices in the first case
*> and k by n matrices in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*> -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
*> Ed Anderson, Cray Research Inc.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* COMPLEX A(LDA,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHERK performs one of the hermitian rank k operations
*>
*> where alpha and beta are real scalars, C is an n by n hermitian
*> matrix and A is an n by k matrix in the first case and a k by n
*> matrix in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*> -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
*> Ed Anderson, Cray Research Inc.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*
* COMPLEX AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n hermitian matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
*
* COMPLEX AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPR performs the hermitian rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n hermitian matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> not be set, they are assumed to be zero, and on exit they
*> are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* COMPLEX AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPR2 performs the hermitian rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an
*> n by n hermitian matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> not be set, they are assumed to be zero, and on exit they
*> are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CROTG(CA,CB,C,S)
*
* REAL C
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CROTG determines a complex Givens rotation.
+*> \verbatim
*>
-*>\endverbatim
+*> CROTG determines a complex Givens rotation.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSCAL(N,CA,CX,INCX)
*
* COMPLEX CX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CSCAL scales a vector by a constant.
+*> \verbatim
*>
-*>\endverbatim
+*> CSCAL scales a vector by a constant.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSROT( N, CX, INCX, CY, INCY, C, S )
*
* COMPLEX CX( * ), CY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSROT applies a plane rotation, where the cos and sin (c and s) are real
*> and the vectors cx and cy are complex.
*> jack dongarra, linpack, 3/11/78.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> S is REAL
*> On entry, S specifies the sine, sin.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSSCAL(N,SA,CX,INCX)
*
* COMPLEX CX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CSSCAL scales a complex vector by a real constant.
+*> \verbatim
*>
-*>\endverbatim
+*> CSSCAL scales a complex vector by a real constant.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSWAP(N,CX,INCX,CY,INCY)
*
* COMPLEX CX(*),CY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CSWAP interchanges two vectors.
+*> \verbatim
*>
-*>\endverbatim
+*> CSWAP interchanges two vectors.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYMM performs one of the matrix-matrix operations
*>
*>
*> where alpha and beta are scalars, A is a symmetric matrix and B and
*> C are m by n matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYR2K performs one of the symmetric rank 2k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A and B are n by k matrices in the first case and k by n
*> matrices in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* COMPLEX A(LDA,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYRK performs one of the symmetric rank k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A is an n by k matrix in the first case and a k by n matrix
*> in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* COMPLEX A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* COMPLEX A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* COMPLEX AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* COMPLEX AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* COMPLEX A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRMM performs one of the matrix-matrix operations
*>
*> non-unit, upper or lower triangular matrix and op( A ) is one of
*>
*> op( A ) = A or op( A ) = A**T or op( A ) = A**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* COMPLEX A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* COMPLEX A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRSM solves one of the matrix equations
*>
*> op( A ) = A or op( A ) = A**T or op( A ) = A**H.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* COMPLEX A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX)
*
* DOUBLE PRECISION DX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DASUM takes the sum of the absolute values.
+*> \verbatim
*>
-*>\endverbatim
+*> DASUM takes the sum of the absolute values.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
*
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DAXPY constant times a vector plus a vector.
*> uses unrolled loops for increments equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DCABS1(Z)
*
* COMPLEX*16 Z
* ..
* ..
-* Purpose
-* =======
+*
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCABS1 computes absolute value of a double complex number
+*> \verbatim
*>
-*>\endverbatim
+*> DCABS1 computes absolute value of a double complex number
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
*
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCOPY copies a vector, x, to a vector, y.
*> uses unrolled loops for increments equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
*
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDOT forms the dot product of two vectors.
*> uses unrolled loops for increments equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEMM performs one of the matrix-matrix operations
*>
*>
*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGER performs the rank 1 operation
*>
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
*
* DOUBLE PRECISION X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DNRM2 returns the euclidean norm of a vector via the function
*> name, so that
*>
*> DNRM2 := sqrt( x'*x )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> -- This version written on 25-October-1982.
*> Modified on 14-October-1993 to inline the call to DLASSQ.
*> Sven Hammarling, Nag Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
*
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DROT applies a plane rotation.
+*> \verbatim
*>
-*>\endverbatim
+*> DROT applies a plane rotation.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DROTG(DA,DB,C,S)
*
* DOUBLE PRECISION C,DA,DB,S
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DROTG construct givens plane rotation.
+*> \verbatim
*>
-*>\endverbatim
+*> DROTG construct givens plane rotation.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM)
*
* DOUBLE PRECISION DPARAM(5),DX(*),DY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
*>
*> H=( ) ( ) ( ) ( )
*> (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0).
*> SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> DPARAM(4)=DH12
*> DPARAM(5)=DH22
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM)
*
* DOUBLE PRECISION DPARAM(5)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
*> THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T.
*> INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
*> OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] DD1
*> \verbatim
*> DPARAM(4)=DH12
*> DPARAM(5)=DH22
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSCAL(N,DA,DX,INCX)
*
* DOUBLE PRECISION DX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSCAL scales a vector by a constant.
*> uses unrolled loops for increment equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSDOT(N,SX,INCX,SY,INCY)
*
* Lawson, C. L., (JPL), Hanson, R. J., (SNLA),
* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*> Compute the inner product of two vectors with extended
*> precision accumulation and result.
*>
*> DSDOT = sum for I = 0 to N-1 of SX(LX+I*INCX) * SY(LY+I*INCY),
*> where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
*> defined in a similar way using INCY.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> DSDOT is DOUBLE PRECISION
*> DSDOT double precision dot product (zero if N.LE.0)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*> \endverbatim
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par References:
+* ================
+*>
*> \verbatim
*>
-*> REFERENCES
*>
*> C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
*> Krogh, Basic linear algebra subprograms for Fortran
*> 920310 Corrected definition of LX in DESCRIPTION. (WRB)
*> 920501 Reformatted the REFERENCES section. (WRB)
*> 070118 Reformat to LAPACK style (JL)
-*>
*> \endverbatim
*>
* =====================================================================
REAL SX(*),SY(*)
* ..
*
-* AUTHORS
-* =======
+* Authors:
+* ========
* Lawson, C. L., (JPL), Hanson, R. J., (SNLA),
* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*
* DOUBLE PRECISION AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
*
* DOUBLE PRECISION AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> AP is overwritten by the lower triangular part of the
*> updated matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* DOUBLE PRECISION AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPR2 performs the symmetric rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an
*> n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> AP is overwritten by the lower triangular part of the
*> updated matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
*
* DOUBLE PRECISION DX(*),DY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> interchanges two vectors.
*> uses unrolled loops for increments equal one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYMM performs one of the matrix-matrix operations
*>
*>
*> where alpha and beta are scalars, A is a symmetric matrix and B and
*> C are m by n matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA)
*
* DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYR2 performs the symmetric rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an n
*> by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYR2K performs one of the symmetric rank 2k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A and B are n by k matrices in the first case and k by n
*> matrices in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* DOUBLE PRECISION A(LDA,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYRK performs one of the symmetric rank k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A is an n by k matrix in the first case and a k by n matrix
*> in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* DOUBLE PRECISION AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* DOUBLE PRECISION AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRMM performs one of the matrix-matrix operations
*>
*> non-unit, upper or lower triangular matrix and op( A ) is one of
*>
*> op( A ) = A or op( A ) = A**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRSM solves one of the matrix equations
*>
*> op( A ) = A or op( A ) = A**T.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX)
*
* COMPLEX*16 ZX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DZASUM takes the sum of the absolute values.
+*> \verbatim
*>
-*>\endverbatim
+*> DZASUM takes the sum of the absolute values.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX)
*
* COMPLEX*16 X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DZNRM2 returns the euclidean norm of a vector via the function
*> name, so that
*>
*> DZNRM2 := sqrt( x**H*x )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> -- This version written on 25-October-1982.
*> Modified on 14-October-1993 to inline the call to ZLASSQ.
*> Sven Hammarling, Nag Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ICAMAX(N,CX,INCX)
*
* COMPLEX CX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ICAMAX finds the index of element having max. absolute value.
+*> \verbatim
*>
-*>\endverbatim
+*> ICAMAX finds the index of element having max. absolute value.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_blas
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION IDAMAX(N,DX,INCX)
*
* DOUBLE PRECISION DX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> IDAMAX finds the index of element having max. absolute value.
+*> \verbatim
*>
-*>\endverbatim
+*> IDAMAX finds the index of element having max. absolute value.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_blas
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ISAMAX(N,SX,INCX)
*
* REAL SX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ISAMAX finds the index of element having max. absolute value.
+*> \verbatim
*>
-*>\endverbatim
+*> ISAMAX finds the index of element having max. absolute value.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_blas
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION IZAMAX(N,ZX,INCX)
*
* COMPLEX*16 ZX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> IZAMAX finds the index of element having max. absolute value.
+*> \verbatim
*>
-*>\endverbatim
+*> IZAMAX finds the index of element having max. absolute value.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_blas
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 1/15/85.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION LSAME(CA,CB)
*
* CHARACTER CA,CB
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
*> case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] CA
*> \verbatim
*> CB is CHARACTER*1
*> CA and CB specify the single characters to be compared.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SASUM(N,SX,INCX)
*
* REAL SX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SASUM takes the sum of the absolute values.
*> uses unrolled loops for increment equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SAXPY(N,SA,SX,INCX,SY,INCY)
*
* REAL SX(*),SY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SAXPY constant times a vector plus a vector.
*> uses unrolled loops for increments equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SCABS1(Z)
*
* COMPLEX Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCABS1 computes absolute value of a complex number
+*> \verbatim
*>
-*>\endverbatim
+*> SCABS1 computes absolute value of a complex number
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SCASUM(N,CX,INCX)
*
* COMPLEX CX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCASUM takes the sum of the absolute values of a complex vector and
*> returns a single precision result.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SCNRM2(N,X,INCX)
*
* COMPLEX X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCNRM2 returns the euclidean norm of a vector via the function
*> name, so that
*>
*> SCNRM2 := sqrt( x**H*x )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> -- This version written on 25-October-1982.
*> Modified on 14-October-1993 to inline the call to CLASSQ.
*> Sven Hammarling, Nag Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCOPY(N,SX,INCX,SY,INCY)
*
* REAL SX(*),SY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCOPY copies a vector, x, to a vector, y.
*> uses unrolled loops for increments equal to 1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SDOT(N,SX,INCX,SY,INCY)
*
* REAL SX(*),SY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDOT forms the dot product of two vectors.
*> uses unrolled loops for increments equal to one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SDSDOT(N,SB,SX,INCX,SY,INCY)
*
* SDSDOT = DSDOT
* RETURN
* END
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*>\endverbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* REAL A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* REAL A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEMM performs one of the matrix-matrix operations
*>
*>
*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* REAL A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* REAL A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGER performs the rank 1 operation
*>
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SNRM2(N,X,INCX)
*
* REAL X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SNRM2 returns the euclidean norm of a vector via the function
*> name, so that
*>
*> SNRM2 := sqrt( x'*x ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> -- This version written on 25-October-1982.
*> Modified on 14-October-1993 to inline the call to SLASSQ.
*> Sven Hammarling, Nag Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SROT(N,SX,INCX,SY,INCY,C,S)
*
* REAL SX(*),SY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> applies a plane rotation.
+*> \verbatim
*>
-*>\endverbatim
+*> applies a plane rotation.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SROTG(SA,SB,C,S)
*
* REAL C,S,SA,SB
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SROTG construct givens plane rotation.
+*> \verbatim
*>
-*>\endverbatim
+*> SROTG construct givens plane rotation.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SROTM(N,SX,INCX,SY,INCY,SPARAM)
*
* REAL SPARAM(5),SX(*),SY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
*>
*> (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0).
*> SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> SPARAM(4)=SH12
*> SPARAM(5)=SH22
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM)
*
* REAL SPARAM(5)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
*> THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T.
*> INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
*> OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] SD1
*> \verbatim
*> SPARAM(4)=SH12
*> SPARAM(5)=SH22
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* REAL A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSCAL(N,SA,SX,INCX)
*
* REAL SX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> scales a vector by a constant.
*> uses unrolled loops for increment equal to 1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*
* REAL AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP)
*
* REAL AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> AP is overwritten by the lower triangular part of the
*> updated matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* REAL AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPR2 performs the symmetric rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an
*> n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> AP is overwritten by the lower triangular part of the
*> updated matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSWAP(N,SX,INCX,SY,INCY)
*
* REAL SX(*),SY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> interchanges two vectors.
*> uses unrolled loops for increments equal to 1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* REAL A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYMM performs one of the matrix-matrix operations
*>
*>
*> where alpha and beta are scalars, A is a symmetric matrix and B and
*> C are m by n matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* REAL A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYR(UPLO,N,ALPHA,X,INCX,A,LDA)
*
* REAL A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* REAL A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYR2 performs the symmetric rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an n
*> by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* REAL A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYR2K performs one of the symmetric rank 2k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A and B are n by k matrices in the first case and k by n
*> matrices in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* REAL A(LDA,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYRK performs one of the symmetric rank k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A is an n by k matrix in the first case and a k by n matrix
*> in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* REAL A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* REAL A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* REAL AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* REAL AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* REAL A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRMM performs one of the matrix-matrix operations
*>
*> non-unit, upper or lower triangular matrix and op( A ) is one of
*>
*> op( A ) = A or op( A ) = A**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* REAL A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* REAL A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRSM solves one of the matrix equations
*>
*> op( A ) = A or op( A ) = A**T.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* REAL A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XERBLA( SRNAME, INFO )
*
* INTEGER INFO
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> XERBLA is an error handler for the LAPACK routines.
*> It is called by an LAPACK routine if an input parameter has an
*>
*> Installers may consider modifying the STOP statement in order to
*> call system-specific exception-handling facilities.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SRNAME
*> \verbatim
*> The position of the invalid parameter in the parameter list
*> of the calling routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XERBLA_ARRAY(SRNAME_ARRAY, SRNAME_LEN, INFO)
*
* CHARACTER(1) SRNAME_ARRAY(SRNAME_LEN)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK
*> and BLAS error handler. Rather than taking a Fortran string argument
*>
*> Providing XERBLA_ARRAY is not necessary for intercepting LAPACK
*> errors. XERBLA_ARRAY calls XERBLA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SRNAME_ARRAY
*> \verbatim
*> The position of the invalid parameter in the parameter list
*> of the calling routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY)
*
* COMPLEX*16 ZX(*),ZY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZAXPY constant times a vector plus a vector.
+*> \verbatim
*>
-*>\endverbatim
+*> ZAXPY constant times a vector plus a vector.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY)
*
* COMPLEX*16 ZX(*),ZY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCOPY copies a vector, x, to a vector, y.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCOPY copies a vector, x, to a vector, y.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, linpack, 4/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY)
*
* COMPLEX*16 ZX(*),ZY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDOTC forms the dot product of a vector.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDOTC forms the dot product of a vector.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX*16 FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY)
*
* COMPLEX*16 ZX(*),ZY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDOTU forms the dot product of two vectors.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDOTU forms the dot product of two vectors.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDROT( N, CX, INCX, CY, INCY, C, S )
*
* COMPLEX*16 CX( * ), CY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Applies a plane rotation, where the cos and sin (c and s) are real
*> and the vectors cx and cy are complex.
*> jack dongarra, linpack, 3/11/78.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> S is DOUBLE PRECISION
*> On entry, S specifies the sine, sin.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDSCAL(N,DA,ZX,INCX)
*
* COMPLEX*16 ZX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDSCAL scales a vector by a constant.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDSCAL scales a vector by a constant.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEMM performs one of the matrix-matrix operations
*>
*>
*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEMV performs one of the matrix-vector operations
*>
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGERC performs the rank 1 operation
*>
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGERU performs the rank 1 operation
*>
*>
*> where alpha is a scalar, x is an m element vector, y is an n element
*> vector and A is an m by n matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n hermitian band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEMM performs one of the matrix-matrix operations
*>
*>
*> where alpha and beta are scalars, A is an hermitian matrix and B and
*> C are m by n matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*
* COMPLEX*16 A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHER performs the hermitian rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* COMPLEX*16 A(LDA,*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHER2 performs the hermitian rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an n
*> by n hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHER2K performs one of the hermitian rank 2k operations
*>
*> where alpha and beta are scalars with beta real, C is an n by n
*> hermitian matrix and A and B are n by k matrices in the first case
*> and k by n matrices in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
*> Ed Anderson, Cray Research Inc.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHERK performs one of the hermitian rank k operations
*>
*> where alpha and beta are real scalars, C is an n by n hermitian
*> matrix and A is an n by k matrix in the first case and a k by n
*> matrix in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
*> Ed Anderson, Cray Research Inc.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*
* COMPLEX*16 AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n hermitian matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
*
* COMPLEX*16 AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPR performs the hermitian rank 1 operation
*>
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n hermitian matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> not be set, they are assumed to be zero, and on exit they
*> are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* COMPLEX*16 AP(*),X(*),Y(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPR2 performs the hermitian rank 2 operation
*>
*>
*> where alpha is a scalar, x and y are n element vectors and A is an
*> n by n hermitian matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> not be set, they are assumed to be zero, and on exit they
*> are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZROTG(CA,CB,C,S)
*
* DOUBLE PRECISION C
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZROTG determines a double complex Givens rotation.
+*> \verbatim
*>
-*>\endverbatim
+*> ZROTG determines a double complex Givens rotation.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSCAL(N,ZA,ZX,INCX)
*
* COMPLEX*16 ZX(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZSCAL scales a vector by a constant.
+*> \verbatim
*>
-*>\endverbatim
+*> ZSCAL scales a vector by a constant.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY)
*
* COMPLEX*16 ZX(*),ZY(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZSWAP interchanges two vectors.
+*> \verbatim
*>
-*>\endverbatim
+*> ZSWAP interchanges two vectors.
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level1
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYMM performs one of the matrix-matrix operations
*>
*>
*> where alpha and beta are scalars, A is a symmetric matrix and B and
*> C are m by n matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYR2K performs one of the symmetric rank 2k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A and B are n by k matrices in the first case and k by n
*> matrices in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* COMPLEX*16 A(LDA,*),C(LDC,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYRK performs one of the symmetric rank k operations
*>
*> where alpha and beta are scalars, C is an n by n symmetric matrix
*> and A is an n by k matrix in the first case and a k by n matrix
*> in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> in the calling (sub) program. LDC must be at least
*> max( 1, n ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* COMPLEX*16 A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* COMPLEX*16 A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* COMPLEX*16 AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* COMPLEX*16 AP(*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* COMPLEX*16 A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRMM performs one of the matrix-matrix operations
*>
*> non-unit, upper or lower triangular matrix and op( A ) is one of
*>
*> op( A ) = A or op( A ) = A**T or op( A ) = A**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* COMPLEX*16 A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRMV performs one of the matrix-vector operations
*>
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* COMPLEX*16 A(LDA,*),B(LDB,*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRSM solves one of the matrix equations
*>
*> op( A ) = A or op( A ) = A**T or op( A ) = A**H.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level3
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 3 Blas routine.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* COMPLEX*16 A(LDA,*),X(*)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRSV solves one of the systems of equations
*>
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_level2
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM CBLAT1
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the COMPLEX Level 1 BLAS.
*> Based upon the original BLAS test routine together with:
*>
*> F06GAF Example Program Text
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_testing
*
-* =====================================================================
- PROGRAM CBLAT1
+* ===================================================================== PROGRAM CBLAT1
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM CBLAT2
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the COMPLEX Level 2 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_testing
*
-* =====================================================================
- PROGRAM CBLAT2
+* ===================================================================== PROGRAM CBLAT2
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM CBLAT3
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the COMPLEX Level 3 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_blas_testing
*
-* =====================================================================
- PROGRAM CBLAT3
+* ===================================================================== PROGRAM CBLAT3
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DBLAT1
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the DOUBLE PRECISION Level 1 BLAS.
*>
*> Based upon the original BLAS test routine together with:
*> F06EAF Example Program Text
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_testing
*
-* =====================================================================
- PROGRAM DBLAT1
+* ===================================================================== PROGRAM DBLAT1
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DBLAT2
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the DOUBLE PRECISION Level 2 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_testing
*
-* =====================================================================
- PROGRAM DBLAT2
+* ===================================================================== PROGRAM DBLAT2
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DBLAT3
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the DOUBLE PRECISION Level 3 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_blas_testing
*
-* =====================================================================
- PROGRAM DBLAT3
+* ===================================================================== PROGRAM DBLAT3
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM SBLAT1
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the REAL Level 1 BLAS.
*>
*> Based upon the original BLAS test routine together with:
*> F06EAF Example Program Text
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_testing
*
-* =====================================================================
- PROGRAM SBLAT1
+* ===================================================================== PROGRAM SBLAT1
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM SBLAT2
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the REAL Level 2 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_testing
*
-* =====================================================================
- PROGRAM SBLAT2
+* ===================================================================== PROGRAM SBLAT2
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM SBLAT3
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the REAL Level 3 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_blas_testing
*
-* =====================================================================
- PROGRAM SBLAT3
+* ===================================================================== PROGRAM SBLAT3
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZBLAT1
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the COMPLEX*16 Level 1 BLAS.
*>
*> Based upon the original BLAS test routine together with:
*> F06GAF Example Program Text
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_testing
*
-* =====================================================================
- PROGRAM ZBLAT1
+* ===================================================================== PROGRAM ZBLAT1
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZBLAT2
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the COMPLEX*16 Level 2 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_testing
*
-* =====================================================================
- PROGRAM ZBLAT2
+* ===================================================================== PROGRAM ZBLAT2
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZBLAT3
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Test program for the COMPLEX*16 Level 3 Blas.
*>
*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
*> can be run multiple times without deleting generated
*> output files (susan)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_blas_testing
*
-* =====================================================================
- PROGRAM ZBLAT3
+* ===================================================================== PROGRAM ZBLAT3
*
* -- Reference BLAS test routine (version 3.4.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM LAPACK_VERSION
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-* =====================================================================
- PROGRAM LAPACK_VERSION
+* ===================================================================== PROGRAM LAPACK_VERSION
*
* -- LAPACK auxiliary routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DLAMCH determines double precision machine parameters.
+*> \verbatim
*>
-*>\endverbatim
+*> DLAMCH determines double precision machine parameters.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] CMACH
*> \verbatim
*> rmax = overflow threshold - (base**emax)*(1-eps)
*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
END
************************************************************************
*> \brief \b DLAMC3
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> DLAMC3 is intended to force A and B to be stored prior to doing
*> the addition of A and B , for use in situations where optimizers
*> might hold one of these in a register.
-*>
-*>\endverbatim
+*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DLAMCHF77 determines double precision machine parameters.
+*> \verbatim
*>
-*>\endverbatim
+*> DLAMCHF77 determines double precision machine parameters.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] CMACH
*> \verbatim
*> rmax = overflow threshold - (base**emax)*(1-eps)
*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
************************************************************************
*
*> \brief \b DLAMC1
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> DLAMC1 determines the machine parameters given by BETA, T, RND, and
*> IEEE1.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \param[out] BETA
*> \verbatim
*> \verbatim
*> Specifies whether rounding appears to be done in the IEEE
*> 'round to nearest' style.
-*>
-*>\endverbatim
+*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
*>
-*>\details \b Further \b Details
+*> \details \b Further \b Details
*> \verbatim
*>
*> The routine is based on the routine ENVRON by Malcolm and
************************************************************************
*
*> \brief \b DLAMC2
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> DLAMC2 determines the machine parameters specified in its argument
*> list.
-*>
-*>\endverbatim
+*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
*> value of BETA.
*> \endverbatim
*>
-*>\details \b Further \b Details
+*> \details \b Further \b Details
*> \verbatim
*>
*> The computation of EPS is based on a routine PARANOIA by
*> W. Kahan of the University of California at Berkeley.
-*>
*> \endverbatim
SUBROUTINE DLAMC2( BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX )
*
************************************************************************
*
*> \brief \b DLAMC3
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> DLAMC3 is intended to force A and B to be stored prior to doing
*> the addition of A and B , for use in situations where optimizers
*> might hold one of these in a register.
-*>\endverbatim
+*> \endverbatim
*>
*> \param[in] A
*>
************************************************************************
*
*> \brief \b DLAMC4
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> DLAMC4 is a service routine for DLAMC2.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \param[out] EMIN
*> \verbatim
************************************************************************
*
*> \brief \b DLAMC5
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> DLAMC5 attempts to compute RMAX, the largest machine floating-point
*> number, without overflow. It assumes that EMAX + abs(EMIN) sum
*> approximately to a power of 2. It will fail on machines where this
*> assumption does not hold, for example, the Cyber 205 (EMIN = -28625,
*> EMAX = 28718). It will also fail if the value supplied for EMIN is
*> too large (i.e. too close to zero), probably with overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DLAMCHTST
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-* =====================================================================
- PROGRAM DLAMCHTST
+* ===================================================================== PROGRAM DLAMCHTST
*
* -- LAPACK test routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSECND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSECND returns the user time for a process in seconds.
*> This version gets the time from the EXTERNAL system function ETIME.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSECND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSECND returns the user time for a process in seconds.
*> This version gets the time from the system function ETIME_.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSECND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSECND returns the user time for a process in seconds.
*> This version gets the time from the INTERNAL function CPU_TIME.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSECND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSECND returns the user time for a process in seconds.
*> This version gets the time from the INTERNAL function ETIME.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSECND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSECND returns nothing instead of returning the user time for a process in seconds.
*> If you are using that routine, it means that neither EXTERNAL ETIME,
*> EXTERNAL ETIME_, INTERNAL ETIME, INTERNAL CPU_TIME is available on
*> your machine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DSECNDTST
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-* =====================================================================
- PROGRAM DSECNDTST
+* ===================================================================== PROGRAM DSECNDTST
*
* -- LAPACK test routine (version 3.3.1) --
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ILAVER( VERS_MAJOR, VERS_MINOR, VERS_PATCH )
*
* INTEGER VERS_MAJOR, VERS_MINOR, VERS_PATCH
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> This subroutine returns the LAPACK version.
+*> \verbatim
*>
-*>\endverbatim
+*> This subroutine returns the LAPACK version.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] VERS_MAJOR
*> return the lapack major version
*> \param[out] VERS_PATCH
*> return the lapack patch version from the minor version
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* =====================================================================
*
INTEGER VERS_MAJOR, VERS_MINOR, VERS_PATCH
-* =====================================================================
- VERS_MAJOR = 3
+* ===================================================================== VERS_MAJOR = 3
VERS_MINOR = 3
VERS_PATCH = 1
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION LSAME( CA, CB )
*
* CHARACTER CA, CB
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> LSAME returns .TRUE. if CA is the same letter as CB regardless of
*> case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] CA
*> \verbatim
*> CA and CB specify the single characters to be compared.
*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM LSAMETST
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-* =====================================================================
- PROGRAM LSAMETST
+* ===================================================================== PROGRAM LSAMETST
*
* -- LAPACK test routine (version 3.2) --
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SECOND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SECOND returns the user time for a process in seconds.
*> This version gets the time from the EXTERNAL system function ETIME.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SECOND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SECOND returns the user time for a process in seconds.
*> This version gets the time from the system function ETIME_.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SECOND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SECOND returns the user time for a process in seconds.
*> This version gets the time from the INTERNAL function CPU_TIME.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SECOND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SECOND returns the user time for a process in seconds.
*> This version gets the time from the INTERNAL function ETIME.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SECOND( )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SECOND returns nothing instead of returning the user time for a process in seconds.
*> If you are using that routine, it means that neither EXTERNAL ETIME,
*> EXTERNAL ETIME_, INTERNAL ETIME, INTERNAL CPU_TIME is available on
*> your machine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* http://www.netlib.org/lapack/explore-html/
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-* =====================================================================
- PROGRAM SECONDTST
+* ===================================================================== PROGRAM SECONDTST
*
* -- LAPACK test routine (version 3.3.1) --
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLAMCH( CMACH )
*
* CHARACTER CMACH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SLAMCH determines single precision machine parameters.
+*> \verbatim
*>
-*>\endverbatim
+*> SLAMCH determines single precision machine parameters.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] CMACH
*> \verbatim
*> emax = largest exponent before overflow
*> rmax = overflow threshold - (base**emax)*(1-eps)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
END
************************************************************************
*> \brief \b SLAMC3
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> SLAMC3 is intended to force A and B to be stored prior to doing
*> the addition of A and B , for use in situations where optimizers
*> might hold one of these in a register.
-*>
-*>\endverbatim
+*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLAMCH( CMACH )
*
* CHARACTER CMACH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SLAMCH determines single precision machine parameters.
+*> \verbatim
*>
-*>\endverbatim
+*> SLAMCH determines single precision machine parameters.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] CMACH
*> \verbatim
*> emax = largest exponent before overflow
*> rmax = overflow threshold - (base**emax)*(1-eps)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
************************************************************************
*
*> \brief \b SLAMC1
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> SLAMC1 determines the machine parameters given by BETA, T, RND, and
*> IEEE1.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \param[out] BETA
*> \verbatim
*> \verbatim
*> Specifies whether rounding appears to be done in the IEEE
*> 'round to nearest' style.
-*>
-*>\endverbatim
+*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
*>
-*>\details \b Further \b Details
+*> \details \b Further \b Details
*> \verbatim
*>
*> The routine is based on the routine ENVRON by Malcolm and
************************************************************************
*
*> \brief \b SLAMC2
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> SLAMC2 determines the machine parameters specified in its argument
*> list.
-*>
-*>\endverbatim
+*> \endverbatim
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> \ingroup auxOTHERauxiliary
*> value of BETA.
*> \endverbatim
*>
-*>\details \b Further \b Details
+*> \details \b Further \b Details
*> \verbatim
*>
*> The computation of EPS is based on a routine PARANOIA by
*> W. Kahan of the University of California at Berkeley.
-*>
*> \endverbatim
SUBROUTINE SLAMC2( BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX )
*
************************************************************************
*
*> \brief \b SLAMC3
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> SLAMC3 is intended to force A and B to be stored prior to doing
*> the addition of A and B , for use in situations where optimizers
*> might hold one of these in a register.
-*>\endverbatim
+*> \endverbatim
*>
*> \param[in] A
*>
************************************************************************
*
*> \brief \b SLAMC4
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> SLAMC4 is a service routine for SLAMC2.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \param[out] EMIN
*> \verbatim
************************************************************************
*
*> \brief \b SLAMC5
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> SLAMC5 attempts to compute RMAX, the largest machine floating-point
*> number, without overflow. It assumes that EMAX + abs(EMIN) sum
*> approximately to a power of 2. It will fail on machines where this
*> assumption does not hold, for example, the Cyber 205 (EMIN = -28625,
*> EMAX = 28718). It will also fail if the value supplied for EMIN is
*> too large (i.e. too close to zero), probably with overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
* http://www.netlib.org/lapack/explore-html/
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-* =====================================================================
- PROGRAM SLAMCHTST
+* ===================================================================== PROGRAM SLAMCHTST
*
* -- LAPACK test routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
-
PROGRAM TSTIEE
*
* -- LAPACK test routine (version 3.2) --
* This routine will not function correctly if it is converted to all
* lower case. Converting it to all upper case is allowed.
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
* ISPEC (input) INTEGER
* Specifies the parameter to be returned as the value of
* IEEECK is called from the ILAENV to verify that Inifinity and
* possibly NaN arithmetic is safe (i.e. will not trap).
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
* ISPEC (input) INTEGER
* Specifies whether to test just for inifinity arithmetic
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOTRF ( UPLO, N, A, LDA, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] UPLO
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETRF( M, N, A, LDA, IPIV, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETRF( M, N, A, LDA, IPIV, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
*
C> \ingroup variantsGEcomputational
*
-*
* Further Details
* ===============
C>\details \b Further \b Details
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
*
C> \ingroup variantsGEcomputational
*
-*
* Further Details
* ===============
C>\details \b Further \b Details
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SCEIL( A )
*
C>\verbatim
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
*
C> \ingroup variantsGEcomputational
*
-*
* Further Details
* ===============
C>\details \b Further \b Details
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
C>
C>\endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
C> \param[in] M
C> \verbatim
C> \endverbatim
C>
*
-* Authors
-* =======
+* Authors:
+* ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
*
C> \ingroup variantsGEcomputational
*
-*
* Further Details
* ===============
C>\details \b Further \b Details
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
* THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T,
* $ V2T( LDV2T, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CBBCSD computes the CS decomposition of a unitary matrix in
*> bidiagonal-block form,
*> The unitary matrices U1, U2, V1T, and V2T are input/output.
*> The input matrices are pre- or post-multiplied by the appropriate
*> singular vector matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> > 0: if CBBCSD did not converge, INFO specifies the number
*> of nonzero entries in PHI, and B11D, B11E, etc.,
*> contain the partially reduced matrix.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Reference
-*> =========
-*>
-*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
-*> Algorithms, 50(1):33-65, 2009.
-*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL REAL, default = MAX(10,MIN(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they
*> are within TOLMUL*EPS of either bound.
*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*> Algorithms, 50(1):33-65, 2009.
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
* LDU, C, LDC, RWORK, INFO )
* COMPLEX C( LDC, * ), U( LDU, * ), VT( LDVT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CBDSQR computes the singular values and, optionally, the right and/or
*> left singular vectors from the singular value decomposition (SVD) of
*> B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
*> Department, University of California at Berkeley, July 1992
*> for a detailed description of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> elements of a bidiagonal matrix which is orthogonally
*> similar to the input matrix B; if INFO = i, i
*> elements of E have not converged to zero.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL REAL, default = max(10,min(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> If it is positive, TOLMUL*EPS is the desired relative
*> (and so fails to converge) if the number of passes
*> through the inner loop exceeds MAXITR*N**2.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
* LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO )
* $ Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBBRD reduces a complex general m-by-n band matrix A to real upper
*> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
*>
*> The routine computes B, and optionally forms Q or P**H, or computes
*> Q**H*C for a given matrix C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
* WORK, RWORK, INFO )
* COMPLEX AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBCON estimates the reciprocal of the condition number of a complex
*> general band matrix A, in either the 1-norm or the infinity-norm,
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBEQU computes row and column scalings intended to equilibrate an
*> M-by-N band matrix A and reduce its condition number. R returns the
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is banded, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBRFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
* COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBSV computes the solution to a complex system of linear equations
*> A * X = B, where A is a band matrix of order N with KL subdiagonals
*> and unit lower triangular matrices with KL subdiagonals, and U is
*> upper triangular with KL+KU superdiagonals. The factored form of A
*> is then used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGBsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBSVX uses the LU factorization to compute the solution to a complex
*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed by this subroutine:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBSVXX uses the LU factorization to compute the solution to a
*> complex system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what CGBSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBTF2 computes an LU factorization of a complex m-by-n band matrix
*> A using partial pivoting with row interchanges.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> + need not be set on entry, but are required by the routine to store
*> elements of U, because of fill-in resulting from the row
*> interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBTRF computes an LU factorization of a complex m-by-n band matrix A
*> using partial pivoting with row interchanges.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
* INFO )
* COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBTRS solves a system of linear equations
*> A * X = B, A**T * X = B, or A**H * X = B
*> with a general band matrix A using the LU factorization computed
*> by CGBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
* INFO )
* COMPLEX V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEBAK forms the right or left eigenvectors of a complex general
*> matrix by backward transformation on the computed eigenvectors of the
*> balanced matrix output by CGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEBAL balances a general complex matrix A. This involves, first,
*> permuting A by a similarity transformation to isolate eigenvalues
*>
*> Balancing may reduce the 1-norm of the matrix, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The permutations consist of row and column interchanges which put
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEBD2 reduces a complex general m by n matrix A to upper or lower
*> real bidiagonal form B by a unitary transformation: Q**H * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \ingroup complexGEcomputational
* @precisions normal c -> s d z
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
* INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEBRD reduces a general complex M-by-N matrix A to upper or lower
*> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
* INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGECON estimates the reciprocal of the condition number of a general
*> complex matrix A, in either the 1-norm or the infinity-norm, using
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEEQU computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
* LDVS, WORK, LWORK, RWORK, BWORK, INFO )
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEES computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues, the Schur form T, and, optionally, the matrix of Schur
*> invariant subspace corresponding to the selected eigenvalues.
*>
*> A complex matrix is in Schur form if it is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> SELECT = .TRUE.. This could also be caused by
*> underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
* VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEESX computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues, the Schur form T, and, optionally, the matrix of Schur
*> these quantities are called s and sep respectively).
*>
*> A complex matrix is in Schur form if it is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> the Schur form no longer satisfy SELECT=.TRUE. This
*> could also be caused by underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
* WORK, LWORK, RWORK, INFO )
* $ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEEV computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*>
*> The computed eigenvectors are normalized to have Euclidean norm
*> equal to 1 and largest component real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> elements and i+1:N of W contain eigenvalues which have
*> converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
* LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
* $ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*> (in exact arithmetic) but diagonal scaling will. For further
*> explanation of balancing, see section 4.10.2 of the LAPACK
*> Users' Guide.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> have been computed; elements 1:ILO-1 and i+1:N of W
*> contain eigenvalues which have converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
* VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine CGGES.
*>
*> CGEGV should be used instead. See CGEGV for a description of the
*> eigenvalues of the generalized nonsymmetric eigenvalue problem
*> (GNEP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> =N+8: error return from CGGBAK (computing VSR)
*> =N+9: error return from CLASCL (various places)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
* VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine CGGEV.
*>
*> are left eigenvectors of (A,B).
*>
*> Note: this routine performs "full balancing" on A and B
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> =N+9: error return from CGGBAK (computing VR)
*> =N+10: error return from CLASCL (various calls)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing
*> are computed, then only the diagonal blocks will be correct.
*>
*> [*] In other words, upper triangular form.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEHD2 reduces a complex general matrix A to upper Hessenberg form H
*> by a unitary similarity transformation: Q**H * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEHRD reduces a complex general matrix A to upper Hessenberg form H by
*> an unitary similarity transformation: Q**H * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> This file is a slight modification of LAPACK-3.0's DGEHRD
*> subroutine incorporating improvements proposed by Quintana-Orti and
*> Van de Geijn (2006). (See DLAHR2.)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGELQ2 computes an LQ factorization of a complex m by n matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
*> A(i,i+1:n), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGELQF computes an LQ factorization of a complex M-by-N matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
*> A(i,i+1:n), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
* INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGELS solves overdetermined or underdetermined complex linear systems
*> involving an M-by-N matrix A, or its conjugate-transpose, using a QR
*> handled in a single call; they are stored as the columns of the
*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
*> matrix X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> full rank; the least squares solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, RWORK, IWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGELSD computes the minimum-norm solution to a real linear least
*> squares problem:
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE CGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
$ WORK, LWORK, RWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, RWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGELSS computes the minimum norm solution to a complex linear
*> least squares problem:
*> The effective rank of A is determined by treating as zero those
*> singular values which are less than RCOND times the largest singular
*> value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, RWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine CGELSY.
*>
*> X = P * Z**H [ inv(T11)*Q1**H*B ]
*> [ 0 ]
*> where Q1 consists of the first RANK columns of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, LWORK, RWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGELSY computes the minimum-norm solution to a complex linear least
*> squares problem:
*> the call to the subroutine xGEQP3. This subroutine is a Blas-3
*> version of the QR factorization with column pivoting.
*> o Matrix B (the right hand side) is updated with Blas-3.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*>
-*> \endverbatim
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n
+*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
+*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
*>
* =====================================================================
SUBROUTINE CGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
* C, LDC, WORK, INFO )
* COMPLEX V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEMQRT overwrites the general complex M-by-N matrix C with
*>
*> generated using the compact WY representation as returned by CGEQRT.
*>
*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQL2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQL2 computes a QL factorization of a complex m by n matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQLF computes a QL factorization of a complex M-by-N matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
* INFO )
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQP3 computes a QR factorization with column pivoting of a
*> matrix A: A*P = Q*R using Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real/complex scalar, and v is a real/complex vector
*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
*> A(i+1:m,i), and tau in TAU(i).
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
$ INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine CGEQP3.
*>
*> CGEQPF computes a QR factorization with column pivoting of a
*> complex M-by-N matrix A: A*P = Q*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> University of Zagreb, Croatia.
*> -- April 2011 --
*> For more details see LAPACK Working Note 176.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQR2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQR2 computes a QR factorization of a complex m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQR2P computes a QR factorization of a complex m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQRF computes a QR factorization of a complex M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQRFP computes a QR factorization of a complex M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
*
* COMPLEX A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> below the diagonal. For example, if M=5 and N=3, the matrix V is
*>
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = (T1 T2 ... TB).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQRT2( M, N, A, LDA, T, LDT, INFO )
*
* COMPLEX A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> H = I - V * T * V**H
*>
*> where V**H is the conjugate transpose of V.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE CGEQRT3( M, N, A, LDA, T, LDT, INFO )
*
* COMPLEX A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A,
*> using the compact WY representation of Q.
*>
*> Based on the algorithm of Elmroth and Gustavson,
*> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> where V**H is the conjugate transpose of V.
*>
*> For details of the algorithm, see Elmroth and Gustavson (cited above).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGERFS improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates for
*> the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGERFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGERQ2 computes an RQ factorization of a complex m by n matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
*> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGERQF computes an RQ factorization of a complex M-by-N matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
*> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
* COMPLEX A( LDA, * ), RHS( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGESC2 solves a system of linear equations
*>
*> with a general N-by-N matrix A using the LU factorization with
*> complete pivoting computed by CGETC2.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On exit, SCALE contains the scale factor. SCALE is chosen
*> 0 <= SCALE <= 1 to prevent owerflow in the solution.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
* WORK, LWORK, RWORK, IWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGESDD computes the singular value decomposition (SVD) of a complex
*> M-by-N matrix A, optionally computing the left and/or right singular
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: The updating process of SBDSDC did not converge.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
$ WORK, LWORK, RWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGESV computes the solution to a complex system of linear equations
*> A * X = B,
*> where P is a permutation matrix, L is unit lower triangular, and U is
*> upper triangular. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
* WORK, LWORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGESVD computes the singular value decomposition (SVD) of a complex
*> M-by-N matrix A, optionally computing the left and/or right singular
*> U and V are the left and right singular vectors of A.
*>
*> Note that the routine returns V**H, not V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> did not converge to zero. See the description of RWORK
*> above for details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGESVX uses the LU factorization to compute the solution to a complex
*> system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGESVXX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, RPVGRW,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGESVXX uses the LU factorization to compute the solution to a
*> complex system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what CGESVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGETC2 computes an LU factorization, using complete pivoting, of the
*> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
*> unit diagonal elements and U is upper triangular.
*>
*> This is a level 1 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> one tries to solve for x in Ax = b. So U is perturbed
*> to avoid the overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETF2( M, N, A, LDA, IPIV, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGETF2 computes an LU factorization of a general m-by-n matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETRF( M, N, A, LDA, IPIV, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGETRF computes an LU factorization of a general M-by-N matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGETRI computes the inverse of a matrix using the LU factorization
*> computed by CGETRF.
*>
*> This method inverts U and then computes inv(A) by solving the system
*> inv(A)*L = inv(U) for inv(A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
*> singular and its inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGETRS solves a system of linear equations
*> A * X = B, A**T * X = B, or A**H * X = B
*> with a general N-by-N matrix A using the LU factorization computed
*> by CGETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
* LDV, INFO )
* COMPLEX V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGBAK forms the right or left eigenvectors of a complex generalized
*> eigenvalue problem A*x = lambda*B*x, by backward transformation on
*> the computed eigenvectors of the balanced pair of matrices output by
*> CGGBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. Ward, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
* RSCALE, WORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGBAL balances a pair of general complex matrices (A,B). This
*> involves, first, permuting A and B by similarity transformations to
*> Balancing may reduce the 1-norm of the matrices, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors in the
*> generalized eigenvalue problem A*x = lambda*B*x.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. WARD, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
* SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGES computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B), the generalized eigenvalues, the generalized complex Schur
*> A pair of matrices (S,T) is in generalized complex Schur form if S
*> and T are upper triangular and, in addition, the diagonal elements
*> of T are non-negative real numbers.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering falied in CTGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
* B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGESX computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B), the generalized eigenvalues, the complex Schur form (S,T),
*> A pair of matrices (S,T) is in generalized complex Schur form if T is
*> upper triangular with non-negative diagonal and S is upper
*> triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering failed in CTGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
* VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGEV computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B), the generalized eigenvalues, and optionally, the left and/or
*> u(j)**H * A = lambda(j) * u(j)**H * B
*>
*> where u(j)**H is the conjugate-transpose of u(j).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> > N: =N+1: other then QZ iteration failed in SHGEQZ,
*> =N+2: error return from STGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
* ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B) the generalized eigenvalues, and optionally, the left and/or
*> u(j)**H * A = lambda(j) * u(j)**H * B.
*> where u(j)**H is the conjugate-transpose of u(j).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> > N: =N+1: other than QZ iteration failed in CHGEQZ.
*> =N+2: error return from CTGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing a matrix pair (A,B) includes, first, permuting rows and
*>
*> For further explanation of the reciprocal condition numbers RCONDE
*> and RCONDV, see section 4.11 of LAPACK User's Guide.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
* INFO )
* $ X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGGLM solves a general Gauss-Markov linear model (GLM) problem:
*>
*> x
*>
*> where inv(B) denotes the inverse of B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> rank( A B ) < N; the least squares solution could not
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
* LDQ, Z, LDZ, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGHRD reduces a pair of complex matrices (A,B) to generalized upper
*> Hessenberg form using unitary transformations, where A is a
*> If Q1 is the unitary matrix from the QR factorization of B in the
*> original equation A*x = lambda*B*x, then CGGHRD reduces the original
*> problem to generalized Hessenberg form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine reduces A to Hessenberg and B to triangular form by
*> an unblocked reduction, as described in _Matrix_Computations_,
*> by Golub and van Loan (Johns Hopkins Press).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
* INFO )
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGLSE solves the linear equality-constrained least squares (LSE)
*> problem:
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> ( (B) )
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGQRF computes a generalized QR factorization of an N-by-M matrix A
*> and an N-by-P matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z' denotes the
*> conjugate transpose of matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine CUNGRQ.
*> To use Z to update another matrix, use LAPACK subroutine CUNMRQ.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGRQF computes a generalized RQ factorization of an M-by-N matrix A
*> and a P-by-N matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
*> conjugate transpose of the matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO=-i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine CUNGQR.
*> To use Z to update another matrix, use LAPACK subroutine CUNMQR.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
* $ U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGSVD computes the generalized singular value decomposition (GSVD)
*> of an M-by-N complex matrix A and P-by-N complex matrix B:
*>
*> X = Q*( I 0 )
*> ( 0 inv(R) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, the Jacobi-type procedure failed to
*> converge. For further details, see subroutine CTGSJA.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLA REAL
*> TOLB REAL
*> TOLA and TOLB are the thresholds to determine the effective
*> The size of TOLA and TOLB may affect the size of backward
*> errors of the decomposition.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> 2-96 Based on modifications by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
$ LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGGSVP computes unitary matrices U, V and Q such that
*>
*> This decomposition is the preprocessing step for computing the
*> Generalized Singular Value Decomposition (GSVD), see subroutine
*> CGGSVD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
*> The subroutine uses LAPACK subroutine CGEQPF for the QR factorization
*> with column pivoting to detect the effective numerical rank of the
*> a matrix. It may be replaced by a better rank determination strategy.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
$ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
* WORK, INFO )
* COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTCON estimates the reciprocal of the condition number of a complex
*> tridiagonal matrix A using the LU factorization as computed by
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is tridiagonal, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTSV solves the equation
*>
*>
*> Note that the equation A**T *X = B may be solved by interchanging the
*> order of the arguments DU and DL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has not been computed. The factorization has not been
*> completed unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTSVX uses the LU factorization to compute the solution to a complex
*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
* COMPLEX D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTTRF computes an LU factorization of a complex tridiagonal matrix A
*> using elimination with partial pivoting and row interchanges.
*> where L is a product of permutation and unit lower bidiagonal
*> matrices and U is upper triangular with nonzeros in only the main
*> diagonal and first two superdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
* INFO )
* COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTTRS solves one of the systems of equations
*> A * X = B, A**T * X = B, or A**H * X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by CGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
* COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTTS2 solves one of the systems of equations
*> A * X = B, A**T * X = B, or A**H * X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by CGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* RWORK, INFO )
* COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBEV computes all the eigenvalues and, optionally, eigenvectors of
*> a complex Hermitian band matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
*> a complex Hermitian band matrix A. If eigenvectors are desired, it
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
*> can be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
* LDX, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBGST reduces a complex Hermitian-definite banded generalized
*> eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
*> split Cholesky factorization. A is overwritten by C = X**H*A*X, where
*> X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
*> bandwidth of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, RWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
*> and banded, and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
* LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBGVX computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> and banded, and B is also positive definite. Eigenvalues and
*> eigenvectors can be selected by specifying either all eigenvalues,
*> a range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
$ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
* WORK, INFO )
* COMPLEX AB( LDAB, * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBTRD reduces a complex Hermitian band matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by Linda Kaufman, Bell Labs.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHECON estimates the reciprocal of the condition number of a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
* REAL S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYEQUB computes row and column scalings intended to equilibrate a
*> symmetric matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
* INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEEV computes all eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
* LRWORK, IWORK, LIWORK, INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix A. If eigenvectors are desired, it uses a
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> lying in rows and columns INFO/(N+1) through
*> mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
+*> \par Further Details:
+* =====================
*>
*> Modified description of INFO. Sven, 16 Feb 05.
-*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
*>
* =====================================================================
SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
* COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEEVR computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
-*> California at Berkeley, USA
+*> California at Berkeley, USA \n
*> Jason Riedy, Computer Science Division, University of
-*> California at Berkeley, USA
-*>
-*> \endverbatim
+*> California at Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
* COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
*> be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEGS2 reduces a complex Hermitian-definite generalized
*> eigenproblem to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
*>
*> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEGST reduces a complex Hermitian-definite generalized
*> eigenproblem to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
*>
*> B must have been previously factorized as U**H*U or L*L**H by CPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, RWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be Hermitian and B is also
*> positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> Based on contributions by
-*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*> \verbatim
*>
*> Modified so that no backsubstitution is performed if CHEEVD fails to
*> converge (NEIG in old code could be greater than N causing out of
*> bounds reference to A - reported by Ralf Meyer). Also corrected the
*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*>
* =====================================================================
SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
* VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHEGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> B are assumed to be Hermitian and B is also positive definite.
*> Eigenvalues and eigenvectors can be selected by specifying either a
*> range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
$ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHERFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHERFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian indefinite, and
*> provides error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_NORM( NRHS, * ),
* $ ERR_BNDS_COMP( NRHS, * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHERFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian indefinite, and
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHESV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, and D is Hermitian and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
*> used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHESVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
* LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHESVX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHESVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHESVXX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B, where
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what CHESVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(R) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHESWAPR( UPLO, N, A, LDA, I1, I2)
*
* .. Array Arguments ..
* COMPLEX A( LDA, N )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHESWAPR applies an elementary permutation on the rows and the columns of
*> a hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> I2 is INTEGER
*> Index of the second row to swap
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETD2( UPLO, N, A, LDA, D, E, TAU, INFO )
*
* COMPLEX A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETD2 reduces a complex Hermitian matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETF2 computes the factorization of a complex Hermitian matrix A
*> using the Bunch-Kaufman diagonal pivoting method:
*> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 09-29-06 - patch from
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRD reduces a complex Hermitian matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRF computes the factorization of a complex Hermitian matrix A
*> using the Bunch-Kaufman diagonal pivoting method. The form of the
*> 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**H, where
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRI computes the inverse of a complex Hermitian indefinite matrix
*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
*> CHETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRI2 computes the inverse of a COMPLEX hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> CHETRF. CHETRI2 set the LEADING DIMENSION of the workspace
*> before calling CHETRI2X that actually computes the inverse.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
* COMPLEX A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRI2X computes the inverse of a complex Hermitian indefinite matrix
*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
*> CHETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRS solves a system of linear equations A*X = B with a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by CHETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHETRS2 solves a system of linear equations A*X = B with a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by CHETRF and converted by CSYCONV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
* C )
* COMPLEX A( LDA, * ), C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for C in RFP Format.
*>
*> where alpha and beta are real scalars, C is an n--by--n Hermitian
*> matrix and A is an n--by--k matrix in the first case and a k--by--n
*> matrix in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> parts of the diagonal elements need not be set, they are
*> assumed to be zero, and on exit they are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
* ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHGEQZ computes the eigenvalues of a complex matrix pair (H,T),
*> where H is an upper Hessenberg matrix and T is upper triangular,
*> Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
*> Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
*> pp. 241--256.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> in Schur form, but ALPHA(i) and BETA(i),
*> i=INFO-N+1,...,N should be correct.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We assume that complex ABS works as long as its value is less than
*> overflow.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* CHARACTER*1 FUNCTION CHLA_TRANSTYPE( TRANS )
*
* INTEGER TRANS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine translates from a BLAST-specified integer constant to
*> the character string specifying a transposition operation.
*> then input is not an integer indicating a transposition operator.
*> Otherwise CHLA_TRANSTYPE returns the constant value corresponding to
*> TRANS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
*
* COMPLEX AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPCON estimates the reciprocal of the condition number of a complex
*> Hermitian packed matrix A using the factorization A = U*D*U**H or
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
* INFO )
* COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPEV computes all the eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix in packed storage.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
* RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
*> a complex Hermitian matrix A in packed storage. If eigenvectors are
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK,
* COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A in packed storage.
*> Eigenvalues/vectors can be selected by specifying either a range of
*> values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPGST( ITYPE, UPLO, N, AP, BP, INFO )
*
* COMPLEX AP( * ), BP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPGST reduces a complex Hermitian-definite generalized
*> eigenproblem to standard form, using packed storage.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
*>
*> B must have been previously factorized as U**H*U or L*L**H by CPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* RWORK, INFO )
* COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPGV computes all the eigenvalues and, optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be Hermitian, stored in packed format,
*> and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPGVD computes all the eigenvalues and, optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
* IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
* COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPGVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> positive definite. Eigenvalues and eigenvectors can be selected by
*> specifying either a range of values or a range of indices for the
*> desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
$ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian indefinite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, D is Hermitian and block diagonal with 1-by-1
*> and 2-by-2 diagonal blocks. The factored form of A is then used to
*> solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, so the solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X,
* LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPSVX uses the diagonal pivoting factorization A = U*D*U**H or
*> A = L*D*L**H to compute the solution to a complex system of linear
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPTRD( UPLO, N, AP, D, E, TAU, INFO )
*
* COMPLEX AP( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPTRD reduces a complex Hermitian matrix A stored in packed form to
*> real symmetric tridiagonal form T by a unitary similarity
*> transformation: Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
*> overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPTRF( UPLO, N, AP, IPIV, INFO )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPTRF computes the factorization of a complex Hermitian packed
*> matrix A using the Bunch-Kaufman diagonal pivoting method:
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is Hermitian and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**H, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> J. Lewis, Boeing Computer Services Company
*>
* =====================================================================
SUBROUTINE CHPTRF( UPLO, N, AP, IPIV, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* COMPLEX AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPTRI computes the inverse of a complex Hermitian indefinite matrix
*> A in packed storage using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by CHPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPTRS solves a system of linear equations A*X = B with a complex
*> Hermitian matrix A stored in packed format using the factorization
*> A = U*D*U**H or A = L*D*L**H computed by CHPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
* LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
* $ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHSEIN uses inverse iteration to find specified right and/or left
*> eigenvectors of a complex upper Hessenberg matrix H.
*> H * x = w * x, y**h * H = w * y**h
*>
*> where y**h denotes the conjugate transpose of the vector y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> failed to converge; see IFAILL and IFAILR for further
*> details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x|+|y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
* WORK, LWORK, INFO )
* .. Array Arguments ..
* COMPLEX H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
-* Purpose
-* =======
+*
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHSEQR computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> If INFO .GT. 0 and COMPZ = 'N', then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
+*> \par Contributors:
+* ==================
+*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Default values supplied by
+*> ILAENV(ISPEC,'CHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
+*> It is suggested that these defaults be adjusted in order
+*> to attain best performance in each particular
+*> computational environment.
+*>
+*> ISPEC=12: The CLAHQR vs CLAQR0 crossover point.
+*> Default: 75. (Must be at least 11.)
+*>
+*> ISPEC=13: Recommended deflation window size.
+*> This depends on ILO, IHI and NS. NS is the
+*> number of simultaneous shifts returned
+*> by ILAENV(ISPEC=15). (See ISPEC=15 below.)
+*> The default for (IHI-ILO+1).LE.500 is NS.
+*> The default for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>
+*> ISPEC=14: Nibble crossover point. (See IPARMQ for
+*> details.) Default: 14% of deflation window
+*> size.
+*>
+*> ISPEC=15: Number of simultaneous shifts in a multishift
+*> QR iteration.
+*>
+*> If IHI-ILO+1 is ...
+*>
+*> greater than ...but less ... the
+*> or equal to ... than default is
+*>
+*> 1 30 NS = 2(+)
+*> 30 60 NS = 4(+)
+*> 60 150 NS = 10(+)
+*> 150 590 NS = **
+*> 590 3000 NS = 64
+*> 3000 6000 NS = 128
+*> 6000 infinity NS = 256
+*>
+*> (+) By default some or all matrices of this order
+*> are passed to the implicit double shift routine
+*> CLAHQR and this parameter is ignored. See
+*> ISPEC=12 above and comments in IPARMQ for
+*> details.
+*>
+*> (**) The asterisks (**) indicate an ad-hoc
+*> function of N increasing from 10 to 64.
+*>
+*> ISPEC=16: Select structured matrix multiply.
+*> If the number of simultaneous shifts (specified
+*> by ISPEC=15) is less than 14, then the default
+*> for ISPEC=16 is 0. Otherwise the default for
+*> ISPEC=16 is 2.
+*> \endverbatim
+*
+*> \par References:
+* ================
+*>
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
+*> \n
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
+*> of Matrix Analysis, volume 23, pages 948--973, 2002.
+*
* =====================================================================
SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
$ WORK, LWORK, INFO )
* .. Array Arguments ..
COMPLEX H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
-* ================================================================
-* Default values supplied by
-* ILAENV(ISPEC,'CHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
-* It is suggested that these defaults be adjusted in order
-* to attain best performance in each particular
-* computational environment.
-*
-* ISPEC=12: The CLAHQR vs CLAQR0 crossover point.
-* Default: 75. (Must be at least 11.)
-*
-* ISPEC=13: Recommended deflation window size.
-* This depends on ILO, IHI and NS. NS is the
-* number of simultaneous shifts returned
-* by ILAENV(ISPEC=15). (See ISPEC=15 below.)
-* The default for (IHI-ILO+1).LE.500 is NS.
-* The default for (IHI-ILO+1).GT.500 is 3*NS/2.
-*
-* ISPEC=14: Nibble crossover point. (See IPARMQ for
-* details.) Default: 14% of deflation window
-* size.
-*
-* ISPEC=15: Number of simultaneous shifts in a multishift
-* QR iteration.
-*
-* If IHI-ILO+1 is ...
-*
-* greater than ...but less ... the
-* or equal to ... than default is
-*
-* 1 30 NS = 2(+)
-* 30 60 NS = 4(+)
-* 60 150 NS = 10(+)
-* 150 590 NS = **
-* 590 3000 NS = 64
-* 3000 6000 NS = 128
-* 6000 infinity NS = 256
-*
-* (+) By default some or all matrices of this order
-* are passed to the implicit double shift routine
-* CLAHQR and this parameter is ignored. See
-* ISPEC=12 above and comments in IPARMQ for
-* details.
-*
-* (**) The asterisks (**) indicate an ad-hoc
-* function of N increasing from 10 to 64.
-*
-* ISPEC=16: Select structured matrix multiply.
-* If the number of simultaneous shifts (specified
-* by ISPEC=15) is less than 14, then the default
-* for ISPEC=16 is 0. Otherwise the default for
-* ISPEC=16 is 2.
-*
-* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* References:
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
-* Performance, SIAM Journal of Matrix Analysis, volume 23, pages
-* 929--947, 2002.
-*
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part II: Aggressive Early Deflation, SIAM Journal
-* of Matrix Analysis, volume 23, pages 948--973, 2002.
-*
-* ================================================================
+*
+* =====================================================================
+*
* .. Parameters ..
*
* ==== Matrices of order NTINY or smaller must be processed by
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
* INCX, BETA, Y, INCY )
* REAL Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_GBAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
* LDAFB, IPIV, C, CAPPLY, INFO, WORK,
* REAL C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_GBRCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a REAL vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB,
* LDAFB, IPIV, X, INFO, WORK, RWORK )
* REAL RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_GBRCOND_X Computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_GBRFSX_EXTENDED ( PREC_TYPE, TRANS_TYPE, N, KL, KU,
* NRHS, AB, LDAB, AFB, LDAFB, IPIV,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_GBRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to CGBTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_GBRPVGRW( N, KL, KU, NCOLS, AB, LDAB, AFB,
* LDAFB )
* COMPLEX AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_GBRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
* Y, INCY )
* REAL Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_GEAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C,
* CAPPLY, INFO, WORK, RWORK )
* REAL C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_GERCOND_C computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a REAL vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_GERCOND_X( TRANS, N, A, LDA, AF, LDAF, IPIV, X,
* INFO, WORK, RWORK )
* REAL RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_GERCOND_X computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
* LDA, AF, LDAF, IPIV, COLEQU, C, B,
* $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_GERFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERRS_C for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERRS_N and ERRS_C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to CGETRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
*
* COMPLEX A( LDA, * ), AF( LDAF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_GERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_HEAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* REAL Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_SYAMV performs the matrix-vector operation
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexHEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Richard Hanson, Sandia National Labs.
*> -- Modified for the absolute-value product, April 2006
*> Jason Riedy, UC Berkeley
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
* CAPPLY, INFO, WORK, RWORK )
* REAL C ( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_HERCOND_C computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a REAL vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
* INFO, WORK, RWORK )
* REAL RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_HERCOND_X computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_HERFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, IPIV, COLEQU, C, B, LDB,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_HERFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to CHETRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_HERPVGRW( UPLO, N, INFO, A, LDA, AF, LDAF, IPIV,
* WORK )
* REAL WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_HERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
*
* COMPLEX RES( N, NRHS )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_LIN_BERR computes componentwise relative backward error from
*> the formula
*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
*> where abs(Z) is the componentwise absolute value of the matrix
*> or vector Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> BERR is COMPLEX array, dimension (NRHS)
*> The componentwise relative backward error from the formula above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY,
* INFO, WORK, RWORK )
* REAL C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_PORCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_PORCOND_X( UPLO, N, A, LDA, AF, LDAF, X, INFO,
* WORK, RWORK )
* REAL RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_PORCOND_X Computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, COLEQU, C, B, LDB, Y,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_PORFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to CPOTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF, WORK )
*
* REAL WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_PORPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* REAL Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_SYAMV performs the matrix-vector operation
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Richard Hanson, Sandia National Labs.
*> -- Modified for the absolute-value product, April 2006
*> Jason Riedy, UC Berkeley
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_SYRCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
* CAPPLY, INFO, WORK, RWORK )
* REAL C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_SYRCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a REAL vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_SYRCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
* INFO, WORK, RWORK )
* REAL RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_SYRCOND_X Computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, IPIV, COLEQU, C, B, LDB,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_SYRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to CSYTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF, LDAF, IPIV,
* WORK )
* INTEGER IPIV( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> CLA_SYRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLA_WWADDW( N, X, Y, W )
*
* COMPLEX X( * ), Y( * ), W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
*>
*> This works for all extant IBM's hex and binary floating point
*> arithmetics, but not for decimal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> W is COMPLEX array, dimension (N)
*> The vector to be added.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
* LDY )
* $ Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLABRD reduces the first NB rows and columns of a complex general
*> m by n matrix A to upper or lower real bidiagonal form by a unitary
*> bidiagonal form.
*>
*> This is an auxiliary routine called by CGEBRD
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where a denotes an element of the original matrix which is unchanged,
*> vi denotes an element of the vector defining H(i), and ui an element
*> of the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACGV( N, X, INCX )
*
* COMPLEX X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CLACGV conjugates a complex vector of length N.
+*> \verbatim
*>
-*>\endverbatim
+*> CLACGV conjugates a complex vector of length N.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive elements of X.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACN2( N, V, X, EST, KASE, ISAVE )
*
* COMPLEX V( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLACN2 estimates the 1-norm of a square, complex matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> ISAVE is INTEGER array, dimension (3)
*> ISAVE is used to save variables between calls to SLACN2
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
-*> Contributed by Nick Higham, University of Manchester.
*> Originally named CONEST, dated March 16, 1988.
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
-*> a real or complex matrix, with applications to condition estimation",
-*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
-*>
*> Last modified: April, 1999
*>
*> This is a thread safe version of CLACON, which uses the array ISAVE
*> JUMP ISAVE(1)
*> J ISAVE(2)
*> ITER ISAVE(3)
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham, University of Manchester
+*
+*> \par References:
+* ================
+*>
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> a real or complex matrix, with applications to condition estimation",
+*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
* =====================================================================
SUBROUTINE CLACN2( N, V, X, EST, KASE, ISAVE )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACON( N, V, X, EST, KASE )
*
* COMPLEX V( N ), X( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLACON estimates the 1-norm of a square, complex matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> whether X should be overwritten by A * X or A**H * X.
*> On the final return from CLACON, KASE will again be 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
+*> \par Further Details:
+* =====================
+*>
+*> Originally named CONEST, dated March 16, 1988. \n
+*> Last modified: April, 1999
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Contributed by Nick Higham, University of Manchester.
-*> Originally named CONEST, dated March 16, 1988.
+*> Nick Higham, University of Manchester
+*
+*> \par References:
+* ================
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
*> a real or complex matrix, with applications to condition estimation",
*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
-*> Last modified: April, 1999
-*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CLACON( N, V, X, EST, KASE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACP2( UPLO, M, N, A, LDA, B, LDB )
*
* COMPLEX B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLACP2 copies all or part of a real two-dimensional matrix A to a
*> complex matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACPY( UPLO, M, N, A, LDA, B, LDB )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLACPY copies all or part of a two-dimensional matrix A to another
*> matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK )
*
* COMPLEX A( LDA, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLACRM performs a very simple matrix-matrix multiplication:
*> C := A * B,
*> where A is M by N and complex; B is N by N and real;
*> C is M by N and complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> RWORK is REAL array, dimension (2*M*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLACRT( N, CX, INCX, CY, INCY, C, S )
*
* COMPLEX CX( * ), CY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLACRT performs the operation
*>
*> ( -s c )( y ) ( y )
*>
*> where c and s are complex and the vectors x and y are complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> [ C S ].
*> [ -S C ]
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX FUNCTION CLADIV( X, Y )
*
* COMPLEX X, Y
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLADIV := X / Y, where X and Y are complex. The computation of X / Y
*> will not overflow on an intermediary step unless the results
*> overflows.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> Y is COMPLEX
*> The complex scalars X and Y.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
* IWORK, INFO )
* COMPLEX Q( LDQ, * ), QSTORE( LDQS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Using the divide and conquer method, CLAED0 computes all eigenvalues
*> of a symmetric tridiagonal matrix which is one diagonal block of
*> those from reducing a dense or band Hermitian matrix and
*> corresponding eigenvectors of the dense or band matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] QSIZ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
* LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM,
* COMPLEX Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAED7 computes the updated eigensystem of a diagonal
*> matrix after modification by a rank-one symmetric matrix. This
*> directly using the updated eigenvalues. The eigenvectors for
*> the current problem are multiplied with the eigenvectors from
*> the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
* COMPLEX Q( LDQ, * ), Q2( LDQ2, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAED8 merges the two sets of eigenvalues together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> eigenvalues are close together or if there is a tiny element in the
*> Z vector. For each such occurrence the order of the related secular
*> equation problem is reduced by one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] K
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK,
* EPS3, SMLNUM, INFO )
* COMPLEX B( LDB, * ), H( LDH, * ), V( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAEIN uses inverse iteration to find a right or left eigenvector
*> corresponding to the eigenvalue W of a complex upper Hessenberg
*> matrix H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RIGHTV
*> \verbatim
*> = 1: inverse iteration did not converge; V is set to the
*> last iterate.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
*
* COMPLEX A, B, C, CS1, EVSCAL, RT1, RT2, SN1
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
*> ( ( A, B );( B, C ) )
*>
*> [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ]
*> [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector
*> for RT1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
* COMPLEX A, B, C, SN1
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
*> [ A B ]
*>
*> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
*> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> SN1 is COMPLEX
*> The vector (CS1, SN1) is a unit right eigenvector for RT1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> RT1 is accurate to a few ulps barring over/underflow.
*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
*> Underflow is harmless if the input data is 0 or exceeds
*> underflow_threshold / macheps.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAG2Z( M, N, SA, LDSA, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAG2Z converts a COMPLEX matrix, SA, to a COMPLEX*16 matrix, A.
*>
*> converting from single to double.
*>
*> This is an auxiliary routine so there is no argument checking.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
* SNV, CSQ, SNQ )
* COMPLEX A2, B2, SNQ, SNU, SNV
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
*> that if ( UPPER ) then
*> then the transformed (2,2) element of B is not zero, except when the
*> first rows of input A and B are parallel and the second rows are
*> zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPPER
*> \verbatim
*> SNQ is COMPLEX
*> The desired unitary matrix Q.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
* B, LDB )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAGTM performs a matrix-vector product of the form
*>
*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
*> matrices, and alpha and beta are real scalars, each of which may be
*> 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
* COMPLEX A( LDA, * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAHEF computes a partial factorization of a complex Hermitian
*> matrix A using the Bunch-Kaufman diagonal pivoting method. The
*> CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code
*> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
*> A22 (if UPLO = 'L').
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
* IHIZ, Z, LDZ, INFO )
* COMPLEX H( LDH, * ), W( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAHQR is an auxiliary routine called by CHSEQR to update the
*> eigenvalues and Schur decomposition already computed by CHSEQR, by
*> dealing with the Hessenberg submatrix in rows and columns ILO to
*> IHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> where U is the orthogonal matrix in (*)
*> (regardless of the value of WANTT.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Contributors:
+* ==================
+*>
*> \verbatim
*>
*> 02-96 Based on modifications by
*> It is (1) more robust against overflow and underflow and
*> (2) adopts the more conservative Ahues & Tisseur stopping
*> criterion (LAWN 122, 1997).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> Q as a block reflector I - V*T*v**H, and also the matrix Y = A * V * T.
*>
*> This is an auxiliary routine called by CGEHRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> Gejin. Note that the entries of A(1:K,2:NB) differ from those
*> returned by the original LAPACK-3.0's DLAHRD routine. (This
*> subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
-*>
-*> References
-*> ==========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
*> performance of reduction to Hessenberg form," ACM Transactions on
*> Mathematical Software, 32(2):180-194, June 2006.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> This is an OBSOLETE auxiliary routine.
*> This routine will be 'deprecated' in a future release.
*> Please use the new routine CLAHR2 instead.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
*
* COMPLEX W( J ), X( J )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAIC1 applies one step of incremental condition estimation in
*> its simplest version:
*> [ conjg(gamma) ]
*>
*> where alpha = x**H*w.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> C is COMPLEX
*> Cosine needed in forming xhat.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
* COMPLEX B( LDB, * ), BX( LDBX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLALS0 applies back the multiplying factors of either the left or the
*> right singular vector matrix of a diagonal matrix appended by a row
*> (3R) The inverse transformation of (2L).
*>
*> (4R) The inverse transformation of (1L).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
$ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
* COMPLEX B( LDB, * ), BX( LDBX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLALSA is an itermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> ICOMPQ = 1, CLALSA applies the right singular vector matrix to the
*> right hand side. The singular vector matrices were generated in
*> compact form by CLALSA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE CLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
$ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
* RANK, WORK, RWORK, IWORK, INFO )
* COMPLEX B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLALSD uses the singular value decomposition of A to solve the least
*> squares problem of finding X to minimize the Euclidean norm of each
*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through MOD(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
$ RANK, WORK, RWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANGB( NORM, N, KL, KU, AB, LDAB,
* WORK )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANGB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANGB returns the value
+*> \return CLANGB
+*> \verbatim
*>
*> CLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANGE( NORM, M, N, A, LDA, WORK )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANGE returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANGE returns the value
+*> \return CLANGE
+*> \verbatim
*>
*> CLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANGT( NORM, N, DL, D, DU )
*
* COMPLEX D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANGT returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANGT returns the value
+*> \return CLANGT
+*> \verbatim
*>
*> CLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> DU is COMPLEX array, dimension (N-1)
*> The (n-1) super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANHB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n hermitian band matrix A, with k super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANHB returns the value
+*> \return CLANHB
+*> \verbatim
*>
*> CLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANHE returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex hermitian matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANHE returns the value
+*> \return CLANHE
+*> \verbatim
*>
*> CLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANHF( NORM, TRANSR, UPLO, N, A, WORK )
*
* COMPLEX A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANHF returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex Hermitian matrix A in RFP format.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANHF returns the value
+*> \return CLANHF
+*> \verbatim
*>
*> CLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANHP( NORM, UPLO, N, AP, WORK )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANHP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex hermitian matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANHP returns the value
+*> \return CLANHP
+*> \verbatim
*>
*> CLANHP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANHS( NORM, N, A, LDA, WORK )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANHS returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> Hessenberg matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANHS returns the value
+*> \return CLANHS
+*> \verbatim
*>
*> CLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANHT( NORM, N, D, E )
*
* COMPLEX E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANHT returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex Hermitian tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANHT returns the value
+*> \return CLANHT
+*> \verbatim
*>
*> CLANHT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> E is COMPLEX array, dimension (N-1)
*> The (n-1) sub-diagonal or super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANSB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANSB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n symmetric band matrix A, with k super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANSB returns the value
+*> \return CLANSB
+*> \verbatim
*>
*> CLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANSP( NORM, UPLO, N, AP, WORK )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANSP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex symmetric matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANSP returns the value
+*> \return CLANSP
+*> \verbatim
*>
*> CLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANSY( NORM, UPLO, N, A, LDA, WORK )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANSY returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex symmetric matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANSY returns the value
+*> \return CLANSY
+*> \verbatim
*>
*> CLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB,
* LDAB, WORK )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANTB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n triangular band matrix A, with ( k + 1 ) diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANTB returns the value
+*> \return CLANTB
+*> \verbatim
*>
*> CLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANTP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> triangular matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANTP returns the value
+*> \return CLANTP
+*> \verbatim
*>
*> CLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
* WORK )
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLANTR returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> trapezoidal or triangular matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> CLANTR returns the value
+*> \return CLANTR
+*> \verbatim
*>
*> CLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
* COMPLEX X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given two column vectors X and Y, let
*>
*> and then computes the SVD of the 2-by-2 upper triangular matrix R.
*> The smaller singular value of R is returned in SSMIN, which is used
*> as the measurement of the linear dependency of the vectors X and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> SSMIN is REAL
*> The smallest singular value of the N-by-2 matrix A = ( X Y ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAPMR( FORWRD, M, N, X, LDX, K )
*
* COMPLEX X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAPMR rearranges the rows of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(M) of the integers 1,...,M.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(I,*) is moved to X(K(I),*) for I = 1,2,...,M.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAPMT( FORWRD, M, N, X, LDX, K )
*
* COMPLEX X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAPMT rearranges the columns of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(N) of the integers 1,...,N.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(*,J) is moved to X(*,K(J)) for J = 1,2,...,N.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, EQUED )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQGB equilibrates a general M by N band matrix A with KL
*> subdiagonals and KU superdiagonals using the row and scaling factors
*> in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* EQUED )
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQGE equilibrates a general M by N matrix A using the row and
*> column scaling factors in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQHB equilibrates an Hermitian band matrix A using the scaling
*> factors in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQHE equilibrates a Hermitian matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQHP equilibrates a Hermitian matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
* WORK )
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQP2 computes a QR factorization with column pivoting of
*> the block A(OFFSET+1:M,1:N).
*> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
-*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE CLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
$ WORK )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
* VN2, AUXV, F, LDF )
* COMPLEX A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQPS computes a step of QR factorization with column pivoting
*> of a complex M-by-N matrix A by using Blas-3. It tries to factorize
*> columns is returned in KB.
*>
*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of the array F. LDF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
$ VN2, AUXV, F, LDF )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
* IHIZ, Z, LDZ, WORK, LWORK, INFO )
* COMPLEX H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQR0 computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQR1( N, H, LDH, S1, S2, V )
*
* COMPLEX H( LDH, * ), V( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given a 2-by-2 or 3-by-3 matrix H, CLAQR1 sets v to a
*> scalar multiple of the first column of the product
*>
*> This is useful for starting double implicit shift bulges
*> in the QR algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> A scalar multiple of the first column of the
*> matrix K in (*).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE CLAQR1( N, H, LDH, S1, S2, V )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT,
* $ WORK( * ), WV( LDWV, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQR2 is identical to CLAQR3 except that it avoids
*> recursion by calling CLAHQR instead of CLAQR4.
*> an unitary similarity transformation of H. It is to be
*> hoped that the final version of H has many zero subdiagonal
*> entries.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE CLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT,
* $ WORK( * ), WV( LDWV, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Aggressive early deflation:
*>
*> an unitary similarity transformation of H. It is to be
*> hoped that the final version of H has many zero subdiagonal
*> entries.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE CLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
* IHIZ, Z, LDZ, WORK, LWORK, INFO )
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQR4 implements one level of recursion for CLAQR0.
*> It is a complete implementation of the small bulge multi-shift
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
* H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,
* $ WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQR5 called by CLAQR0 performs a
*> single small-bulge multi-shift QR sweep.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> LDWV is the leading dimension of WV as declared in the
*> in the calling subroutine. LDWV.GE.NV.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> \par Contributors:
+* ==================
*>
-*> Reference:
-*>
-*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-*> Algorithm Part I: Maintaining Well Focused Shifts, and
-*> Level 3 Performance, SIAM Journal of Matrix Analysis,
-*> volume 23, pages 929--947, 2002.
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> \endverbatim
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
*>
* =====================================================================
SUBROUTINE CLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQSB equilibrates a symmetric band matrix A using the scaling
*> factors in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQSP equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAQSY equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
* PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
* COMPLEX Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAR1V computes the (scaled) r-th column of the inverse of
*> the sumbmatrix in rows B1 through BN of the tridiagonal matrix
*> (d) Computation of the (scaled) r-th column of the inverse using the
*> twisted factorization obtained by combining the top part of the
*> the stationary and the bottom part of the progressive transform.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (4*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE CLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
$ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* COMPLEX S( * ), X( * ), Y( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAR2V applies a vector of complex plane rotations with real cosines
*> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
*>
*> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
*> ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARCM( M, N, A, LDA, B, LDB, C, LDC, RWORK )
*
* COMPLEX B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARCM performs a very simple matrix-matrix multiplication:
*> C := A * B,
*> where A is M by M and real; B is M by N and complex;
*> C is M by N and complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> RWORK is REAL array, dimension (2*M*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARF applies a complex elementary reflector H to a complex M-by-N
*> matrix C, from either the left or the right. H is represented in the
*>
*> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
*> tau.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
* T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARFB applies a complex block reflector H or its transpose H**H to a
*> complex M-by-N matrix C, from either the left or the right.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )
*
* COMPLEX X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARFG generates a complex elementary reflector H of order n, such
*> that
*> and H is taken to be the unit matrix.
*>
*> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is COMPLEX
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARFGP( N, ALPHA, X, INCX, TAU )
*
* COMPLEX X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARFGP generates a complex elementary reflector H of order n, such
*> that
*>
*> If the elements of x are all zero and alpha is real, then tau = 0
*> and H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is COMPLEX
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* COMPLEX T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARFT forms the triangular factor T of a complex block reflector H
*> of order n, which is defined as a product of k elementary reflectors.
*> H(i) is stored in the i-th row of the array V, and
*>
*> H = I - V**H * T * V
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARFX( SIDE, M, N, V, TAU, C, LDC, WORK )
*
* COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARFX applies a complex elementary reflector H to a complex m by n
*> matrix C, from either the left or the right. H is represented in the
*> If tau = 0, then H is taken to be the unit matrix
*>
*> This version uses inline code if H has order < 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> or (M) if SIDE = 'R'
*> WORK is not referenced if H has order < 11.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* COMPLEX X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARGV generates a vector of complex plane rotations with real
*> cosines, determined by elements of the complex vectors x and y.
*> but differ from the BLAS1 routine CROTG):
*> If y(i)=0, then c(i)=1 and s(i)=0.
*> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*>
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARNV( IDIST, ISEED, N, X )
*
* COMPLEX X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARNV returns a vector of n random complex numbers from a uniform or
*> normal distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> X is COMPLEX array, dimension (N)
*> The generated random numbers.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine SLARUV to generate random
*> real numbers from a uniform (0,1) distribution, in batches of up to
*> 128 using vectorisable code. The Box-Muller method is used to
*> transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARRV( N, VL, VU, D, L, PIVMIN,
* ISPLIT, M, DOL, DOU, MINRGP,
* COMPLEX Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARRV computes the eigenvectors of the tridiagonal matrix
*> T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
*> The input eigenvalues should have been computed by SLARRE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 5: The Rayleigh Quotient Iteration failed to converge to
*> full accuracy in MAXITR steps.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE CLARRV( N, VL, VU, D, L, PIVMIN,
$ ISPLIT, M, DOL, DOU, MINRGP,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARSCL2 ( M, N, D, X, LDX )
*
* REAL D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARSCL2 performs a reciprocal diagonal scaling on an vector:
*> x <-- inv(D) * x
*>
*> Eventually to be replaced by BLAS_cge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARTG( F, G, CS, SN, R )
*
* COMPLEX F, G, R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARTG generates a plane rotation so that
*>
*> F and G are unchanged on return.
*> If G=0, then CS=1 and SN=0.
*> If F=0, then CS=0 and SN is chosen so that R is real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> R is COMPLEX
*> The nonzero component of the rotated vector.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*>
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARTV( N, X, INCX, Y, INCY, C, S, INCC )
*
* COMPLEX S( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARTV applies a vector of complex plane rotations with real cosines
*> to elements of the complex vectors x and y. For i = 1,2,...,n
*>
*> ( x(i) ) := ( c(i) s(i) ) ( x(i) )
*> ( y(i) ) ( -conjg(s(i)) c(i) ) ( y(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARZ applies a complex elementary reflector H to a complex
*> M-by-N matrix C, from either the left or the right. H is represented
*> tau.
*>
*> H is a product of k elementary reflectors as returned by CTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
* LDV, T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARZB applies a complex block reflector H or its transpose H**H
*> to a complex distributed M-by-N C from the left or the right.
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* COMPLEX T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARZT forms the triangular factor T of a complex block reflector
*> H of order > n, which is defined as a product of k elementary
*> H = I - V**H * T * V
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> the H(i) is best illustrated by the following example with n = 5 and
*> V = ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> ( v1 v2 v3 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASCL multiplies the M by N complex matrix A by the real scalar
*> CTO/CFROM. This is done without over/underflow as long as the final
*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
*> A may be full, upper triangular, lower triangular, upper Hessenberg,
*> or banded.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> 0 - successful exit
*> <0 - if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASCL2 ( M, N, D, X, LDX )
*
* COMPLEX X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASCL2 performs a diagonal scaling on a vector:
*> x <-- D * x
*>
*> Eventually to be replaced by BLAS_cge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASET initializes a 2-D array A to BETA on the diagonal and
*> ALPHA on the offdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASR applies a sequence of real plane rotations to a complex matrix
*> A, from either the left or the right.
*>
*> where R(k) appears in rows and columns k and z. The rotations are
*> performed without ever forming P(k) explicitly.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* COMPLEX X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASSQ returns the values scl and ssq such that
*>
*> SCALE and SUMSQ are overwritten by scl and ssq respectively.
*>
*> The routine makes only one pass through the vector X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On entry, the value sumsq in the equation above.
*> On exit, SUMSQ is overwritten with the value ssq .
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASWP( N, A, LDA, K1, K2, IPIV, INCX )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASWP performs a series of row interchanges on the matrix A.
*> One row interchange is initiated for each of rows K1 through K2 of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of IPIV. If IPIV
*> is negative, the pivots are applied in reverse order.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by
*> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
* COMPLEX A( LDA, * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLASYF computes a partial factorization of a complex symmetric matrix
*> A using the Bunch-Kaufman diagonal pivoting method. The partial
*> CLASYF is an auxiliary routine called by CSYTRF. It uses blocked code
*> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
*> A22 (if UPLO = 'L').
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
* SCALE, CNORM, INFO )
* COMPLEX AB( LDAB, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATBS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine CTBSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, CTBSV
*>
*> and we can safely call CTBSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
* JPIV )
* COMPLEX RHS( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATDF computes the contribution to the reciprocal Dif-estimate
*> by solving for x in Z * x = b, where b is chosen such that the norm
*> The factorization of Z returned by CGETC2 has the form
*> Z = P * L * U * Q, where P and Q are permutation matrices. L is lower
*> triangular with unit diagonal elements and U is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> The pivot indices; for 1 <= j <= N, column j of the
*> matrix has been interchanged with column JPIV(j).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
+*> \par Further Details:
+* =====================
+*>
+*> This routine is a further developed implementation of algorithm
+*> BSOLVE in [1] using complete pivoting in the LU factorization.
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> This routine is a further developed implementation of algorithm
-*> BSOLVE in [1] using complete pivoting in the LU factorization.
+*
+*> \par References:
+* ================
*>
*> [1] Bo Kagstrom and Lars Westin,
*> Generalized Schur Methods with Condition Estimators for
*> Condition Estimation. Report UMINF-95.05, Department of
*> Computing Science, Umea University, S-901 87 Umea, Sweden,
*> 1995.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
$ JPIV )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATPS( UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE,
* CNORM, INFO )
* COMPLEX AP( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATPS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine CTPSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, CTPSV
*>
*> and we can safely call CTPSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
* COMPLEX A( LDA, * ), TAU( * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATRD reduces NB rows and columns of a complex Hermitian matrix A to
*> Hermitian tridiagonal form by a unitary similarity
*> matrix, of which the lower triangle is supplied.
*>
*> This is an auxiliary routine called by CHETRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDW is INTEGER
*> The leading dimension of the array W. LDW >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where d denotes a diagonal element of the reduced matrix, a denotes
*> an element of the original matrix that is unchanged, and vi denotes
*> an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
* CNORM, INFO )
* COMPLEX A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATRS solves one of the triangular systems
*>
*> unscaled problem will not cause overflow, the Level 2 BLAS routine
*> CTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j),
*> then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, CTRSV
*>
*> and we can safely call CTRSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATRZ( M, N, L, A, LDA, TAU, WORK )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
*> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means
*> of unitary transformations, where Z is an (M+L)-by-(M+L) unitary
*> matrix and, R and A1 are M-by-M upper triangular matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension (M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
* COMPLEX C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine CUNMRZ.
*>
*> C = [ C1, C2 ] m
*> 1 n-1
*> Then C is overwritten by C*P.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAUU2( UPLO, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAUU2 computes the product U * U**H or L**H * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the unblocked form of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAUUM( UPLO, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAUUM computes the product U * U**H or L**H * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the blocked form of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
* RWORK, INFO )
* COMPLEX AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite band matrix using
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBEQU computes row and column scalings intended to equilibrate a
*> Hermitian positive definite band matrix A and reduce its condition
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B,
* LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite
*> and banded, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBSTF( UPLO, N, KD, AB, LDAB, INFO )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBSTF computes a split Cholesky factorization of a complex
*> Hermitian positive definite band matrix A.
*>
*> where U is upper triangular of order m = (n+kd)/2, and L is lower
*> triangular of order n-m.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> because the updated element a(i,i) was negative; the
*> matrix A is not positive definite.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*>
*> Array elements marked * are not used by the routine; s12**H denotes
*> conjg(s12); the diagonal elements of S are real.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular band matrix, with the same number of superdiagonals or
*> subdiagonals as A. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBSVX( FACT, UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB,
* EQUED, S, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
*> compute the solution to a complex system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBTF2 computes the Cholesky factorization of a complex Hermitian
*> positive definite band matrix A.
*> of U, and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite band matrix A.
*> A = U**H * U, if UPLO = 'U', or
*> A = L * L**H, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
-*> Contributed by
-*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
+*
* =====================================================================
SUBROUTINE CPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite band matrix A using the Cholesky factorization
*> A = U**H*U or A = L*L**H computed by CPBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPFTRF( TRANSR, UPLO, N, A, INFO )
*
* .. Array Arguments ..
* COMPLEX A( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPFTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPFTRI( TRANSR, UPLO, N, A, INFO )
*
* COMPLEX A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPFTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by CPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* COMPLEX A( 0: * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPFTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A using the Cholesky factorization
*> A = U**H*U or A = L*L**H computed by CPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
* INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite matrix using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOEQU computes row and column scalings intended to equilibrate a
*> Hermitian positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
*
* REAL S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOEQUB computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X,
* LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPORFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite,
*> and provides error bounds and backward error estimates for the
*> solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
* LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPORFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOSV computes the solution to a complex system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
*> compute the solution to a complex system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
*> to compute the solution to a complex system of linear equations
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what CPOSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOTF2 computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOTRF( UPLO, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOTRI( UPLO, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by CPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A using the Cholesky factorization
*> A = U**H*U or A = L*L**H computed by CPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
*
* COMPLEX AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite packed matrix using
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPEQU computes row and column scalings intended to equilibrate a
*> Hermitian positive definite matrix A in packed storage and reduce
*> This choice of S puts the condition number of B within a factor N of
*> the smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR,
* BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPSV computes the solution to a complex system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPSVX( FACT, UPLO, N, NRHS, AP, AFP, EQUED, S, B, LDB,
* X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
*> compute the solution to a complex system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPTRF( UPLO, N, AP, INFO )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A stored in packed format.
*> A = U**H * U, if UPLO = 'U', or
*> A = L * L**H, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPTRI( UPLO, N, AP, INFO )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by CPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A in packed storage using the Cholesky
*> factorization A = U**H*U or A = L*L**H computed by CPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPSTF2 computes the Cholesky factorization with complete
*> pivoting of a complex Hermitian positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPSTRF computes the Cholesky factorization with complete
*> pivoting of a complex Hermitian positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
*
* COMPLEX E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTCON computes the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite tridiagonal matrix
*> Norm(inv(A)) is computed by a direct method, and the reciprocal of
*> the condition number is computed as
*> RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The method used is described in Nicholas J. Higham, "Efficient
*> Algorithms for Computing the Condition Number of a Tridiagonal
*> Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* COMPLEX Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric positive definite tridiagonal matrix by first factoring the
*> tridiagonal form, however, may preclude the possibility of obtaining
*> high relative accuracy in the small eigenvalues of the original
*> matrix, if these eigenvalues range over many orders of magnitude.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> if INFO = N+i, i off-diagonal elements of the
*> bidiagonal factor did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite
*> and tridiagonal, and provides error bounds and backward error
*> estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTSV( N, NRHS, D, E, B, LDB, INFO )
*
* COMPLEX B( LDB, * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTSV computes the solution to a complex system of linear equations
*> A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
*>
*> A is factored as A = L*D*L**H, and the factored form of A is then
*> used to solve the system of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> computed. The factorization has not been completed
*> unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
* RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTSVX uses the factorization A = L*D*L**H to compute the solution
*> to a complex system of linear equations A*X = B, where A is an
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTTRF( N, D, E, INFO )
*
* COMPLEX E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTTRF computes the L*D*L**H factorization of a complex Hermitian
*> positive definite tridiagonal matrix A. The factorization may also
*> be regarded as having the form A = U**H *D*U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be completed, while if k = N, the factorization was
*> completed, but D(N) <= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
*
* COMPLEX B( LDB, * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTTRS solves a tridiagonal system of the form
*> A * X = B
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
*
* COMPLEX B( LDB, * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTTS2 solves a tridiagonal system of the form
*> A * X = B
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IUPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CROT( N, CX, INCX, CY, INCY, C, S )
*
* COMPLEX CX( * ), CY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CROT applies a plane rotation, where the cos (C) is real and the
*> sin (S) is complex, and the vectors CX and CY are complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> [ -conjg(S) C ]
*> where C*C + S*CONJG(S) = 1.0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
*
* COMPLEX AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex symmetric packed matrix A using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*
* COMPLEX AP( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP )
*
* COMPLEX AP( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a complex scalar, x is an n element vector and A is an
*> n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> not be set, they are assumed to be zero, and on exit they
*> are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, D is symmetric and block diagonal with 1-by-1
*> and 2-by-2 diagonal blocks. The factored form of A is then used to
*> solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, so the solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X,
* LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
*> A = L*D*L**T to compute the solution to a complex system of linear
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPTRF( UPLO, N, AP, IPIV, INFO )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPTRF computes the factorization of a complex symmetric matrix A
*> stored in packed format using the Bunch-Kaufman diagonal pivoting
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* COMPLEX AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPTRI computes the inverse of a complex symmetric indefinite matrix
*> A in packed storage using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by CSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPTRS solves a system of linear equations A*X = B with a complex
*> symmetric matrix A stored in packed format using the factorization
*> A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSRSCL( N, SA, SX, INCX )
*
* COMPLEX SX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSRSCL multiplies an n-element complex vector x by the real scalar
*> 1/a. This is done without overflow or underflow as long as
*> the final result x/a does not overflow or underflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of the vector SX.
*> > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,
* LRWORK, IWORK, LIWORK, INFO )
* COMPLEX WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none. See SLAED3 for details.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,
$ LRWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
* COMPLEX Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTEGR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> NaNs. Normal execution may create these exceptiona values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by SLARRE or
*> CLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, LBNL/NERSC, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
* IWORK, IFAIL, INFO )
* COMPLEX Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTEIN computes the eigenvectors of a real symmetric tridiagonal
*> matrix T corresponding to specified eigenvalues, using inverse
*> transformation to the eigenvectors of a complex Hermitian matrix
*> which was reduced to tridiagonal form.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge
*> in MAXITS iterations. Their indices are stored in
*> array IFAIL.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> MAXITS INTEGER, default = 5
*> The maximum number of iterations performed.
*>
*> The number of iterations performed after norm growth
*> criterion is satisfied, should be at least 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
* COMPLEX Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTEMR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> Since LAPACK drivers overwrite the matrix data with the eigenvectors,
*> CSTEMR accepts complex workspace to facilitate interoperability
*> with CUNMTR or CUPMTR.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by SLARRE or
*> CLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE CSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* COMPLEX Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the implicit QL or QR method.
*> The eigenvectors of a full or band complex Hermitian matrix can also
*> be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
*> matrix to tridiagonal form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> matrix which is unitarily similar to the original
*> matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex symmetric matrix A using the factorization
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYCONV( UPLO, WAY, N, A, LDA, IPIV, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYCONV convert A given by TRF into L and D and vice-versa.
*> Get Non-diag elements of D (returned in workspace) and
*> apply or reverse permutation done in TRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
* REAL S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYEQUB computes row and column scalings intended to equilibrate a
*> symmetric matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par References:
+* ================
*>
-*> Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
-*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
-*> DOI 10.1023/B:NUMA.0000016606.32820.69
+*> Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n
+*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n
+*> DOI 10.1023/B:NUMA.0000016606.32820.69 \n
*> Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
*
* COMPLEX A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
*
* COMPLEX A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a complex scalar, x is an n element vector and A is an
*> n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> max( 1, N ).
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> provides error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYRFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
*> used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
* LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYSVX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYSVXX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B, where
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what CSYSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(R) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYSWAPR( UPLO, N, A, LDA, I1, I2)
*
* .. Array Arguments ..
* COMPLEX A( LDA, N )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYSWAPR applies an elementary permutation on the rows and the columns of
*> a symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> I2 is INTEGER
*> Index of the second row to swap
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTF2 computes the factorization of a complex symmetric matrix A
*> using the Bunch-Kaufman diagonal pivoting method:
*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 09-29-06 - patch from
-*> Bobby Cheng, MathWorks
-*>
-*> Replace l.209 and l.377
-*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
-*> by
-*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
-*>
-*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
+*>
+*> 09-29-06 - patch from
+*> Bobby Cheng, MathWorks
*>
+*> Replace l.209 and l.377
+*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*> by
+*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
+*>
+*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
+*> Company
+*> \endverbatim
+*
* =====================================================================
SUBROUTINE CSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTRF computes the factorization of a complex symmetric matrix A
*> using the Bunch-Kaufman diagonal pivoting method. The form of the
*> with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTRI computes the inverse of a complex symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> CSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTRI2 computes the inverse of a COMPLEX hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> CSYTRF. CSYTRI2 sets the LEADING DIMENSION of the workspace
*> before calling CSYTRI2X that actually computes the inverse.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
* COMPLEX A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTRI2X computes the inverse of a real symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> CSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTRS solves a system of linear equations A*X = B with a complex
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by CSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYTRS2 solves a system of linear equations A*X = B with a COMPLEX
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by CSYTRF and converted by CSYCONV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
* RWORK, INFO )
* COMPLEX AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBCON estimates the reciprocal of the condition number of a
*> triangular band matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular band
*> The solution matrix X must be computed by CTBTRS or some other
*> means before entering this routine. CTBRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, INFO )
* COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBTRS solves a triangular system of the form
*>
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by-NRHS matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
* B, LDB )
* COMPLEX A( 0: * ), B( 0: LDB-1, 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for A in RFP Format.
*>
*> A is in Rectangular Full Packed (RFP) Format.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> max( 1, m ).
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
* COMPLEX A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTFTRI computes the inverse of a triangular matrix A stored in RFP
*> format.
*>
*> This is a Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* COMPLEX AP( 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTFTTP copies a triangular matrix A from rectangular full packed
*> format (TF) to standard packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
* COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTFTTR copies a triangular matrix A from rectangular full packed
*> format (TF) to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGEVC computes some or all of the right and/or left eigenvectors of
*> a pair of complex matrices (S,P), where S and P are upper triangular.
*> If Q and Z are the unitary factors from the generalized Schur
*> factorization of a matrix pair (A,B), then Z*X and Q*Y
*> are the matrices of right and left eigenvectors of (A,B).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, J1, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
*> in an upper triangular matrix pair (A, B) by an unitary equivalence
*> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
*> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> from generalized Schur form; the problem is ill-
*> conditioned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
-*> Umea University, S-901 87 Umea, Sweden.
+*> \par Further Details:
+* =====================
*>
*> In the current code both weak and strong stability tests are
*> performed. The user can omit the strong stability test by changing
*> the internal logical parameter WANDS to .FALSE.. See ref. [2] for
*> details.
+*
+*> \par Contributors:
+* ==================
+*>
+*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
+*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
+*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report UMINF-94.04,
*> Sweden, 1994. Also as LAPACK Working Note 87. To appear in
*> Numerical Algorithms, 1996.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, J1, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, IFST, ILST, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGEXC reorders the generalized Schur decomposition of a complex
*> matrix pair (A,B), using an unitary equivalence transformation
*>
*> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
*> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> and ILST points to the first row of the current
*> position of the block being moved.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
+*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report
*> UMINF - 94.04, Department of Computing Science, Umea University,
*> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
*> To appear in Numerical Algorithms, 1996.
-*>
+*> \n
*> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB,
* ALPHA, BETA, Q, LDQ, Z, LDZ, M, PL, PR, DIF,
* $ BETA( * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGSEN reorders the generalized Schur decomposition of a complex
*> matrix pair (A, B) (in terms of an unitary equivalence trans-
*> and norms of "projections" onto left and right eigenspaces w.r.t.
*> the selected cluster in the (1,1)-block.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> (A, B) may have been partially reordered.
*> If requested, 0 is returned in DIF(*), PL and PR.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> CTGSEN first collects the selected eigenvalues by computing unitary
*> based estimate DIF is not wanted (see CLATDF), then the parameter
*> IDIFJB (see below) should be changed from 3 to 4 (routine CLATDF
*> (IJOB = 2 will be used)). See CTGSYL for more details.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> References
-*> ==========
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
+*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report
*> UMINF - 94.04, Department of Computing Science, Umea University,
*> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
*> To appear in Numerical Algorithms, 1996.
-*>
+*> \n
*> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB,
$ ALPHA, BETA, Q, LDQ, Z, LDZ, M, PL, PR, DIF,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
* $ U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGSJA computes the generalized singular value decomposition (GSVD)
*> of two complex upper triangular (or trapezoidal) matrices A and B.
*> The computation of the unitary transformation matrices U, V or Q
*> is optional. These matrices may either be formed explicitly, or they
*> may be postmultiplied into input matrices U1, V1, or Q1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the procedure does not converge after MAXIT cycles.
*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
*> \verbatim
*> MAXIT INTEGER
*> MAXIT specifies the total loops that the iterative procedure
*> may take. If after MAXIT cycles, the routine fails to
*> converge, we return INFO = 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> CTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
*> C1**2 + S1**2 = I,
*>
*> and R1 is an L-by-L nonsingular upper triangular matrix.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK,
* $ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or eigenvectors of a matrix pair (A, B).
*>
*> (A, B) must be in generalized Schur canonical form, that is, A and
*> B are both upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: Successful exit
*> < 0: If INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of the i-th generalized
*> EPS * norm(A, B) / DIF(i).
*>
*> See ref. [2-3] for more details and further references.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75.
*> To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
* $ D( LDD, * ), E( LDE, * ), F( LDF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGSY2 solves the generalized Sylvester equation
*>
*> of an upper bound on the separation between to matrix pairs. Then
*> the input (A, D), (B, E) are sub-pencils of two matrix pairs in
*> CTGSYL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> >0: The matrix pairs (A, D) and (B, E) have common or very
*> close eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexSYauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE CTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTGSYL solves the generalized Sylvester equation:
*>
*> reciprocal of the smallest singular value of Z.
*>
*> This is a level-3 BLAS algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> >0: (A, D) and (B, E) have common or very close
*> eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
*> No 1, 1996.
-*>
+*> \n
*> [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
*> Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
*> Appl., 15(4):1045-1060, 1994.
-*>
+*> \n
*> [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
*> Condition Estimators for Solving the Generalized Sylvester
*> Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
*> July 1989, pp 745-751.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK,
* INFO )
* COMPLEX AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPCON estimates the reciprocal of the condition number of a packed
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
* A, LDA, B, LDB, WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPMQRT applies a complex orthogonal matrix Q obtained from a
*> "triangular-pentagonal" complex block reflector H to a general
*> complex matrix C, which consists of two blocks A and B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The columns of the pentagonal matrix V contain the elementary reflectors
*> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
*>
*> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
* INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPQRT computes a blocked QR factorization of a complex
*> "triangular-pentagonal" matrix C, which is composed of a
*> triangular block A and pentagonal block B, using the compact
*> WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> C = [ A ]
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = [T1 T2 ... TB].
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPQRT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
* COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPQRT2 computes a QR factorization of a complex "triangular-pentagonal"
*> matrix C, which is composed of a triangular block A and pentagonal block B,
*> using the compact WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> where W**H is the conjugate transpose of W and T is the upper triangular
*> factor of the block reflector.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L,
* V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK )
* $ V( LDV, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPRFB applies a complex "triangular-pentagonal" block reflector H or its
*> conjugate transpose H**H to a complex matrix C, which is composed of two
*> blocks A and B, either from the left or right.
*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= K;
*> if SIDE = 'R', LDWORK >= M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix C is a composite matrix formed from blocks A and B.
*> If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
*>
*> If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular packed
*> The solution matrix X must be computed by CTPTRS or some other
*> means before entering this routine. CTPRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPTRI( UPLO, DIAG, N, AP, INFO )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPTRI computes the inverse of a complex upper or lower triangular
*> matrix A stored in packed format.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A triangular matrix A can be transferred to packed storage using one
*> 1 CONTINUE 1 CONTINUE
*> JC = JC + J JC = JC + N - J + 1
*> 2 CONTINUE 2 CONTINUE
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
*
* COMPLEX AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPTRS solves a triangular system of the form
*>
*> where A is a triangular matrix of order N stored in packed format,
*> and B is an N-by-NRHS matrix. A check is made to verify that A is
*> nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
*
* .. Array Arguments ..
* COMPLEX AP( 0: * ), ARF( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPTTF copies a triangular matrix A from standard packed format (TP)
*> to rectangular full packed format (TF).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPTTR( UPLO, N, AP, A, LDA, INFO )
*
* COMPLEX A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPTTR copies a triangular matrix A from standard packed format (TP)
*> to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
* RWORK, INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRCON estimates the reciprocal of the condition number of a
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, MM, M, WORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTREVC computes some or all of the right and/or left eigenvectors of
*> a complex upper triangular matrix T.
*> input matrix. If Q is the unitary factor that reduces a matrix A to
*> Schur form T, then Q*X and Q*Y are the matrices of right and left
*> eigenvectors of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The algorithm used in this program is basically backward (forward)
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x| + |y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
* COMPLEX Q( LDQ, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTREXC reorders the Schur factorization of a complex matrix
*> A = Q*T*Q**H, so that the diagonal element of T with row index IFST
*> The Schur form T is reordered by a unitary similarity transformation
*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
*> postmultplying it with Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular
*> The solution matrix X must be computed by CTRTRS or some other
*> means before entering this routine. CTRRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, W, M, S,
* SEP, WORK, LWORK, INFO )
* COMPLEX Q( LDQ, * ), T( LDT, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRSEN reorders the Schur factorization of a complex matrix
*> A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in
*>
*> Optionally the routine computes the reciprocal condition numbers of
*> the cluster of eigenvalues and/or the invariant subspace.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> CTRSEN first collects the selected eigenvalues by computing a unitary
*> error in the computed right invariant subspace is
*>
*> EPS * norm(T) / SEP
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, S, SEP, MM, M, WORK, LDWORK, RWORK,
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or right eigenvectors of a complex upper triangular
*> matrix T (or of any matrix Q*T*Q**H with Q unitary).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of an eigenvalue lambda is
*> is given by
*>
*> EPS * norm(T) / SEP(i)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
* LDC, SCALE, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRSYL solves the complex Sylvester matrix equation:
*>
*> M-by-M and B is N-by-N; the right hand side C and the solution X are
*> M-by-N; and scale is an output scale factor, set <= 1 to avoid
*> overflow in X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANA
*> \verbatim
*> values were used to solve the equation (but the matrices
*> A and B are unchanged).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRTI2 computes the inverse of a complex upper or lower triangular
*> matrix.
*>
*> This is the Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRTRI( UPLO, DIAG, N, A, LDA, INFO )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRTRI computes the inverse of a complex upper or lower triangular
*> matrix A.
*>
*> This is the Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
* INFO )
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRTRS solves a triangular system of the form
*>
*>
*> where A is a triangular matrix of order N, and B is an N-by-NRHS
*> matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the solutions
*> X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRTTF copies a triangular matrix A from standard full format (TR)
*> to rectangular full packed format (TF) .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRTTP( UPLO, N, A, LDA, AP, INFO )
*
* COMPLEX A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRTTP copies a triangular matrix A from full format (TR) to standard
*> packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTZRQF( M, N, A, LDA, TAU, INFO )
*
* COMPLEX A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine CTZRZF.
*>
*>
*> where Z is an N-by-N unitary matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
*> to upper triangular form by means of unitary transformations.
*>
*> where Z is an N-by-N unitary matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
* $ X21( LDX21, * ), X22( LDX22, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
*> partitioned unitary matrix X:
*>
*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
*> implicitly by angles THETA, PHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The bidiagonal blocks B11, B12, B21, and B22 are represented
*> P1, P2, Q1, and Q2 are represented as products of elementary
*> reflectors. See CUNCSD for details on generating P1, P2, Q1, and Q2
*> using CUNGQR and CUNGLQ.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE CUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
* SIGNS, M, P, Q, X11, LDX11, X12,
* $ * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNCSD computes the CS decomposition of an M-by-M partitioned
*> unitary matrix X:
*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
*> which R = MIN(P,M-P,Q,M-Q).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: CBBCSD did not converge. See the description of RWORK
*> above for details.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
-*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNG2L generates an m by n complex matrix Q with orthonormal columns,
*> which is defined as the last n columns of a product of k elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by CGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNG2R generates an m by n complex matrix Q with orthonormal columns,
*> which is defined as the first n columns of a product of k elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by CGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGBR generates one of the complex unitary matrices Q or P**H
*> determined by CGEBRD when reducing a complex matrix A to bidiagonal
*> rows of P**H, where n >= m >= k;
*> if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
*> an N-by-N matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGHR generates a complex unitary matrix Q which is defined as the
*> product of IHI-ILO elementary reflectors of order N, as returned by
*> CGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
*> which is defined as the first m rows of a product of k elementary
*> Q = H(k)**H . . . H(2)**H H(1)**H
*>
*> as returned by CGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
*> which is defined as the first M rows of a product of K elementary
*> Q = H(k)**H . . . H(2)**H H(1)**H
*>
*> as returned by CGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit;
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
*> which is defined as the last N columns of a product of K elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by CGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
*> which is defined as the first N columns of a product of K elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by CGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGR2 generates an m by n complex matrix Q with orthonormal rows,
*> which is defined as the last m rows of a product of k elementary
*> Q = H(1)**H H(2)**H . . . H(k)**H
*>
*> as returned by CGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,
*> which is defined as the last M rows of a product of K elementary
*> Q = H(1)**H H(2)**H . . . H(k)**H
*>
*> as returned by CGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNGTR generates a complex unitary matrix Q which is defined as the
*> product of n-1 elementary reflectors of order N, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNM2L overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by CGEQLF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNM2R overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by CGEQRF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
*> with
*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
*> if k < nq, P = G(1) G(2) . . . G(k);
*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMHR overwrites the general complex M-by-N matrix C with
*>
*> IHI-ILO elementary reflectors, as returned by CGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNML2 overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by CGELQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMLQ overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by CGELQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMQL overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by CGEQLF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMQR overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by CGEQRF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMR2 overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by CGERQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMR3 overwrites the general complex m by n matrix C with
*>
*>
*> as returned by CTZRZF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMRQ overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by CGERQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMRZ overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by CTZRZF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNMTR overwrites the general complex M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
* COMPLEX AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUPGTR generates a complex unitary matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
* INFO )
* COMPLEX AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUPMTR overwrites the general complex M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
* THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T,
* $ V2T( LDV2T, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DBBCSD computes the CS decomposition of an orthogonal matrix in
*> bidiagonal-block form,
*> The orthogonal matrices U1, U2, V1T, and V2T are input/output.
*> The input matrices are pre- or post-multiplied by the appropriate
*> singular vector matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> > 0: if DBBCSD did not converge, INFO specifies the number
*> of nonzero entries in PHI, and B11D, B11E, etc.,
*> contain the partially reduced matrix.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Reference
-*> =========
-*>
-*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
-*> Algorithms, 50(1):33-65, 2009.
-*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they
*> are within TOLMUL*EPS of either bound.
*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*> Algorithms, 50(1):33-65, 2009.
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
* WORK, IWORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DBDSDC computes the singular value decomposition (SVD) of a real
*> N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,
*> The code currently calls DLASDQ if singular values only are desired.
*> However, it can be slightly modified to compute singular values
*> using the divide and conquer method.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: The algorithm failed to compute a singular value.
*> The update process of divide and conquer failed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
$ WORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
* LDU, C, LDC, WORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DBDSQR computes the singular values and, optionally, the right and/or
*> left singular vectors from the singular value decomposition (SVD) of
*> B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
*> Department, University of California at Berkeley, July 1992
*> for a detailed description of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> elements of a bidiagonal matrix which is orthogonally
*> similar to the input matrix B; if INFO = i, i
*> elements of E have not converged to zero.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> If it is positive, TOLMUL*EPS is the desired relative
*> (and so fails to converge) if the number of passes
*> through the inner loop exceeds MAXITR*N**2.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO )
*
* DOUBLE PRECISION D( * ), SEP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDISNA computes the reciprocal condition numbers for the eigenvectors
*> of a real symmetric or complex Hermitian matrix or for the left or
*>
*> DDISNA may also be used to compute error bounds for eigenvectors of
*> the generalized symmetric definite eigenproblem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
* LDQ, PT, LDPT, C, LDC, WORK, INFO )
* $ PT( LDPT, * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBBRD reduces a real general m-by-n band matrix A to upper
*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
*>
*> The routine computes B, and optionally forms Q or P**T, or computes
*> Q**T*C for a given matrix C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
* WORK, IWORK, INFO )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBCON estimates the reciprocal of the condition number of a real
*> general band matrix A, in either the 1-norm or the infinity-norm,
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBEQU computes row and column scalings intended to equilibrate an
*> M-by-N band matrix A and reduce its condition number. R returns the
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK,
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is banded, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBRFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBSV computes the solution to a real system of linear equations
*> A * X = B, where A is a band matrix of order N with KL subdiagonals
*> and unit lower triangular matrices with KL subdiagonals, and U is
*> upper triangular with KL+KU superdiagonals. The factored form of A
*> is then used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGBsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBSVX uses the LU factorization to compute the solution to a real
*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed by this subroutine:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBSVXX uses the LU factorization to compute the solution to a
*> double precision system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what DGBSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* DOUBLE PRECISION AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBTF2 computes an LU factorization of a real m-by-n band matrix A
*> using partial pivoting with row interchanges.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> + need not be set on entry, but are required by the routine to store
*> elements of U, because of fill-in resulting from the row
*> interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* DOUBLE PRECISION AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBTRF computes an LU factorization of a real m-by-n band matrix A
*> using partial pivoting with row interchanges.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
* INFO )
* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBTRS solves a system of linear equations
*> A * X = B or A**T * X = B
*> with a general band matrix A using the LU factorization computed
*> by DGBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
* INFO )
* DOUBLE PRECISION SCALE( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEBAK forms the right or left eigenvectors of a real general matrix
*> by backward transformation on the computed eigenvectors of the
*> balanced matrix output by DGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
*
* DOUBLE PRECISION A( LDA, * ), SCALE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEBAL balances a general real matrix A. This involves, first,
*> permuting A by a similarity transformation to isolate eigenvalues
*>
*> Balancing may reduce the 1-norm of the matrix, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The permutations consist of row and column interchanges which put
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
*
* $ TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEBD2 reduces a real general m by n matrix A to upper or lower
*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
* INFO )
* $ TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEBRD reduces a general real M-by-N matrix A to upper or lower
*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
* INFO )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGECON estimates the reciprocal of the condition number of a general
*> real matrix A, in either the 1-norm or the infinity-norm, using
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEEQU computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI,
* VS, LDVS, WORK, LWORK, BWORK, INFO )
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEES computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues, the real Schur form T, and, optionally, the matrix of
*> [ c a ]
*>
*> where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> the Schur form no longer satisfy SELECT=.TRUE. This
*> could also be caused by underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM,
* WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK,
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEESX computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues, the real Schur form T, and, optionally, the matrix of
*> [ c a ]
*>
*> where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> the Schur form no longer satisfy SELECT=.TRUE. This
*> could also be caused by underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
* LDVR, WORK, LWORK, INFO )
* $ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEEV computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*>
*> The computed eigenvectors are normalized to have Euclidean norm
*> equal to 1 and largest component real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> elements i+1:N of WR and WI contain eigenvalues which
*> have converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
* VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
* $ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEEVX computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*> (in exact arithmetic) but diagonal scaling will. For further
*> explanation of balancing, see section 4.10.2 of the LAPACK
*> Users' Guide.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> have been computed; elements 1:ILO-1 and i+1:N of WR
*> and WI contain eigenvalues which have converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR,
* ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
* $ VSR( LDVSR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DGGES.
*>
*> DGEGV should be used instead. See DGEGV for a description of the
*> eigenvalues of the generalized nonsymmetric eigenvalue problem
*> (GNEP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> =N+8: error return from DGGBAK (computing VSR)
*> =N+9: error return from DLASCL (various places)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
* $ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DGGEV.
*>
*> are left eigenvectors of (A,B).
*>
*> Note: this routine performs "full balancing" on A and B
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> =N+9: error return from DGGBAK (computing VR)
*> =N+10: error return from DLASCL (various calls)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing
*>
*> [*] See DHGEQZ, DGEGS, or read the book "Matrix Computations",
*> by Golub & van Loan, pub. by Johns Hopkins U. Press.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
*> an orthogonal similarity transformation: Q**T * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEHRD reduces a real general matrix A to upper Hessenberg form H by
*> an orthogonal similarity transformation: Q**T * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> This file is a slight modification of LAPACK-3.0's DGEHRD
*> subroutine incorporating improvements proposed by Quintana-Orti and
*> Van de Geijn (2006). (See DLAHR2.)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
* M, N, A, LDA, SVA, U, LDU, V, LDV,
* CHARACTER*1 JOBA, JOBP, JOBR, JOBT, JOBU, JOBV
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEJSV computes the singular value decomposition (SVD) of a real M-by-N
*> matrix [A], where M >= N. The SVD of [A] is written as
*> the right singular vectors of [A], respectively. The matrices [U] and [V]
*> are computed and stored in the arrays U and V, respectively. The diagonal
*> of [SIGMA] is computed and stored in the array SVA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBA
*> \verbatim
*> > 0 : DGEJSV did not converge in the maximal allowed number
*> of sweeps. The computed values may be inaccurate.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> DGEJSV implements a preconditioned Jacobi SVD algorithm. It uses DGEQP3,
*> this extra QRF step easily. The implementer can also improve data movement
*> (matrix transpose, matrix copy, matrix transposed copy) - this
*> implementation of DGEJSV uses only the simplest, naive data movement.
-*>
-*> Contributors
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*
+*> \par References:
+* ================
*>
-*> References
+*> \verbatim
*>
*> [1] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I.
*> SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342.
*> [4] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,
*> QSVD, (H,K)-SVD computations.
*> Department of Mathematics, University of Zagreb, 2008.
-*>
-*> Bugs, examples and comments
+*> \endverbatim
+*
+*> \par Bugs, examples and comments:
+* =================================
*>
*> Please report all bugs and send interesting examples and/or comments to
*> drmac@math.hr. Thank you.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
$ M, N, A, LDA, SVA, U, LDU, V, LDV,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGELQ2 computes an LQ factorization of a real m by n matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGELQF computes an LQ factorization of a real M-by-N matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
* INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGELS solves overdetermined or underdetermined real linear systems
*> involving an M-by-N matrix A, or its transpose, using a QR or LQ
*> handled in a single call; they are stored as the columns of the
*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
*> matrix X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> full rank; the least squares solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, IWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGELSD computes the minimum-norm solution to a real linear least
*> squares problem:
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
$ WORK, LWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGELSS computes the minimum norm solution to a real linear least
*> squares problem:
*> The effective rank of A is determined by treating as zero those
*> singular values which are less than RCOND times the largest singular
*> value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DGELSY.
*>
*> X = P * Z**T [ inv(T11)*Q1**T*B ]
*> [ 0 ]
*> where Q1 consists of the first RANK columns of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGELSY computes the minimum-norm solution to a real linear least
*> squares problem:
*> o Matrix B (the right hand side) is updated with Blas-3.
*> o The permutation of matrix B (the right hand side) is faster and
*> more simple.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: If INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*>
-*> \endverbatim
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n
+*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
+*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
*>
* =====================================================================
SUBROUTINE DGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
* C, LDC, WORK, INFO )
* DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEMQRT overwrites the general real M-by-N matrix C with
*>
*> generated using the compact WY representation as returned by DGEQRT.
*>
*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQL2 computes a QL factorization of a real m by n matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQLF computes a QL factorization of a real M-by-N matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQP3 computes a QR factorization with column pivoting of a
*> matrix A: A*P = Q*R using Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real/complex scalar, and v is a real/complex vector
*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
*> A(i+1:m,i), and tau in TAU(i).
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DGEQP3.
*>
*> DGEQPF computes a QR factorization with column pivoting of a
*> real M-by-N matrix A: A*P = Q*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> University of Zagreb, Croatia.
*> -- April 2011 --
*> For more details see LAPACK Working Note 176.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQR2 computes a QR factorization of a real m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQR2 computes a QR factorization of a real m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQRF computes a QR factorization of a real M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQRFP computes a QR factorization of a real M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQRT computes a blocked QR factorization of a real M-by-N matrix A
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> below the diagonal. For example, if M=5 and N=3, the matrix V is
*>
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = (T1 T2 ... TB).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQRT2( M, N, A, LDA, T, LDT, INFO )
*
* DOUBLE PRECISION A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQRT2 computes a QR factorization of a real M-by-N matrix A,
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> H = I - V * T * V**T
*>
*> where V**T is the transpose of V.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE DGEQRT3( M, N, A, LDA, T, LDT, INFO )
*
* DOUBLE PRECISION A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGEQRT3 recursively computes a QR factorization of a real M-by-N
*> matrix A, using the compact WY representation of Q.
*>
*> Based on the algorithm of Elmroth and Gustavson,
*> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> where V**T is the transpose of V.
*>
*> For details of the algorithm, see Elmroth and Gustavson (cited above).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGERFS improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates for
*> the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGERFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGERQ2 computes an RQ factorization of a real m by n matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
*> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGERQF computes an RQ factorization of a real M-by-N matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
*> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
* DOUBLE PRECISION A( LDA, * ), RHS( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESC2 solves a system of linear equations
*>
*>
*> with a general N-by-N matrix A using the LU factorization with
*> complete pivoting computed by DGETC2.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On exit, SCALE contains the scale factor. SCALE is chosen
*> 0 <= SCALE <= 1 to prevent owerflow in the solution.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
* LWORK, IWORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESDD computes the singular value decomposition (SVD) of a real
*> M-by-N matrix A, optionally computing the left and right singular
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: DBDSDC did not converge, updating process failed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
$ LWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESV computes the solution to a real system of linear equations
*> A * X = B,
*> where P is a permutation matrix, L is unit lower triangular, and U is
*> upper triangular. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
* WORK, LWORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESVD computes the singular value decomposition (SVD) of a real
*> M-by-N matrix A, optionally computing the left and/or right singular
*> U and V are the left and right singular vectors of A.
*>
*> Note that the routine returns V**T, not V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> did not converge to zero. See the description of WORK
*> above for details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
* LDV, WORK, LWORK, INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESVJ computes the singular value decomposition (SVD) of a real
*> M-by-N matrix A, where M >= N. The SVD of A is written as
*> matrix, and V is an N-by-N orthogonal matrix. The diagonal elements
*> of SIGMA are the singular values of A. The columns of U and V are the
*> left and the right singular vectors of A, respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBA
*> \verbatim
*> of sweeps. The output may still be useful. See the
*> description of WORK.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane
*> number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even
*> denormalized singular values can be computed with the corresponding
*> gradual loss of accurate digits.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
*>
-*> Contributors
*> ============
*>
*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling.
*> SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174.
*> [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,
*> QSVD, (H,K)-SVD computations.
*> Department of Mathematics, University of Zagreb, 2008.
+*> \endverbatim
+*
+*> \par Bugs, examples and comments:
+* =================================
*>
-*> Bugs, Examples and Comments
+*> \verbatim
*> ===========================
*> Please report all bugs and send interesting test examples and comments to
*> drmac@math.hr. Thank you.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESVX uses the LU factorization to compute the solution to a real
*> system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGESVXX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, RPVGRW,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGESVXX uses the LU factorization to compute the solution to a
*> double precision system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what DGESVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGETC2 computes an LU factorization with complete pivoting of the
*> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
*> unit diagonal elements and U is upper triangular.
*>
*> This is the Level 2 BLAS algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> we try to solve for x in Ax = b. So U is perturbed to
*> avoid the overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGETF2 computes an LU factorization of a general m-by-n matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGETRF computes an LU factorization of a general M-by-N matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGETRI computes the inverse of a matrix using the LU factorization
*> computed by DGETRF.
*>
*> This method inverts U and then computes inv(A) by solving the system
*> inv(A)*L = inv(U) for inv(A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
*> singular and its inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGETRS solves a system of linear equations
*> A * X = B or A**T * X = B
*> with a general N-by-N matrix A using the LU factorization computed
*> by DGETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
* LDV, INFO )
* DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGBAK forms the right or left eigenvectors of a real generalized
*> eigenvalue problem A*x = lambda*B*x, by backward transformation on
*> the computed eigenvectors of the balanced pair of matrices output by
*> DGGBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. Ward, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
* RSCALE, WORK, INFO )
* $ RSCALE( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGBAL balances a pair of general real matrices (A,B). This
*> involves, first, permuting A and B by similarity transformations to
*> Balancing may reduce the 1-norm of the matrices, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors in the
*> generalized eigenvalue problem A*x = lambda*B*x.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. WARD, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
* SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
*> the generalized eigenvalues, the generalized real Schur form (S,T),
*> and the pair of corresponding 2-by-2 blocks in S and T will have a
*> complex conjugate pair of generalized eigenvalues.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering failed in DTGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
* B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGESX computes for a pair of N-by-N real nonsymmetric matrices
*> (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
*> and the pair of corresponding 2-by-2 blocks in S and T will have a
*> complex conjugate pair of generalized eigenvalues.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering failed in DTGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> An approximate (asymptotic) bound on the average absolute error of
*> EPS * norm((A, B)) / RCONDV( 2 ).
*>
*> See LAPACK User's Guide, section 4.11 for more information.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
* $ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
*> the generalized eigenvalues, and optionally, the left and/or right
*>
*> where u(j)**H is the conjugate-transpose of u(j).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> > N: =N+1: other than QZ iteration failed in DHGEQZ.
*> =N+2: error return from DTGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
* ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, ILO,
* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGEVX computes for a pair of N-by-N real nonsymmetric matrices (A,B)
*> the generalized eigenvalues, and optionally, the left and/or right
*>
*> where u(j)**H is the conjugate-transpose of u(j).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> > N: =N+1: other than QZ iteration failed in DHGEQZ.
*> =N+2: error return from DTGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing a matrix pair (A,B) includes, first, permuting rows and
*>
*> For further explanation of the reciprocal condition numbers RCONDE
*> and RCONDV, see section 4.11 of LAPACK User's Guide.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
* INFO )
* $ X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGGLM solves a general Gauss-Markov linear model (GLM) problem:
*>
*> x
*>
*> where inv(B) denotes the inverse of B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> rank( A B ) < N; the least squares solution could not
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
* LDQ, Z, LDZ, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGHRD reduces a pair of real matrices (A,B) to generalized upper
*> Hessenberg form using orthogonal transformations, where A is a
*> If Q1 is the orthogonal matrix from the QR factorization of B in the
*> original equation A*x = lambda*B*x, then DGGHRD reduces the original
*> problem to generalized Hessenberg form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine reduces A to Hessenberg and B to triangular form by
*> an unblocked reduction, as described in _Matrix_Computations_,
*> by Golub and Van Loan (Johns Hopkins Press.)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
* INFO )
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGLSE solves the linear equality-constrained least squares (LSE)
*> problem:
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> ( (B) )
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGQRF computes a generalized QR factorization of an N-by-M matrix A
*> and an N-by-P matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
*> transpose of the matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine DORGRQ.
*> To use Z to update another matrix, use LAPACK subroutine DORMRQ.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGRQF computes a generalized RQ factorization of an M-by-N matrix A
*> and a P-by-N matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
*> transpose of the matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INF0= -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine DORGQR.
*> To use Z to update another matrix, use LAPACK subroutine DORMQR.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGSVD computes the generalized singular value decomposition (GSVD)
*> of an M-by-N real matrix A and P-by-N real matrix B:
*>
*> X = Q*( I 0 )
*> ( 0 inv(R) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, the Jacobi-type procedure failed to
*> converge. For further details, see subroutine DTGSJA.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLA DOUBLE PRECISION
*> TOLB DOUBLE PRECISION
*> TOLA and TOLB are the thresholds to determine the effective
*> The size of TOLA and TOLB may affect the size of backward
*> errors of the decomposition.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> 2-96 Based on modifications by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
$ LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGGSVP computes orthogonal matrices U, V and Q such that
*>
*> This decomposition is the preprocessing step for computing the
*> Generalized Singular Value Decomposition (GSVD), see subroutine
*> DGGSVD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
*> The subroutine uses LAPACK subroutine DGEQPF for the QR factorization
*> with column pivoting to detect the effective numerical rank of the
*> a matrix. It may be replaced by a better rank determination strategy.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
$ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGSVJ0 is called from DGESVJ as a pre-processor and that is its main
*> purpose. It applies Jacobi rotations in the same way as DGESVJ does, but
*> it does not check convergence (stopping criterion). Few tuning
*> parameters (marked by [TP]) are available for the implementer.
-*>
-*> Further Details
-*> ~~~~~~~~~~~~~~~
-*> DGSVJ0 is used just to enable SGESVJ to call a simplified version of
-*> itself to work on a submatrix of the original matrix.
-*>
-*> Contributors
-*> ~~~~~~~~~~~~
-*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
-*>
-*> Bugs, Examples and Comments
-*> ~~~~~~~~~~~~~~~~~~~~~~~~~~~
-*> Please report all bugs and send interesting test examples and comments to
-*> drmac@math.hr. Thank you.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBV
*> \verbatim
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
+*> \par Further Details:
+* =====================
+*>
+*> DGSVJ0 is used just to enable DGESVJ to call a simplified version of
+*> itself to work on a submatrix of the original matrix.
+*>
+*> \par Contributors:
+* ==================
+*>
+*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*>
+*> \par Bugs, Examples and Comments:
+* =================================
+*>
+*> Please report all bugs and send interesting test examples and comments to
+*> drmac@math.hr. Thank you.
+*
* =====================================================================
SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGSVJ1 is called from SGESVJ as a pre-processor and that is its main
*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
*> The number of sweeps is given in NSWEEP and the orthogonality threshold
*> is given in TOL.
-*>
-*> Contributors
-*> ~~~~~~~~~~~~
-*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBV
*> \verbatim
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
+*> \par Contributors:
+* ==================
+*>
+*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*
* =====================================================================
SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
* WORK, IWORK, INFO )
* DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTCON estimates the reciprocal of the condition number of a real
*> tridiagonal matrix A using the LU factorization as computed by
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK,
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is tridiagonal, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTSV solves the equation
*>
*>
*> Note that the equation A**T*X = B may be solved by interchanging the
*> order of the arguments DU and DL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has not been computed. The factorization has not been
*> completed unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTSVX uses the LU factorization to compute the solution to a real
*> system of linear equations A * X = B or A**T * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
* DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTTRF computes an LU factorization of a real tridiagonal matrix A
*> using elimination with partial pivoting and row interchanges.
*> where L is a product of permutation and unit lower bidiagonal
*> matrices and U is upper triangular with nonzeros in only the main
*> diagonal and first two superdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
* INFO )
* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTTRS solves one of the systems of equations
*> A*X = B or A**T*X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by DGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTTS2 solves one of the systems of equations
*> A*X = B or A**T*X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by DGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DHGEQZ computes the eigenvalues of a real matrix pair (H,T),
*> where H is an upper Hessenberg matrix and T is upper triangular,
*> Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
*> Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
*> pp. 241--256.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> in Schur form, but ALPHAR(i), ALPHAI(i), and
*> BETA(i), i=INFO-N+1,...,N should be correct.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Iteration counters:
*> IITER -- counts iterations run since ILAST was last
*> changed. This is therefore reset only when a 1-by-1 or
*> 2-by-2 block deflates off the bottom.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI,
* VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL,
* $ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DHSEIN uses inverse iteration to find specified right and/or left
*> eigenvectors of a real upper Hessenberg matrix H.
*> H * x = w * x, y**h * H = w * y**h
*>
*> where y**h denotes the conjugate transpose of the vector y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> failed to converge; see IFAILL and IFAILR for further
*> details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x|+|y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z,
* LDZ, WORK, LWORK, INFO )
* DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ),
* $ Z( LDZ, * )
* ..
-* Purpose
-* =======
+*
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DHSEQR computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> If INFO .GT. 0 and COMPZ = 'N', then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
+*> \par Contributors:
+* ==================
+*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Default values supplied by
+*> ILAENV(ISPEC,'DHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
+*> It is suggested that these defaults be adjusted in order
+*> to attain best performance in each particular
+*> computational environment.
+*>
+*> ISPEC=12: The DLAHQR vs DLAQR0 crossover point.
+*> Default: 75. (Must be at least 11.)
+*>
+*> ISPEC=13: Recommended deflation window size.
+*> This depends on ILO, IHI and NS. NS is the
+*> number of simultaneous shifts returned
+*> by ILAENV(ISPEC=15). (See ISPEC=15 below.)
+*> The default for (IHI-ILO+1).LE.500 is NS.
+*> The default for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>
+*> ISPEC=14: Nibble crossover point. (See IPARMQ for
+*> details.) Default: 14% of deflation window
+*> size.
+*>
+*> ISPEC=15: Number of simultaneous shifts in a multishift
+*> QR iteration.
+*>
+*> If IHI-ILO+1 is ...
+*>
+*> greater than ...but less ... the
+*> or equal to ... than default is
+*>
+*> 1 30 NS = 2(+)
+*> 30 60 NS = 4(+)
+*> 60 150 NS = 10(+)
+*> 150 590 NS = **
+*> 590 3000 NS = 64
+*> 3000 6000 NS = 128
+*> 6000 infinity NS = 256
+*>
+*> (+) By default some or all matrices of this order
+*> are passed to the implicit double shift routine
+*> DLAHQR and this parameter is ignored. See
+*> ISPEC=12 above and comments in IPARMQ for
+*> details.
+*>
+*> (**) The asterisks (**) indicate an ad-hoc
+*> function of N increasing from 10 to 64.
+*>
+*> ISPEC=16: Select structured matrix multiply.
+*> If the number of simultaneous shifts (specified
+*> by ISPEC=15) is less than 14, then the default
+*> for ISPEC=16 is 0. Otherwise the default for
+*> ISPEC=16 is 2.
+*> \endverbatim
+*
+*> \par References:
+* ================
+*>
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
+*> \n
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
+*> of Matrix Analysis, volume 23, pages 948--973, 2002.
+*
* =====================================================================
SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z,
$ LDZ, WORK, LWORK, INFO )
DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ),
$ Z( LDZ, * )
* ..
-* ================================================================
-* Default values supplied by
-* ILAENV(ISPEC,'DHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
-* It is suggested that these defaults be adjusted in order
-* to attain best performance in each particular
-* computational environment.
-*
-* ISPEC=12: The DLAHQR vs DLAQR0 crossover point.
-* Default: 75. (Must be at least 11.)
-*
-* ISPEC=13: Recommended deflation window size.
-* This depends on ILO, IHI and NS. NS is the
-* number of simultaneous shifts returned
-* by ILAENV(ISPEC=15). (See ISPEC=15 below.)
-* The default for (IHI-ILO+1).LE.500 is NS.
-* The default for (IHI-ILO+1).GT.500 is 3*NS/2.
-*
-* ISPEC=14: Nibble crossover point. (See IPARMQ for
-* details.) Default: 14% of deflation window
-* size.
-*
-* ISPEC=15: Number of simultaneous shifts in a multishift
-* QR iteration.
-*
-* If IHI-ILO+1 is ...
-*
-* greater than ...but less ... the
-* or equal to ... than default is
-*
-* 1 30 NS = 2(+)
-* 30 60 NS = 4(+)
-* 60 150 NS = 10(+)
-* 150 590 NS = **
-* 590 3000 NS = 64
-* 3000 6000 NS = 128
-* 6000 infinity NS = 256
-*
-* (+) By default some or all matrices of this order
-* are passed to the implicit double shift routine
-* DLAHQR and this parameter is ignored. See
-* ISPEC=12 above and comments in IPARMQ for
-* details.
-*
-* (**) The asterisks (**) indicate an ad-hoc
-* function of N increasing from 10 to 64.
-*
-* ISPEC=16: Select structured matrix multiply.
-* If the number of simultaneous shifts (specified
-* by ISPEC=15) is less than 14, then the default
-* for ISPEC=16 is 0. Otherwise the default for
-* ISPEC=16 is 2.
-*
-* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* References:
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
-* Performance, SIAM Journal of Matrix Analysis, volume 23, pages
-* 929--947, 2002.
-*
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part II: Aggressive Early Deflation, SIAM Journal
-* of Matrix Analysis, volume 23, pages 948--973, 2002.
-*
-* ================================================================
+*
+* =====================================================================
+*
* .. Parameters ..
*
* ==== Matrices of order NTINY or smaller must be processed by
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION DISNAN( DIN )
*
* DOUBLE PRECISION DIN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE.
*> otherwise. To be replaced by the Fortran 2003 intrinsic in the
*> future.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIN
*> \verbatim
*> DIN is DOUBLE PRECISION
*> Input to test for NaN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
* INCX, BETA, Y, INCY )
* DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_GBAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB,
* AFB, LDAFB, IPIV, CMODE, C,
* $ C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
* NRHS, AB, LDAB, AFB, LDAFB, IPIV,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> DLA_GBRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to DGBTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
* LDAB, AFB, LDAFB )
* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_GBRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
* Y, INCY )
* DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_GEAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_GERCOND ( TRANS, N, A, LDA, AF,
* LDAF, IPIV, CMODE, C,
* $ C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
* LDA, AF, LDAF, IPIV, COLEQU, C, B,
* $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> DLA_GERFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERRS_C for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERRS_N and ERRS_C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to DGETRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF,
* LDAF )
* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> DLA_GERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
*
* DOUBLE PRECISION RES( N, NRHS )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_LIN_BERR computes component-wise relative backward error from
*> the formula
*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
*> where abs(Z) is the component-wise absolute value of the matrix
*> or vector Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> BERR is DOUBLE PRECISION array, dimension (NRHS)
*> The component-wise relative backward error from the formula above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
* CMODE, C, INFO, WORK,
* INTEGER IWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, COLEQU, C, B, LDB, Y,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_PORFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to DPOTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
* LDAF, WORK )
* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> DLA_PORPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_SYAMV performs the matrix-vector operation
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Richard Hanson, Sandia National Labs.
*> -- Modified for the absolute-value product, April 2006
*> Jason Riedy, UC Berkeley
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
* IPIV, CMODE, C, INFO, WORK,
* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, IPIV, COLEQU, C, B, LDB,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> DLA_SYRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to DSYTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF,
* LDAF, IPIV, WORK )
* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> DLA_SYRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLA_WWADDW( N, X, Y, W )
*
* DOUBLE PRECISION X( * ), Y( * ), W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
*>
*> This works for all extant IBM's hex and binary floating point
*> arithmetics, but not for decimal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> W is DOUBLE PRECISION array, dimension (N)
*> The vector to be added.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLABAD( SMALL, LARGE )
*
* DOUBLE PRECISION LARGE, SMALL
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLABAD takes as input the values computed by DLAMCH for underflow and
*> overflow, and returns the square root of each of these values if the
*> the values computed by DLAMCH. This subroutine is needed because
*> DLAMCH does not compensate for poor arithmetic in the upper half of
*> the exponent range, as is found on a Cray.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] SMALL
*> \verbatim
*> On exit, if LOG10(LARGE) is sufficiently large, the square
*> root of LARGE, otherwise unchanged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
* LDY )
* $ TAUQ( * ), X( LDX, * ), Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLABRD reduces the first NB rows and columns of a real general
*> m by n matrix A to upper or lower bidiagonal form by an orthogonal
*> bidiagonal form.
*>
*> This is an auxiliary routine called by DGEBRD
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where a denotes an element of the original matrix which is unchanged,
*> vi denotes an element of the vector defining H(i), and ui an element
*> of the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
*
* DOUBLE PRECISION V( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLACN2 estimates the 1-norm of a square, real matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> ISAVE is INTEGER array, dimension (3)
*> ISAVE is used to save variables between calls to DLACN2
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
-*> Contributed by Nick Higham, University of Manchester.
*> Originally named SONEST, dated March 16, 1988.
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
-*> a real or complex matrix, with applications to condition estimation",
-*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
-*>
*> This is a thread safe version of DLACON, which uses the array ISAVE
*> in place of a SAVE statement, as follows:
*>
*> JUMP ISAVE(1)
*> J ISAVE(2)
*> ITER ISAVE(3)
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham, University of Manchester
+*
+*> \par References:
+* ================
+*>
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> a real or complex matrix, with applications to condition estimation",
+*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
* =====================================================================
SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
*
* DOUBLE PRECISION V( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLACON estimates the 1-norm of a square, real matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> whether X should be overwritten by A * X or A**T * X.
*> On the final return from DLACON, KASE will again be 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Contributed by Nick Higham, University of Manchester.
+*> Nick Higham, University of Manchester. \n
*> Originally named SONEST, dated March 16, 1988.
+*
+*> \par References:
+* ================
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
*> a real or complex matrix, with applications to condition estimation",
*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLACPY copies all or part of a two-dimensional matrix A to another
*> matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLADIV( A, B, C, D, P, Q )
*
* DOUBLE PRECISION A, B, C, D, P, Q
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLADIV performs complex division in real arithmetic
*>
*>
*> The algorithm is due to Robert L. Smith and can be found
*> in D. Knuth, The art of Computer Programming, Vol.2, p.195
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> Q is DOUBLE PRECISION
*> The scalars p and q in the above expression.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
*
* DOUBLE PRECISION A, B, C, RT1, RT2
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
*> [ A B ]
*> [ B C ].
*> On return, RT1 is the eigenvalue of larger absolute value, and RT2
*> is the eigenvalue of smaller absolute value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> RT2 is DOUBLE PRECISION
*> The eigenvalue of smaller absolute value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> RT1 is accurate to a few ulps barring over/underflow.
*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
*> Underflow is harmless if the input data is 0 or exceeds
*> underflow_threshold / macheps.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL,
* RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAEBZ contains the iteration loops which compute and use the
*> function N(w), which is the count of eigenvalues of a symmetric
*>
*> Note: the arguments are, in general, *not* checked for unreasonable
*> values.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> = 1--MMAX: The last INFO intervals did not converge.
*> = MMAX+1: More than MMAX intervals were generated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine is intended to be called only by other LAPACK
*> >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and
*> N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and
*> w(l-r)=...=w(l+k) are handled similarly.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
* WORK, IWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED0 computes all eigenvalues and corresponding eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
$ WORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
* INFO )
* DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED1 computes the updated eigensystem of a diagonal
*> matrix after modification by a rank-one symmetric matrix. This
*> directly using the updated eigenvalues. The eigenvectors for
*> the current problem are multiplied with the eigenvectors from
*> the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
* Q2, INDX, INDXC, INDXP, COLTYP, INFO )
* $ W( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED2 merges the two sets of eigenvalues together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> eigenvalues are close together or if there is a tiny entry in the
*> Z vector. For each such occurrence the order of the related secular
*> equation problem is reduced by one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] K
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
* CTOT, W, S, INFO )
* $ S( * ), W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED3 finds the roots of the secular equation, as defined by the
*> values in D, W, and RHO, between 1 and K. It makes the
*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] K
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
*
* DOUBLE PRECISION D( * ), DELTA( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the I-th updated eigenvalue of a symmetric
*> rank-one modification to a diagonal matrix whose elements are
*>
*> The method consists of approximating the rational functions in the
*> secular equation by simpler interpolating rational functions.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> > 0: if INFO = 1, the updating process failed.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> Logical variable ORGATI (origin-at-i?) is used for distinguishing
*> whether D(i) or D(i+1) is treated as the origin.
*>
*> MAXIT is the maximum number of iterations allowed for each
*> eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
*
* DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the I-th eigenvalue of a symmetric rank-one
*> modification of a 2-by-2 diagonal matrix
*>
*> We also assume RHO > 0 and that the Euclidean norm of the vector
*> Z is one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I
*> \verbatim
*> DLAM is DOUBLE PRECISION
*> The computed lambda_I, the I-th updated eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
*
* DOUBLE PRECISION D( 3 ), Z( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED6 computes the positive or negative root (closest to the origin)
*> of
*> This routine will be called by DLAED4 when necessary. In most cases,
*> the root sought is the smallest in magnitude, though it might not be
*> in some extremely rare situations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] KNITER
*> \verbatim
*> = 0: successful exit
*> > 0: if INFO = 1, failure to converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 30/06/99: Based on contributions by
-*> Ren-Cang Li, Computer Science Division, University of California
-*> at Berkeley, USA
+*> \verbatim
*>
*> 10/02/03: This version has a few statements commented out for thread
*> safety (machine parameters are computed on each entry). SJH.
*>
*> 05/10/06: Modified from a new version of Ren-Cang Li, use
*> Gragg-Thornton-Warner cubic convergent scheme for better stability.
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ren-Cang Li, Computer Science Division, University of California
+*> at Berkeley, USA
*>
* =====================================================================
SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
* $ QSTORE( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED7 computes the updated eigensystem of a diagonal
*> matrix after modification by a rank-one symmetric matrix. This
*> directly using the updated eigenvalues. The eigenvectors for
*> the current problem are multiplied with the eigenvectors from
*> the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
$ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED8 merges the two sets of eigenvalues together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> eigenvalues are close together or if there is a tiny element in the
*> Z vector. For each such occurrence the order of the related secular
*> equation problem is reduced by one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
$ CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
* S, LDS, INFO )
* $ W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAED9 finds the roots of the secular equation, as defined by the
*> values in D, Z, and RHO, between KSTART and KSTOP. It makes the
*> appropriate calls to DLAED4 and then stores the new matrix of
*> eigenvectors for use in calculating the next level of Z vectors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] K
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
$ S, LDS, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
* DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAEDA computes the Z vector corresponding to the merge step in the
*> CURLVLth step of the merge process with TLVLS steps for the CURPBMth
*> problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
$ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B,
* LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAEIN uses inverse iteration to find a right or left eigenvector
*> corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
*> matrix H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RIGHTV
*> \verbatim
*> = 1: inverse iteration did not converge; VR is set to the
*> last iterate, and so is VI if WI.ne.0.0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
* DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
*> [ A B ]
*>
*> [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
*> [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> SN1 is DOUBLE PRECISION
*> The vector (CS1, SN1) is a unit right eigenvector for RT1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> RT1 is accurate to a few ulps barring over/underflow.
*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
*> Underflow is harmless if the input data is 0 or exceeds
*> underflow_threshold / macheps.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAEXC( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK,
* INFO )
* DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in
*> an upper quasi-triangular matrix T by an orthogonal similarity
*> with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block
*> has its diagonal elemnts equal and its off-diagonal elements of
*> opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> form; the blocks are not swapped and T and Q are
*> unchanged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,
* WR2, WI )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue
*> problem A - w B, with scaling as necessary to avoid over-/underflow.
*>
*> where s is a non-negative scaling factor chosen so that w, w B,
*> and s A do not overflow and, if possible, do not underflow, either.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> eigenvalue is complex, then WI is SCALE1 times the imaginary
*> part of the eigenvalues. WI will always be non-negative.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAG2S( M, N, A, LDA, SA, LDSA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAG2S converts a DOUBLE PRECISION matrix, SA, to a SINGLE
*> PRECISION matrix, A.
*> RMAX. If not the convertion is aborted and a flag is raised.
*>
*> This is an auxiliary routine so there is no argument checking.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> PRECISION overflow threshold, in this case, the content
*> of SA in exit is unspecified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
* SNV, CSQ, SNQ )
* $ SNU, SNV
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
*> that if ( UPPER ) then
*>
*> Z**T denotes the transpose of Z.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPPER
*> \verbatim
*> SNQ is DOUBLE PRECISION
*> The desired orthogonal matrix Q.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
*
* DOUBLE PRECISION A( * ), B( * ), C( * ), D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n
*> tridiagonal matrix and lambda is a scalar, as
*> The parameter LAMBDA is included in the routine so that DLAGTF may
*> be used, in conjunction with DLAGTS, to obtain eigenvectors of T by
*> inverse iteration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0 : successful exit
*> .lt. 0: if INFO = -k, the kth argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
* B, LDB )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGTM performs a matrix-vector product of the form
*>
*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
*> matrices, and alpha and beta are real scalars, each of which may be
*> 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
*
* DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGTS may be used to solve one of the systems of equations
*>
*> controlled by the argument JOB, and in each case there is an option
*> to perturb zero or very small diagonal elements of U, this option
*> being intended for use in applications such as inverse iteration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> the elements of the right-hand side vector y are very
*> large.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
* CSR, SNR )
* $ B( LDB, * ), BETA( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGV2 computes the Generalized Schur factorization of a real 2-by-2
*> matrix pencil (A,B) where B is upper triangular. This routine
*>
*> where b11 >= b22 > 0.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] A
*> \verbatim
*> SNR is DOUBLE PRECISION
*> The sine of the right rotation matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
$ CSR, SNR )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, INFO )
* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAHQR is an auxiliary routine called by DHSEQR to update the
*> eigenvalues and Schur decomposition already computed by DHSEQR, by
*> dealing with the Hessenberg submatrix in rows and columns ILO to
*> IHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> where U is the orthogonal matrix in (*)
*> (regardless of the value of WANTT.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 02-96 Based on modifications by
*> It is (1) more robust against overflow and underflow and
*> (2) adopts the more conservative Ahues & Tisseur stopping
*> criterion (LAWN 122, 1997).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
*>
*> This is an auxiliary routine called by DGEHRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> Gejin. Note that the entries of A(1:K,2:NB) differ from those
*> returned by the original LAPACK-3.0's DLAHRD routine. (This
*> subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
-*>
-*> References
-*> ==========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
*> performance of reduction to Hessenberg form," ACM Transactions on
*> Mathematical Software, 32(2):180-194, June 2006.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAHRD reduces the first NB columns of a real general n-by-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> This is an OBSOLETE auxiliary routine.
*> This routine will be 'deprecated' in a future release.
*> Please use the new routine DLAHR2 instead.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
*
* DOUBLE PRECISION W( J ), X( J )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAIC1 applies one step of incremental condition estimation in
*> its simplest version:
*> [ gamma ]
*>
*> where alpha = x**T*w.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> C is DOUBLE PRECISION
*> Cosine needed in forming xhat.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
*
* DOUBLE PRECISION DIN1, DIN2
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is not for general use. It exists solely to avoid
*> over-optimization in DISNAN.
*> Interprocedural or whole-program optimization may delete this
*> test. The ISNAN functions will be replaced by the correct
*> Fortran 03 intrinsic once the intrinsic is widely available.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIN1
*> \verbatim
*> DIN2 is DOUBLE PRECISION
*> Two numbers to compare for inequality.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B,
* LDB, WR, WI, X, LDX, SCALE, XNORM, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLALN2 solves a system of the form (ca A - w D ) X = s B
*> or (ca A**T - w D) X = s B with possible scaling ("s") and
*>
*> Note: all input quantities are assumed to be smaller than overflow
*> by a reasonable factor. (See BIGNUM.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LTRANS
*> \verbatim
*> NOTE: In the interests of speed, this routine does not
*> check the inputs for errors.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
* $ POLES( LDGNUM, * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLALS0 applies back the multiplying factors of either the left or the
*> right singular vector matrix of a diagonal matrix appended by a row
*> (3R) The inverse transformation of (2L).
*>
*> (4R) The inverse transformation of (1L).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
$ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
* $ Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLALSA is an itermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> ICOMPQ = 1, DLALSA applies the right singular vector matrix to the
*> right hand side. The singular vector matrices were generated in
*> compact form by DLALSA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
$ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
* RANK, WORK, IWORK, INFO )
* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLALSD uses the singular value decomposition of A to solve the least
*> squares problem of finding X to minimize the Euclidean norm of each
*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through MOD(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
$ RANK, WORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX )
*
* DOUBLE PRECISION A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAMRG will create a permutation list which will merge the elements
*> of A (which is composed of two independently sorted sets) into a
*> single set which is sorted in ascending order.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N1
*> \verbatim
*> if B( I ) = A( INDEX( I ) ) for I=1,N1+N2, then B will be
*> sorted in ascending order.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )
*
* DOUBLE PRECISION D( * ), LLD( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANEG computes the Sturm count, the number of negative pivots
*> encountered while factoring tridiagonal T - sigma I = L D L^T.
*> Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
*> Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624
*> (Tech report version in LAWN 172 with the same title.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The twist index for the twisted factorization that is used
*> for the negcount.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*> Jason Riedy, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
+*> Jason Riedy, University of California, Berkeley, USA \n
*>
* =====================================================================
INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
* WORK )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANGB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANGB returns the value
+*> \return DLANGB
+*> \verbatim
*>
*> DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANGE returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANGE returns the value
+*> \return DLANGE
+*> \verbatim
*>
*> DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU )
*
* DOUBLE PRECISION D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANGT returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANGT returns the value
+*> \return DLANGT
+*> \verbatim
*>
*> DLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> DU is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANHS returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> Hessenberg matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANHS returns the value
+*> \return DLANHS
+*> \verbatim
*>
*> DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANSB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n symmetric band matrix A, with k super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANSB returns the value
+*> \return DLANSB
+*> \verbatim
*>
*> DLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
*
* DOUBLE PRECISION A( 0: * ), WORK( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANSF returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric matrix A in RFP format.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANSF returns the value
+*> \return DLANSF
+*> \verbatim
*>
*> DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
*
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANSP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANSP returns the value
+*> \return DLANSP
+*> \verbatim
*>
*> DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
*
* DOUBLE PRECISION D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANST returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANST returns the value
+*> \return DLANST
+*> \verbatim
*>
*> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) sub-diagonal or super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANSY returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANSY returns the value
+*> \return DLANSY
+*> \verbatim
*>
*> DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB,
* LDAB, WORK )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANTB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n triangular band matrix A, with ( k + 1 ) diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANTB returns the value
+*> \return DLANTB
+*> \verbatim
*>
*> DLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANTP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> triangular matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANTP returns the value
+*> \return DLANTP
+*> \verbatim
*>
*> DLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
* WORK )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANTR returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> trapezoidal or triangular matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> DLANTR returns the value
+*> \return DLANTR
+*> \verbatim
*>
*> DLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
*
* DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
*> matrix in standard form:
*> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
*> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
*> conjugate eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] A
*> \verbatim
*> SN is DOUBLE PRECISION
*> Parameters of the rotation matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by V. Sima, Research Institute for Informatics, Bucharest,
*> Romania, to reduce the risk of cancellation errors,
*> when computing real eigenvalues, and to ensure, if possible, that
*> abs(RT1R) >= abs(RT2R).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
* DOUBLE PRECISION X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given two column vectors X and Y, let
*>
*> and then computes the SVD of the 2-by-2 upper triangular matrix R.
*> The smaller singular value of R is returned in SSMIN, which is used
*> as the measurement of the linear dependency of the vectors X and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> SSMIN is DOUBLE PRECISION
*> The smallest singular value of the N-by-2 matrix A = ( X Y ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAPMR( FORWRD, M, N, X, LDX, K )
*
* DOUBLE PRECISION X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAPMR rearranges the rows of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(M) of the integers 1,...,M.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(I,*) is moved to X(K(I),*) for I = 1,2,...,M.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAPMT( FORWRD, M, N, X, LDX, K )
*
* DOUBLE PRECISION X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAPMT rearranges the columns of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(N) of the integers 1,...,N.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(*,J) is moved to X(*,K(J)) for J = 1,2,...,N.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
*
* DOUBLE PRECISION X, Y
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary
*> overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> Y is DOUBLE PRECISION
*> X and Y specify the values x and y.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z )
*
* DOUBLE PRECISION X, Y, Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause
*> unnecessary overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> Z is DOUBLE PRECISION
*> X, Y and Z specify the values x, y and z.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, EQUED )
* DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQGB equilibrates a general M by N band matrix A with KL
*> subdiagonals and KU superdiagonals using the row and scaling factors
*> in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* EQUED )
* DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQGE equilibrates a general M by N matrix A using the row and
*> column scaling factors in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
* WORK )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQP2 computes a QR factorization with column pivoting of
*> the block A(OFFSET+1:M,1:N).
*> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
-*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
$ WORK )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
* VN2, AUXV, F, LDF )
* $ VN1( * ), VN2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQPS computes a step of QR factorization with column pivoting
*> of a real M-by-N matrix A by using Blas-3. It tries to factorize
*> columns is returned in KB.
*>
*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of the array F. LDF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
-*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
$ VN2, AUXV, F, LDF )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQR0 computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*>
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
-*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
*
* DOUBLE PRECISION H( LDH, * ), V( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a
*> scalar multiple of the first column of the product
*>
*> This is useful for starting double implicit shift bulges
*> in the QR algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> A scalar multiple of the first column of the
*> matrix K in (*).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQR2 is identical to DLAQR3 except that it avoids
*> recursion by calling DLAHQR instead of DLAQR4.
*> an orthogonal similarity transformation of H. It is to be
*> hoped that the final version of H has many zero subdiagonal
*> entries.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Aggressive early deflation:
*>
*> an orthogonal similarity transformation of H. It is to be
*> hoped that the final version of H has many zero subdiagonal
*> entries.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE DLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQR4 implements one level of recursion for DLAQR0.
*> It is a complete implementation of the small bulge multi-shift
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
$ ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
* SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQR5, called by DLAQR0, performs a
*> single small-bulge multi-shift QR sweep.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> LDWV is the leading dimension of WV as declared in the
*> in the calling subroutine. LDWV.GE.NV.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> \par Contributors:
+* ==================
*>
-*> Reference:
-*>
-*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-*> Algorithm Part I: Maintaining Well Focused Shifts, and
-*> Level 3 Performance, SIAM Journal of Matrix Analysis,
-*> volume 23, pages 929--947, 2002.
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> \endverbatim
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
*>
* =====================================================================
SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* DOUBLE PRECISION AB( LDAB, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQSB equilibrates a symmetric band matrix A using the scaling
*> factors in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* DOUBLE PRECISION AP( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQSP equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* DOUBLE PRECISION A( LDA, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQSY equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK,
* INFO )
* DOUBLE PRECISION B( * ), T( LDT, * ), WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAQTR solves the real quasi-triangular system
*>
*>
*> This subroutine is designed for the condition number estimation
*> in routine DTRSNA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LTRAN
*> \verbatim
*> NOTE: In the interests of speed, this routine does not
*> check the inputs for errors.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
* PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
* DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAR1V computes the (scaled) r-th column of the inverse of
*> the sumbmatrix in rows B1 through BN of the tridiagonal matrix
*> (d) Computation of the (scaled) r-th column of the inverse using the
*> twisted factorization obtained by combining the top part of the
*> the stationary and the bottom part of the progressive transform.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (4*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
$ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* DOUBLE PRECISION C( * ), S( * ), X( * ), Y( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAR2V applies a vector of real plane rotations from both sides to
*> a sequence of 2-by-2 real symmetric matrices, defined by the elements
*>
*> ( x(i) z(i) ) := ( c(i) s(i) ) ( x(i) z(i) ) ( c(i) -s(i) )
*> ( z(i) y(i) ) ( -s(i) c(i) ) ( z(i) y(i) ) ( s(i) c(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARF applies a real elementary reflector H to a real m by n matrix
*> C, from either the left or the right. H is represented in the form
*> where tau is a real scalar and v is a real vector.
*>
*> If tau = 0, then H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
* T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARFB applies a real block reflector H or its transpose H**T to a
*> real m by n matrix C, from either the left or the right.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
*
* DOUBLE PRECISION X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARFG generates a real elementary reflector H of order n, such
*> that
*> the unit matrix.
*>
*> Otherwise 1 <= tau <= 2.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is DOUBLE PRECISION
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )
*
* DOUBLE PRECISION X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARFGP generates a real elementary reflector H of order n, such
*> that
*>
*> If the elements of x are all zero, then tau = 0 and H is taken to be
*> the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is DOUBLE PRECISION
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARFT forms the triangular factor T of a real block reflector H
*> of order n, which is defined as a product of k elementary reflectors.
*> H(i) is stored in the i-th row of the array V, and
*>
*> H = I - V**T * T * V
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARFX( SIDE, M, N, V, TAU, C, LDC, WORK )
*
* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARFX applies a real elementary reflector H to a real m by n
*> matrix C, from either the left or the right. H is represented in the
*> If tau = 0, then H is taken to be the unit matrix
*>
*> This version uses inline code if H has order < 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> or (M) if SIDE = 'R'
*> WORK is not referenced if H has order < 11.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* DOUBLE PRECISION C( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARGV generates a vector of real plane rotations, determined by
*> elements of the real vectors x and y. For i = 1,2,...,n
*>
*> ( c(i) s(i) ) ( x(i) ) = ( a(i) )
*> ( -s(i) c(i) ) ( y(i) ) = ( 0 )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARNV( IDIST, ISEED, N, X )
*
* DOUBLE PRECISION X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARNV returns a vector of n random real numbers from a uniform or
*> normal distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (N)
*> The generated random numbers.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine DLARUV to generate random
*> real numbers from a uniform (0,1) distribution, in batches of up to
*> 128 using vectorisable code. The Box-Muller method is used to
*> transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
* NSPLIT, ISPLIT, INFO )
* DOUBLE PRECISION D( * ), E( * ), E2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute the splitting points with threshold SPLTOL.
*> DLARRA sets any "small" off-diagonal elements to zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
$ NSPLIT, ISPLIT, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
* RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK,
* $ WERR( * ), WGAP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given the relatively robust representation(RRR) L D L^T, DLARRB
*> does "limited" bisection to refine the eigenvalues of L D L^T,
*> and WGAP, respectively. During bisection, intervals
*> [left, right] are maintained by storing their mid-points and
*> semi-widths in the arrays W and WERR respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> Error flag.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
$ RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
* EIGCNT, LCNT, RCNT, INFO )
* DOUBLE PRECISION D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Find the number of eigenvalues of the symmetric tridiagonal matrix T
*> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
*> if JOBT = 'L'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBT
*> \verbatim
*> \verbatim
*> INFO is INTEGER
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
$ EIGCNT, LCNT, RCNT, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS,
* RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT,
* $ GERS( * ), W( * ), WERR( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARRD computes the eigenvalues of a symmetric tridiagonal
*> matrix T to suitable accuracy. This is an auxiliary code to be
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RANGE
*> \verbatim
*> floating-point arithmetic.
*> Cure: Increase the PARAMETER "FUDGE",
*> recompile, and try again.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> FUDGE DOUBLE PRECISION, default = 2
*> A "fudge factor" to widen the Gershgorin intervals. Ideally,
*> a value of 1 should work, but on machines with sloppy
*> publicly released versions should be large enough to handle
*> the worst machine around. Note that this has no effect
*> on accuracy of the solution.
-*>
-*> Based on contributions by
-*> W. Kahan, University of California, Berkeley, USA
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
*> \endverbatim
*>
+*> \par Contributors:
+* ==================
+*>
+*> W. Kahan, University of California, Berkeley, USA \n
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,
* RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M,
* $ W( * ),WERR( * ), WGAP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> To find the desired eigenvalues of a given real symmetric
*> tridiagonal matrix T, DLARRE sets any "small" off-diagonal
*> conpute all and then discard any unwanted one.
*> As an added benefit, DLARRE also outputs the n
*> Gerschgorin intervals for the matrices L_i D_i L_i^T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RANGE
*> \verbatim
*> =-5: Problem in DLASQ2.
*> =-6: Problem in DLASQ2.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The base representations are required to suffer very little
*> element growth and consequently define all their eigenvalues to
*> high relative accuracy.
-*> ===============
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRF( N, D, L, LD, CLSTRT, CLEND,
* W, WGAP, WERR,
* $ LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given the initial representation L D L^T and its cluster of close
*> eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
*> W( CLEND ), DLARRF finds a new relatively robust representation
*> L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the
*> eigenvalues of L(+) D(+) L(+)^T is relatively isolated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> Signals processing OK (=0) or failure (=1)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRF( N, D, L, LD, CLSTRT, CLEND,
$ W, WGAP, WERR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
* RTOL, OFFSET, W, WERR, WORK, IWORK,
* $ WERR( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given the initial eigenvalue approximations of T, DLARRJ
*> does bisection to refine the eigenvalues of T,
*> of the error in these guesses in WERR. During bisection, intervals
*> [left, right] are maintained by storing their mid-points and
*> semi-widths in the arrays W and WERR respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> Error flag.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
$ RTOL, OFFSET, W, WERR, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRK( N, IW, GL, GU,
* D, E2, PIVMIN, RELTOL, W, WERR, INFO)
* DOUBLE PRECISION D( * ), E2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARRK computes one eigenvalue of a symmetric tridiagonal
*> matrix T to suitable accuracy. This is an auxiliary code to be
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: Eigenvalue converged
*> = -1: Eigenvalue did NOT converge
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> FUDGE DOUBLE PRECISION, default = 2
*> A "fudge factor" to widen the Gershgorin intervals.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRR( N, D, E, INFO )
*
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Perform tests to decide whether the symmetric tridiagonal matrix T
*> warrants expensive computations which guarantee high relative accuracy
*> in the eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO = 1 : the matrix warrants computations guaranteeing
*> only absolute accuracy.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRR( N, D, E, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN,
* ISPLIT, M, DOL, DOU, MINRGP,
* DOUBLE PRECISION Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARRV computes the eigenvectors of the tridiagonal matrix
*> T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
*> The input eigenvalues should have been computed by DLARRE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 5: The Rayleigh Quotient Iteration failed to converge to
*> full accuracy in MAXITR steps.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN,
$ ISPLIT, M, DOL, DOU, MINRGP,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARSCL2 ( M, N, D, X, LDX )
*
* DOUBLE PRECISION D( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARSCL2 performs a reciprocal diagonal scaling on an vector:
*> x <-- inv(D) * x
*>
*> Eventually to be replaced by BLAS_dge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARTG( F, G, CS, SN, R )
*
* DOUBLE PRECISION CS, F, G, R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARTG generate a plane rotation so that
*>
*> there are zeros on the diagonal).
*>
*> If F exceeds G in magnitude, CS will be positive.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARTGP( F, G, CS, SN, R )
*
* DOUBLE PRECISION CS, F, G, R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARTGP generates a plane rotation so that
*>
*> If F=0 and (G .ne. 0), then CS=0 and SN=(+/-)1.
*>
*> The sign is chosen so that R >= 0.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )
*
* DOUBLE PRECISION CS, SIGMA, SN, X, Y
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARTGS generates a plane rotation designed to introduce a bulge in
*> Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
*>
*> with R nonnegative. If X^2 - SIGMA and X * Y are 0, then the
*> rotation is by PI/2.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> SN is DOUBLE PRECISION
*> The sine of the rotation.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARTV( N, X, INCX, Y, INCY, C, S, INCC )
*
* DOUBLE PRECISION C( * ), S( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARTV applies a vector of real plane rotations to elements of the
*> real vectors x and y. For i = 1,2,...,n
*>
*> ( x(i) ) := ( c(i) s(i) ) ( x(i) )
*> ( y(i) ) ( -s(i) c(i) ) ( y(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARUV( ISEED, N, X )
*
* DOUBLE PRECISION X( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARUV returns a vector of n random real numbers from a uniform (0,1)
*> distribution (n <= 128).
*>
*> This is an auxiliary routine called by DLARNV and ZLARNV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] ISEED
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (N)
*> The generated random numbers.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine uses a multiplicative congruential method with modulus
*> 48-bit integers are stored in 4 integer array elements with 12 bits
*> per element. Hence the routine is portable across machines with
*> integers of 32 bits or more.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARZ applies a real elementary reflector H to a real M-by-N
*> matrix C, from either the left or the right. H is represented in the
*>
*>
*> H is a product of k elementary reflectors as returned by DTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
* LDV, T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARZB applies a real block reflector H or its transpose H**T to
*> a real distributed M-by-N C from the left or the right.
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARZT forms the triangular factor T of a real block reflector
*> H of order > n, which is defined as a product of k elementary
*> H = I - V**T * T * V
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> the H(i) is best illustrated by the following example with n = 5 and
*> V = ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> ( v1 v2 v3 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
*
* DOUBLE PRECISION F, G, H, SSMAX, SSMIN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAS2 computes the singular values of the 2-by-2 matrix
*> [ F G ]
*> [ 0 H ].
*> On return, SSMIN is the smaller singular value and SSMAX is the
*> larger singular value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> SSMAX is DOUBLE PRECISION
*> The larger singular value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Barring over/underflow, all output quantities are correct to within
*> Underflow is harmless if underflow is gradual. Otherwise, results
*> may correspond to a matrix modified by perturbations of size near
*> the underflow threshold.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASCL multiplies the M by N real matrix A by the real scalar
*> CTO/CFROM. This is done without over/underflow as long as the final
*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
*> A may be full, upper triangular, lower triangular, upper Hessenberg,
*> or banded.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> 0 - successful exit
*> <0 - if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASCL2 ( M, N, D, X, LDX )
*
* DOUBLE PRECISION D( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASCL2 performs a diagonal scaling on a vector:
*> x <-- D * x
*>
*> Eventually to be replaced by BLAS_dge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
* WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Using a divide and conquer approach, DLASD0 computes the singular
*> value decomposition (SVD) of a real upper bidiagonal N-by-M
*>
*> A related subroutine, DLASDA, computes only the singular values,
*> and optionally, the singular vectors in compact form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
$ WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD1( NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT,
* IDXQ, IWORK, WORK, INFO )
* DOUBLE PRECISION D( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B,
*> where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0.
*> directly using the updated singular values. The singular vectors
*> for the current problem are multiplied with the singular vectors
*> from the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NL
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD1( NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT,
$ IDXQ, IWORK, WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT,
* LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX,
* $ Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASD2 merges the two sets of singular values together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> equation problem is reduced by one.
*>
*> DLASD2 is called from DLASD1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NL
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT,
$ LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
* LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z,
* $ Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASD3 finds all the square roots of the roots of the secular
*> equation, as defined by the values in D and Z. It makes the
*> without guard digits, but we know of none.
*>
*> DLASD3 is called from DLASD1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NL
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
$ LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the square root of the I-th updated
*> eigenvalue of a positive symmetric rank-one modification to
*>
*> The method consists of approximating the rational functions in the
*> secular equation by simpler interpolating rational functions.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> > 0: if INFO = 1, the updating process failed.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> Logical variable ORGATI (origin-at-i?) is used for distinguishing
*> whether D(i) or D(i+1) is treated as the origin.
*>
*> MAXIT is the maximum number of iterations allowed for each
*> eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
*
* DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the square root of the I-th eigenvalue
*> of a positive symmetric rank-one modification of a 2-by-2 diagonal
*>
*> We also assume RHO > 0 and that the Euclidean norm of the vector
*> Z is one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension ( 2 )
*> WORK contains (D(j) + sigma_I) in its j-th component.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
* $ VF( * ), VL( * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASD6 computes the SVD of an updated upper bidiagonal matrix B
*> obtained by merging two smaller ones by appending a row. This
*> values.
*>
*> DLASD6 is called from DLASDA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
$ IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL,
* VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ,
* $ ZW( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASD7 merges the two sets of singular values together into a single
*> sorted set. Then it tries to deflate the size of the problem. There
*> secular equation problem is reduced by one.
*>
*> DLASD7 is called from DLASD6.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL,
$ VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
* DSIGMA, WORK, INFO )
* $ Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASD8 finds the square roots of the roots of the secular equation,
*> as defined by the values in DSIGMA and Z. It makes the appropriate
*> right singular vectors of the original bidiagonal matrix.
*>
*> DLASD8 is called from DLASD6.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
$ DSIGMA, WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
* $ Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Using a divide and conquer approach, DLASDA computes the singular
*> value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
*>
*> A related subroutine, DLASD0, computes the singular values and
*> the singular vectors in explicit form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
$ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT,
* U, LDU, C, LDC, WORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASDQ computes the singular value decomposition (SVD) of a real
*> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
*> See "Computing Small Singular Values of Bidiagonal Matrices With
*> Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
*> LAPACK Working Note #3, for a detailed description of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If INFO > 0, the algorithm did not converge, and INFO
*> specifies how many superdiagonals did not converge.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT,
$ U, LDU, C, LDC, WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
* INTEGER INODE( * ), NDIML( * ), NDIMR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASDT creates a tree of subproblems for bidiagonal divide and
*> conquer.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On entry, the maximum row dimension each subproblem at the
*> bottom of the tree can be of.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASET initializes an m-by-n matrix A to BETA on the diagonal and
*> ALPHA on the offdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
*
* DOUBLE PRECISION D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASQ1 computes the singular values of a real N-by-N bidiagonal
*> matrix with diagonal D and off-diagonal E. The singular values
*>
*> and the present implementation is described in "An implementation of
*> the dqds Algorithm (Positive Case)", LAPACK Working Note.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 3, termination criterion of outer while loop not met
*> (program created more than N unreduced blocks)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASQ2( N, Z, INFO )
*
* DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASQ2 computes all the eigenvalues of the symmetric positive
*> definite tridiagonal matrix associated with the qd array Z to high
*> on machines which follow ieee-754 floating-point standard in their
*> handling of infinities and NaNs, and false otherwise. This variable
*> is passed to DLASQ3.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 3, termination criterion of outer while loop not met
*> (program created more than N unreduced blocks)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Local Variables: I0:N0 defines a current unreduced segment of Z.
*> The shifts are accumulated in SIGMA. Iteration count is in ITER.
*> Ping-pong is controlled by PP (alternates between 0 and 1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
* DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
*> In case of failure it changes shifts, and tries again until output
*> is positive.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> These are passed as arguments in order to save their values
*> between calls to DLASQ3.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
* DN1, DN2, TAU, TTYPE, G )
* DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASQ4 computes an approximation TAU to the smallest eigenvalue
*> using values of d from the previous transform.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> G is passed as an argument in order to save its value between
*> calls to DLASQ4.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> CNST1 = 9/16
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2, IEEE )
* DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASQ5 computes one dqds transform in ping-pong form, one
*> version for IEEE machines another for non IEEE machines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> IEEE is LOGICAL
*> Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2 )
* DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASQ6 computes one dqd (shift equal to zero) transform in
*> ping-pong form, with protection against underflow and overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> DNM2 is DOUBLE PRECISION
*> d(N0-2).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
* DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASR applies a sequence of plane rotations to a real matrix A,
*> from either the left or the right.
*>
*> where R(k) appears in rows and columns k and z. The rotations are
*> performed without ever forming P(k) explicitly.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASRT( ID, N, D, INFO )
*
* DOUBLE PRECISION D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Sort the numbers in D in increasing order (if ID = 'I') or
*> in decreasing order (if ID = 'D' ).
*>
*> Use Quick Sort, reverting to Insertion sort on arrays of
*> size <= 20. Dimension of STACK limits N to about 2**32.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ID
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* DOUBLE PRECISION X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASSQ returns the values scl and smsq such that
*>
*> scl and smsq are overwritten on SCALE and SUMSQ respectively.
*>
*> The routine makes only one pass through the vector x.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On exit, SUMSQ is overwritten with smsq , the basic sum of
*> squares from which scl has been factored out.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
*
* DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASV2 computes the singular value decomposition of a 2-by-2
*> triangular matrix
*>
*> [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ]
*> [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ].
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> The vector (CSR, SNR) is a unit right singular vector for the
*> singular value abs(SSMAX).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Any input parameter may be aliased with any output parameter.
*> Underflow is harmless if underflow is gradual. Otherwise, results
*> may correspond to a matrix modified by perturbations of size near
*> the underflow threshold.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASWP performs a series of row interchanges on the matrix A.
*> One row interchange is initiated for each of rows K1 through K2 of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of IPIV. If IPIV
*> is negative, the pivots are applied in reverse order.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by
*> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR,
* LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in
*>
*>
*> where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or
*> -1. op(T) = T or T**T, where T**T denotes the transpose of T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LTRANL
*> \verbatim
*> NOTE: In the interests of speed, this routine does not
*> check the inputs for errors.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
* DOUBLE PRECISION A( LDA, * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLASYF computes a partial factorization of a real symmetric matrix A
*> using the Bunch-Kaufman diagonal pivoting method. The partial
*> DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code
*> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
*> A22 (if UPLO = 'L').
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAT2S( UPLO, N, A, LDA, SA, LDSA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAT2S converts a DOUBLE PRECISION triangular matrix, SA, to a SINGLE
*> PRECISION triangular matrix, A.
*> RMAX. If not the convertion is aborted and a flag is raised.
*>
*> This is an auxiliary routine so there is no argument checking.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> PRECISION overflow threshold, in this case, the content
*> of the UPLO part of SA in exit is unspecified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
* SCALE, CNORM, INFO )
* DOUBLE PRECISION AB( LDAB, * ), CNORM( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATBS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine DTBSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, DTBSV
*>
*> and we can safely call DTBSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
* JPIV )
* DOUBLE PRECISION RHS( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATDF uses the LU factorization of the n-by-n matrix Z computed by
*> DGETC2 and computes a contribution to the reciprocal Dif-estimate
*> The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,
*> where P and Q are permutation matrices. L is lower triangular with
*> unit diagonal elements and U is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> The pivot indices; for 1 <= j <= N, column j of the
*> matrix has been interchanged with column JPIV(j).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
+*> \par Further Details:
+* =====================
+*>
+*> This routine is a further developed implementation of algorithm
+*> BSOLVE in [1] using complete pivoting in the LU factorization.
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
-*> This routine is a further developed implementation of algorithm
-*> BSOLVE in [1] using complete pivoting in the LU factorization.
*>
*> [1] Bo Kagstrom and Lars Westin,
*> Generalized Schur Methods with Condition Estimators for
*> between two Regular Matrix Pairs with Applications in
*> Condition Estimation. Report IMINF-95.05, Departement of
*> Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATPS( UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE,
* CNORM, INFO )
* DOUBLE PRECISION AP( * ), CNORM( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATPS solves one of the triangular systems
*>
*> unscaled problem will not cause overflow, the Level 2 BLAS routine
*> DTPSV is called. If the matrix A is singular (A(j,j) = 0 for some j),
*> then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, DTPSV
*>
*> and we can safely call DTPSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
* DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATRD reduces NB rows and columns of a real symmetric matrix A to
*> symmetric tridiagonal form by an orthogonal similarity
*> matrix, of which the lower triangle is supplied.
*>
*> This is an auxiliary routine called by DSYTRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDW is INTEGER
*> The leading dimension of the array W. LDW >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where d denotes a diagonal element of the reduced matrix, a denotes
*> an element of the original matrix that is unchanged, and vi denotes
*> an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
* CNORM, INFO )
* DOUBLE PRECISION A( LDA, * ), CNORM( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATRS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine DTRSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, DTRSV
*>
*> and we can safely call DTRSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
*> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means
*> of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal
*> matrix and, R and A1 are M-by-M upper triangular matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
* DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DORMRZ.
*>
*> C = [ C1, C2 ] m
*> 1 n-1
*> Then C is overwritten by C*P.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAUU2( UPLO, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAUU2 computes the product U * U**T or L**T * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the unblocked form of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAUUM computes the product U * U**T or L**T * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the blocked form of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
* DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DOPGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
* INFO )
* DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DOPMTR overwrites the general real M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
* $ X21( LDX21, * ), X22( LDX22, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORBDB simultaneously bidiagonalizes the blocks of an M-by-M
*> partitioned orthogonal matrix X:
*>
*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
*> implicitly by angles THETA, PHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The bidiagonal blocks B11, B12, B21, and B22 are represented
*> P1, P2, Q1, and Q2 are represented as products of elementary
*> reflectors. See DORCSD for details on generating P1, P2, Q1, and Q2
*> using DORGQR and DORGLQ.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
* SIGNS, M, P, Q, X11, LDX11, X12,
* $ * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORCSD computes the CS decomposition of an M-by-M partitioned
*> orthogonal matrix X:
*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
*> which R = MIN(P,M-P,Q,M-Q).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: DBBCSD did not converge. See the description of WORK
*> above for details.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
-*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORG2L generates an m by n real matrix Q with orthonormal columns,
*> which is defined as the last n columns of a product of k elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by DGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORG2R generates an m by n real matrix Q with orthonormal columns,
*> which is defined as the first n columns of a product of k elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by DGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGBR generates one of the real orthogonal matrices Q or P**T
*> determined by DGEBRD when reducing a real matrix A to bidiagonal
*> rows of P**T, where n >= m >= k;
*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
*> an N-by-N matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGHR generates a real orthogonal matrix Q which is defined as the
*> product of IHI-ILO elementary reflectors of order N, as returned by
*> DGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGL2 generates an m by n real matrix Q with orthonormal rows,
*> which is defined as the first m rows of a product of k elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by DGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGLQ generates an M-by-N real matrix Q with orthonormal rows,
*> which is defined as the first M rows of a product of K elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by DGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGQL generates an M-by-N real matrix Q with orthonormal columns,
*> which is defined as the last N columns of a product of K elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by DGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGQR generates an M-by-N real matrix Q with orthonormal columns,
*> which is defined as the first N columns of a product of K elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by DGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGR2 generates an m by n real matrix Q with orthonormal rows,
*> which is defined as the last m rows of a product of k elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by DGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGRQ generates an M-by-N real matrix Q with orthonormal rows,
*> which is defined as the last M rows of a product of K elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by DGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors of order N, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORM2L overwrites the general real m by n matrix C with
*>
*>
*> as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORM2R overwrites the general real m by n matrix C with
*>
*>
*> as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
*> with
*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
*> if k < nq, P = G(1) G(2) . . . G(k);
*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMHR overwrites the general real M-by-N matrix C with
*>
*> IHI-ILO elementary reflectors, as returned by DGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORML2 overwrites the general real m by n matrix C with
*>
*>
*> as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMLQ overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMQL overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMQR overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMR2 overwrites the general real m by n matrix C with
*>
*>
*> as returned by DGERQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMR3 overwrites the general real m by n matrix C with
*>
*>
*> as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMRQ overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMRZ overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORMTR overwrites the general real M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
* IWORK, INFO )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite band matrix using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )
*
* DOUBLE PRECISION AB( LDAB, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite band matrix A and reduce its condition
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B,
* LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite
*> and banded, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO )
*
* DOUBLE PRECISION AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBSTF computes a split Cholesky factorization of a real
*> symmetric positive definite band matrix A.
*>
*> where U is upper triangular of order m = (n+kd)/2, and L is lower
*> triangular of order n-m.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> because the updated element a(i,i) was negative; the
*> matrix A is not positive definite.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBSV computes the solution to a real system of linear equations
*> A * X = B,
*> triangular band matrix, with the same number of superdiagonals or
*> subdiagonals as A. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBSVX( FACT, UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB,
* EQUED, S, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
*> compute the solution to a real system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
* DOUBLE PRECISION AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBTF2 computes the Cholesky factorization of a real symmetric
*> positive definite band matrix A.
*> L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
* DOUBLE PRECISION AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBTRF computes the Cholesky factorization of a real symmetric
*> positive definite band matrix A.
*> A = U**T * U, if UPLO = 'U', or
*> A = L * L**T, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
-*> Contributed by
-*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
+*
* =====================================================================
SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite band matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by DPBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO )
*
* .. Array Arguments ..
* DOUBLE PRECISION A( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPFTRF computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
*
* DOUBLE PRECISION A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPFTRI computes the inverse of a (real) symmetric positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by DPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* DOUBLE PRECISION A( 0: * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPFTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by DPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
* INFO )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite matrix using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
*
* DOUBLE PRECISION A( LDA, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
*
* DOUBLE PRECISION A( LDA, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X,
* LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPORFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite,
*> and provides error bounds and backward error estimates for the
*> solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
* LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPORFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOSV computes the solution to a real system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK,
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
*> compute the solution to a real system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
*> to compute the solution to a double precision system of linear equations
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what DPOSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOTF2 computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOTRF computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOTRI( UPLO, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOTRI computes the inverse of a real symmetric positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by DPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by DPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )
*
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite packed matrix using
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
*
* DOUBLE PRECISION AP( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A in packed storage and reduce
*> This choice of S puts the condition number of B within a factor N of
*> the smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR,
* BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* DOUBLE PRECISION AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPSV computes the solution to a real system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPSVX( FACT, UPLO, N, NRHS, AP, AFP, EQUED, S, B, LDB,
* X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), S( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
*> compute the solution to a real system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
*
* DOUBLE PRECISION AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPTRF computes the Cholesky factorization of a real symmetric
*> positive definite matrix A stored in packed format.
*> A = U**T * U, if UPLO = 'U', or
*> A = L * L**T, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPTRI( UPLO, N, AP, INFO )
*
* DOUBLE PRECISION AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPTRI computes the inverse of a real symmetric positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by DPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* DOUBLE PRECISION AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A in packed storage using the Cholesky
*> factorization A = U**T*U or A = L*L**T computed by DPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPSTF2 computes the Cholesky factorization with complete
*> pivoting of a real symmetric positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPSTRF computes the Cholesky factorization with complete
*> pivoting of a real symmetric positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
*
* DOUBLE PRECISION D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTCON computes the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite tridiagonal matrix
*> Norm(inv(A)) is computed by a direct method, and the reciprocal of
*> the condition number is computed as
*> RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The method used is described in Nicholas J. Higham, "Efficient
*> Algorithms for Computing the Condition Number of a Tridiagonal
*> Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric positive definite tridiagonal matrix by first factoring the
*> form, however, may preclude the possibility of obtaining high
*> relative accuracy in the small eigenvalues of the original matrix, if
*> these eigenvalues range over many orders of magnitude.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> if INFO = N+i, i off-diagonal elements of the
*> bidiagonal factor did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
* BERR, WORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite
*> and tridiagonal, and provides error bounds and backward error
*> estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTSV( N, NRHS, D, E, B, LDB, INFO )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTSV computes the solution to a real system of linear equations
*> A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
*>
*> A is factored as A = L*D*L**T, and the factored form of A is then
*> used to solve the system of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> computed. The factorization has not been completed
*> unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
* RCOND, FERR, BERR, WORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTSVX uses the factorization A = L*D*L**T to compute the solution
*> to a real system of linear equations A*X = B, where A is an N-by-N
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTTRF( N, D, E, INFO )
*
* DOUBLE PRECISION D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTTRF computes the L*D*L**T factorization of a real symmetric
*> positive definite tridiagonal matrix A. The factorization may also
*> be regarded as having the form A = U**T*D*U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be completed, while if k = N, the factorization was
*> completed, but D(N) <= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTTRS( N, NRHS, D, E, B, LDB, INFO )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTTRS solves a tridiagonal system of the form
*> A * X = B
*> diagonal matrix specified in the vector D, L is a unit bidiagonal
*> matrix whose subdiagonal is specified in the vector E, and X and B
*> are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTTS2 solves a tridiagonal system of the form
*> A * X = B
*> diagonal matrix specified in the vector D, L is a unit bidiagonal
*> matrix whose subdiagonal is specified in the vector E, and X and B
*> are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DRSCL( N, SA, SX, INCX )
*
* DOUBLE PRECISION SX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DRSCL multiplies an n-element real vector x by the real scalar 1/a.
*> This is done without overflow or underflow as long as
*> the final result x/a does not overflow or underflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of the vector SX.
*> > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* INFO )
* DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBEV computes all the eigenvalues and, optionally, eigenvectors of
*> a real symmetric band matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* LWORK, IWORK, LIWORK, INFO )
* DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
*> a real symmetric band matrix A. If eigenvectors are desired, it uses
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric band matrix A. Eigenvalues and eigenvectors can
*> be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
* LDX, WORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBGST reduces a real symmetric-definite banded generalized
*> eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
*> split Cholesky factorization. A is overwritten by C = X**T*A*X, where
*> X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
*> bandwidth of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
*> and banded, and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of the
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
* LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
* $ W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of
*> and banded, and B is also positive definite. Eigenvalues and
*> eigenvectors can be selected by specifying either all eigenvalues,
*> a range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
$ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
* WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBTRD reduces a real symmetric band matrix A to symmetric
*> tridiagonal form T by an orthogonal similarity transformation:
*> Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by Linda Kaufman, Bell Labs.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
* C )
* DOUBLE PRECISION A( LDA, * ), C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for C in RFP Format.
*>
*> where alpha and beta are real scalars, C is an n--by--n symmetric
*> matrix and A is an n--by--k matrix in the first case and a k--by--n
*> matrix in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP
*> Format. RFP Format is described by TRANSR, UPLO and N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,
* SWORK, ITER, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSGESV computes the solution to a real system of linear equations
*> A * X = B,
*> o EPS is the machine epsilon returned by DLAMCH('Epsilon')
*> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
*> respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> but the factor U is exactly singular, so the solution
*> could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
* INFO )
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric packed matrix A using the factorization
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
*
* DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A in packed storage.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
* IWORK, LIWORK, INFO )
* DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPEVD computes all the eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A in packed storage. If eigenvectors are
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL,
* DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A in packed storage. Eigenvalues/vectors
*> can be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
*
* DOUBLE PRECISION AP( * ), BP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPGST reduces a real symmetric-definite generalized eigenproblem
*> to standard form, using packed storage.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
*>
*> B must have been previously factorized as U**T*U or L*L**T by DPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPGV computes all the eigenvalues and, optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be symmetric, stored in packed format,
*> and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* LWORK, IWORK, LIWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ LWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
* IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> is also positive definite. Eigenvalues and eigenvectors can be
*> selected by specifying either a range of values or a range of indices
*> for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
$ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,
* SWORK, ITER, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPOSV computes the solution to a real system of linear equations
*> A * X = B,
*> o EPS is the machine epsilon returned by DLAMCH('Epsilon')
*> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
*> respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> factorization could not be completed, and the solution
*> has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
* FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* DOUBLE PRECISION AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPSV computes the solution to a real system of linear equations
*> A * X = B,
*> triangular matrices, D is symmetric and block diagonal with 1-by-1
*> and 2-by-2 diagonal blocks. The factored form of A is then used to
*> solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, so the solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X,
* LDX, RCOND, FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
*> A = L*D*L**T to compute the solution to a real system of linear
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )
*
* DOUBLE PRECISION AP( * ), D( * ), E( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPTRD reduces a real symmetric matrix A stored in packed form to
*> symmetric tridiagonal form T by an orthogonal similarity
*> transformation: Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where tau is a real scalar, and v is a real vector with
*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
*> overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO )
*
* DOUBLE PRECISION AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPTRF computes the factorization of a real symmetric matrix A stored
*> in packed format using the Bunch-Kaufman diagonal pivoting method:
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> J. Lewis, Boeing Computer Services Company
*>
* =====================================================================
SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPTRI computes the inverse of a real symmetric indefinite matrix
*> A in packed storage using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by DSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* DOUBLE PRECISION AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPTRS solves a system of linear equations A*X = B with a real
*> symmetric matrix A stored in packed format using the factorization
*> A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E,
* M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK,
* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEBZ computes the eigenvalues of a symmetric tridiagonal
*> matrix T. The user may ask for all eigenvalues, all eigenvalues
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RANGE
*> \verbatim
*> floating-point arithmetic.
*> Cure: Increase the PARAMETER "FUDGE",
*> recompile, and try again.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> RELFAC DOUBLE PRECISION, default = 2.0e0
*> The relative tolerance. An interval (a,b] lies within
*> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|),
*> the worst machine around. Note that this has no effect
*> on accuracy of the solution.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
* LIWORK, INFO )
* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none. See DLAED3 for details.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
* DOUBLE PRECISION Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEGR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> NaNs. Normal execution may create these exceptiona values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by DLARRE or
*> DLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, LBNL/NERSC, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
* IWORK, IFAIL, INFO )
* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEIN computes the eigenvectors of a real symmetric tridiagonal
*> matrix T corresponding to specified eigenvalues, using inverse
*>
*> The maximum number of iterations allowed for each eigenvector is
*> specified by an internal parameter MAXITS (currently set to 5).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge
*> in MAXITS iterations. Their indices are stored in
*> array IFAIL.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> MAXITS INTEGER, default = 5
*> The maximum number of iterations performed.
*>
*> The number of iterations performed after norm growth
*> criterion is satisfied, should be at least 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
* DOUBLE PRECISION Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEMR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> floating-point standard in their handling of infinities and NaNs.
*> This permits the use of efficient inner loops avoiding a check for
*> zero divisors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by DLARRE or
*> DLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the implicit QL or QR method.
*> The eigenvectors of a full or band symmetric matrix can also be found
*> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to
*> tridiagonal form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> matrix which is orthogonally similar to the original
*> matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTERF( N, D, E, INFO )
*
* DOUBLE PRECISION D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTERF computes all eigenvalues of a symmetric tridiagonal matrix
*> using the Pal-Walker-Kahan variant of the QL or QR algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> a total of 30*N iterations; if INFO = i, then i
*> elements of E have not converged to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
*
* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEV computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric tridiagonal matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, the algorithm failed to converge; i
*> off-diagonal elements of E did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
* LIWORK, INFO )
* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric tridiagonal matrix. If eigenvectors are desired, it
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, the algorithm failed to converge; i
*> off-diagonal elements of E did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
* M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEVR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Eigenvalues and
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
-*> California at Berkeley, USA
-*>
-*> \endverbatim
+*> California at Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
* M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix A. Eigenvalues and
*> eigenvectors can be selected by specifying either a range of values
*> or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* IWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric matrix A using the factorization
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYCONV( UPLO, WAY, N, A, LDA, IPIV, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYCONV convert A given by TRF into L and D and vice-versa.
*> Get Non-diag elements of D (returned in workspace) and
*> apply or reverse permutation done in TRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYEQUB computes row and column scalings intended to equilibrate a
*> symmetric matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par References:
+* ================
*>
-*> Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
-*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
-*> DOI 10.1023/B:NUMA.0000016606.32820.69
+*> Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n
+*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n
+*> DOI 10.1023/B:NUMA.0000016606.32820.69 \n
*> Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYEV computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
* LIWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A. If eigenvectors are desired, it uses a
*>
*> Because of large use of BLAS of level 3, DSYEVD needs N**2 more
*> workspace than DSYEVX.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> lying in rows and columns INFO/(N+1) through
*> mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> Modified description of INFO. Sven, 16 Feb 05.
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee \n
+*> Modified description of INFO. Sven, 16 Feb 05. \n
+
+
*>
* =====================================================================
SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYEVR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A. Eigenvalues and eigenvectors can be
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
-*> California at Berkeley, USA
+*> California at Berkeley, USA \n
*> Jason Riedy, Computer Science Division, University of
-*> California at Berkeley, USA
-*>
-*> \endverbatim
+*> California at Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK,
* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A. Eigenvalues and eigenvectors can be
*> selected by specifying either a range of values or a range of indices
*> for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYGS2 reduces a real symmetric-definite generalized eigenproblem
*> to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
*>
*> B must have been previously factorized as U**T *U or L*L**T by DPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYGST reduces a real symmetric-definite generalized eigenproblem
*> to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
*>
*> B must have been previously factorized as U**T*U or L*L**T by DPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be symmetric and B is also
*> positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, IWORK, LIWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> Based on contributions by
-*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*> \verbatim
*>
*> Modified so that no backsubstitution is performed if DSYEVD fails to
*> converge (NEIG in old code could be greater than N causing out of
*> bounds reference to A - reported by Ralf Meyer). Also corrected the
*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*>
* =====================================================================
SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
* VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> and B are assumed to be symmetric and B is also positive definite.
*> Eigenvalues and eigenvectors can be selected by specifying either a
*> range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
$ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> provides error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYRFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYSV computes the solution to a real system of linear equations
*> A * X = B,
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
*> used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
* LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK,
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYSVX uses the diagonal pivoting factorization to compute the
*> solution to a real system of linear equations A * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYSVXX uses the diagonal pivoting factorization to compute the
*> solution to a double precision system of linear equations A * X = B, where A
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what DSYSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(R) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYSWAPR( UPLO, N, A, LDA, I1, I2)
*
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, N )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYSWAPR applies an elementary permutation on the rows and the columns of
*> a symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> I2 is INTEGER
*> Index of the second row to swap
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )
*
* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
*> form T by an orthogonal similarity transformation: Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTF2 computes the factorization of a real symmetric matrix A using
*> the Bunch-Kaufman diagonal pivoting method:
*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 09-29-06 - patch from
-*> Bobby Cheng, MathWorks
-*>
-*> Replace l.204 and l.372
-*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
-*> by
-*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
-*>
-*> 01-01-96 - Based on modifications by
-*> J. Lewis, Boeing Computer Services Company
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
*>
+*> 09-29-06 - patch from
+*> Bobby Cheng, MathWorks
+*>
+*> Replace l.204 and l.372
+*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*> by
+*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
+*>
+*> 01-01-96 - Based on modifications by
+*> J. Lewis, Boeing Computer Services Company
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
+*> Company
+*> \endverbatim
+*
* =====================================================================
SUBROUTINE DSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRD reduces a real symmetric matrix A to real symmetric
*> tridiagonal form T by an orthogonal similarity transformation:
*> Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRF computes the factorization of a real symmetric matrix A using
*> the Bunch-Kaufman diagonal pivoting method. The form of the
*> 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRI computes the inverse of a real symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> DSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRI2 computes the inverse of a DOUBLE PRECISION hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> DSYTRF. DSYTRI2 sets the LEADING DIMENSION of the workspace
*> before calling DSYTRI2X that actually computes the inverse.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRI2X computes the inverse of a real symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> DSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRS solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by DSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYTRS2 solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by DSYTRF and converted by DSYCONV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
* IWORK, INFO )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBCON estimates the reciprocal of the condition number of a
*> triangular band matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular band
*> The solution matrix X must be computed by DTBTRS or some other
*> means before entering this routine. DTBRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, INFO )
* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBTRS solves a triangular system of the form
*>
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by NRHS matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
* B, LDB )
* DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for A in RFP Format.
*>
*> A is in Rectangular Full Packed (RFP) Format.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> max( 1, m ).
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
$ B, LDB )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
* DOUBLE PRECISION A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTFTRI computes the inverse of a triangular matrix A stored in RFP
*> format.
*>
*> This is a Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTFTTP copies a triangular matrix A from rectangular full packed
*> format (TF) to standard packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
* DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTFTTR copies a triangular matrix A from rectangular full packed
*> format (TF) to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
* LDVL, VR, LDVR, MM, M, WORK, INFO )
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGEVC computes some or all of the right and/or left eigenvectors of
*> a pair of real matrices (S,P), where S is a quasi-triangular matrix
*> factorization of a matrix pair (A,B), then Z*X and Q*Y
*> are the matrices of right and left eigenvectors of (A,B).
*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> > 0: the 2-by-2 block (INFO:INFO+1) does not have a complex
*> eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Allocation of workspace:
*> transpose of the one in storage, so the rowwise method then
*> actually accesses columns of A and B at each step, and so is the
*> preferred method.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, J1, N1, N2, WORK, LWORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
*> of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
*> Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
*> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> <0: If INFO = -16: LWORK is too small. Appropriate value
*> for LWORK is returned in WORK(1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
-*> Umea University, S-901 87 Umea, Sweden.
+*> \par Further Details:
+* =====================
*>
*> In the current code both weak and strong stability tests are
*> performed. The user can omit the strong stability test by changing
*> the internal logical parameter WANDS to .FALSE.. See ref. [2] for
*> details.
+*
+*> \par Contributors:
+* ==================
+*>
+*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
+*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Report UMINF - 94.04, Department of Computing Science, Umea
*> University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
*> Note 87. To appear in Numerical Algorithms, 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, IFST, ILST, WORK, LWORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGEXC reorders the generalized real Schur decomposition of a real
*> matrix pair (A,B) using an orthogonal equivalence transformation
*> Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
*> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> and ILST points to the first row of the current
*> position of the block being moved.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB,
* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL,
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGSEN reorders the generalized real Schur decomposition of a real
*> matrix pair (A, B) (in terms of an orthonormal equivalence trans-
*> the selected cluster and the eigenvalues outside the cluster, resp.,
*> and norms of "projections" onto left and right eigenspaces w.r.t.
*> the selected cluster in the (1,1)-block.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> (A, B) may have been partially reordered.
*> If requested, 0 is returned in DIF(*), PL and PR.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> DTGSEN first collects the selected eigenvalues by computing
*> based estimate DIF is not wanted (see DLATDF), then the parameter
*> IDIFJB (see below) should be changed from 3 to 4 (routine DLATDF
*> (IJOB = 2 will be used)). See DTGSYL for more details.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGSJA computes the generalized singular value decomposition (GSVD)
*> of two real upper triangular (or trapezoidal) matrices A and B.
*> The computation of the orthogonal transformation matrices U, V or Q
*> is optional. These matrices may either be formed explicitly, or they
*> may be postmultiplied into input matrices U1, V1, or Q1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> may take. If after MAXIT cycles, the routine fails to
*> converge, we return INFO = 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> DTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
*> C1**2 + S1**2 = I,
*>
*> and R1 is an L-by-L nonsingular upper triangular matrix.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK,
* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or eigenvectors of a matrix pair (A, B) in
*> i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal
*> blocks. B is upper triangular.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> =0: Successful exit
*> <0: If INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of a generalized eigenvalue
*> EPS * norm(A, B) / DIF(i).
*>
*> See ref. [2-3] for more details and further references.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
*> No 1, 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
* $ D( LDD, * ), E( LDE, * ), F( LDF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGSY2 solves the generalized Sylvester equation:
*>
*> of an upper bound on the separation between to matrix pairs. Then
*> the input (A, D), (B, E) are sub-pencils of the matrix pair in
*> DTGSYL. See DTGSYL for details.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> >0: The matrix pairs (A, D) and (B, E) have common or very
*> close eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTGSYL solves the generalized Sylvester equation:
*>
*> information.
*>
*> This is a level 3 BLAS algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> <0: If INFO = -i, the i-th argument had an illegal value.
*> >0: (A, D) and (B, E) have common or close eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
*> [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Condition Estimators for Solving the Generalized Sylvester
*> Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
*> July 1989, pp 745-751.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK,
* INFO )
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPCON estimates the reciprocal of the condition number of a packed
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
* A, LDA, B, LDB, WORK, INFO )
* $ T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPMQRT applies a real orthogonal matrix Q obtained from a
*> "triangular-pentagonal" real block reflector H to a general
*> real matrix C, which consists of two blocks A and B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The columns of the pentagonal matrix V contain the elementary reflectors
*> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
*>
*> If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
* INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPQRT computes a blocked QR factorization of a real
*> "triangular-pentagonal" matrix C, which is composed of a
*> triangular block A and pentagonal block B, using the compact
*> WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> C = [ A ]
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = [T1 T2 ... TB].
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPQRT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPQRT2 computes a QR factorization of a real "triangular-pentagonal"
*> matrix C, which is composed of a triangular block A and pentagonal block B,
*> using the compact WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> where W^H is the conjugate transpose of W and T is the upper triangular
*> factor of the block reflector.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L,
* V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK )
* $ V( LDV, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPRFB applies a real "triangular-pentagonal" block reflector H or its
*> transpose H**T to a real matrix C, which is composed of two
*> blocks A and B, either from the left or right.
*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= K;
*> if SIDE = 'R', LDWORK >= M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix C is a composite matrix formed from blocks A and B.
*> If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
*>
*> If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* FERR, BERR, WORK, IWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular packed
*> The solution matrix X must be computed by DTPTRS or some other
*> means before entering this routine. DTPRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPTRI( UPLO, DIAG, N, AP, INFO )
*
* DOUBLE PRECISION AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPTRI computes the inverse of a real upper or lower triangular
*> matrix A stored in packed format.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A triangular matrix A can be transferred to packed storage using one
*> 1 CONTINUE 1 CONTINUE
*> JC = JC + J JC = JC + N - J + 1
*> 2 CONTINUE 2 CONTINUE
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
*
* DOUBLE PRECISION AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPTRS solves a triangular system of the form
*>
*> where A is a triangular matrix of order N stored in packed format,
*> and B is an N-by-NRHS matrix. A check is made to verify that A is
*> nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
*
* .. Array Arguments ..
* DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPTTF copies a triangular matrix A from standard packed format (TP)
*> to rectangular full packed format (TF).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPTTR( UPLO, N, AP, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPTTR copies a triangular matrix A from standard packed format (TP)
*> to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
* IWORK, INFO )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRCON estimates the reciprocal of the condition number of a
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, MM, M, WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTREVC computes some or all of the right and/or left eigenvectors of
*> a real upper quasi-triangular matrix T.
*> input matrix. If Q is the orthogonal factor that reduces a matrix
*> A to Schur form T, then Q*X and Q*Y are the matrices of right and
*> left eigenvectors of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The algorithm used in this program is basically backward (forward)
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x| + |y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
* INFO )
* DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTREXC reorders the real Schur factorization of a real matrix
*> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
*> 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> reordered, and ILST points to the first row of the
*> current position of the block being moved.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, FERR, BERR, WORK, IWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular
*> The solution matrix X must be computed by DTRTRS or some other
*> means before entering this routine. DTRRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI,
* M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO )
* $ WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRSEN reorders the real Schur factorization of a real matrix
*> A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in
*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
*> 2-by-2 diagonal block has its diagonal elemnts equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> contain the eigenvalues in the same order as in T; S and
*> SEP (if requested) are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> DTRSEN first collects the selected eigenvalues by computing an
*> error in the computed right invariant subspace is
*>
*> EPS * norm(T) / SEP
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, S, SEP, MM, M, WORK, LDWORK, IWORK,
* $ VR( LDVR, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or right eigenvectors of a real upper
*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
*> 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of an eigenvalue lambda is
*> is given by
*>
*> EPS * norm(T) / SEP(i)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
* LDC, SCALE, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRSYL solves the real Sylvester matrix equation:
*>
*> is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
*> each 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANA
*> \verbatim
*> values were used to solve the equation (but the matrices
*> A and B are unchanged).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRTI2 computes the inverse of a real upper or lower triangular
*> matrix.
*>
*> This is the Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRTRI computes the inverse of a real upper or lower triangular
*> matrix A.
*>
*> This is the Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
* INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRTRS solves a triangular system of the form
*>
*>
*> where A is a triangular matrix of order N, and B is an N-by-NRHS
*> matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the solutions
*> X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRTTF copies a triangular matrix A from standard full format (TR)
*> to rectangular full packed format (TF) .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE DTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRTTP( UPLO, N, A, LDA, AP, INFO )
*
* DOUBLE PRECISION A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRTTP copies a triangular matrix A from full format (TR) to standard
*> packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DTZRZF.
*>
*>
*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
*> to upper triangular form by means of orthogonal transformations.
*>
*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DZSUM1( N, CX, INCX )
*
* COMPLEX*16 CX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DZSUM1 takes the sum of the absolute values of a complex
*> vector and returns a double precision result.
*>
*> Based on DZASUM from the Level 1 BLAS.
*> The change is to use the 'genuine' absolute value.
-*>
-*> Contributed by Nick Higham for use with ZLACON.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive values of CX. INCX > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham for use with ZLACON.
+*
* =====================================================================
DOUBLE PRECISION FUNCTION DZSUM1( N, CX, INCX )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ICMAX1( N, CX, INCX )
*
* COMPLEX CX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ICMAX1 finds the index of the element whose real part has maximum
*> absolute value.
*>
*> Based on ICAMAX from Level 1 BLAS.
*> The change is to use the 'genuine' absolute value.
-*>
-*> Contributed by Nick Higham for use with CLACON.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive values of CX. INCX >= 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham for use with CLACON.
+*
* =====================================================================
INTEGER FUNCTION ICMAX1( N, CX, INCX )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE )
*
* REAL ONE, ZERO
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> IEEECK is called from the ILAENV to verify that Infinity and
*> possibly NaN arithmetic is safe (i.e. will not trap).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> = 0: Arithmetic failed to produce the correct answers
*> = 1: Arithmetic produced the correct answers
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILACLC( M, N, A, LDA )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILACLC scans A for its last non-zero column.
+*> \verbatim
*>
-*>\endverbatim
+*> ILACLC scans A for its last non-zero column.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILACLR( M, N, A, LDA )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILACLR scans A for its last non-zero row.
+*> \verbatim
*>
-*>\endverbatim
+*> ILACLR scans A for its last non-zero row.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILADIAG( DIAG )
*
* CHARACTER DIAG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine translated from a character string specifying if a
*> matrix has unit diagonal or not to the relevant BLAST-specified
*> ILADIAG returns an INTEGER. If ILADIAG < 0, then the input is not a
*> character indicating a unit or non-unit diagonal. Otherwise ILADIAG
*> returns the constant value corresponding to DIAG.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILADLC( M, N, A, LDA )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILADLC scans A for its last non-zero column.
+*> \verbatim
*>
-*>\endverbatim
+*> ILADLC scans A for its last non-zero column.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILADLR( M, N, A, LDA )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILADLR scans A for its last non-zero row.
+*> \verbatim
*>
-*>\endverbatim
+*> ILADLR scans A for its last non-zero row.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
*
* INTEGER ISPEC, N1, N2, N3, N4
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ILAENV is called from the LAPACK routines to choose problem-dependent
*> parameters for the local environment. See ISPEC for a description of
*>
*> This routine will not function correctly if it is converted to all
*> lower case. Converting it to all upper case is allowed.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> Problem dimensions for the subroutine NAME; these may not all
*> be required.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The following conventions have been used when calling ILAENV from the
*>
*> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
*> IF( NB.LE.1 ) NB = MAX( 1, N )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAPREC( PREC )
*
* CHARACTER PREC
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine translated from a character string specifying an
*> intermediate precision to the relevant BLAST-specified integer
*> ILAPREC returns an INTEGER. If ILAPREC < 0, then the input is not a
*> character indicating a supported intermediate precision. Otherwise
*> ILAPREC returns the constant value corresponding to PREC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILASLC( M, N, A, LDA )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILASLC scans A for its last non-zero column.
+*> \verbatim
*>
-*>\endverbatim
+*> ILASLC scans A for its last non-zero column.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILASLR( M, N, A, LDA )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILASLR scans A for its last non-zero row.
+*> \verbatim
*>
-*>\endverbatim
+*> ILASLR scans A for its last non-zero row.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILATRANS( TRANS )
*
* CHARACTER TRANS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine translates from a character string specifying a
*> transposition operation to the relevant BLAST-specified integer
*> ILATRANS returns an INTEGER. If ILATRANS < 0, then the input is not
*> a character indicating a transposition operator. Otherwise ILATRANS
*> returns the constant value corresponding to TRANS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAUPLO( UPLO )
*
* CHARACTER UPLO
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine translated from a character string specifying a
*> upper- or lower-triangular matrix to the relevant BLAST-specified
*> ILAUPLO returns an INTEGER. If ILAUPLO < 0, then the input is not
*> a character indicating an upper- or lower-triangular matrix.
*> Otherwise ILAUPLO returns the constant value corresponding to UPLO.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \brief \b ILAVER returns the LAPACK version.
-*>\details
+*> \details
*> \b Purpose:
-*>\verbatim
-*>
+*> \verbatim
*> This subroutine returns the LAPACK version.
-*>
-*>\endverbatim
+*> \endverbatim
*>
*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
*> \date November 2011
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAZLC( M, N, A, LDA )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILAZLC scans A for its last non-zero column.
+*> \verbatim
*>
-*>\endverbatim
+*> ILAZLC scans A for its last non-zero column.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAZLR( M, N, A, LDA )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ILAZLR scans A for its last non-zero row.
+*> \verbatim
*>
-*>\endverbatim
+*> ILAZLR scans A for its last non-zero row.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
*
* INTEGER IHI, ILO, ISPEC, LWORK, N
* CHARACTER NAME*( * ), OPTS*( * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This program sets problem and machine dependent parameters
*> useful for xHSEQR and its subroutines. It is called whenever
*> ILAENV is called with 12 <= ISPEC <= 16
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> LWORK is integer scalar
*> The amount of workspace available.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Little is known about how best to choose these parameters.
*> IPARMQ(ISPEC=16) Select structured matrix multiply.
*> (See ISPEC=16 above for details.)
*> Default: 3.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION IZMAX1( N, CX, INCX )
*
* COMPLEX*16 CX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> IZMAX1 finds the index of the element whose real part has maximum
*> absolute value.
*>
*> Based on IZAMAX from Level 1 BLAS.
*> The change is to use the 'genuine' absolute value.
-*>
-*> Contributed by Nick Higham for use with ZLACON.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive values of CX. INCX >= 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham for use with ZLACON.
+*
* =====================================================================
INTEGER FUNCTION IZMAX1( N, CX, INCX )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION LSAMEN( N, CA, CB )
*
* INTEGER N
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> LSAMEN tests if the first N letters of CA are the same as the
*> first N letters of CB, regardless of case.
*> LSAMEN returns .TRUE. if CA and CB are equivalent except for case
*> and .FALSE. otherwise. LSAMEN also returns .FALSE. if LEN( CA )
*> or LEN( CB ) is less than N.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> CA and CB specify two character strings of length at least N.
*> Only the first N characters of each string will be accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
* THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T,
* $ V2T( LDV2T, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SBBCSD computes the CS decomposition of an orthogonal matrix in
*> bidiagonal-block form,
*> The orthogonal matrices U1, U2, V1T, and V2T are input/output.
*> The input matrices are pre- or post-multiplied by the appropriate
*> singular vector matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> > 0: if SBBCSD did not converge, INFO specifies the number
*> of nonzero entries in PHI, and B11D, B11E, etc.,
*> contain the partially reduced matrix.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Reference
-*> =========
-*>
-*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
-*> Algorithms, 50(1):33-65, 2009.
-*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL REAL, default = MAX(10,MIN(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they
*> are within TOLMUL*EPS of either bound.
*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*> Algorithms, 50(1):33-65, 2009.
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
* WORK, IWORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SBDSDC computes the singular value decomposition (SVD) of a real
*> N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,
*> The code currently calls SLASDQ if singular values only are desired.
*> However, it can be slightly modified to compute singular values
*> using the divide and conquer method.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: The algorithm failed to compute a singular value.
*> The update process of divide and conquer failed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
-*> \endverbatim
*>
* =====================================================================
SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
* LDU, C, LDC, WORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SBDSQR computes the singular values and, optionally, the right and/or
*> left singular vectors from the singular value decomposition (SVD) of
*> B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
*> Department, University of California at Berkeley, July 1992
*> for a detailed description of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> elements of a bidiagonal matrix which is orthogonally
*> similar to the input matrix B; if INFO = i, i
*> elements of E have not converged to zero.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL REAL, default = max(10,min(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> If it is positive, TOLMUL*EPS is the desired relative
*> (and so fails to converge) if the number of passes
*> through the inner loop exceeds MAXITR*N**2.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SCSUM1( N, CX, INCX )
*
* COMPLEX CX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCSUM1 takes the sum of the absolute values of a complex
*> vector and returns a single precision result.
*>
*> Based on SCASUM from the Level 1 BLAS.
*> The change is to use the 'genuine' absolute value.
-*>
-*> Contributed by Nick Higham for use with CLACON.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive values of CX. INCX > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complexOTHERauxiliary
*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham for use with CLACON.
+*
* =====================================================================
REAL FUNCTION SCSUM1( N, CX, INCX )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDISNA( JOB, M, N, D, SEP, INFO )
*
* REAL D( * ), SEP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDISNA computes the reciprocal condition numbers for the eigenvectors
*> of a real symmetric or complex Hermitian matrix or for the left or
*>
*> SDISNA may also be used to compute error bounds for eigenvectors of
*> the generalized symmetric definite eigenproblem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
* LDQ, PT, LDPT, C, LDC, WORK, INFO )
* $ PT( LDPT, * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBBRD reduces a real general m-by-n band matrix A to upper
*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
*>
*> The routine computes B, and optionally forms Q or P**T, or computes
*> Q**T*C for a given matrix C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
* WORK, IWORK, INFO )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBCON estimates the reciprocal of the condition number of a real
*> general band matrix A, in either the 1-norm or the infinity-norm,
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* REAL AB( LDAB, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBEQU computes row and column scalings intended to equilibrate an
*> M-by-N band matrix A and reduce its condition number. R returns the
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* REAL AB( LDAB, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK,
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is banded, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBRFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
* REAL AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBSV computes the solution to a real system of linear equations
*> A * X = B, where A is a band matrix of order N with KL subdiagonals
*> and unit lower triangular matrices with KL subdiagonals, and U is
*> upper triangular with KL+KU superdiagonals. The factored form of A
*> is then used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGBsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBSVX uses the LU factorization to compute the solution to a real
*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed by this subroutine:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> there are a number of situations where the
*> computed solution can be more accurate than the
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBSVXX uses the LU factorization to compute the solution to a
*> real system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what SGBSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* REAL AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBTF2 computes an LU factorization of a real m-by-n band matrix A
*> using partial pivoting with row interchanges.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> + need not be set on entry, but are required by the routine to store
*> elements of U, because of fill-in resulting from the row
*> interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* REAL AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBTRF computes an LU factorization of a real m-by-n band matrix A
*> using partial pivoting with row interchanges.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
* INFO )
* REAL AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBTRS solves a system of linear equations
*> A * X = B or A**T * X = B
*> with a general band matrix A using the LU factorization computed
*> by SGBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
* INFO )
* REAL V( LDV, * ), SCALE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEBAK forms the right or left eigenvectors of a real general matrix
*> by backward transformation on the computed eigenvectors of the
*> balanced matrix output by SGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
*
* REAL A( LDA, * ), SCALE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEBAL balances a general real matrix A. This involves, first,
*> permuting A by a similarity transformation to isolate eigenvalues
*>
*> Balancing may reduce the 1-norm of the matrix, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The permutations consist of row and column interchanges which put
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
*
* $ TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEBD2 reduces a real general m by n matrix A to upper or lower
*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
* INFO )
* $ TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEBRD reduces a general real M-by-N matrix A to upper or lower
*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
* INFO )
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGECON estimates the reciprocal of the condition number of a general
*> real matrix A, in either the 1-norm or the infinity-norm, using
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* REAL A( LDA, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEEQU computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* REAL A( LDA, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI,
* VS, LDVS, WORK, LWORK, BWORK, INFO )
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEES computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues, the real Schur form T, and, optionally, the matrix of
*> [ c a ]
*>
*> where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> the Schur form no longer satisfy SELECT=.TRUE. This
*> could also be caused by underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM,
* WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK,
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEESX computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues, the real Schur form T, and, optionally, the matrix of
*> [ c a ]
*>
*> where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> the Schur form no longer satisfy SELECT=.TRUE. This
*> could also be caused by underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
* LDVR, WORK, LWORK, INFO )
* $ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEEV computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*>
*> The computed eigenvectors are normalized to have Euclidean norm
*> equal to 1 and largest component real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> elements i+1:N of WR and WI contain eigenvalues which
*> have converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
* VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
* $ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEEVX computes for an N-by-N real nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*> (in exact arithmetic) but diagonal scaling will. For further
*> explanation of balancing, see section 4.10.2 of the LAPACK
*> Users' Guide.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> have been computed; elements 1:ILO-1 and i+1:N of WR
*> and WI contain eigenvalues which have converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR,
* ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
* $ VSR( LDVSR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine SGGES.
*>
*> SGEGV should be used instead. See SGEGV for a description of the
*> eigenvalues of the generalized nonsymmetric eigenvalue problem
*> (GNEP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> =N+8: error return from SGGBAK (computing VSR)
*> =N+9: error return from SLASCL (various places)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
* $ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine SGGEV.
*>
*> are left eigenvectors of (A,B).
*>
*> Note: this routine performs "full balancing" on A and B
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> =N+9: error return from SGGBAK (computing VR)
*> =N+10: error return from SLASCL (various calls)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing
*>
*> [*] See SHGEQZ, SGEGS, or read the book "Matrix Computations",
*> by Golub & van Loan, pub. by Johns Hopkins U. Press.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEHD2 reduces a real general matrix A to upper Hessenberg form H by
*> an orthogonal similarity transformation: Q**T * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEHRD reduces a real general matrix A to upper Hessenberg form H by
*> an orthogonal similarity transformation: Q**T * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> This file is a slight modification of LAPACK-3.0's DGEHRD
*> subroutine incorporating improvements proposed by Quintana-Orti and
*> Van de Geijn (2006). (See DLAHR2.)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
* M, N, A, LDA, SVA, U, LDU, V, LDV,
* CHARACTER*1 JOBA, JOBP, JOBR, JOBT, JOBU, JOBV
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEJSV computes the singular value decomposition (SVD) of a real M-by-N
*> matrix [A], where M >= N. The SVD of [A] is written as
*> the right singular vectors of [A], respectively. The matrices [U] and [V]
*> are computed and stored in the arrays U and V, respectively. The diagonal
*> of [SIGMA] is computed and stored in the array SVA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBA
*> \verbatim
*> > 0 : SGEJSV did not converge in the maximal allowed number
*> of sweeps. The computed values may be inaccurate.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> SGEJSV implements a preconditioned Jacobi SVD algorithm. It uses SGEQP3,
*> this extra QRF step easily. The implementer can also improve data movement
*> (matrix transpose, matrix copy, matrix transposed copy) - this
*> implementation of SGEJSV uses only the simplest, naive data movement.
-*>
-*> Contributors
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*
+*> \par References:
+* ================
*>
-*> References
+*> \verbatim
*>
*> [1] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I.
*> SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342.
*> [4] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,
*> QSVD, (H,K)-SVD computations.
*> Department of Mathematics, University of Zagreb, 2008.
-*>
-*> Bugs, examples and comments
+*> \endverbatim
+*
+*> \par Bugs, examples and comments:
+* =================================
*>
*> Please report all bugs and send interesting examples and/or comments to
*> drmac@math.hr. Thank you.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
$ M, N, A, LDA, SVA, U, LDU, V, LDV,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGELQ2 computes an LQ factorization of a real m by n matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGELQF computes an LQ factorization of a real M-by-N matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
* INFO )
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGELS solves overdetermined or underdetermined real linear systems
*> involving an M-by-N matrix A, or its transpose, using a QR or LQ
*> handled in a single call; they are stored as the columns of the
*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
*> matrix X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> full rank; the least squares solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND,
* RANK, WORK, LWORK, IWORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGELSD computes the minimum-norm solution to a real linear least
*> squares problem:
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE SGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND,
$ RANK, WORK, LWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGELSS computes the minimum norm solution to a real linear least
*> squares problem:
*> The effective rank of A is determined by treating as zero those
*> singular values which are less than RCOND times the largest singular
*> value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine SGELSY.
*>
*> X = P * Z**T [ inv(T11)*Q1**T*B ]
*> [ 0 ]
*> where Q1 consists of the first RANK columns of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, LWORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGELSY computes the minimum-norm solution to a real linear least
*> squares problem:
*> o Matrix B (the right hand side) is updated with Blas-3.
*> o The permutation of matrix B (the right hand side) is faster and
*> more simple.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: If INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*>
-*> \endverbatim
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n
+*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
+*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
*>
* =====================================================================
SUBROUTINE SGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
* C, LDC, WORK, INFO )
* REAL V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEMQRT overwrites the general real M-by-N matrix C with
*>
*> generated using the compact WY representation as returned by SGEQRT.
*>
*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQL2( M, N, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQL2 computes a QL factorization of a real m by n matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQLF computes a QL factorization of a real M-by-N matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQP3 computes a QR factorization with column pivoting of a
*> matrix A: A*P = Q*R using Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real/complex scalar, and v is a real/complex vector
*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
*> A(i+1:m,i), and tau in TAU(i).
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine SGEQP3.
*>
*> SGEQPF computes a QR factorization with column pivoting of a
*> real M-by-N matrix A: A*P = Q*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> University of Zagreb, Croatia.
*> -- April 2011 --
*> For more details see LAPACK Working Note 176.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQR2 computes a QR factorization of a real m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQR2P computes a QR factorization of a real m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQRF computes a QR factorization of a real M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQRFP computes a QR factorization of a real M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
*
* REAL A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQRT computes a blocked QR factorization of a real M-by-N matrix A
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> below the diagonal. For example, if M=5 and N=3, the matrix V is
*>
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = (T1 T2 ... TB).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQRT2( M, N, A, LDA, T, LDT, INFO )
*
* REAL A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQRT2 computes a QR factorization of a real M-by-N matrix A,
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> H = I - V * T * V**T
*>
*> where V**T is the transpose of V.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE SGEQRT3( M, N, A, LDA, T, LDT, INFO )
*
* REAL A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGEQRT3 recursively computes a QR factorization of a real M-by-N
*> matrix A, using the compact WY representation of Q.
*>
*> Based on the algorithm of Elmroth and Gustavson,
*> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> where V**T is the transpose of V.
*>
*> For details of the algorithm, see Elmroth and Gustavson (cited above).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGERFS improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates for
*> the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGERFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGERQ2 computes an RQ factorization of a real m by n matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
*> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGERQF computes an RQ factorization of a real M-by-N matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real scalar, and v is a real vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
*> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
* REAL A( LDA, * ), RHS( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESC2 solves a system of linear equations
*>
*>
*> with a general N-by-N matrix A using the LU factorization with
*> complete pivoting computed by SGETC2.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On exit, SCALE contains the scale factor. SCALE is chosen
*> 0 <= SCALE <= 1 to prevent owerflow in the solution.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
* LWORK, IWORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESDD computes the singular value decomposition (SVD) of a real
*> M-by-N matrix A, optionally computing the left and right singular
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: SBDSDC did not converge, updating process failed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
$ LWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESV computes the solution to a real system of linear equations
*> A * X = B,
*> where P is a permutation matrix, L is unit lower triangular, and U is
*> upper triangular. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
* WORK, LWORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESVD computes the singular value decomposition (SVD) of a real
*> M-by-N matrix A, optionally computing the left and/or right singular
*> U and V are the left and right singular vectors of A.
*>
*> Note that the routine returns V**T, not V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> did not converge to zero. See the description of WORK
*> above for details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
* LDV, WORK, LWORK, INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESVJ computes the singular value decomposition (SVD) of a real
*> M-by-N matrix A, where M >= N. The SVD of A is written as
*> matrix, and V is an N-by-N orthogonal matrix. The diagonal elements
*> of SIGMA are the singular values of A. The columns of U and V are the
*> left and the right singular vectors of A, respectively.
-*>
-*> Further Details
-*> ~~~~~~~~~~~~~~~
-*> The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane
-*> rotations. The rotations are implemented as fast scaled rotations of
-*> Anda and Park [1]. In the case of underflow of the Jacobi angle, a
-*> modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses
-*> column interchanges of de Rijk [2]. The relative accuracy of the computed
-*> singular values and the accuracy of the computed singular vectors (in
-*> angle metric) is as guaranteed by the theory of Demmel and Veselic [3].
-*> The condition number that determines the accuracy in the full rank case
-*> is essentially min_{D=diag} kappa(A*D), where kappa(.) is the
-*> spectral condition number. The best performance of this Jacobi SVD
-*> procedure is achieved if used in an accelerated version of Drmac and
-*> Veselic [5,6], and it is the kernel routine in the SIGMA library [7].
-*> Some tunning parameters (marked with [TP]) are available for the
-*> implementer.
-*> The computational range for the nonzero singular values is the machine
-*> number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even
-*> denormalized singular values can be computed with the corresponding
-*> gradual loss of accurate digits.
-*>
-*> Contributors
-*> ~~~~~~~~~~~~
-*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
-*>
-*> References
-*> ~~~~~~~~~~
-*> [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling.
-*> SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174.
-*> [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the
-*> singular value decomposition on a vector computer.
-*> SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371.
-*> [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR.
-*> [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular
-*> value computation in floating point arithmetic.
-*> SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222.
-*> [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I.
-*> SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342.
-*> LAPACK Working note 169.
-*> [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II.
-*> SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362.
-*> LAPACK Working note 170.
-*> [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,
-*> QSVD, (H,K)-SVD computations.
-*> Department of Mathematics, University of Zagreb, 2008.
-*>
-*> Bugs, Examples and Comments
-*> ~~~~~~~~~~~~~~~~~~~~~~~~~~~
-*> Please report all bugs and send interesting test examples and comments to
-*> drmac@math.hr. Thank you.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBA
*> \verbatim
*> of sweeps. The output may still be useful. See the
*> description of WORK.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
+*> \par Further Details:
+* =====================
+*>
+*> The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane
+*> rotations. The rotations are implemented as fast scaled rotations of
+*> Anda and Park [1]. In the case of underflow of the Jacobi angle, a
+*> modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses
+*> column interchanges of de Rijk [2]. The relative accuracy of the computed
+*> singular values and the accuracy of the computed singular vectors (in
+*> angle metric) is as guaranteed by the theory of Demmel and Veselic [3].
+*> The condition number that determines the accuracy in the full rank case
+*> is essentially min_{D=diag} kappa(A*D), where kappa(.) is the
+*> spectral condition number. The best performance of this Jacobi SVD
+*> procedure is achieved if used in an accelerated version of Drmac and
+*> Veselic [5,6], and it is the kernel routine in the SIGMA library [7].
+*> Some tunning parameters (marked with [TP]) are available for the
+*> implementer. \n
+*> The computational range for the nonzero singular values is the machine
+*> number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even
+*> denormalized singular values can be computed with the corresponding
+*> gradual loss of accurate digits.
+*>
+*> \par Contributors:
+* ==================
+*>
+*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*>
+*> \par References:
+* ================
+*>
+*> [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling. \n
+*> SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174. \n\n
+*> [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the
+*> singular value decomposition on a vector computer. \n
+*> SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371. \n\n
+*> [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR. \n
+*> [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular
+*> value computation in floating point arithmetic. \n
+*> SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222. \n\n
+*> [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I. \n
+*> SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. \n
+*> LAPACK Working note 169. \n\n
+*> [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II. \n
+*> SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. \n
+*> LAPACK Working note 170. \n\n
+*> [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,
+*> QSVD, (H,K)-SVD computations.\n
+*> Department of Mathematics, University of Zagreb, 2008.
+*>
+*> \par Bugs, Examples and Comments:
+* =================================
+*>
+*> Please report all bugs and send interesting test examples and comments to
+*> drmac@math.hr. Thank you.
+*
* =====================================================================
SUBROUTINE SGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
$ LDV, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESVX uses the LU factorization to compute the solution to a real
*> system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGESVXX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, RPVGRW,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGESVXX uses the LU factorization to compute the solution to a
*> real system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what SGESVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGETC2 computes an LU factorization with complete pivoting of the
*> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
*> unit diagonal elements and U is upper triangular.
*>
*> This is the Level 2 BLAS algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> we try to solve for x in Ax = b. So U is perturbed to
*> avoid the overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETF2( M, N, A, LDA, IPIV, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGETF2 computes an LU factorization of a general m-by-n matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETRF( M, N, A, LDA, IPIV, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGETRF computes an LU factorization of a general M-by-N matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGETRI computes the inverse of a matrix using the LU factorization
*> computed by SGETRF.
*>
*> This method inverts U and then computes inv(A) by solving the system
*> inv(A)*L = inv(U) for inv(A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
*> singular and its inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGETRS solves a system of linear equations
*> A * X = B or A**T * X = B
*> with a general N-by-N matrix A using the LU factorization computed
*> by SGETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
* LDV, INFO )
* REAL LSCALE( * ), RSCALE( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGBAK forms the right or left eigenvectors of a real generalized
*> eigenvalue problem A*x = lambda*B*x, by backward transformation on
*> the computed eigenvectors of the balanced pair of matrices output by
*> SGGBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. Ward, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
* RSCALE, WORK, INFO )
* $ RSCALE( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGBAL balances a pair of general real matrices (A,B). This
*> involves, first, permuting A and B by similarity transformations to
*> Balancing may reduce the 1-norm of the matrices, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors in the
*> generalized eigenvalue problem A*x = lambda*B*x.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. WARD, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
* SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
*> the generalized eigenvalues, the generalized real Schur form (S,T),
*> and the pair of corresponding 2-by-2 blocks in S and T will have a
*> complex conjugate pair of generalized eigenvalues.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering failed in STGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
* B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGESX computes for a pair of N-by-N real nonsymmetric matrices
*> (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
*> and the pair of corresponding 2-by-2 blocks in S and T will have a
*> complex conjugate pair of generalized eigenvalues.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering failed in STGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> An approximate (asymptotic) bound on the average absolute error of
*> EPS * norm((A, B)) / RCONDV( 2 ).
*>
*> See LAPACK User's Guide, section 4.11 for more information.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
* $ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
*> the generalized eigenvalues, and optionally, the left and/or right
*>
*> where u(j)**H is the conjugate-transpose of u(j).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> > N: =N+1: other than QZ iteration failed in SHGEQZ.
*> =N+2: error return from STGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
* ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, ILO,
* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGEVX computes for a pair of N-by-N real nonsymmetric matrices (A,B)
*> the generalized eigenvalues, and optionally, the left and/or right
*>
*> where u(j)**H is the conjugate-transpose of u(j).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> > N: =N+1: other than QZ iteration failed in SHGEQZ.
*> =N+2: error return from STGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing a matrix pair (A,B) includes, first, permuting rows and
*>
*> For further explanation of the reciprocal condition numbers RCONDE
*> and RCONDV, see section 4.11 of LAPACK User's Guide.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
* INFO )
* $ X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGGLM solves a general Gauss-Markov linear model (GLM) problem:
*>
*> x
*>
*> where inv(B) denotes the inverse of B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> rank( A B ) < N; the least squares solution could not
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
* LDQ, Z, LDZ, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGHRD reduces a pair of real matrices (A,B) to generalized upper
*> Hessenberg form using orthogonal transformations, where A is a
*> If Q1 is the orthogonal matrix from the QR factorization of B in the
*> original equation A*x = lambda*B*x, then SGGHRD reduces the original
*> problem to generalized Hessenberg form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine reduces A to Hessenberg and B to triangular form by
*> an unblocked reduction, as described in _Matrix_Computations_,
*> by Golub and Van Loan (Johns Hopkins Press.)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
* INFO )
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGLSE solves the linear equality-constrained least squares (LSE)
*> problem:
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> ( (B) )
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGQRF computes a generalized QR factorization of an N-by-M matrix A
*> and an N-by-P matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
*> transpose of the matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine SORGRQ.
*> To use Z to update another matrix, use LAPACK subroutine SORMRQ.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGRQF computes a generalized RQ factorization of an M-by-N matrix A
*> and a P-by-N matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
*> transpose of the matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INF0= -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine SORGQR.
*> To use Z to update another matrix, use LAPACK subroutine SORMQR.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGSVD computes the generalized singular value decomposition (GSVD)
*> of an M-by-N real matrix A and P-by-N real matrix B:
*>
*> X = Q*( I 0 )
*> ( 0 inv(R) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, the Jacobi-type procedure failed to
*> converge. For further details, see subroutine STGSJA.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLA REAL
*> TOLB REAL
*> TOLA and TOLB are the thresholds to determine the effective
*> The size of TOLA and TOLB may affect the size of backward
*> errors of the decomposition.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> 2-96 Based on modifications by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
$ LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGGSVP computes orthogonal matrices U, V and Q such that
*>
*> This decomposition is the preprocessing step for computing the
*> Generalized Singular Value Decomposition (GSVD), see subroutine
*> SGGSVD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
*> The subroutine uses LAPACK subroutine SGEQPF for the QR factorization
*> with column pivoting to detect the effective numerical rank of the
*> a matrix. It may be replaced by a better rank determination strategy.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
$ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGSVJ0 is called from SGESVJ as a pre-processor and that is its main
*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
*> it does not check convergence (stopping criterion). Few tuning
*> parameters (marked by [TP]) are available for the implementer.
-*>
-*> Further Details
-*> ~~~~~~~~~~~~~~~
-*> SGSVJ0 is used just to enable SGESVJ to call a simplified version of
-*> itself to work on a submatrix of the original matrix.
-*>
-*> Contributors
-*> ~~~~~~~~~~~~
-*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
-*>
-*> Bugs, Examples and Comments
-*> ~~~~~~~~~~~~~~~~~~~~~~~~~~~
-*> Please report all bugs and send interesting test examples and comments to
-*> drmac@math.hr. Thank you.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBV
*> \verbatim
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
+*> \par Further Details:
+* =====================
+*>
+*> SGSVJ0 is used just to enable SGESVJ to call a simplified version of
+*> itself to work on a submatrix of the original matrix.
+*>
+*> \par Contributors:
+* ==================
+*>
+*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*>
+*> \par Bugs, Examples and Comments:
+* =================================
+*>
+*> Please report all bugs and send interesting test examples and comments to
+*> drmac@math.hr. Thank you.
+*
* =====================================================================
SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGSVJ1 is called from SGESVJ as a pre-processor and that is its main
*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
*> The number of sweeps is given in NSWEEP and the orthogonality threshold
*> is given in TOL.
-*>
-*> Contributors
-*> ~~~~~~~~~~~~
-*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBV
*> \verbatim
*> = 0 : successful exit.
*> < 0 : if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
+*> \par Contributors:
+* ==================
+*>
+*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*
* =====================================================================
SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
* WORK, IWORK, INFO )
* REAL D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTCON estimates the reciprocal of the condition number of a real
*> tridiagonal matrix A using the LU factorization as computed by
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK,
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is tridiagonal, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* REAL B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTSV solves the equation
*>
*>
*> Note that the equation A**T*X = B may be solved by interchanging the
*> order of the arguments DU and DL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has not been computed. The factorization has not been
*> completed unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTSVX uses the LU factorization to compute the solution to a real
*> system of linear equations A * X = B or A**T * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
* REAL D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTTRF computes an LU factorization of a real tridiagonal matrix A
*> using elimination with partial pivoting and row interchanges.
*> where L is a product of permutation and unit lower bidiagonal
*> matrices and U is upper triangular with nonzeros in only the main
*> diagonal and first two superdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
* INFO )
* REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTTRS solves one of the systems of equations
*> A*X = B or A**T*X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by SGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
* REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTTS2 solves one of the systems of equations
*> A*X = B or A**T*X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by SGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SHGEQZ computes the eigenvalues of a real matrix pair (H,T),
*> where H is an upper Hessenberg matrix and T is upper triangular,
*> Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
*> Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
*> pp. 241--256.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> in Schur form, but ALPHAR(i), ALPHAI(i), and
*> BETA(i), i=INFO-N+1,...,N should be correct.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Iteration counters:
*> IITER -- counts iterations run since ILAST was last
*> changed. This is therefore reset only when a 1-by-1 or
*> 2-by-2 block deflates off the bottom.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI,
* VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL,
* $ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SHSEIN uses inverse iteration to find specified right and/or left
*> eigenvectors of a real upper Hessenberg matrix H.
*> H * x = w * x, y**h * H = w * y**h
*>
*> where y**h denotes the conjugate transpose of the vector y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> failed to converge; see IFAILL and IFAILR for further
*> details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x|+|y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z,
* LDZ, WORK, LWORK, INFO )
* REAL H( LDH, * ), WI( * ), WORK( * ), WR( * ),
* $ Z( LDZ, * )
* ..
-* Purpose
-* =======
+*
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SHSEQR computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> If INFO .GT. 0 and COMPZ = 'N', then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
+*> \par Contributors:
+* ==================
+*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Default values supplied by
+*> ILAENV(ISPEC,'SHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
+*> It is suggested that these defaults be adjusted in order
+*> to attain best performance in each particular
+*> computational environment.
+*>
+*> ISPEC=12: The SLAHQR vs SLAQR0 crossover point.
+*> Default: 75. (Must be at least 11.)
+*>
+*> ISPEC=13: Recommended deflation window size.
+*> This depends on ILO, IHI and NS. NS is the
+*> number of simultaneous shifts returned
+*> by ILAENV(ISPEC=15). (See ISPEC=15 below.)
+*> The default for (IHI-ILO+1).LE.500 is NS.
+*> The default for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>
+*> ISPEC=14: Nibble crossover point. (See IPARMQ for
+*> details.) Default: 14% of deflation window
+*> size.
+*>
+*> ISPEC=15: Number of simultaneous shifts in a multishift
+*> QR iteration.
+*>
+*> If IHI-ILO+1 is ...
+*>
+*> greater than ...but less ... the
+*> or equal to ... than default is
+*>
+*> 1 30 NS = 2(+)
+*> 30 60 NS = 4(+)
+*> 60 150 NS = 10(+)
+*> 150 590 NS = **
+*> 590 3000 NS = 64
+*> 3000 6000 NS = 128
+*> 6000 infinity NS = 256
+*>
+*> (+) By default some or all matrices of this order
+*> are passed to the implicit double shift routine
+*> SLAHQR and this parameter is ignored. See
+*> ISPEC=12 above and comments in IPARMQ for
+*> details.
+*>
+*> (**) The asterisks (**) indicate an ad-hoc
+*> function of N increasing from 10 to 64.
+*>
+*> ISPEC=16: Select structured matrix multiply.
+*> If the number of simultaneous shifts (specified
+*> by ISPEC=15) is less than 14, then the default
+*> for ISPEC=16 is 0. Otherwise the default for
+*> ISPEC=16 is 2.
+*> \endverbatim
+*
+*> \par References:
+* ================
+*>
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
+*> \n
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
+*> of Matrix Analysis, volume 23, pages 948--973, 2002.
+*
* =====================================================================
SUBROUTINE SHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z,
$ LDZ, WORK, LWORK, INFO )
REAL H( LDH, * ), WI( * ), WORK( * ), WR( * ),
$ Z( LDZ, * )
* ..
-* ================================================================
-* Default values supplied by
-* ILAENV(ISPEC,'SHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
-* It is suggested that these defaults be adjusted in order
-* to attain best performance in each particular
-* computational environment.
-*
-* ISPEC=12: The SLAHQR vs SLAQR0 crossover point.
-* Default: 75. (Must be at least 11.)
-*
-* ISPEC=13: Recommended deflation window size.
-* This depends on ILO, IHI and NS. NS is the
-* number of simultaneous shifts returned
-* by ILAENV(ISPEC=15). (See ISPEC=15 below.)
-* The default for (IHI-ILO+1).LE.500 is NS.
-* The default for (IHI-ILO+1).GT.500 is 3*NS/2.
-*
-* ISPEC=14: Nibble crossover point. (See IPARMQ for
-* details.) Default: 14% of deflation window
-* size.
-*
-* ISPEC=15: Number of simultaneous shifts in a multishift
-* QR iteration.
-*
-* If IHI-ILO+1 is ...
-*
-* greater than ...but less ... the
-* or equal to ... than default is
-*
-* 1 30 NS = 2(+)
-* 30 60 NS = 4(+)
-* 60 150 NS = 10(+)
-* 150 590 NS = **
-* 590 3000 NS = 64
-* 3000 6000 NS = 128
-* 6000 infinity NS = 256
-*
-* (+) By default some or all matrices of this order
-* are passed to the implicit double shift routine
-* SLAHQR and this parameter is ignored. See
-* ISPEC=12 above and comments in IPARMQ for
-* details.
-*
-* (**) The asterisks (**) indicate an ad-hoc
-* function of N increasing from 10 to 64.
-*
-* ISPEC=16: Select structured matrix multiply.
-* If the number of simultaneous shifts (specified
-* by ISPEC=15) is less than 14, then the default
-* for ISPEC=16 is 0. Otherwise the default for
-* ISPEC=16 is 2.
-*
-* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* References:
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
-* Performance, SIAM Journal of Matrix Analysis, volume 23, pages
-* 929--947, 2002.
-*
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part II: Aggressive Early Deflation, SIAM Journal
-* of Matrix Analysis, volume 23, pages 948--973, 2002.
-*
-* ================================================================
+*
+* =====================================================================
+*
* .. Parameters ..
*
* ==== Matrices of order NTINY or smaller must be processed by
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION SISNAN( SIN )
*
* REAL SIN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SISNAN returns .TRUE. if its argument is NaN, and .FALSE.
*> otherwise. To be replaced by the Fortran 2003 intrinsic in the
*> future.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIN
*> \verbatim
*> SIN is REAL
*> Input to test for NaN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
* INCX, BETA, Y, INCY )
* REAL AB( LDAB, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GBAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* ..
*
* =====================================================================
-
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB,
* IPIV, CMODE, C, INFO, WORK, IWORK )
* $ C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
* NRHS, AB, LDAB, AFB, LDAFB, IPIV,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GBRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to SGBTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_GBRPVGRW( N, KL, KU, NCOLS, AB, LDAB, AFB,
* LDAFB )
* REAL AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GBRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
* Y, INCY )
* REAL A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GEAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_GERCOND ( TRANS, N, A, LDA, AF, LDAF, IPIV,
* CMODE, C, INFO, WORK, IWORK )
* $ C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.2
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
* LDA, AF, LDAF, IPIV, COLEQU, C, B,
* $ ERRS_C( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GERFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERRS_C for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERRS_N and ERRS_C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to SGETRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
*
* REAL A( LDA, * ), AF( LDAF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_GERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
*
* REAL RES( N, NRHS )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_LIN_BERR computes componentwise relative backward error from
*> the formula
*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
*> where abs(Z) is the componentwise absolute value of the matrix
*> or vector Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> BERR is REAL array, dimension (NRHS)
*> The componentwise relative backward error from the formula above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C,
* INFO, WORK, IWORK )
* INTEGER IWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, COLEQU, C, B, LDB, Y,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_PORFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to SPOTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, LDAF, WORK )
*
* REAL A( LDA, * ), AF( LDAF, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> SLA_PORPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* REAL A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_SYAMV performs the matrix-vector operation
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Richard Hanson, Sandia National Labs.
*> -- Modified for the absolute-value product, April 2006
*> Jason Riedy, UC Berkeley
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE,
* C, INFO, WORK, IWORK )
* REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, IPIV, COLEQU, C, B, LDB,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> SLA_SYRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to SSYTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF, LDAF, IPIV,
* WORK )
* REAL A( LDA, * ), AF( LDAF, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> SLA_SYRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLA_WWADDW( N, X, Y, W )
*
* REAL X( * ), Y( * ), W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
*>
*> This works for all extant IBM's hex and binary floating point
*> arithmetics, but not for decimal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> W is REAL array, dimension (N)
*> The vector to be added.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLABAD( SMALL, LARGE )
*
* REAL LARGE, SMALL
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLABAD takes as input the values computed by SLAMCH for underflow and
*> overflow, and returns the square root of each of these values if the
*> the values computed by SLAMCH. This subroutine is needed because
*> SLAMCH does not compensate for poor arithmetic in the upper half of
*> the exponent range, as is found on a Cray.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] SMALL
*> \verbatim
*> On exit, if LOG10(LARGE) is sufficiently large, the square
*> root of LARGE, otherwise unchanged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
* LDY )
* $ TAUQ( * ), X( LDX, * ), Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLABRD reduces the first NB rows and columns of a real general
*> m by n matrix A to upper or lower bidiagonal form by an orthogonal
*> bidiagonal form.
*>
*> This is an auxiliary routine called by SGEBRD
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where a denotes an element of the original matrix which is unchanged,
*> vi denotes an element of the vector defining H(i), and ui an element
*> of the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
*
* REAL V( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLACN2 estimates the 1-norm of a square, real matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> ISAVE is INTEGER array, dimension (3)
*> ISAVE is used to save variables between calls to SLACN2
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
-*> Contributed by Nick Higham, University of Manchester.
*> Originally named SONEST, dated March 16, 1988.
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
-*> a real or complex matrix, with applications to condition estimation",
-*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
-*>
*> This is a thread safe version of SLACON, which uses the array ISAVE
*> in place of a SAVE statement, as follows:
*>
*> JUMP ISAVE(1)
*> J ISAVE(2)
*> ITER ISAVE(3)
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham, University of Manchester
+*
+*> \par References:
+* ================
+*>
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> a real or complex matrix, with applications to condition estimation",
+*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
* =====================================================================
SUBROUTINE SLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLACON( N, V, X, ISGN, EST, KASE )
*
* REAL V( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLACON estimates the 1-norm of a square, real matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> whether X should be overwritten by A * X or A**T * X.
*> On the final return from SLACON, KASE will again be 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Contributed by Nick Higham, University of Manchester.
+*> Nick Higham, University of Manchester. \n
*> Originally named SONEST, dated March 16, 1988.
+*
+*> \par References:
+* ================
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
*> a real or complex matrix, with applications to condition estimation",
*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLACON( N, V, X, ISGN, EST, KASE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLACPY( UPLO, M, N, A, LDA, B, LDB )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLACPY copies all or part of a two-dimensional matrix A to another
*> matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLADIV( A, B, C, D, P, Q )
*
* REAL A, B, C, D, P, Q
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLADIV performs complex division in real arithmetic
*>
*>
*> The algorithm is due to Robert L. Smith and can be found
*> in D. Knuth, The art of Computer Programming, Vol.2, p.195
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> Q is REAL
*> The scalars p and q in the above expression.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAE2( A, B, C, RT1, RT2 )
*
* REAL A, B, C, RT1, RT2
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
*> [ A B ]
*> [ B C ].
*> On return, RT1 is the eigenvalue of larger absolute value, and RT2
*> is the eigenvalue of smaller absolute value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> RT2 is REAL
*> The eigenvalue of smaller absolute value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> RT1 is accurate to a few ulps barring over/underflow.
*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
*> Underflow is harmless if the input data is 0 or exceeds
*> underflow_threshold / macheps.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL,
* RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAEBZ contains the iteration loops which compute and use the
*> function N(w), which is the count of eigenvalues of a symmetric
*>
*> Note: the arguments are, in general, *not* checked for unreasonable
*> values.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> = 1--MMAX: The last INFO intervals did not converge.
*> = MMAX+1: More than MMAX intervals were generated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine is intended to be called only by other LAPACK
*> >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and
*> N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and
*> w(l-r)=...=w(l+k) are handled similarly.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
* WORK, IWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED0 computes all eigenvalues and corresponding eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
$ WORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
* INFO )
* REAL D( * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED1 computes the updated eigensystem of a diagonal
*> matrix after modification by a rank-one symmetric matrix. This
*> directly using the updated eigenvalues. The eigenvectors for
*> the current problem are multiplied with the eigenvectors from
*> the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE SLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
* Q2, INDX, INDXC, INDXP, COLTYP, INFO )
* $ W( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED2 merges the two sets of eigenvalues together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> eigenvalues are close together or if there is a tiny entry in the
*> Z vector. For each such occurrence the order of the related secular
*> equation problem is reduced by one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] K
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
* CTOT, W, S, INFO )
* $ S( * ), W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED3 finds the roots of the secular equation, as defined by the
*> values in D, W, and RHO, between 1 and K. It makes the
*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] K
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
*
* REAL D( * ), DELTA( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the I-th updated eigenvalue of a symmetric
*> rank-one modification to a diagonal matrix whose elements are
*>
*> The method consists of approximating the rational functions in the
*> secular equation by simpler interpolating rational functions.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> > 0: if INFO = 1, the updating process failed.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> Logical variable ORGATI (origin-at-i?) is used for distinguishing
*> whether D(i) or D(i+1) is treated as the origin.
*>
*> MAXIT is the maximum number of iterations allowed for each
*> eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED5( I, D, Z, DELTA, RHO, DLAM )
*
* REAL D( 2 ), DELTA( 2 ), Z( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the I-th eigenvalue of a symmetric rank-one
*> modification of a 2-by-2 diagonal matrix
*>
*> We also assume RHO > 0 and that the Euclidean norm of the vector
*> Z is one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I
*> \verbatim
*> DLAM is REAL
*> The computed lambda_I, the I-th updated eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLAED5( I, D, Z, DELTA, RHO, DLAM )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
*
* REAL D( 3 ), Z( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED6 computes the positive or negative root (closest to the origin)
*> of
*> This routine will be called by SLAED4 when necessary. In most cases,
*> the root sought is the smallest in magnitude, though it might not be
*> in some extremely rare situations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] KNITER
*> \verbatim
*> = 0: successful exit
*> > 0: if INFO = 1, failure to converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 30/06/99: Based on contributions by
-*> Ren-Cang Li, Computer Science Division, University of California
-*> at Berkeley, USA
+*> \verbatim
*>
-*> 10/02/03: This version has a few statements commented out for thread safety
-*> (machine parameters are computed on each entry). SJH.
+*> 10/02/03: This version has a few statements commented out for thread
+*> safety (machine parameters are computed on each entry). SJH.
*>
*> 05/10/06: Modified from a new version of Ren-Cang Li, use
*> Gragg-Thornton-Warner cubic convergent scheme for better stability.
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ren-Cang Li, Computer Science Division, University of California
+*> at Berkeley, USA
*>
* =====================================================================
SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
* $ QSTORE( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED7 computes the updated eigensystem of a diagonal
*> matrix after modification by a rank-one symmetric matrix. This
*> directly using the updated eigenvalues. The eigenvectors for
*> the current problem are multiplied with the eigenvectors from
*> the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
$ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED8 merges the two sets of eigenvalues together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> eigenvalues are close together or if there is a tiny element in the
*> Z vector. For each such occurrence the order of the related secular
*> equation problem is reduced by one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
$ CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
* S, LDS, INFO )
* $ W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAED9 finds the roots of the secular equation, as defined by the
*> values in D, Z, and RHO, between KSTART and KSTOP. It makes the
*> appropriate calls to SLAED4 and then stores the new matrix of
*> eigenvectors for use in calculating the next level of Z vectors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] K
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
$ S, LDS, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
* REAL GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAEDA computes the Z vector corresponding to the merge step in the
*> CURLVLth step of the merge process with TLVLS steps for the CURPBMth
*> problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
$ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B,
* LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAEIN uses inverse iteration to find a right or left eigenvector
*> corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
*> matrix H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RIGHTV
*> \verbatim
*> = 1: inverse iteration did not converge; VR is set to the
*> last iterate, and so is VI if WI.ne.0.0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
* REAL A, B, C, CS1, RT1, RT2, SN1
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
*> [ A B ]
*>
*> [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
*> [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> SN1 is REAL
*> The vector (CS1, SN1) is a unit right eigenvector for RT1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> RT1 is accurate to a few ulps barring over/underflow.
*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
*> Underflow is harmless if the input data is 0 or exceeds
*> underflow_threshold / macheps.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAEXC( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK,
* INFO )
* REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in
*> an upper quasi-triangular matrix T by an orthogonal similarity
*> with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block
*> has its diagonal elemnts equal and its off-diagonal elements of
*> opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> form; the blocks are not swapped and T and Q are
*> unchanged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,
* WR2, WI )
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue
*> problem A - w B, with scaling as necessary to avoid over-/underflow.
*>
*> where s is a non-negative scaling factor chosen so that w, w B,
*> and s A do not overflow and, if possible, do not underflow, either.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> eigenvalue is complex, then WI is SCALE1 times the imaginary
*> part of the eigenvalues. WI will always be non-negative.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAG2D( M, N, SA, LDSA, A, LDA, INFO )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAG2D converts a SINGLE PRECISION matrix, SA, to a DOUBLE
*> PRECISION matrix, A.
*> converting from single to double.
*>
*> This is an auxiliary routine so there is no argument checking.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
* SNV, CSQ, SNQ )
* $ SNU, SNV
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
*> that if ( UPPER ) then
*>
*> Z**T denotes the transpose of Z.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPPER
*> \verbatim
*> SNQ is REAL
*> The desired orthogonal matrix Q.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
*
* REAL A( * ), B( * ), C( * ), D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGTF factorizes the matrix (T - lambda*I), where T is an n by n
*> tridiagonal matrix and lambda is a scalar, as
*> The parameter LAMBDA is included in the routine so that SLAGTF may
*> be used, in conjunction with SLAGTS, to obtain eigenvectors of T by
*> inverse iteration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0 : successful exit
*> .lt. 0: if INFO = -k, the kth argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
* B, LDB )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGTM performs a matrix-vector product of the form
*>
*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
*> matrices, and alpha and beta are real scalars, each of which may be
*> 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
*
* REAL A( * ), B( * ), C( * ), D( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGTS may be used to solve one of the systems of equations
*>
*> controlled by the argument JOB, and in each case there is an option
*> to perturb zero or very small diagonal elements of U, this option
*> being intended for use in applications such as inverse iteration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> the elements of the right-hand side vector y are very
*> large.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
* CSR, SNR )
* $ B( LDB, * ), BETA( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGV2 computes the Generalized Schur factorization of a real 2-by-2
*> matrix pencil (A,B) where B is upper triangular. This routine
*>
*> where b11 >= b22 > 0.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] A
*> \verbatim
*> SNR is REAL
*> The sine of the right rotation matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
$ CSR, SNR )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, INFO )
* REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAHQR is an auxiliary routine called by SHSEQR to update the
*> eigenvalues and Schur decomposition already computed by SHSEQR, by
*> dealing with the Hessenberg submatrix in rows and columns ILO to
*> IHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> where U is the orthogonal matrix in (*)
*> (regardless of the value of WANTT.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 02-96 Based on modifications by
*> It is (1) more robust against overflow and underflow and
*> (2) adopts the more conservative Ahues & Tisseur stopping
*> criterion (LAWN 122, 1997).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
*>
*> This is an auxiliary routine called by SGEHRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> Gejin. Note that the entries of A(1:K,2:NB) differ from those
*> returned by the original LAPACK-3.0's DLAHRD routine. (This
*> subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
-*>
-*> References
-*> ==========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
*> performance of reduction to Hessenberg form," ACM Transactions on
*> Mathematical Software, 32(2):180-194, June 2006.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAHRD reduces the first NB columns of a real general n-by-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> This is an OBSOLETE auxiliary routine.
*> This routine will be 'deprecated' in a future release.
*> Please use the new routine SLAHR2 instead.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
*
* REAL W( J ), X( J )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAIC1 applies one step of incremental condition estimation in
*> its simplest version:
*> [ gamma ]
*>
*> where alpha = x**T*w.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> C is REAL
*> Cosine needed in forming xhat.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION SLAISNAN( SIN1, SIN2 )
*
* REAL SIN1, SIN2
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is not for general use. It exists solely to avoid
*> over-optimization in SISNAN.
*> Interprocedural or whole-program optimization may delete this
*> test. The ISNAN functions will be replaced by the correct
*> Fortran 03 intrinsic once the intrinsic is widely available.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIN1
*> \verbatim
*> SIN2 is REAL
*> Two numbers to compare for inequality.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B,
* LDB, WR, WI, X, LDX, SCALE, XNORM, INFO )
* REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLALN2 solves a system of the form (ca A - w D ) X = s B
*> or (ca A**T - w D) X = s B with possible scaling ("s") and
*>
*> Note: all input quantities are assumed to be smaller than overflow
*> by a reasonable factor. (See BIGNUM.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LTRANS
*> \verbatim
*> NOTE: In the interests of speed, this routine does not
*> check the inputs for errors.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
* $ POLES( LDGNUM, * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLALS0 applies back the multiplying factors of either the left or the
*> right singular vector matrix of a diagonal matrix appended by a row
*> (3R) The inverse transformation of (2L).
*>
*> (4R) The inverse transformation of (1L).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE SLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
$ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
* $ Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLALSA is an itermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> ICOMPQ = 1, SLALSA applies the right singular vector matrix to the
*> right hand side. The singular vector matrices were generated in
*> compact form by SLALSA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE SLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
$ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
* RANK, WORK, IWORK, INFO )
* REAL B( LDB, * ), D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLALSD uses the singular value decomposition of A to solve the least
*> squares problem of finding X to minimize the Euclidean norm of each
*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through MOD(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
$ RANK, WORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAMRG( N1, N2, A, STRD1, STRD2, INDEX )
*
* REAL A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAMRG will create a permutation list which will merge the elements
*> of A (which is composed of two independently sorted sets) into a
*> single set which is sorted in ascending order.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N1
*> \verbatim
*> if B( I ) = A( INDEX( I ) ) for I=1,N1+N2, then B will be
*> sorted in ascending order.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION SLANEG( N, D, LLD, SIGMA, PIVMIN, R )
*
* REAL D( * ), LLD( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANEG computes the Sturm count, the number of negative pivots
*> encountered while factoring tridiagonal T - sigma I = L D L^T.
*> Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
*> Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624
*> (Tech report version in LAWN 172 with the same title.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The twist index for the twisted factorization that is used
*> for the negcount.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*> Jason Riedy, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
+*> Jason Riedy, University of California, Berkeley, USA \n
*>
* =====================================================================
INTEGER FUNCTION SLANEG( N, D, LLD, SIGMA, PIVMIN, R )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANGB( NORM, N, KL, KU, AB, LDAB,
* WORK )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANGB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANGB returns the value
+*> \return SLANGB
+*> \verbatim
*>
*> SLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANGE( NORM, M, N, A, LDA, WORK )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANGE returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANGE returns the value
+*> \return SLANGE
+*> \verbatim
*>
*> SLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANGT( NORM, N, DL, D, DU )
*
* REAL D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANGT returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANGT returns the value
+*> \return SLANGT
+*> \verbatim
*>
*> SLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> DU is REAL array, dimension (N-1)
*> The (n-1) super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANHS( NORM, N, A, LDA, WORK )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANHS returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> Hessenberg matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANHS returns the value
+*> \return SLANHS
+*> \verbatim
*>
*> SLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANSB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n symmetric band matrix A, with k super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANSB returns the value
+*> \return SLANSB
+*> \verbatim
*>
*> SLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANSF( NORM, TRANSR, UPLO, N, A, WORK )
*
* REAL A( 0: * ), WORK( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANSF returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric matrix A in RFP format.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANSF returns the value
+*> \return SLANSF
+*> \verbatim
*>
*> SLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
REAL FUNCTION SLANSF( NORM, TRANSR, UPLO, N, A, WORK )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANSP( NORM, UPLO, N, AP, WORK )
*
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANSP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANSP returns the value
+*> \return SLANSP
+*> \verbatim
*>
*> SLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANST( NORM, N, D, E )
*
* REAL D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANST returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANST returns the value
+*> \return SLANST
+*> \verbatim
*>
*> SLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> E is REAL array, dimension (N-1)
*> The (n-1) sub-diagonal or super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANSY returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> real symmetric matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANSY returns the value
+*> \return SLANSY
+*> \verbatim
*>
*> SLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANTB( NORM, UPLO, DIAG, N, K, AB,
* LDAB, WORK )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANTB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n triangular band matrix A, with ( k + 1 ) diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANTB returns the value
+*> \return SLANTB
+*> \verbatim
*>
*> SLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANTP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> triangular matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANTP returns the value
+*> \return SLANTP
+*> \verbatim
*>
*> SLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
* WORK )
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANTR returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> trapezoidal or triangular matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> SLANTR returns the value
+*> \return SLANTR
+*> \verbatim
*>
*> SLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
*
* REAL A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
*> matrix in standard form:
*> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
*> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
*> conjugate eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] A
*> \verbatim
*> SN is REAL
*> Parameters of the rotation matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by V. Sima, Research Institute for Informatics, Bucharest,
*> Romania, to reduce the risk of cancellation errors,
*> when computing real eigenvalues, and to ensure, if possible, that
*> abs(RT1R) >= abs(RT2R).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
* REAL X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given two column vectors X and Y, let
*>
*> and then computes the SVD of the 2-by-2 upper triangular matrix R.
*> The smaller singular value of R is returned in SSMIN, which is used
*> as the measurement of the linear dependency of the vectors X and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> SSMIN is REAL
*> The smallest singular value of the N-by-2 matrix A = ( X Y ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAPMR( FORWRD, M, N, X, LDX, K )
*
* REAL X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAPMR rearranges the rows of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(M) of the integers 1,...,M.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(I,*) is moved to X(K(I),*) for I = 1,2,...,M.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAPMT( FORWRD, M, N, X, LDX, K )
*
* REAL X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAPMT rearranges the columns of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(N) of the integers 1,...,N.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(*,J) is moved to X(*,K(J)) for J = 1,2,...,N.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLAPY2( X, Y )
*
* REAL X, Y
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary
*> overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> Y is REAL
*> X and Y specify the values x and y.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLAPY3( X, Y, Z )
*
* REAL X, Y, Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause
*> unnecessary overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> Z is REAL
*> X, Y and Z specify the values x, y and z.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, EQUED )
* REAL AB( LDAB, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQGB equilibrates a general M by N band matrix A with KL
*> subdiagonals and KU superdiagonals using the row and scaling factors
*> in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* EQUED )
* REAL A( LDA, * ), C( * ), R( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQGE equilibrates a general M by N matrix A using the row and
*> column scaling factors in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
* WORK )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQP2 computes a QR factorization with column pivoting of
*> the block A(OFFSET+1:M,1:N).
*> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
-*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE SLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
$ WORK )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
* VN2, AUXV, F, LDF )
* $ VN1( * ), VN2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQPS computes a step of QR factorization with column pivoting
*> of a real M-by-N matrix A by using Blas-3. It tries to factorize
*> columns is returned in KB.
*>
*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of the array F. LDF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE SLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
$ VN2, AUXV, F, LDF )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQR0 computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
$ ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
*
* REAL H( LDH, * ), V( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a
*> scalar multiple of the first column of the product
*>
*> This is useful for starting double implicit shift bulges
*> in the QR algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> A scalar multiple of the first column of the
*> matrix K in (*).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE SLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQR2 is identical to SLAQR3 except that it avoids
*> recursion by calling SLAHQR instead of SLAQR4.
*> an orthogonal similarity transformation of H. It is to be
*> hoped that the final version of H has many zero subdiagonal
*> entries.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE SLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Aggressive early deflation:
*>
*> an orthogonal similarity transformation of H. It is to be
*> hoped that the final version of H has many zero subdiagonal
*> entries.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE SLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQR4 implements one level of recursion for SLAQR0.
*> It is a complete implementation of the small bulge multi-shift
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
$ ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
* SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQR5, called by SLAQR0, performs a
*> single small-bulge multi-shift QR sweep.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> LDWV is the leading dimension of WV as declared in the
*> in the calling subroutine. LDWV.GE.NV.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> \par Contributors:
+* ==================
*>
-*> Reference:
-*>
-*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-*> Algorithm Part I: Maintaining Well Focused Shifts, and
-*> Level 3 Performance, SIAM Journal of Matrix Analysis,
-*> volume 23, pages 929--947, 2002.
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> \endverbatim
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
*>
* =====================================================================
SUBROUTINE SLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* REAL AB( LDAB, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQSB equilibrates a symmetric band matrix A using the scaling
*> factors in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* REAL AP( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQSP equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* REAL A( LDA, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQSY equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK,
* INFO )
* REAL B( * ), T( LDT, * ), WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAQTR solves the real quasi-triangular system
*>
*>
*> This subroutine is designed for the condition number estimation
*> in routine STRSNA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LTRAN
*> \verbatim
*> NOTE: In the interests of speed, this routine does not
*> check the inputs for errors.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
* PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
* REAL Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAR1V computes the (scaled) r-th column of the inverse of
*> the sumbmatrix in rows B1 through BN of the tridiagonal matrix
*> (d) Computation of the (scaled) r-th column of the inverse using the
*> twisted factorization obtained by combining the top part of the
*> the stationary and the bottom part of the progressive transform.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (4*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
$ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* REAL C( * ), S( * ), X( * ), Y( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAR2V applies a vector of real plane rotations from both sides to
*> a sequence of 2-by-2 real symmetric matrices, defined by the elements
*>
*> ( x(i) z(i) ) := ( c(i) s(i) ) ( x(i) z(i) ) ( c(i) -s(i) )
*> ( z(i) y(i) ) ( -s(i) c(i) ) ( z(i) y(i) ) ( s(i) c(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* REAL C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARF applies a real elementary reflector H to a real m by n matrix
*> C, from either the left or the right. H is represented in the form
*> where tau is a real scalar and v is a real vector.
*>
*> If tau = 0, then H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
* T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARFB applies a real block reflector H or its transpose H**T to a
*> real m by n matrix C, from either the left or the right.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU )
*
* REAL X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARFG generates a real elementary reflector H of order n, such
*> that
*> the unit matrix.
*>
*> Otherwise 1 <= tau <= 2.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is REAL
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARFGP( N, ALPHA, X, INCX, TAU )
*
* REAL X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARFGP generates a real elementary reflector H of order n, such
*> that
*>
*> If the elements of x are all zero, then tau = 0 and H is taken to be
*> the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is REAL
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* REAL T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARFT forms the triangular factor T of a real block reflector H
*> of order n, which is defined as a product of k elementary reflectors.
*> H(i) is stored in the i-th row of the array V, and
*>
*> H = I - V**T * T * V
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARFX( SIDE, M, N, V, TAU, C, LDC, WORK )
*
* REAL C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARFX applies a real elementary reflector H to a real m by n
*> matrix C, from either the left or the right. H is represented in the
*> If tau = 0, then H is taken to be the unit matrix
*>
*> This version uses inline code if H has order < 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> or (M) if SIDE = 'R'
*> WORK is not referenced if H has order < 11.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* REAL C( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARGV generates a vector of real plane rotations, determined by
*> elements of the real vectors x and y. For i = 1,2,...,n
*>
*> ( c(i) s(i) ) ( x(i) ) = ( a(i) )
*> ( -s(i) c(i) ) ( y(i) ) = ( 0 )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARNV( IDIST, ISEED, N, X )
*
* REAL X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARNV returns a vector of n random real numbers from a uniform or
*> normal distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> X is REAL array, dimension (N)
*> The generated random numbers.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine SLARUV to generate random
*> real numbers from a uniform (0,1) distribution, in batches of up to
*> 128 using vectorisable code. The Box-Muller method is used to
*> transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM,
* NSPLIT, ISPLIT, INFO )
* REAL D( * ), E( * ), E2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute the splitting points with threshold SPLTOL.
*> SLARRA sets any "small" off-diagonal elements to zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM,
$ NSPLIT, ISPLIT, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
* RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK,
* $ WERR( * ), WGAP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given the relatively robust representation(RRR) L D L^T, SLARRB
*> does "limited" bisection to refine the eigenvalues of L D L^T,
*> and WGAP, respectively. During bisection, intervals
*> [left, right] are maintained by storing their mid-points and
*> semi-widths in the arrays W and WERR respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> Error flag.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
$ RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
* EIGCNT, LCNT, RCNT, INFO )
* REAL D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Find the number of eigenvalues of the symmetric tridiagonal matrix T
*> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
*> if JOBT = 'L'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBT
*> \verbatim
*> \verbatim
*> INFO is INTEGER
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
$ EIGCNT, LCNT, RCNT, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS,
* RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT,
* $ GERS( * ), W( * ), WERR( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARRD computes the eigenvalues of a symmetric tridiagonal
*> matrix T to suitable accuracy. This is an auxiliary code to be
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RANGE
*> \verbatim
*> floating-point arithmetic.
*> Cure: Increase the PARAMETER "FUDGE",
*> recompile, and try again.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
-*> FUDGE REAL , default = 2
+*> \verbatim
+*> FUDGE REAL, default = 2
*> A "fudge factor" to widen the Gershgorin intervals. Ideally,
*> a value of 1 should work, but on machines with sloppy
*> arithmetic, this needs to be larger. The default for
*> publicly released versions should be large enough to handle
*> the worst machine around. Note that this has no effect
*> on accuracy of the solution.
-*>
-*> Based on contributions by
-*> W. Kahan, University of California, Berkeley, USA
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
*> \endverbatim
*>
+*> \par Contributors:
+* ==================
+*>
+*> W. Kahan, University of California, Berkeley, USA \n
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,
* RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M,
* $ W( * ),WERR( * ), WGAP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> To find the desired eigenvalues of a given real symmetric
*> tridiagonal matrix T, SLARRE sets any "small" off-diagonal
*> conpute all and then discard any unwanted one.
*> As an added benefit, SLARRE also outputs the n
*> Gerschgorin intervals for the matrices L_i D_i L_i^T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RANGE
*> \verbatim
*> =-5: Problem in SLASQ2.
*> =-6: Problem in SLASQ2.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The base representations are required to suffer very little
*> element growth and consequently define all their eigenvalues to
*> high relative accuracy.
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE SLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRF( N, D, L, LD, CLSTRT, CLEND,
* W, WGAP, WERR,
* $ LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given the initial representation L D L^T and its cluster of close
*> eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
*> W( CLEND ), SLARRF finds a new relatively robust representation
*> L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the
*> eigenvalues of L(+) D(+) L(+)^T is relatively isolated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> Signals processing OK (=0) or failure (=1)
*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRF( N, D, L, LD, CLSTRT, CLEND,
$ W, WGAP, WERR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST,
* RTOL, OFFSET, W, WERR, WORK, IWORK,
* $ WERR( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given the initial eigenvalue approximations of T, SLARRJ
*> does bisection to refine the eigenvalues of T,
*> of the error in these guesses in WERR. During bisection, intervals
*> [left, right] are maintained by storing their mid-points and
*> semi-widths in the arrays W and WERR respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> Error flag.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST,
$ RTOL, OFFSET, W, WERR, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRK( N, IW, GL, GU,
* D, E2, PIVMIN, RELTOL, W, WERR, INFO)
* REAL D( * ), E2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARRK computes one eigenvalue of a symmetric tridiagonal
*> matrix T to suitable accuracy. This is an auxiliary code to be
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: Eigenvalue converged
*> = -1: Eigenvalue did NOT converge
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> FUDGE REAL , default = 2
*> A "fudge factor" to widen the Gershgorin intervals.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRR( N, D, E, INFO )
*
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Perform tests to decide whether the symmetric tridiagonal matrix T
*> warrants expensive computations which guarantee high relative accuracy
*> in the eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO = 1 : the matrix warrants computations guaranteeing
*> only absolute accuracy.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRR( N, D, E, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARRV( N, VL, VU, D, L, PIVMIN,
* ISPLIT, M, DOL, DOU, MINRGP,
* REAL Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARRV computes the eigenvectors of the tridiagonal matrix
*> T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
*> The input eigenvalues should have been computed by SLARRE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 5: The Rayleigh Quotient Iteration failed to converge to
*> full accuracy in MAXITR steps.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SLARRV( N, VL, VU, D, L, PIVMIN,
$ ISPLIT, M, DOL, DOU, MINRGP,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARSCL2 ( M, N, D, X, LDX )
*
* REAL D( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARSCL2 performs a reciprocal diagonal scaling on an vector:
*> x <-- inv(D) * x
*>
*> Eventually to be replaced by BLAS_sge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARTG( F, G, CS, SN, R )
*
* REAL CS, F, G, R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARTG generate a plane rotation so that
*>
*> there are zeros on the diagonal).
*>
*> If F exceeds G in magnitude, CS will be positive.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARTGP( F, G, CS, SN, R )
*
* REAL CS, F, G, R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARTGP generates a plane rotation so that
*>
*> If F=0 and (G .ne. 0), then CS=0 and SN=(+/-)1.
*>
*> The sign is chosen so that R >= 0.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARTGS( X, Y, SIGMA, CS, SN )
*
* REAL CS, SIGMA, SN, X, Y
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARTGS generates a plane rotation designed to introduce a bulge in
*> Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
*>
*> with R nonnegative. If X^2 - SIGMA and X * Y are 0, then the
*> rotation is by PI/2.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> SN is REAL
*> The sine of the rotation.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARTV( N, X, INCX, Y, INCY, C, S, INCC )
*
* REAL C( * ), S( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARTV applies a vector of real plane rotations to elements of the
*> real vectors x and y. For i = 1,2,...,n
*>
*> ( x(i) ) := ( c(i) s(i) ) ( x(i) )
*> ( y(i) ) ( -s(i) c(i) ) ( y(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARUV( ISEED, N, X )
*
* REAL X( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARUV returns a vector of n random real numbers from a uniform (0,1)
*> distribution (n <= 128).
*>
*> This is an auxiliary routine called by SLARNV and CLARNV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] ISEED
*> \verbatim
*> X is REAL array, dimension (N)
*> The generated random numbers.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine uses a multiplicative congruential method with modulus
*> 48-bit integers are stored in 4 integer array elements with 12 bits
*> per element. Hence the routine is portable across machines with
*> integers of 32 bits or more.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* REAL C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARZ applies a real elementary reflector H to a real M-by-N
*> matrix C, from either the left or the right. H is represented in the
*>
*>
*> H is a product of k elementary reflectors as returned by STZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
* LDV, T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARZB applies a real block reflector H or its transpose H**T to
*> a real distributed M-by-N C from the left or the right.
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* REAL T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARZT forms the triangular factor T of a real block reflector
*> H of order > n, which is defined as a product of k elementary
*> H = I - V**T * T * V
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> the H(i) is best illustrated by the following example with n = 5 and
*> V = ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> ( v1 v2 v3 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )
*
* REAL F, G, H, SSMAX, SSMIN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAS2 computes the singular values of the 2-by-2 matrix
*> [ F G ]
*> [ 0 H ].
*> On return, SSMIN is the smaller singular value and SSMAX is the
*> larger singular value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> SSMAX is REAL
*> The larger singular value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Barring over/underflow, all output quantities are correct to within
*> Underflow is harmless if underflow is gradual. Otherwise, results
*> may correspond to a matrix modified by perturbations of size near
*> the underflow threshold.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASCL multiplies the M by N real matrix A by the real scalar
*> CTO/CFROM. This is done without over/underflow as long as the final
*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
*> A may be full, upper triangular, lower triangular, upper Hessenberg,
*> or banded.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> 0 - successful exit
*> <0 - if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASCL2 ( M, N, D, X, LDX )
*
* REAL D( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASCL2 performs a diagonal scaling on a vector:
*> x <-- D * x
*>
*> Eventually to be replaced by BLAS_sge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
* WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Using a divide and conquer approach, SLASD0 computes the singular
*> value decomposition (SVD) of a real upper bidiagonal N-by-M
*>
*> A related subroutine, SLASDA, computes only the singular values,
*> and optionally, the singular vectors in compact form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
$ WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD1( NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT,
* IDXQ, IWORK, WORK, INFO )
* REAL D( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B,
*> where N = NL + NR + 1 and M = N + SQRE. SLASD1 is called from SLASD0.
*> directly using the updated singular values. The singular vectors
*> for the current problem are multiplied with the singular vectors
*> from the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NL
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD1( NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT,
$ IDXQ, IWORK, WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT,
* LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX,
* $ Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASD2 merges the two sets of singular values together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> equation problem is reduced by one.
*>
*> SLASD2 is called from SLASD1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NL
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT,
$ LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
* LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z,
* $ Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASD3 finds all the square roots of the roots of the secular
*> equation, as defined by the values in D and Z. It makes the
*> without guard digits, but we know of none.
*>
*> SLASD3 is called from SLASD1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NL
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
$ LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
* REAL D( * ), DELTA( * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the square root of the I-th updated
*> eigenvalue of a positive symmetric rank-one modification to
*>
*> The method consists of approximating the rational functions in the
*> secular equation by simpler interpolating rational functions.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> > 0: if INFO = 1, the updating process failed.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> Logical variable ORGATI (origin-at-i?) is used for distinguishing
*> whether D(i) or D(i+1) is treated as the origin.
*>
*> MAXIT is the maximum number of iterations allowed for each
*> eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
*
* REAL D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This subroutine computes the square root of the I-th eigenvalue
*> of a positive symmetric rank-one modification of a 2-by-2 diagonal
*>
*> We also assume RHO > 0 and that the Euclidean norm of the vector
*> Z is one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I
*> \verbatim
*> WORK is REAL array, dimension (2)
*> WORK contains (D(j) + sigma_I) in its j-th component.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ren-Cang Li, Computer Science Division, University of California
*> at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
* $ VF( * ), VL( * ), WORK( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASD6 computes the SVD of an updated upper bidiagonal matrix B
*> obtained by merging two smaller ones by appending a row. This
*> values.
*>
*> SLASD6 is called from SLASDA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
$ IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL,
* VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ,
* $ ZW( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASD7 merges the two sets of singular values together into a single
*> sorted set. Then it tries to deflate the size of the problem. There
*> secular equation problem is reduced by one.
*>
*> SLASD7 is called from SLASD6.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL,
$ VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
* DSIGMA, WORK, INFO )
* $ Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASD8 finds the square roots of the roots of the secular equation,
*> as defined by the values in DSIGMA and Z. It makes the appropriate
*> right singular vectors of the original bidiagonal matrix.
*>
*> SLASD8 is called from SLASD6.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
$ DSIGMA, WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
* $ Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Using a divide and conquer approach, SLASDA computes the singular
*> value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
*>
*> A related subroutine, SLASD0, computes the singular values and
*> the singular vectors in explicit form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, a singular value did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
$ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT,
* U, LDU, C, LDC, WORK, INFO )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASDQ computes the singular value decomposition (SVD) of a real
*> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
*> See "Computing Small Singular Values of Bidiagonal Matrices With
*> Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
*> LAPACK Working Note #3, for a detailed description of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If INFO > 0, the algorithm did not converge, and INFO
*> specifies how many superdiagonals did not converge.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT,
$ U, LDU, C, LDC, WORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
* INTEGER INODE( * ), NDIML( * ), NDIMR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASDT creates a tree of subproblems for bidiagonal divide and
*> conquer.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On entry, the maximum row dimension each subproblem at the
*> bottom of the tree can be of.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASET initializes an m-by-n matrix A to BETA on the diagonal and
*> ALPHA on the offdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASQ1( N, D, E, WORK, INFO )
*
* REAL D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASQ1 computes the singular values of a real N-by-N bidiagonal
*> matrix with diagonal D and off-diagonal E. The singular values
*>
*> and the present implementation is described in "An implementation of
*> the dqds Algorithm (Positive Case)", LAPACK Working Note.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 3, termination criterion of outer while loop not met
*> (program created more than N unreduced blocks)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASQ2( N, Z, INFO )
*
* REAL Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASQ2 computes all the eigenvalues of the symmetric positive
*> definite tridiagonal matrix associated with the qd array Z to high
*> on machines which follow ieee-754 floating-point standard in their
*> handling of infinities and NaNs, and false otherwise. This variable
*> is passed to SLASQ3.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 3, termination criterion of outer while loop not met
*> (program created more than N unreduced blocks)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> Local Variables: I0:N0 defines a current unreduced segment of Z.
*> The shifts are accumulated in SIGMA. Iteration count is in ITER.
*> Ping-pong is controlled by PP (alternates between 0 and 1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
* REAL Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
*> In case of failure it changes shifts, and tries again until output
*> is positive.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> These are passed as arguments in order to save their values
*> between calls to SLASQ3.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
* DN1, DN2, TAU, TTYPE, G )
* REAL Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASQ4 computes an approximation TAU to the smallest eigenvalue
*> using values of d from the previous transform.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> G is passed as an argument in order to save its value between
*> calls to SLASQ4.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
-*> CNST1 = 9/16
*>
+*> CNST1 = 9/16
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2, IEEE )
* REAL Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASQ5 computes one dqds transform in ping-pong form, one
*> version for IEEE machines another for non IEEE machines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> IEEE is LOGICAL
*> Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2 )
* REAL Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASQ6 computes one dqd (shift equal to zero) transform in
*> ping-pong form, with protection against underflow and overflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] I0
*> \verbatim
*> DNM2 is REAL
*> d(N0-2).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
* REAL A( LDA, * ), C( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASR applies a sequence of plane rotations to a real matrix A,
*> from either the left or the right.
*>
*> where R(k) appears in rows and columns k and z. The rotations are
*> performed without ever forming P(k) explicitly.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASRT( ID, N, D, INFO )
*
* REAL D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Sort the numbers in D in increasing order (if ID = 'I') or
*> in decreasing order (if ID = 'D' ).
*>
*> Use Quick Sort, reverting to Insertion sort on arrays of
*> size <= 20. Dimension of STACK limits N to about 2**32.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ID
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* REAL X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASSQ returns the values scl and smsq such that
*>
*> scl and smsq are overwritten on SCALE and SUMSQ respectively.
*>
*> The routine makes only one pass through the vector x.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On exit, SUMSQ is overwritten with smsq , the basic sum of
*> squares from which scl has been factored out.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
*
* REAL CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASV2 computes the singular value decomposition of a 2-by-2
*> triangular matrix
*>
*> [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ]
*> [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ].
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> The vector (CSR, SNR) is a unit right singular vector for the
*> singular value abs(SSMAX).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Any input parameter may be aliased with any output parameter.
*> Underflow is harmless if underflow is gradual. Otherwise, results
*> may correspond to a matrix modified by perturbations of size near
*> the underflow threshold.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASWP( N, A, LDA, K1, K2, IPIV, INCX )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASWP performs a series of row interchanges on the matrix A.
*> One row interchange is initiated for each of rows K1 through K2 of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of IPIV. If IPIV
*> is negative, the pivots are applied in reverse order.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by
*> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR,
* LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in
*>
*>
*> where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or
*> -1. op(T) = T or T**T, where T**T denotes the transpose of T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LTRANL
*> \verbatim
*> NOTE: In the interests of speed, this routine does not
*> check the inputs for errors.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
* REAL A( LDA, * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLASYF computes a partial factorization of a real symmetric matrix A
*> using the Bunch-Kaufman diagonal pivoting method. The partial
*> SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code
*> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
*> A22 (if UPLO = 'L').
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
* SCALE, CNORM, INFO )
* REAL AB( LDAB, * ), CNORM( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATBS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine STBSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, STBSV
*>
*> and we can safely call STBSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
* JPIV )
* REAL RHS( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATDF uses the LU factorization of the n-by-n matrix Z computed by
*> SGETC2 and computes a contribution to the reciprocal Dif-estimate
*> The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q,
*> where P and Q are permutation matrices. L is lower triangular with
*> unit diagonal elements and U is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> The pivot indices; for 1 <= j <= N, column j of the
*> matrix has been interchanged with column JPIV(j).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
+*> \par Further Details:
+* =====================
+*>
+*> This routine is a further developed implementation of algorithm
+*> BSOLVE in [1] using complete pivoting in the LU factorization.
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
-*> This routine is a further developed implementation of algorithm
-*> BSOLVE in [1] using complete pivoting in the LU factorization.
*>
*> [1] Bo Kagstrom and Lars Westin,
*> Generalized Schur Methods with Condition Estimators for
*> between two Regular Matrix Pairs with Applications in
*> Condition Estimation. Report IMINF-95.05, Departement of
*> Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATPS( UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE,
* CNORM, INFO )
* REAL AP( * ), CNORM( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATPS solves one of the triangular systems
*>
*> unscaled problem will not cause overflow, the Level 2 BLAS routine
*> STPSV is called. If the matrix A is singular (A(j,j) = 0 for some j),
*> then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, STPSV
*>
*> and we can safely call STPSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
* REAL A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATRD reduces NB rows and columns of a real symmetric matrix A to
*> symmetric tridiagonal form by an orthogonal similarity
*> matrix, of which the lower triangle is supplied.
*>
*> This is an auxiliary routine called by SSYTRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDW is INTEGER
*> The leading dimension of the array W. LDW >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup doubleOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where d denotes a diagonal element of the reduced matrix, a denotes
*> an element of the original matrix that is unchanged, and vi denotes
*> an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
* CNORM, INFO )
* REAL A( LDA, * ), CNORM( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATRS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine STRSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, STRSV
*>
*> and we can safely call STRSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATRZ( M, N, L, A, LDA, TAU, WORK )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
*> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means
*> of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal
*> matrix and, R and A1 are M-by-M upper triangular matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
* REAL C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine SORMRZ.
*>
*> C = [ C1, C2 ] m
*> 1 n-1
*> Then C is overwritten by C*P.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAUU2( UPLO, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAUU2 computes the product U * U**T or L**T * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the unblocked form of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAUUM( UPLO, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAUUM computes the product U * U**T or L**T * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the blocked form of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
* REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SOPGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
* INFO )
* REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SOPMTR overwrites the general real M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
* $ X21( LDX21, * ), X22( LDX22, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORBDB simultaneously bidiagonalizes the blocks of an M-by-M
*> partitioned orthogonal matrix X:
*>
*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
*> implicitly by angles THETA, PHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The bidiagonal blocks B11, B12, B21, and B22 are represented
*> P1, P2, Q1, and Q2 are represented as products of elementary
*> reflectors. See SORCSD for details on generating P1, P2, Q1, and Q2
*> using SORGQR and SORGLQ.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE SORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
* SIGNS, M, P, Q, X11, LDX11, X12,
* $ * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORCSD computes the CS decomposition of an M-by-M partitioned
*> orthogonal matrix X:
*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
*> which R = MIN(P,M-P,Q,M-Q).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: SBBCSD did not converge. See the description of WORK
*> above for details.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
-*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORG2L generates an m by n real matrix Q with orthonormal columns,
*> which is defined as the last n columns of a product of k elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by SGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORG2R generates an m by n real matrix Q with orthonormal columns,
*> which is defined as the first n columns of a product of k elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by SGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGBR generates one of the real orthogonal matrices Q or P**T
*> determined by SGEBRD when reducing a real matrix A to bidiagonal
*> rows of P**T, where n >= m >= k;
*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as
*> an N-by-N matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGHR generates a real orthogonal matrix Q which is defined as the
*> product of IHI-ILO elementary reflectors of order N, as returned by
*> SGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGL2 generates an m by n real matrix Q with orthonormal rows,
*> which is defined as the first m rows of a product of k elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by SGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGLQ generates an M-by-N real matrix Q with orthonormal rows,
*> which is defined as the first M rows of a product of K elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by SGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGQL generates an M-by-N real matrix Q with orthonormal columns,
*> which is defined as the last N columns of a product of K elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by SGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGQR generates an M-by-N real matrix Q with orthonormal columns,
*> which is defined as the first N columns of a product of K elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by SGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGR2 generates an m by n real matrix Q with orthonormal rows,
*> which is defined as the last m rows of a product of k elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by SGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGRQ generates an M-by-N real matrix Q with orthonormal rows,
*> which is defined as the last M rows of a product of K elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by SGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors of order N, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORM2L overwrites the general real m by n matrix C with
*>
*>
*> as returned by SGEQLF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORM2R overwrites the general real m by n matrix C with
*>
*>
*> as returned by SGEQRF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
*> with
*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
*> if k < nq, P = G(1) G(2) . . . G(k);
*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMHR overwrites the general real M-by-N matrix C with
*>
*> IHI-ILO elementary reflectors, as returned by SGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORML2 overwrites the general real m by n matrix C with
*>
*>
*> as returned by SGELQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMLQ overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMQL overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by SGEQLF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMQR overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by SGEQRF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMR2 overwrites the general real m by n matrix C with
*>
*>
*> as returned by SGERQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, INFO )
* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMR3 overwrites the general real m by n matrix C with
*>
*>
*> as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMRQ overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMRZ overwrites the general real M-by-N matrix C with
*>
*>
*> as returned by STZRZF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORMTR overwrites the general real M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
* IWORK, INFO )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite band matrix using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )
*
* REAL AB( LDAB, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite band matrix A and reduce its condition
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B,
* LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite
*> and banded, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBSTF( UPLO, N, KD, AB, LDAB, INFO )
*
* REAL AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBSTF computes a split Cholesky factorization of a real
*> symmetric positive definite band matrix A.
*>
*> where U is upper triangular of order m = (n+kd)/2, and L is lower
*> triangular of order n-m.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> because the updated element a(i,i) was negative; the
*> matrix A is not positive definite.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* REAL AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBSV computes the solution to a real system of linear equations
*> A * X = B,
*> triangular band matrix, with the same number of superdiagonals or
*> subdiagonals as A. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBSVX( FACT, UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB,
* EQUED, S, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
*> compute the solution to a real system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
* REAL AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBTF2 computes the Cholesky factorization of a real symmetric
*> positive definite band matrix A.
*> L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
* REAL AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBTRF computes the Cholesky factorization of a real symmetric
*> positive definite band matrix A.
*> A = U**T * U, if UPLO = 'U', or
*> A = L * L**T, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
-*> Contributed by
-*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
+*
* =====================================================================
SUBROUTINE SPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* REAL AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite band matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by SPBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPFTRF( TRANSR, UPLO, N, A, INFO )
*
* .. Array Arguments ..
* REAL A( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPFTRF computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPFTRI( TRANSR, UPLO, N, A, INFO )
*
* REAL A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPFTRI computes the inverse of a real (symmetric) positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by SPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* REAL A( 0: * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPFTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by SPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
* INFO )
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite matrix using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
*
* REAL A( LDA, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
*
* REAL A( LDA, * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X,
* LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPORFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite,
*> and provides error bounds and backward error estimates for the
*> solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
* LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPORFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOSV computes the solution to a real system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK,
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
*> compute the solution to a real system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
*> to compute the solution to a real system of linear equations
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what SPOSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOTF2 computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOTRF computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOTRI( UPLO, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOTRI computes the inverse of a real symmetric positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by SPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by SPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )
*
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite packed matrix using
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
*
* REAL AP( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPEQU computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A in packed storage and reduce
*> This choice of S puts the condition number of B within a factor N of
*> the smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR,
* BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* REAL AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPSV computes the solution to a real system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPSVX( FACT, UPLO, N, NRHS, AP, AFP, EQUED, S, B, LDB,
* X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), S( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
*> compute the solution to a real system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPTRF( UPLO, N, AP, INFO )
*
* REAL AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPTRF computes the Cholesky factorization of a real symmetric
*> positive definite matrix A stored in packed format.
*> A = U**T * U, if UPLO = 'U', or
*> A = L * L**T, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPTRI( UPLO, N, AP, INFO )
*
* REAL AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPTRI computes the inverse of a real symmetric positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by SPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* REAL AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite matrix A in packed storage using the Cholesky
*> factorization A = U**T*U or A = L*L**T computed by SPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPSTF2 computes the Cholesky factorization with complete
*> pivoting of a real symmetric positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPSTRF computes the Cholesky factorization with complete
*> pivoting of a real symmetric positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
*
* REAL D( * ), E( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTCON computes the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric positive definite tridiagonal matrix
*> Norm(inv(A)) is computed by a direct method, and the reciprocal of
*> the condition number is computed as
*> RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The method used is described in Nicholas J. Higham, "Efficient
*> Algorithms for Computing the Condition Number of a Tridiagonal
*> Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric positive definite tridiagonal matrix by first factoring the
*> form, however, may preclude the possibility of obtaining high
*> relative accuracy in the small eigenvalues of the original matrix, if
*> these eigenvalues range over many orders of magnitude.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> if INFO = N+i, i off-diagonal elements of the
*> bidiagonal factor did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
* BERR, WORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive definite
*> and tridiagonal, and provides error bounds and backward error
*> estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTSV( N, NRHS, D, E, B, LDB, INFO )
*
* REAL B( LDB, * ), D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTSV computes the solution to a real system of linear equations
*> A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
*>
*> A is factored as A = L*D*L**T, and the factored form of A is then
*> used to solve the system of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> computed. The factorization has not been completed
*> unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
* RCOND, FERR, BERR, WORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTSVX uses the factorization A = L*D*L**T to compute the solution
*> to a real system of linear equations A*X = B, where A is an N-by-N
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTTRF( N, D, E, INFO )
*
* REAL D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTTRF computes the L*D*L**T factorization of a real symmetric
*> positive definite tridiagonal matrix A. The factorization may also
*> be regarded as having the form A = U**T*D*U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be completed, while if k = N, the factorization was
*> completed, but D(N) <= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTTRS( N, NRHS, D, E, B, LDB, INFO )
*
* REAL B( LDB, * ), D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTTRS solves a tridiagonal system of the form
*> A * X = B
*> diagonal matrix specified in the vector D, L is a unit bidiagonal
*> matrix whose subdiagonal is specified in the vector E, and X and B
*> are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
*
* REAL B( LDB, * ), D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTTS2 solves a tridiagonal system of the form
*> A * X = B
*> diagonal matrix specified in the vector D, L is a unit bidiagonal
*> matrix whose subdiagonal is specified in the vector E, and X and B
*> are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SRSCL( N, SA, SX, INCX )
*
* REAL SX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SRSCL multiplies an n-element real vector x by the real scalar 1/a.
*> This is done without overflow or underflow as long as
*> the final result x/a does not overflow or underflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of the vector SX.
*> > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* INFO )
* REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBEV computes all the eigenvalues and, optionally, eigenvectors of
*> a real symmetric band matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* LWORK, IWORK, LIWORK, INFO )
* REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBEVD computes all the eigenvalues and, optionally, eigenvectors of
*> a real symmetric band matrix A. If eigenvectors are desired, it uses
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric band matrix A. Eigenvalues and eigenvectors can
*> be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
* LDX, WORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBGST reduces a real symmetric-definite banded generalized
*> eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
*> split Cholesky factorization. A is overwritten by C = X**T*A*X, where
*> X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
*> bandwidth of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
*> and banded, and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of the
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
* LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
* $ W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of
*> and banded, and B is also positive definite. Eigenvalues and
*> eigenvectors can be selected by specifying either all eigenvalues,
*> a range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
$ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
* WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBTRD reduces a real symmetric band matrix A to symmetric
*> tridiagonal form T by an orthogonal similarity transformation:
*> Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by Linda Kaufman, Bell Labs.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
* C )
* REAL A( LDA, * ), C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for C in RFP Format.
*>
*> where alpha and beta are real scalars, C is an n--by--n symmetric
*> matrix and A is an n--by--k matrix in the first case and a k--by--n
*> matrix in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP
*> Format. RFP Format is described by TRANSR, UPLO and N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
* INFO )
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric packed matrix A using the factorization
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
*
* REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPEV computes all the eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A in packed storage.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
* IWORK, LIWORK, INFO )
* REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPEVD computes all the eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A in packed storage. If eigenvectors are
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL,
* REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A in packed storage. Eigenvalues/vectors
*> can be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPGST( ITYPE, UPLO, N, AP, BP, INFO )
*
* REAL AP( * ), BP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPGST reduces a real symmetric-definite generalized eigenproblem
*> to standard form, using packed storage.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
*>
*> B must have been previously factorized as U**T*U or L*L**T by SPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPGV computes all the eigenvalues and, optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be symmetric, stored in packed format,
*> and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* LWORK, IWORK, LIWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ LWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
* IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> is also positive definite. Eigenvalues and eigenvectors can be
*> selected by specifying either a range of values or a range of indices
*> for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
$ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
* FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* REAL AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPSV computes the solution to a real system of linear equations
*> A * X = B,
*> triangular matrices, D is symmetric and block diagonal with 1-by-1
*> and 2-by-2 diagonal blocks. The factored form of A is then used to
*> solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, so the solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X,
* LDX, RCOND, FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
*> A = L*D*L**T to compute the solution to a real system of linear
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPTRD( UPLO, N, AP, D, E, TAU, INFO )
*
* REAL AP( * ), D( * ), E( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPTRD reduces a real symmetric matrix A stored in packed form to
*> symmetric tridiagonal form T by an orthogonal similarity
*> transformation: Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where tau is a real scalar, and v is a real vector with
*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
*> overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPTRF( UPLO, N, AP, IPIV, INFO )
*
* REAL AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPTRF computes the factorization of a real symmetric matrix A stored
*> in packed format using the Bunch-Kaufman diagonal pivoting method:
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPTRI computes the inverse of a real symmetric indefinite matrix
*> A in packed storage using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by SSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* REAL AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPTRS solves a system of linear equations A*X = B with a real
*> symmetric matrix A stored in packed format using the factorization
*> A = U*D*U**T or A = L*D*L**T computed by SSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E,
* M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK,
* REAL D( * ), E( * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEBZ computes the eigenvalues of a symmetric tridiagonal
*> matrix T. The user may ask for all eigenvalues, all eigenvalues
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RANGE
*> \verbatim
*> floating-point arithmetic.
*> Cure: Increase the PARAMETER "FUDGE",
*> recompile, and try again.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> RELFAC REAL, default = 2.0e0
*> The relative tolerance. An interval (a,b] lies within
*> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|),
*> the worst machine around. Note that this has no effect
*> on accuracy of the solution.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
* LIWORK, INFO )
* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none. See SLAED3 for details.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup auxOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
*>
* =====================================================================
SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
* REAL Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEGR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> NaNs. Normal execution may create these exceptiona values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by SLARRE or
*> SLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, LBNL/NERSC, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
* IWORK, IFAIL, INFO )
* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEIN computes the eigenvectors of a real symmetric tridiagonal
*> matrix T corresponding to specified eigenvalues, using inverse
*>
*> The maximum number of iterations allowed for each eigenvector is
*> specified by an internal parameter MAXITS (currently set to 5).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge
*> in MAXITS iterations. Their indices are stored in
*> array IFAIL.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> MAXITS INTEGER, default = 5
*> The maximum number of iterations performed.
*>
*> The number of iterations performed after norm growth
*> criterion is satisfied, should be at least 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
* REAL Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEMR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> floating-point standard in their handling of infinities and NaNs.
*> This permits the use of efficient inner loops avoiding a check for
*> zero divisors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by SLARRE or
*> SLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the implicit QL or QR method.
*> The eigenvectors of a full or band symmetric matrix can also be found
*> if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to
*> tridiagonal form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> matrix which is orthogonally similar to the original
*> matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTERF( N, D, E, INFO )
*
* REAL D( * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTERF computes all eigenvalues of a symmetric tridiagonal matrix
*> using the Pal-Walker-Kahan variant of the QL or QR algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> a total of 30*N iterations; if INFO = i, then i
*> elements of E have not converged to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
*
* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEV computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric tridiagonal matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, the algorithm failed to converge; i
*> off-diagonal elements of E did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
* LIWORK, INFO )
* REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEVD computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric tridiagonal matrix. If eigenvectors are desired, it
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, the algorithm failed to converge; i
*> off-diagonal elements of E did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
* M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEVR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Eigenvalues and
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
-*> California at Berkeley, USA
+*> California at Berkeley, USA \n
*> Jason Riedy, Computer Science Division, University of
-*> California at Berkeley, USA
-*>
-*> \endverbatim
+*> California at Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
* M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix A. Eigenvalues and
*> eigenvectors can be selected by specifying either a range of values
*> or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* IWORK, INFO )
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric matrix A using the factorization
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYCONV( UPLO, WAY, N, A, LDA, IPIV, WORK, INFO )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYCONV convert A given by TRF into L and D and vice-versa.
*> Get Non-diag elements of D (returned in workspace) and
*> apply or reverse permutation done in TRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
* REAL A( LDA, * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYEQUB computes row and column scalings intended to equilibrate a
*> symmetric matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par References:
+* ================
*>
-*> Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
-*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
-*> DOI 10.1023/B:NUMA.0000016606.32820.69
+*> Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n
+*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n
+*> DOI 10.1023/B:NUMA.0000016606.32820.69 \n
*> Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE SSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYEV computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
* LIWORK, INFO )
* REAL A( LDA, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYEVD computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A. If eigenvectors are desired, it uses a
*>
*> Because of large use of BLAS of level 3, SSYEVD needs N**2 more
*> workspace than SSYEVX.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> lying in rows and columns INFO/(N+1) through
*> mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*> Modified by Francoise Tisseur, University of Tennessee.
-*>
-*> Modified description of INFO. Sven, 16 Feb 05.
-*> \endverbatim
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee \n
+*> Modified description of INFO. Sven, 16 Feb 05. \n
*>
* =====================================================================
SUBROUTINE SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
* REAL A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYEVR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A. Eigenvalues and eigenvectors can be
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
-*> California at Berkeley, USA
+*> California at Berkeley, USA \n
*> Jason Riedy, Computer Science Division, University of
-*> California at Berkeley, USA
-*>
-*> \endverbatim
+*> California at Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE SSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK,
* REAL A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric matrix A. Eigenvalues and eigenvectors can be
*> selected by specifying either a range of values or a range of indices
*> for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYGS2 reduces a real symmetric-definite generalized eigenproblem
*> to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
*>
*> B must have been previously factorized as U**T *U or L*L**T by SPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYGST reduces a real symmetric-definite generalized eigenproblem
*> to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
*>
*> B must have been previously factorized as U**T*U or L*L**T by SPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be symmetric and B is also
*> positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, IWORK, LIWORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> Based on contributions by
-*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*> \verbatim
*>
*> Modified so that no backsubstitution is performed if SSYEVD fails to
*> converge (NEIG in old code could be greater than N causing out of
*> bounds reference to A - reported by Ralf Meyer). Also corrected the
*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*>
* =====================================================================
SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
* VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite eigenproblem, of the form
*> and B are assumed to be symmetric and B is also positive definite.
*> Eigenvalues and eigenvectors can be selected by specifying either a
*> range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE SSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
$ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> provides error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYRFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYSV computes the solution to a real system of linear equations
*> A * X = B,
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
*> used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
* LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK,
* $ BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYSVX uses the diagonal pivoting factorization to compute the
*> solution to a real system of linear equations A * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYSVXX uses the diagonal pivoting factorization to compute the
*> solution to a real system of linear equations A * X = B, where A
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what SSYSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(R) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYSWAPR( UPLO, N, A, LDA, I1, I2)
*
* .. Array Arguments ..
* REAL A( LDA, N )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYSWAPR applies an elementary permutation on the rows and the columns of
*> a symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> I2 is INTEGER
*> Index of the second row to swap
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )
*
* REAL A( LDA, * ), D( * ), E( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
*> form T by an orthogonal similarity transformation: Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTF2 computes the factorization of a real symmetric matrix A using
*> the Bunch-Kaufman diagonal pivoting method:
*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> 09-29-06 - patch from
-*> Bobby Cheng, MathWorks
-*>
-*> Replace l.204 and l.372
-*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
-*> by
-*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
+*> \par Further Details:
+* =====================
*>
-*> 01-01-96 - Based on modifications by
-*> J. Lewis, Boeing Computer Services Company
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> \verbatim
+*>
+*> 09-29-06 - patch from
+*> Bobby Cheng, MathWorks
+*>
+*> Replace l.204 and l.372
+*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*> by
+*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
+*>
+*> 01-01-96 - Based on modifications by
+*> J. Lewis, Boeing Computer Services Company
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
+*> Company
+*>
+*> \endverbatim
+*
* =====================================================================
SUBROUTINE SSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRD reduces a real symmetric matrix A to real symmetric
*> tridiagonal form T by an orthogonal similarity transformation:
*> Q**T * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRF computes the factorization of a real symmetric matrix A using
*> the Bunch-Kaufman diagonal pivoting method. The form of the
*> 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRI computes the inverse of a real symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> SSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRI2 computes the inverse of a REAL hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> SSYTRF. SSYTRI2 sets the LEADING DIMENSION of the workspace
*> before calling SSYTRI2X that actually computes the inverse.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
* REAL A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRI2X computes the inverse of a real symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> SSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRS solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by SSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYTRS2 solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by SSYTRF and converted by SSYCONV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
* IWORK, INFO )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBCON estimates the reciprocal of the condition number of a
*> triangular band matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
* $ FERR( * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular band
*> The solution matrix X must be computed by STBTRS or some other
*> means before entering this routine. STBRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, INFO )
* REAL AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBTRS solves a triangular system of the form
*>
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by NRHS matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
* B, LDB )
* REAL A( 0: * ), B( 0: LDB-1, 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for A in RFP Format.
*>
*> A is in Rectangular Full Packed (RFP) Format.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> max( 1, m ).
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE STFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
$ B, LDB )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
* REAL A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STFTRI computes the inverse of a triangular matrix A stored in RFP
*> format.
*>
*> This is a Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* REAL AP( 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STFTTP copies a triangular matrix A from rectangular full packed
*> format (TF) to standard packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
* REAL A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STFTTR copies a triangular matrix A from rectangular full packed
*> format (TF) to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE STFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
* LDVL, VR, LDVR, MM, M, WORK, INFO )
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGEVC computes some or all of the right and/or left eigenvectors of
*> a pair of real matrices (S,P), where S is a quasi-triangular matrix
*> factorization of a matrix pair (A,B), then Z*X and Q*Y
*> are the matrices of right and left eigenvectors of (A,B).
*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> > 0: the 2-by-2 block (INFO:INFO+1) does not have a complex
*> eigenvalue.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Allocation of workspace:
*> transpose of the one in storage, so the rowwise method then
*> actually accesses columns of A and B at each step, and so is the
*> preferred method.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, J1, N1, N2, WORK, LWORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
*> of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
*> Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
*> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> <0: If INFO = -16: LWORK is too small. Appropriate value
*> for LWORK is returned in WORK(1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
-*> Umea University, S-901 87 Umea, Sweden.
+*> \par Further Details:
+* =====================
*>
*> In the current code both weak and strong stability tests are
*> performed. The user can omit the strong stability test by changing
*> the internal logical parameter WANDS to .FALSE.. See ref. [2] for
*> details.
+*
+*> \par Contributors:
+* ==================
+*>
+*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
+*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Report UMINF - 94.04, Department of Computing Science, Umea
*> University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
*> Note 87. To appear in Numerical Algorithms, 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, IFST, ILST, WORK, LWORK, INFO )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGEXC reorders the generalized real Schur decomposition of a real
*> matrix pair (A,B) using an orthogonal equivalence transformation
*> Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
*> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> and ILST points to the first row of the current
*> position of the block being moved.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realGEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB,
* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL,
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGSEN reorders the generalized real Schur decomposition of a real
*> matrix pair (A, B) (in terms of an orthonormal equivalence trans-
*> the selected cluster and the eigenvalues outside the cluster, resp.,
*> and norms of "projections" onto left and right eigenspaces w.r.t.
*> the selected cluster in the (1,1)-block.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> (A, B) may have been partially reordered.
*> If requested, 0 is returned in DIF(*), PL and PR.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> STGSEN first collects the selected eigenvalues by computing
*> based estimate DIF is not wanted (see SLATDF), then the parameter
*> IDIFJB (see below) should be changed from 3 to 4 (routine SLATDF
*> (IJOB = 2 will be used)). See STGSYL for more details.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGSJA computes the generalized singular value decomposition (GSVD)
*> of two real upper triangular (or trapezoidal) matrices A and B.
*> The computation of the orthogonal transformation matrices U, V or Q
*> is optional. These matrices may either be formed explicitly, or they
*> may be postmultiplied into input matrices U1, V1, or Q1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> may take. If after MAXIT cycles, the routine fails to
*> converge, we return INFO = 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> STGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
*> C1**2 + S1**2 = I,
*>
*> and R1 is an L-by-L nonsingular upper triangular matrix.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK,
* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or eigenvectors of a matrix pair (A, B) in
*> i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal
*> blocks. B is upper triangular.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> =0: Successful exit
*> <0: If INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of a generalized eigenvalue
*> EPS * norm(A, B) / DIF(i).
*>
*> See ref. [2-3] for more details and further references.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
*> No 1, 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
* $ D( LDD, * ), E( LDE, * ), F( LDF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGSY2 solves the generalized Sylvester equation:
*>
*> of an upper bound on the separation between to matrix pairs. Then
*> the input (A, D), (B, E) are sub-pencils of the matrix pair in
*> STGSYL. See STGSYL for details.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> >0: The matrix pairs (A, D) and (B, E) have common or very
*> close eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE STGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STGSYL solves the generalized Sylvester equation:
*>
*> information.
*>
*> This is a level 3 BLAS algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> <0: If INFO = -i, the i-th argument had an illegal value.
*> >0: (A, D) and (B, E) have common or close eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realSYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
+*>
+*> \verbatim
*>
*> [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Condition Estimators for Solving the Generalized Sylvester
*> Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
*> July 1989, pp 745-751.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK,
* INFO )
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPCON estimates the reciprocal of the condition number of a packed
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
* A, LDA, B, LDB, WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPMQRT applies a real orthogonal matrix Q obtained from a
*> "triangular-pentagonal" real block reflector H to a general
*> real matrix C, which consists of two blocks A and B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The columns of the pentagonal matrix V contain the elementary reflectors
*> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
*>
*> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q^H.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
* INFO )
* REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPQRT computes a blocked QR factorization of a real
*> "triangular-pentagonal" matrix C, which is composed of a
*> triangular block A and pentagonal block B, using the compact
*> WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> C = [ A ]
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = [T1 T2 ... TB].
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPQRT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
* REAL A( LDA, * ), B( LDB, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPQRT2 computes a QR factorization of a real "triangular-pentagonal"
*> matrix C, which is composed of a triangular block A and pentagonal block B,
*> using the compact WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> where W^H is the conjugate transpose of W and T is the upper triangular
*> factor of the block reflector.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L,
* V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK )
* $ V( LDV, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPRFB applies a real "triangular-pentagonal" block reflector H or its
*> conjugate transpose H^H to a real matrix C, which is composed of two
*> blocks A and B, either from the left or right.
*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= K;
*> if SIDE = 'R', LDWORK >= M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix C is a composite matrix formed from blocks A and B.
*> If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
*>
*> If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* FERR, BERR, WORK, IWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular packed
*> The solution matrix X must be computed by STPTRS or some other
*> means before entering this routine. STPRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPTRI( UPLO, DIAG, N, AP, INFO )
*
* REAL AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPTRI computes the inverse of a real upper or lower triangular
*> matrix A stored in packed format.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A triangular matrix A can be transferred to packed storage using one
*> 1 CONTINUE 1 CONTINUE
*> JC = JC + J JC = JC + N - J + 1
*> 2 CONTINUE 2 CONTINUE
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
*
* REAL AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPTRS solves a triangular system of the form
*>
*> where A is a triangular matrix of order N stored in packed format,
*> and B is an N-by-NRHS matrix. A check is made to verify that A is
*> nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
*
* .. Array Arguments ..
* REAL AP( 0: * ), ARF( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPTTF copies a triangular matrix A from standard packed format (TP)
*> to rectangular full packed format (TF).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPTTR( UPLO, N, AP, A, LDA, INFO )
*
* REAL A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPTTR copies a triangular matrix A from standard packed format (TP)
*> to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
* IWORK, INFO )
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRCON estimates the reciprocal of the condition number of a
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, MM, M, WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STREVC computes some or all of the right and/or left eigenvectors of
*> a real upper quasi-triangular matrix T.
*> input matrix. If Q is the orthogonal factor that reduces a matrix
*> A to Schur form T, then Q*X and Q*Y are the matrices of right and
*> left eigenvectors of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The algorithm used in this program is basically backward (forward)
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x| + |y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
* INFO )
* REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STREXC reorders the real Schur factorization of a real matrix
*> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
*> 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> reordered, and ILST points to the first row of the
*> current position of the block being moved.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, FERR, BERR, WORK, IWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular
*> The solution matrix X must be computed by STRTRS or some other
*> means before entering this routine. STRRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI,
* M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO )
* $ WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRSEN reorders the real Schur factorization of a real matrix
*> A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in
*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
*> 2-by-2 diagonal block has its diagonal elemnts equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> contain the eigenvalues in the same order as in T; S and
*> SEP (if requested) are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> STRSEN first collects the selected eigenvalues by computing an
*> error in the computed right invariant subspace is
*>
*> EPS * norm(T) / SEP
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, S, SEP, MM, M, WORK, LDWORK, IWORK,
* $ VR( LDVR, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or right eigenvectors of a real upper
*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
*> 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of an eigenvalue lambda is
*> is given by
*>
*> EPS * norm(T) / SEP(i)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
* LDC, SCALE, INFO )
* REAL A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRSYL solves the real Sylvester matrix equation:
*>
*> is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
*> each 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANA
*> \verbatim
*> values were used to solve the equation (but the matrices
*> A and B are unchanged).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRTI2 computes the inverse of a real upper or lower triangular
*> matrix.
*>
*> This is the Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRTRI( UPLO, DIAG, N, A, LDA, INFO )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRTRI computes the inverse of a real upper or lower triangular
*> matrix A.
*>
*> This is the Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
* INFO )
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRTRS solves a triangular system of the form
*>
*>
*> where A is a triangular matrix of order N, and B is an N-by-NRHS
*> matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the solutions
*> X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* REAL A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRTTF copies a triangular matrix A from standard full format (TR)
*> to rectangular full packed format (TF) .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
-*> Reference
-*> =========
-*>
*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE STRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRTTP( UPLO, N, A, LDA, AP, INFO )
*
* REAL A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRTTP copies a triangular matrix A from full format (TR) to standard
*> packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STZRQF( M, N, A, LDA, TAU, INFO )
*
* REAL A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine STZRZF.
*>
*>
*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
*> to upper triangular form by means of orthogonal transformations.
*>
*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup realOTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XERBLA( SRNAME, INFO )
*
* INTEGER INFO
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> XERBLA is an error handler for the LAPACK routines.
*> It is called by an LAPACK routine if an input parameter has an
*>
*> Installers may consider modifying the STOP statement in order to
*> call system-specific exception-handling facilities.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SRNAME
*> \verbatim
*> The position of the invalid parameter in the parameter list
*> of the calling routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XERBLA_ARRAY( SRNAME_ARRAY, SRNAME_LEN, INFO)
*
* CHARACTER(1) SRNAME_ARRAY(SRNAME_LEN)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK
*> and BLAS error handler. Rather than taking a Fortran string argument
*>
*> Providing XERBLA_ARRAY is not necessary for intercepting LAPACK
*> errors. XERBLA_ARRAY calls XERBLA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SRNAME_ARRAY
*> \verbatim
*> The position of the invalid parameter in the parameter list
*> of the calling routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
* THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T,
* $ V2T( LDV2T, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZBBCSD computes the CS decomposition of a unitary matrix in
*> bidiagonal-block form,
*> The unitary matrices U1, U2, V1T, and V2T are input/output.
*> The input matrices are pre- or post-multiplied by the appropriate
*> singular vector matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> > 0: if ZBBCSD did not converge, INFO specifies the number
*> of nonzero entries in PHI, and B11D, B11E, etc.,
*> contain the partially reduced matrix.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Reference
-*> =========
-*>
-*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
-*> Algorithms, 50(1):33-65, 2009.
-*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they
*> are within TOLMUL*EPS of either bound.
*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*> Algorithms, 50(1):33-65, 2009.
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
* LDU, C, LDC, RWORK, INFO )
* COMPLEX*16 C( LDC, * ), U( LDU, * ), VT( LDVT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZBDSQR computes the singular values and, optionally, the right and/or
*> left singular vectors from the singular value decomposition (SVD) of
*> B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
*> Department, University of California at Berkeley, July 1992
*> for a detailed description of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> elements of a bidiagonal matrix which is orthogonally
*> similar to the input matrix B; if INFO = i, i
*> elements of E have not converged to zero.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8)))
*> TOLMUL controls the convergence criterion of the QR loop.
*> If it is positive, TOLMUL*EPS is the desired relative
*> (and so fails to converge) if the number of passes
*> through the inner loop exceeds MAXITR*N**2.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,
* SWORK, RWORK, ITER, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCGESV computes the solution to a complex system of linear equations
*> A * X = B,
*> o EPS is the machine epsilon returned by DLAMCH('Epsilon')
*> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
*> respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> factor U is exactly singular, so the solution
*> could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,
* SWORK, RWORK, ITER, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCPOSV computes the solution to a complex system of linear equations
*> A * X = B,
*> o EPS is the machine epsilon returned by DLAMCH('Epsilon')
*> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
*> respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> factorization could not be completed, and the solution
*> has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRSCL( N, SA, SX, INCX )
*
* COMPLEX*16 SX( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRSCL multiplies an n-element complex vector x by the real scalar
*> 1/a. This is done without overflow or underflow as long as
*> the final result x/a does not overflow or underflow.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of the vector SX.
*> > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
* LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO )
* $ Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBBRD reduces a complex general m-by-n band matrix A to real upper
*> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
*>
*> The routine computes B, and optionally forms Q or P**H, or computes
*> Q**H*C for a given matrix C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
* WORK, RWORK, INFO )
* COMPLEX*16 AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBCON estimates the reciprocal of the condition number of a complex
*> general band matrix A, in either the 1-norm or the infinity-norm,
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBEQU computes row and column scalings intended to equilibrate an
*> M-by-N band matrix A and reduce its condition number. R returns the
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, INFO )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is banded, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBRFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBSV computes the solution to a complex system of linear equations
*> A * X = B, where A is a band matrix of order N with KL subdiagonals
*> and unit lower triangular matrices with KL subdiagonals, and U is
*> upper triangular with KL+KU superdiagonals. The factored form of A
*> is then used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GBsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBSVX uses the LU factorization to compute the solution to a complex
*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed by this subroutine:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBSVXX uses the LU factorization to compute the solution to a
*> complex*16 system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what ZGBSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBTF2 computes an LU factorization of a complex m-by-n band matrix
*> A using partial pivoting with row interchanges.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> + need not be set on entry, but are required by the routine to store
*> elements of U, because of fill-in resulting from the row
*> interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBTRF computes an LU factorization of a complex m-by-n band matrix A
*> using partial pivoting with row interchanges.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
* INFO )
* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBTRS solves a system of linear equations
*> A * X = B, A**T * X = B, or A**H * X = B
*> with a general band matrix A using the LU factorization computed
*> by ZGBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
* INFO )
* COMPLEX*16 V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEBAK forms the right or left eigenvectors of a complex general
*> matrix by backward transformation on the computed eigenvectors of the
*> balanced matrix output by ZGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEBAL balances a general complex matrix A. This involves, first,
*> permuting A by a similarity transformation to isolate eigenvalues
*>
*> Balancing may reduce the 1-norm of the matrix, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The permutations consist of row and column interchanges which put
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEBD2 reduces a complex general m by n matrix A to upper or lower
*> real bidiagonal form B by a unitary transformation: Q**H * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
* INFO )
* COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEBRD reduces a general complex M-by-N matrix A to upper or lower
*> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
*>
*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where d and e denote diagonal and off-diagonal elements of B, vi
*> denotes an element of the vector defining H(i), and ui an element of
*> the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
* INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGECON estimates the reciprocal of the condition number of a general
*> complex matrix A, in either the 1-norm or the infinity-norm, using
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEEQU computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> number and BIGNUM = largest safe number. Use of these scaling
*> factors is not guaranteed to reduce the condition number of A but
*> works well in practice.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* INFO )
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEEQUB computes row and column scalings intended to equilibrate an
*> M-by-N matrix A and reduce its condition number. R returns the row
*> these factors introduces no additional rounding errors. However, the
*> scaled entries' magnitured are no longer approximately 1 but lie
*> between sqrt(radix) and 1/sqrt(radix).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> <= M: the i-th row of A is exactly zero
*> > M: the (i-M)-th column of A is exactly zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
* LDVS, WORK, LWORK, RWORK, BWORK, INFO )
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEES computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues, the Schur form T, and, optionally, the matrix of Schur
*> invariant subspace corresponding to the selected eigenvalues.
*>
*> A complex matrix is in Schur form if it is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> SELECT = .TRUE.. This could also be caused by
*> underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
* VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
* EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues, the Schur form T, and, optionally, the matrix of Schur
*> these quantities are called s and sep respectively).
*>
*> A complex matrix is in Schur form if it is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVS
*> \verbatim
*> the Schur form no longer satisfy SELECT=.TRUE. This
*> could also be caused by underflow due to scaling.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
* WORK, LWORK, RWORK, INFO )
* $ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*>
*> The computed eigenvectors are normalized to have Euclidean norm
*> equal to 1 and largest component real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> elements and i+1:N of W contain eigenvalues which have
*> converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
* LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
* $ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
*> eigenvalues and, optionally, the left and/or right eigenvectors.
*> (in exact arithmetic) but diagonal scaling will. For further
*> explanation of balancing, see section 4.10.2 of the LAPACK
*> Users' Guide.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> have been computed; elements 1:ILO-1 and i+1:N of W
*> contain eigenvalues which have converged.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
* VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine ZGGES.
*>
*> ZGEGV should be used instead. See ZGEGV for a description of the
*> eigenvalues of the generalized nonsymmetric eigenvalue problem
*> (GNEP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> =N+8: error return from ZGGBAK (computing VSR)
*> =N+9: error return from ZLASCL (various places)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
* VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine ZGGEV.
*>
*> are left eigenvectors of (A,B).
*>
*> Note: this routine performs "full balancing" on A and B
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> =N+9: error return from ZGGBAK (computing VR)
*> =N+10: error return from ZLASCL (various calls)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing
*> are computed, then only the diagonal blocks will be correct.
*>
*> [*] In other words, upper triangular form.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
*> by a unitary similarity transformation: Q**H * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
*> an unitary similarity transformation: Q**H * A * Q = H .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of (ihi-ilo) elementary
*> This file is a slight modification of LAPACK-3.0's DGEHRD
*> subroutine incorporating improvements proposed by Quintana-Orti and
*> Van de Geijn (2006). (See DLAHR2.)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGELQ2 computes an LQ factorization of a complex m by n matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
*> A(i,i+1:n), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
*> A = L * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
*> A(i,i+1:n), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
* INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGELS solves overdetermined or underdetermined complex linear systems
*> involving an M-by-N matrix A, or its conjugate-transpose, using a QR
*> handled in a single call; they are stored as the columns of the
*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
*> matrix X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> full rank; the least squares solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, RWORK, IWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGELSD computes the minimum-norm solution to a real linear least
*> squares problem:
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
$ WORK, LWORK, RWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
* WORK, LWORK, RWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGELSS computes the minimum norm solution to a complex linear
*> least squares problem:
*> The effective rank of A is determined by treating as zero those
*> singular values which are less than RCOND times the largest singular
*> value.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> if INFO = i, i off-diagonal elements of an intermediate
*> bidiagonal form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, RWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine ZGELSY.
*>
*> X = P * Z**H [ inv(T11)*Q1**H*B ]
*> [ 0 ]
*> where Q1 consists of the first RANK columns of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
* WORK, LWORK, RWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGELSY computes the minimum-norm solution to a complex linear least
*> squares problem:
*> the call to the subroutine xGEQP3. This subroutine is a Blas-3
*> version of the QR factorization with column pivoting.
*> o Matrix B (the right hand side) is updated with Blas-3.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-*>
-*> \endverbatim
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n
+*> E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
+*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n
*>
* =====================================================================
SUBROUTINE ZGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
* C, LDC, WORK, INFO )
* COMPLEX*16 V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEMQRT overwrites the general complex M-by-N matrix C with
*>
*> generated using the compact WY representation as returned by ZGEQRT.
*>
*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQL2 computes a QL factorization of a complex m by n matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQLF computes a QL factorization of a complex M-by-N matrix A:
*> A = Q * L.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
*> A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
* INFO )
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQP3 computes a QR factorization with column pivoting of a
*> matrix A: A*P = Q*R using Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a real/complex scalar, and v is a real/complex vector
*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
*> A(i+1:m,i), and tau in TAU(i).
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
$ INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine ZGEQP3.
*>
*> ZGEQPF computes a QR factorization with column pivoting of a
*> complex M-by-N matrix A: A*P = Q*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> University of Zagreb, Croatia.
*> -- April 2011 --
*> For more details see LAPACK Working Note 176.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQR2 computes a QR factorization of a complex m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQR2P computes a QR factorization of a complex m by n matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQRF computes a QR factorization of a complex M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQRFP computes a QR factorization of a complex M-by-N matrix A:
*> A = Q * R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
*> and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> below the diagonal. For example, if M=5 and N=3, the matrix V is
*>
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = (T1 T2 ... TB).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQRT2( M, N, A, LDA, T, LDT, INFO )
*
* COMPLEX*16 A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
*> using the compact WY representation of Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> H = I - V * T * V**H
*>
*> where V**H is the conjugate transpose of V.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE ZGEQRT3( M, N, A, LDA, T, LDT, INFO )
*
* COMPLEX*16 A( LDA, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGEQRT3 recursively computes a QR factorization of a complex M-by-N
*> matrix A, using the compact WY representation of Q.
*>
*> Based on the algorithm of Elmroth and Gustavson,
*> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix V stores the elementary reflectors H(i) in the i-th column
*> where V**H is the conjugate transpose of V.
*>
*> For details of the algorithm, see Elmroth and Gustavson (cited above).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGERFS improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates for
*> the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGERFSX improves the computed solution to a system of linear
*> equations and provides error bounds and backward error estimates
*> before calling this routine, as described by arguments EQUED, R
*> and C below. In this case, the solution and error bounds returned
*> are for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERQ2( M, N, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
*> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGERQF computes an RQ factorization of a complex M-by-N matrix A:
*> A = R * Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> where tau is a complex scalar, and v is a complex vector with
*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
*> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
* COMPLEX*16 A( LDA, * ), RHS( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGESC2 solves a system of linear equations
*>
*> with a general N-by-N matrix A using the LU factorization with
*> complete pivoting computed by ZGETC2.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On exit, SCALE contains the scale factor. SCALE is chosen
*> 0 <= SCALE <= 1 to prevent owerflow in the solution.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
* LWORK, RWORK, IWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGESDD computes the singular value decomposition (SVD) of a complex
*> M-by-N matrix A, optionally computing the left and/or right singular
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: The updating process of DBDSDC did not converge.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
$ LWORK, RWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGESV computes the solution to a complex system of linear equations
*> A * X = B,
*> where P is a permutation matrix, L is unit lower triangular, and U is
*> upper triangular. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has been completed, but the factor U is exactly
*> singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
* WORK, LWORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGESVD computes the singular value decomposition (SVD) of a complex
*> M-by-N matrix A, optionally computing the left and/or right singular
*> U and V are the left and right singular vectors of A.
*>
*> Note that the routine returns V**H, not V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> did not converge to zero. See the description of RWORK
*> above for details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGESVX uses the LU factorization to compute the solution to a complex
*> system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGESVXX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, R, C, B, LDB, X, LDX, RCOND, RPVGRW,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGESVXX uses the LU factorization to compute the solution to a
*> complex*16 system of linear equations A * X = B, where A is an
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what ZGESVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
*> that it solves the original system before equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGETC2 computes an LU factorization, using complete pivoting, of the
*> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
*> unit diagonal elements and U is upper triangular.
*>
*> This is a level 1 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> one tries to solve for x in Ax = b. So U is perturbed
*> to avoid the overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETF2( M, N, A, LDA, IPIV, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGETF2 computes an LU factorization of a general m-by-n matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGETRF computes an LU factorization of a general M-by-N matrix A
*> using partial pivoting with row interchanges.
*> triangular (upper trapezoidal if m < n).
*>
*> This is the right-looking Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGETRI computes the inverse of a matrix using the LU factorization
*> computed by ZGETRF.
*>
*> This method inverts U and then computes inv(A) by solving the system
*> inv(A)*L = inv(U) for inv(A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
*> singular and its inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGETRS solves a system of linear equations
*> A * X = B, A**T * X = B, or A**H * X = B
*> with a general N-by-N matrix A using the LU factorization computed
*> by ZGETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
* LDV, INFO )
* COMPLEX*16 V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGBAK forms the right or left eigenvectors of a complex generalized
*> eigenvalue problem A*x = lambda*B*x, by backward transformation on
*> the computed eigenvectors of the balanced pair of matrices output by
*> ZGGBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. Ward, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
* RSCALE, WORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGBAL balances a pair of general complex matrices (A,B). This
*> involves, first, permuting A and B by similarity transformations to
*> Balancing may reduce the 1-norm of the matrices, and improve the
*> accuracy of the computed eigenvalues and/or eigenvectors in the
*> generalized eigenvalue problem A*x = lambda*B*x.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GBcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> See R.C. WARD, Balancing the generalized eigenvalue problem,
*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
* SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B), the generalized eigenvalues, the generalized complex Schur
*> A pair of matrices (S,T) is in generalized complex Schur form if S
*> and T are upper triangular and, in addition, the diagonal elements
*> of T are non-negative real numbers.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering falied in ZTGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
* B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR,
* EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B), the generalized eigenvalues, the complex Schur form (S,T),
*> A pair of matrices (S,T) is in generalized complex Schur form if T is
*> upper triangular with non-negative diagonal and S is upper
*> triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVSL
*> \verbatim
*> be caused due to scaling.
*> =N+3: reordering failed in ZTGSEN.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
* VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B), the generalized eigenvalues, and optionally, the left and/or
*> u(j)**H * A = lambda(j) * u(j)**H * B
*>
*> where u(j)**H is the conjugate-transpose of u(j).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBVL
*> \verbatim
*> > N: =N+1: other then QZ iteration failed in DHGEQZ,
*> =N+2: error return from DTGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
* ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B) the generalized eigenvalues, and optionally, the left and/or
*> u(j)**H * A = lambda(j) * u(j)**H * B.
*> where u(j)**H is the conjugate-transpose of u(j).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] BALANC
*> \verbatim
*> > N: =N+1: other than QZ iteration failed in ZHGEQZ.
*> =N+2: error return from ZTGEVC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Balancing a matrix pair (A,B) includes, first, permuting rows and
*>
*> For further explanation of the reciprocal condition numbers RCONDE
*> and RCONDV, see section 4.11 of LAPACK User's Guide.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
* INFO )
* $ X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
*>
*> x
*>
*> where inv(B) denotes the inverse of B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> rank( A B ) < N; the least squares solution could not
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q,
* LDQ, Z, LDZ, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper
*> Hessenberg form using unitary transformations, where A is a
*> If Q1 is the unitary matrix from the QR factorization of B in the
*> original equation A*x = lambda*B*x, then ZGGHRD reduces the original
*> problem to generalized Hessenberg form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine reduces A to Hessenberg and B to triangular form by
*> an unblocked reduction, as described in _Matrix_Computations_,
*> by Golub and van Loan (Johns Hopkins Press).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
* INFO )
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGLSE solves the linear equality-constrained least squares (LSE)
*> problem:
*> matrices (B, A) given by
*>
*> B = (0 R)*Q, A = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> ( (B) )
*> be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGQRF computes a generalized QR factorization of an N-by-M matrix A
*> and an N-by-P matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
*> conjugate transpose of matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine ZUNGRQ.
*> To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGRQF computes a generalized RQ factorization of an M-by-N matrix A
*> and a P-by-N matrix B:
*>
*> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
*> conjugate transpose of the matrix Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO=-i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of elementary reflectors
*> and taub in TAUB(i).
*> To form Z explicitly, use LAPACK subroutine ZUNGQR.
*> To use Z to update another matrix, use LAPACK subroutine ZUNMQR.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
* $ U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGSVD computes the generalized singular value decomposition (GSVD)
*> of an M-by-N complex matrix A and P-by-N complex matrix B:
*>
*> X = Q*( I 0 )
*> ( 0 inv(R) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, the Jacobi-type procedure failed to
*> converge. For further details, see subroutine ZTGSJA.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> TOLA DOUBLE PRECISION
*> TOLB DOUBLE PRECISION
*> TOLA and TOLB are the thresholds to determine the effective
*> The size of TOLA and TOLB may affect the size of backward
*> errors of the decomposition.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsing
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> 2-96 Based on modifications by
*> Ming Gu and Huan Ren, Computer Science Division, University of
*> California at Berkeley, USA
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
$ LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGGSVP computes unitary matrices U, V and Q such that
*>
*> This decomposition is the preprocessing step for computing the
*> Generalized Singular Value Decomposition (GSVD), see subroutine
*> ZGGSVD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
*> with column pivoting to detect the effective numerical rank of the
*> a matrix. It may be replaced by a better rank determination strategy.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
* WORK, INFO )
* COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTCON estimates the reciprocal of the condition number of a complex
*> tridiagonal matrix A using the LU factorization as computed by
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is tridiagonal, and provides
*> error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTSV solves the equation
*>
*>
*> Note that the equation A**T *X = B may be solved by interchanging the
*> order of the arguments DU and DL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> has not been computed. The factorization has not been
*> completed unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTSVX uses the LU factorization to compute the solution to a complex
*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
* COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
*> using elimination with partial pivoting and row interchanges.
*> where L is a product of permutation and unit lower bidiagonal
*> matrices and U is upper triangular with nonzeros in only the main
*> diagonal and first two superdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> singular, and division by zero will occur if it is used
*> to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
* INFO )
* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTTRS solves one of the systems of equations
*> A * X = B, A**T * X = B, or A**H * X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by ZGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTTS2 solves one of the systems of equations
*> A * X = B, A**T * X = B, or A**H * X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by ZGTTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* RWORK, INFO )
* COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
*> a complex Hermitian band matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
*> a complex Hermitian band matrix A. If eigenvectors are desired, it
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
*> can be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
* LDX, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBGST reduces a complex Hermitian-definite banded generalized
*> eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
*> split Cholesky factorization. A is overwritten by C = X**H*A*X, where
*> X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
*> bandwidth of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, RWORK, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
*> and banded, and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
* LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBGVX computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> and banded, and B is also positive definite. Eigenvalues and
*> eigenvectors can be selected by specifying either all eigenvalues,
*> a range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
$ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
* WORK, INFO )
* COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBTRD reduces a complex Hermitian band matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by Linda Kaufman, Bell Labs.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHECON estimates the reciprocal of the condition number of a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
* DOUBLE PRECISION S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYEQUB computes row and column scalings intended to equilibrate a
*> symmetric matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
* INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
* LRWORK, IWORK, LIWORK, INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix A. If eigenvectors are desired, it uses a
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> lying in rows and columns INFO/(N+1) through
*> mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
+*> \par Further Details:
+* =====================
*>
*> Modified description of INFO. Sven, 16 Feb 05.
-*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
*>
* =====================================================================
SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
* COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEEVR computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
-*> California at Berkeley, USA
+*> California at Berkeley, USA \n
*> Jason Riedy, Computer Science Division, University of
-*> California at Berkeley, USA
-*>
-*> \endverbatim
+*> California at Berkeley, USA \n
*>
* =====================================================================
SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
* COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
*> be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEGS2 reduces a complex Hermitian-definite generalized
*> eigenproblem to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
*>
*> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEGST reduces a complex Hermitian-definite generalized
*> eigenproblem to standard form.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
*>
*> B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, RWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be Hermitian and B is also
*> positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> Based on contributions by
-*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*> \verbatim
*>
*> Modified so that no backsubstitution is performed if ZHEEVD fails to
*> converge (NEIG in old code could be greater than N causing out of
*> bounds reference to A - reported by Ralf Meyer). Also corrected the
*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*>
* =====================================================================
SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
* VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> B are assumed to be Hermitian and B is also positive definite.
*> Eigenvalues and eigenvectors can be selected by specifying either a
*> range of values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEeigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
$ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHERFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHERFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian indefinite, and
*> provides error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_NORM( NRHS, * ),
* $ ERR_BNDS_COMP( NRHS, * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHERFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian indefinite, and
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHESV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, and D is Hermitian and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
*> used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHESVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
* LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHESVX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHESVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHESVXX uses the diagonal pivoting factorization to compute the
*> solution to a complex*16 system of linear equations A * X = B, where
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what ZHESVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(R) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHESWAPR( UPLO, N, A, LDA, I1, I2)
*
* .. Array Arguments ..
* COMPLEX*16 A( LDA, N )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHESWAPR applies an elementary permutation on the rows and the columns of
*> a hermitian matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> I2 is INTEGER
*> Index of the second row to swap
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETD2 reduces a complex Hermitian matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETF2 computes the factorization of a complex Hermitian matrix A
*> using the Bunch-Kaufman diagonal pivoting method:
*> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 09-29-06 - patch from
-*> Bobby Cheng, MathWorks
-*>
-*> Replace l.210 and l.393
-*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
-*> by
-*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
-*>
-*> 01-01-96 - Based on modifications by
-*> J. Lewis, Boeing Computer Services Company
-*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**H, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
+*> 09-29-06 - patch from
+*> Bobby Cheng, MathWorks
+*>
+*> Replace l.210 and l.393
+*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*> by
+*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
*>
+*> 01-01-96 - Based on modifications by
+*> J. Lewis, Boeing Computer Services Company
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> \endverbatim
+*
* =====================================================================
SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRD reduces a complex Hermitian matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*>
*> where d and e denote diagonal and off-diagonal elements of T, and vi
*> denotes an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRF computes the factorization of a complex Hermitian matrix A
*> using the Bunch-Kaufman diagonal pivoting method. The form of the
*> 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**H, where
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRI computes the inverse of a complex Hermitian indefinite matrix
*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
*> ZHETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRI2 computes the inverse of a COMPLEX*16 hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> ZHETRF. ZHETRI2 set the LEADING DIMENSION of the workspace
*> before calling ZHETRI2X that actually computes the inverse.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRI2X computes the inverse of a COMPLEX*16 Hermitian indefinite matrix
*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
*> ZHETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRS solves a system of linear equations A*X = B with a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by ZHETRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHETRS2 solves a system of linear equations A*X = B with a complex
*> Hermitian matrix A using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by ZHETRF and converted by ZSYCONV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
* C )
* COMPLEX*16 A( LDA, * ), C( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for C in RFP Format.
*>
*> where alpha and beta are real scalars, C is an n--by--n Hermitian
*> matrix and A is an n--by--k matrix in the first case and a k--by--n
*> matrix in the second case.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> parts of the diagonal elements need not be set, they are
*> assumed to be zero, and on exit they are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
* ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHGEQZ computes the eigenvalues of a complex matrix pair (H,T),
*> where H is an upper Hessenberg matrix and T is upper triangular,
*> Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
*> Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
*> pp. 241--256.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> in Schur form, but ALPHA(i) and BETA(i),
*> i=INFO-N+1,...,N should be correct.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We assume that complex ABS works as long as its value is less than
*> overflow.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
*
* COMPLEX*16 AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPCON estimates the reciprocal of the condition number of a complex
*> Hermitian packed matrix A using the factorization A = U*D*U**H or
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
* INFO )
* COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix in packed storage.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
* RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
*> a complex Hermitian matrix A in packed storage. If eigenvectors are
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK,
* COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A in packed storage.
*> Eigenvalues/vectors can be selected by specifying either a range of
*> values or a range of indices for the desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge.
*> Their indices are stored in array IFAIL.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
*
* COMPLEX*16 AP( * ), BP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPGST reduces a complex Hermitian-definite generalized
*> eigenproblem to standard form, using packed storage.
*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
*>
*> B must have been previously factorized as U**H*U or L*L**H by ZPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* RWORK, INFO )
* COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
*> Here A and B are assumed to be Hermitian, stored in packed format,
*> and B is also positive definite.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
* COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
* IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
* COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPGVX computes selected eigenvalues and, optionally, eigenvectors
*> of a complex generalized Hermitian-definite eigenproblem, of the form
*> positive definite. Eigenvalues and eigenvectors can be selected by
*> specifying either a range of values or a range of indices for the
*> desired eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> The factorization of B could not be completed and
*> no eigenvalues or eigenvectors were computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHEReigen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
$ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian indefinite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, D is Hermitian and block diagonal with 1-by-1
*> and 2-by-2 diagonal blocks. The factored form of A is then used to
*> solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, so the solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X,
* LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPSVX uses the diagonal pivoting factorization A = U*D*U**H or
*> A = L*D*L**H to compute the solution to a complex system of linear
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO )
*
* COMPLEX*16 AP( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPTRD reduces a complex Hermitian matrix A stored in packed form to
*> real symmetric tridiagonal form T by a unitary similarity
*> transformation: Q**H * A * Q = T.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where tau is a complex scalar, and v is a complex vector with
*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
*> overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPTRF( UPLO, N, AP, IPIV, INFO )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPTRF computes the factorization of a complex Hermitian packed
*> matrix A using the Bunch-Kaufman diagonal pivoting method:
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is Hermitian and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**H, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> J. Lewis, Boeing Computer Services Company
+*
* =====================================================================
SUBROUTINE ZHPTRF( UPLO, N, AP, IPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* COMPLEX*16 AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
*> A in packed storage using the factorization A = U*D*U**H or
*> A = L*D*L**H computed by ZHPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPTRS solves a system of linear equations A*X = B with a complex
*> Hermitian matrix A stored in packed format using the factorization
*> A = U*D*U**H or A = L*D*L**H computed by ZHPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
* LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
* $ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHSEIN uses inverse iteration to find specified right and/or left
*> eigenvectors of a complex upper Hessenberg matrix H.
*> H * x = w * x, y**h * H = w * y**h
*>
*> where y**h denotes the conjugate transpose of the vector y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> failed to converge; see IFAILL and IFAILR for further
*> details.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x|+|y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
* WORK, LWORK, INFO )
* .. Array Arguments ..
* COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
-* Purpose
-* =======
+*
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHSEQR computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> If INFO .GT. 0 and COMPZ = 'N', then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
+*> \par Contributors:
+* ==================
+*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Default values supplied by
+*> ILAENV(ISPEC,'ZHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
+*> It is suggested that these defaults be adjusted in order
+*> to attain best performance in each particular
+*> computational environment.
+*>
+*> ISPEC=12: The ZLAHQR vs ZLAQR0 crossover point.
+*> Default: 75. (Must be at least 11.)
+*>
+*> ISPEC=13: Recommended deflation window size.
+*> This depends on ILO, IHI and NS. NS is the
+*> number of simultaneous shifts returned
+*> by ILAENV(ISPEC=15). (See ISPEC=15 below.)
+*> The default for (IHI-ILO+1).LE.500 is NS.
+*> The default for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>
+*> ISPEC=14: Nibble crossover point. (See IPARMQ for
+*> details.) Default: 14% of deflation window
+*> size.
+*>
+*> ISPEC=15: Number of simultaneous shifts in a multishift
+*> QR iteration.
+*>
+*> If IHI-ILO+1 is ...
+*>
+*> greater than ...but less ... the
+*> or equal to ... than default is
+*>
+*> 1 30 NS = 2(+)
+*> 30 60 NS = 4(+)
+*> 60 150 NS = 10(+)
+*> 150 590 NS = **
+*> 590 3000 NS = 64
+*> 3000 6000 NS = 128
+*> 6000 infinity NS = 256
+*>
+*> (+) By default some or all matrices of this order
+*> are passed to the implicit double shift routine
+*> ZLAHQR and this parameter is ignored. See
+*> ISPEC=12 above and comments in IPARMQ for
+*> details.
+*>
+*> (**) The asterisks (**) indicate an ad-hoc
+*> function of N increasing from 10 to 64.
+*>
+*> ISPEC=16: Select structured matrix multiply.
+*> If the number of simultaneous shifts (specified
+*> by ISPEC=15) is less than 14, then the default
+*> for ISPEC=16 is 0. Otherwise the default for
+*> ISPEC=16 is 2.
+*> \endverbatim
+*
+*> \par References:
+* ================
+*>
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
+*> \n
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
+*> of Matrix Analysis, volume 23, pages 948--973, 2002.
+*
* =====================================================================
SUBROUTINE ZHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
$ WORK, LWORK, INFO )
* .. Array Arguments ..
COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
-* ================================================================
-* Default values supplied by
-* ILAENV(ISPEC,'ZHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).
-* It is suggested that these defaults be adjusted in order
-* to attain best performance in each particular
-* computational environment.
-*
-* ISPEC=12: The ZLAHQR vs ZLAQR0 crossover point.
-* Default: 75. (Must be at least 11.)
-*
-* ISPEC=13: Recommended deflation window size.
-* This depends on ILO, IHI and NS. NS is the
-* number of simultaneous shifts returned
-* by ILAENV(ISPEC=15). (See ISPEC=15 below.)
-* The default for (IHI-ILO+1).LE.500 is NS.
-* The default for (IHI-ILO+1).GT.500 is 3*NS/2.
-*
-* ISPEC=14: Nibble crossover point. (See IPARMQ for
-* details.) Default: 14% of deflation window
-* size.
-*
-* ISPEC=15: Number of simultaneous shifts in a multishift
-* QR iteration.
-*
-* If IHI-ILO+1 is ...
-*
-* greater than ...but less ... the
-* or equal to ... than default is
-*
-* 1 30 NS = 2(+)
-* 30 60 NS = 4(+)
-* 60 150 NS = 10(+)
-* 150 590 NS = **
-* 590 3000 NS = 64
-* 3000 6000 NS = 128
-* 6000 infinity NS = 256
-*
-* (+) By default some or all matrices of this order
-* are passed to the implicit double shift routine
-* ZLAHQR and this parameter is ignored. See
-* ISPEC=12 above and comments in IPARMQ for
-* details.
-*
-* (**) The asterisks (**) indicate an ad-hoc
-* function of N increasing from 10 to 64.
-*
-* ISPEC=16: Select structured matrix multiply.
-* If the number of simultaneous shifts (specified
-* by ISPEC=15) is less than 14, then the default
-* for ISPEC=16 is 0. Otherwise the default for
-* ISPEC=16 is 2.
-*
-* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* References:
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
-* Performance, SIAM Journal of Matrix Analysis, volume 23, pages
-* 929--947, 2002.
-*
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part II: Aggressive Early Deflation, SIAM Journal
-* of Matrix Analysis, volume 23, pages 948--973, 2002.
-*
-* ================================================================
+*
+* =====================================================================
+*
* .. Parameters ..
*
* ==== Matrices of order NTINY or smaller must be processed by
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
* INCX, BETA, Y, INCY )
* DOUBLE PRECISION Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GBAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GBRCOND_C( TRANS, N, KL, KU, AB,
* LDAB, AFB, LDAFB, IPIV,
* DOUBLE PRECISION C( * ), RWORK( * )
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GBRCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
* LDAB, AFB, LDAFB, IPIV,
* DOUBLE PRECISION RWORK( * )
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GBRCOND_X Computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX*16 vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
* NRHS, AB, LDAB, AFB, LDAFB, IPIV,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GBRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to ZGBTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
* LDAB, AFB, LDAFB )
* COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GBRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAFB is INTEGER
*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
* Y, INCY )
* DOUBLE PRECISION Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GEAMV performs one of the matrix-vector operations
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*>
*> Level 2 Blas routine.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF,
* LDAF, IPIV, C, CAPPLY,
* DOUBLE PRECISION C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GERCOND_C computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, N, A, LDA, AF,
* LDAF, IPIV, X, INFO,
* DOUBLE PRECISION RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GERCOND_X computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX*16 vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
* LDA, AF, LDAF, IPIV, COLEQU, C, B,
* $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_GERFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERRS_C for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERRS_N and ERRS_C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to ZGETRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
* LDAF )
* COMPLEX*16 A( LDA, * ), AF( LDAF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> ZLA_GERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_HEAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* DOUBLE PRECISION Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_SYAMV performs the matrix-vector operation
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16HEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Richard Hanson, Sandia National Labs.
*> -- Modified for the absolute-value product, April 2006
*> Jason Riedy, UC Berkeley
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF,
* LDAF, IPIV, C, CAPPLY,
* DOUBLE PRECISION C ( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_HERCOND_C computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF,
* LDAF, IPIV, X, INFO,
* DOUBLE PRECISION RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_HERCOND_X computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX*16 vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_HERFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, IPIV, COLEQU, C, B, LDB,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_HERFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to ZHETRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_HERPVGRW( UPLO, N, INFO, A, LDA, AF,
* LDAF, IPIV, WORK )
* DOUBLE PRECISION WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> ZLA_HERPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
*
* COMPLEX*16 RES( N, NRHS )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_LIN_BERR computes componentwise relative backward error from
*> the formula
*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
*> where abs(Z) is the componentwise absolute value of the matrix
*> or vector Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> BERR is COMPLEX*16 array, dimension (NRHS)
*> The componentwise relative backward error from the formula above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_PORCOND_C( UPLO, N, A, LDA, AF,
* LDAF, C, CAPPLY, INFO,
* DOUBLE PRECISION C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_PORCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_PORCOND_X( UPLO, N, A, LDA, AF,
* LDAF, X, INFO, WORK,
* DOUBLE PRECISION RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_PORCOND_X Computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX*16 vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, COLEQU, C, B, LDB, Y,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_PORFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to ZPOTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
* LDAF, WORK )
* DOUBLE PRECISION WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> ZLA_PORPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* DOUBLE PRECISION Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_SYAMV performs the matrix-vector operation
*>
*> "symbolically" zero components are not perturbed. A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16SYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> Richard Hanson, Sandia National Labs.
*> -- Modified for the absolute-value product, April 2006
*> Jason Riedy, UC Berkeley
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_SYRCOND_C( UPLO, N, A, LDA, AF,
* LDAF, IPIV, C, CAPPLY,
* DOUBLE PRECISION C( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_SYRCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_SYRCOND_X( UPLO, N, A, LDA, AF,
* LDAF, IPIV, X, INFO,
* DOUBLE PRECISION RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_SYRCOND_X Computes the infinity norm condition number of
*> op(A) * diag(X) where X is a COMPLEX*16 vector.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N).
*> Workspace.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
* AF, LDAF, IPIV, COLEQU, C, B, LDB,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_SYRFSX_EXTENDED improves the computed solution to a system of
*> linear equations by performing extra-precise iterative refinement
*> and ERR_BNDS_COMP for details of the error bounds. Note that this
*> subroutine is only resonsible for setting the second fields of
*> ERR_BNDS_NORM and ERR_BNDS_COMP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PREC_TYPE
*> \verbatim
*> < 0: if INFO = -i, the ith argument to ZSYTRS had an illegal
*> value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF,
* LDAF, IPIV, WORK )
* INTEGER IPIV( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*>
*> ZLA_SYRPVGRW computes the reciprocal pivot growth factor
*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
*> (equilibrated) matrix A could be poor. This also means that the
*> solution X, estimated condition numbers, and error bounds could be
*> unreliable.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (2*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLA_WWADDW( N, X, Y, W )
*
* COMPLEX*16 X( * ), Y( * ), W( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
*>
*> This works for all extant IBM's hex and binary floating point
*> arithmetics, but not for decimal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> W is COMPLEX*16 array, dimension (N)
*> The vector to be added.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
* LDY )
* $ Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLABRD reduces the first NB rows and columns of a complex general
*> m by n matrix A to upper or lower real bidiagonal form by a unitary
*> bidiagonal form.
*>
*> This is an auxiliary routine called by ZGEBRD
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrices Q and P are represented as products of elementary
*> where a denotes an element of the original matrix which is unchanged,
*> vi denotes an element of the vector defining H(i), and ui an element
*> of the vector defining G(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACGV( N, X, INCX )
*
* COMPLEX*16 X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZLACGV conjugates a complex vector of length N.
+*> \verbatim
*>
-*>\endverbatim
+*> ZLACGV conjugates a complex vector of length N.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive elements of X.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
*
* COMPLEX*16 V( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLACN2 estimates the 1-norm of a square, complex matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> ISAVE is INTEGER array, dimension (3)
*> ISAVE is used to save variables between calls to ZLACN2
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
-*> Contributed by Nick Higham, University of Manchester.
*> Originally named CONEST, dated March 16, 1988.
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
-*> a real or complex matrix, with applications to condition estimation",
-*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
-*>
*> Last modified: April, 1999
*>
*> This is a thread safe version of ZLACON, which uses the array ISAVE
*> JUMP ISAVE(1)
*> J ISAVE(2)
*> ITER ISAVE(3)
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Nick Higham, University of Manchester
+*
+*> \par References:
+* ================
+*>
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> a real or complex matrix, with applications to condition estimation",
+*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
* =====================================================================
SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACON( N, V, X, EST, KASE )
*
* COMPLEX*16 V( N ), X( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLACON estimates the 1-norm of a square, complex matrix A.
*> Reverse communication is used for evaluating matrix-vector products.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> whether X should be overwritten by A * X or A**H * X.
*> On the final return from ZLACON, KASE will again be 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
+*> \par Further Details:
+* =====================
+*>
+*> Originally named CONEST, dated March 16, 1988. \n
+*> Last modified: April, 1999
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Contributed by Nick Higham, University of Manchester.
-*> Originally named CONEST, dated March 16, 1988.
+*> Nick Higham, University of Manchester
+*
+*> \par References:
+* ================
*>
-*> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
+*> N.J. Higham, "FORTRAN codes for estimating the one-norm of
*> a real or complex matrix, with applications to condition estimation",
*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
-*> Last modified: April, 1999
-*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZLACON( N, V, X, EST, KASE )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACP2( UPLO, M, N, A, LDA, B, LDB )
*
* COMPLEX*16 B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLACP2 copies all or part of a real two-dimensional matrix A to a
*> complex matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLACPY copies all or part of a two-dimensional matrix A to another
*> matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK )
*
* COMPLEX*16 A( LDA, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLACRM performs a very simple matrix-matrix multiplication:
*> C := A * B,
*> where A is M by N and complex; B is N by N and real;
*> C is M by N and complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (2*M*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLACRT( N, CX, INCX, CY, INCY, C, S )
*
* COMPLEX*16 CX( * ), CY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLACRT performs the operation
*>
*> ( -s c )( y ) ( y )
*>
*> where c and s are complex and the vectors x and y are complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> [ C S ].
*> [ -S C ]
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX*16 FUNCTION ZLADIV( X, Y )
*
* COMPLEX*16 X, Y
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLADIV := X / Y, where X and Y are complex. The computation of X / Y
*> will not overflow on an intermediary step unless the results
*> overflows.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] X
*> \verbatim
*> Y is COMPLEX*16
*> The complex scalars X and Y.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
* IWORK, INFO )
* COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Using the divide and conquer method, ZLAED0 computes all eigenvalues
*> of a symmetric tridiagonal matrix which is one diagonal block of
*> those from reducing a dense or band Hermitian matrix and
*> corresponding eigenvectors of the dense or band matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] QSIZ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
* LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM,
* COMPLEX*16 Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAED7 computes the updated eigensystem of a diagonal
*> matrix after modification by a rank-one symmetric matrix. This
*> directly using the updated eigenvalues. The eigenvectors for
*> the current problem are multiplied with the eigenvectors from
*> the overall problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = 1, an eigenvalue did not converge
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA,
* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR,
* COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAED8 merges the two sets of eigenvalues together into a single
*> sorted set. Then it tries to deflate the size of the problem.
*> eigenvalues are close together or if there is a tiny element in the
*> Z vector. For each such occurrence the order of the related secular
*> equation problem is reduced by one.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] K
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK,
* EPS3, SMLNUM, INFO )
* COMPLEX*16 B( LDB, * ), H( LDH, * ), V( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAEIN uses inverse iteration to find a right or left eigenvector
*> corresponding to the eigenvalue W of a complex upper Hessenberg
*> matrix H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RIGHTV
*> \verbatim
*> = 1: inverse iteration did not converge; V is set to the
*> last iterate.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
*
* COMPLEX*16 A, B, C, CS1, EVSCAL, RT1, RT2, SN1
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
*> ( ( A, B );( B, C ) )
*>
*> [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ]
*> [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector
*> for RT1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
* COMPLEX*16 A, B, C, SN1
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
*> [ A B ]
*>
*> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
*> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> SN1 is COMPLEX*16
*> The vector (CS1, SN1) is a unit right eigenvector for RT1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> RT1 is accurate to a few ulps barring over/underflow.
*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
*> Underflow is harmless if the input data is 0 or exceeds
*> underflow_threshold / macheps.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAG2C( M, N, A, LDA, SA, LDSA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAG2C converts a COMPLEX*16 matrix, SA, to a COMPLEX matrix, A.
*>
*> RMAX. If not the convertion is aborted and a flag is raised.
*>
*> This is an auxiliary routine so there is no argument checking.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> PRECISION overflow threshold, in this case, the content
*> of SA in exit is unspecified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
* SNV, CSQ, SNQ )
* COMPLEX*16 A2, B2, SNQ, SNU, SNV
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
*> that if ( UPPER ) then
*> then the transformed (2,2) element of B is not zero, except when the
*> first rows of input A and B are parallel and the second rows are
*> zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPPER
*> \verbatim
*> SNQ is COMPLEX*16
*> The desired unitary matrix Q.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
* B, LDB )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAGTM performs a matrix-vector product of the form
*>
*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
*> matrices, and alpha and beta are real scalars, each of which may be
*> 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
* COMPLEX*16 A( LDA, * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAHEF computes a partial factorization of a complex Hermitian
*> matrix A using the Bunch-Kaufman diagonal pivoting method. The
*> ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code
*> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
*> A22 (if UPLO = 'L').
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
* IHIZ, Z, LDZ, INFO )
* COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAHQR is an auxiliary routine called by CHSEQR to update the
*> eigenvalues and Schur decomposition already computed by CHSEQR, by
*> dealing with the Hessenberg submatrix in rows and columns ILO to
*> IHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> where U is the orthogonal matrix in (*)
*> (regardless of the value of WANTT.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Contributors:
+* ==================
+*>
*> \verbatim
*>
*> 02-96 Based on modifications by
*> It is (1) more robust against overflow and underflow and
*> (2) adopts the more conservative Ahues & Tisseur stopping
*> criterion (LAWN 122, 1997).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
*>
*> This is an auxiliary routine called by ZGEHRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> Gejin. Note that the entries of A(1:K,2:NB) differ from those
*> returned by the original LAPACK-3.0's DLAHRD routine. (This
*> subroutine is not backward compatible with LAPACK-3.0's DLAHRD.)
-*>
-*> References
-*> ==========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> Gregorio Quintana-Orti and Robert van de Geijn, "Improving the
*> performance of reduction to Hessenberg form," ACM Transactions on
*> Mathematical Software, 32(2):180-194, June 2006.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
* $ Y( LDY, NB )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
*> matrix A so that elements below the k-th subdiagonal are zero. The
*> This is an OBSOLETE auxiliary routine.
*> This routine will be 'deprecated' in a future release.
*> Please use the new routine ZLAHR2 instead.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of the array Y. LDY >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix Q is represented as a product of nb elementary reflectors
*> where a denotes an element of the original matrix A, h denotes a
*> modified element of the upper Hessenberg matrix H, and vi denotes an
*> element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
*
* COMPLEX*16 W( J ), X( J )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAIC1 applies one step of incremental condition estimation in
*> its simplest version:
*> [ conjg(gamma) ]
*>
*> where alpha = x**H * w.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> C is COMPLEX*16
*> Cosine needed in forming xhat.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
* COMPLEX*16 B( LDB, * ), BX( LDBX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLALS0 applies back the multiplying factors of either the left or the
*> right singular vector matrix of a diagonal matrix appended by a row
*> (3R) The inverse transformation of (2L).
*>
*> (4R) The inverse transformation of (1L).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE ZLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
$ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
* COMPLEX*16 B( LDB, * ), BX( LDBX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLALSA is an itermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the
*> right hand side. The singular vector matrices were generated in
*> compact form by ZLALSA.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ICOMPQ
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE ZLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
$ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
* RANK, WORK, RWORK, IWORK, INFO )
* COMPLEX*16 B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLALSD uses the singular value decomposition of A to solve the least
*> squares problem of finding X to minimize the Euclidean norm of each
*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through MOD(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Ming Gu and Ren-Cang Li, Computer Science Division, University of
-*> California at Berkeley, USA
-*> Osni Marques, LBNL/NERSC, USA
-*>
-*> \endverbatim
-*>
+*> California at Berkeley, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE ZLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
$ RANK, WORK, RWORK, IWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
* WORK )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANGB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANGB returns the value
+*> \return ZLANGB
+*> \verbatim
*>
*> ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANGE returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANGE returns the value
+*> \return ZLANGE
+*> \verbatim
*>
*> ZLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANGT( NORM, N, DL, D, DU )
*
* COMPLEX*16 D( * ), DL( * ), DU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANGT returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANGT returns the value
+*> \return ZLANGT
+*> \verbatim
*>
*> ZLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> DU is COMPLEX*16 array, dimension (N-1)
*> The (n-1) super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANHB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n hermitian band matrix A, with k super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANHB returns the value
+*> \return ZLANHB
+*> \verbatim
*>
*> ZLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANHE returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex hermitian matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANHE returns the value
+*> \return ZLANHE
+*> \verbatim
*>
*> ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK )
*
* COMPLEX*16 A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANHF returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex Hermitian matrix A in RFP format.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANHF returns the value
+*> \return ZLANHF
+*> \verbatim
*>
*> ZLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANHP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex hermitian matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANHP returns the value
+*> \return ZLANHP
+*> \verbatim
*>
*> ZLANHP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANHS( NORM, N, A, LDA, WORK )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANHS returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> Hessenberg matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANHS returns the value
+*> \return ZLANHS
+*> \verbatim
*>
*> ZLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E )
*
* COMPLEX*16 E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANHT returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex Hermitian tridiagonal matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANHT returns the value
+*> \return ZLANHT
+*> \verbatim
*>
*> ZLANHT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> E is COMPLEX*16 array, dimension (N-1)
*> The (n-1) sub-diagonal or super-diagonal elements of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
* WORK )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANSB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n symmetric band matrix A, with k super-diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANSB returns the value
+*> \return ZLANSB
+*> \verbatim
*>
*> ZLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANSP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex symmetric matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANSP returns the value
+*> \return ZLANSP
+*> \verbatim
*>
*> ZLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANSY returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> complex symmetric matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANSY returns the value
+*> \return ZLANSY
+*> \verbatim
*>
*> ZLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*> WORK is not referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANTB( NORM, UPLO, DIAG, N, K, AB,
* LDAB, WORK )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANTB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n triangular band matrix A, with ( k + 1 ) diagonals.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANTB returns the value
+*> \return ZLANTB
+*> \verbatim
*>
*> ZLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANTP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> triangular matrix A, supplied in packed form.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANTP returns the value
+*> \return ZLANTP
+*> \verbatim
*>
*> ZLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
* WORK )
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLANTR returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> trapezoidal or triangular matrix A.
+*> \endverbatim
*>
-*> Description
-*> ===========
-*>
-*> ZLANTR returns the value
+*> \return ZLANTR
+*> \verbatim
*>
*> ZLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*> (
*> normI denotes the infinity norm of a matrix (maximum row sum) and
*> normF denotes the Frobenius norm of a matrix (square root of sum of
*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
* COMPLEX*16 X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given two column vectors X and Y, let
*>
*> and then computes the SVD of the 2-by-2 upper triangular matrix R.
*> The smaller singular value of R is returned in SSMIN, which is used
*> as the measurement of the linear dependency of the vectors X and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> SSMIN is DOUBLE PRECISION
*> The smallest singular value of the N-by-2 matrix A = ( X Y ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAPMR( FORWRD, M, N, X, LDX, K )
*
* COMPLEX*16 X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAPMR rearranges the rows of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(M) of the integers 1,...,M.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(I,*) is moved to X(K(I),*) for I = 1,2,...,M.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAPMT( FORWRD, M, N, X, LDX, K )
*
* COMPLEX*16 X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAPMT rearranges the columns of the M by N matrix X as specified
*> by the permutation K(1),K(2),...,K(N) of the integers 1,...,N.
*> If FORWRD = .FALSE., backward permutation:
*>
*> X(*,J) is moved to X(*,K(J)) for J = 1,2,...,N.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FORWRD
*> \verbatim
*> internal workspace, but reset to its original value on
*> output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
* AMAX, EQUED )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQGB equilibrates a general M by N band matrix A with KL
*> subdiagonals and KU superdiagonals using the row and scaling factors
*> in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* EQUED )
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQGE equilibrates a general M by N matrix A using the row and
*> column scaling factors in the vectors R and C.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQHB equilibrates a Hermitian band matrix A
*> using the scaling factors in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQHP equilibrates a Hermitian matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
* WORK )
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQP2 computes a QR factorization with column pivoting of
*> the block A(OFFSET+1:M,1:N).
*> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
-*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
$ WORK )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
* VN2, AUXV, F, LDF )
* COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQPS computes a step of QR factorization with column pivoting
*> of a complex M-by-N matrix A by using Blas-3. It tries to factorize
*> columns is returned in KB.
*>
*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of the array F. LDF >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
-*>
-*> Partial column norm updating strategy modified by
+*> \n
+*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
-*> -- April 2011 --
-*> For more details see LAPACK Working Note 176.
-*> \endverbatim
+*
+*> \par References:
+* ================
*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
+*> \endhtmlonly
+*
* =====================================================================
SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
$ VN2, AUXV, F, LDF )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
* IHIZ, Z, LDZ, WORK, LWORK, INFO )
* COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQR0 computes the eigenvalues of a Hessenberg matrix H
*> and, optionally, the matrices T and Z from the Schur decomposition
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V )
*
* COMPLEX*16 H( LDH, * ), V( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a
*> scalar multiple of the first column of the product
*>
*> This is useful for starting double implicit shift bulges
*> in the QR algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> A scalar multiple of the first column of the
*> matrix K in (*).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT,
* $ WORK( * ), WV( LDWV, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQR2 is identical to ZLAQR3 except that it avoids
*> recursion by calling ZLAHQR instead of ZLAQR4.
*> hoped that the final version of H has many zero subdiagonal
*> entries.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
* IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT,
* $ WORK( * ), WV( LDWV, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Aggressive early deflation:
*>
*> hoped that the final version of H has many zero subdiagonal
*> entries.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> in WORK(1). No error message related to LWORK is issued
*> by XERBLA. Neither H nor Z are accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
-*>
-*> \endverbatim
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
*>
* =====================================================================
SUBROUTINE ZLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
* IHIZ, Z, LDZ, WORK, LWORK, INFO )
* COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQR4 implements one level of recursion for ZLAQR0.
*> It is a complete implementation of the small bulge multi-shift
*> matrix Q so that this routine can give the Schur factorization
*> of a matrix A which has been reduced to the Hessenberg form H
*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
-*> Karen Braman and Ralph Byers, Department of Mathematics,
-*> University of Kansas, USA
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
*>
-*> References:
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
*> 929--947, 2002.
-*>
+*> \n
*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
*> of Matrix Analysis, volume 23, pages 948--973, 2002.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, WORK, LWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
* H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,
* $ WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQR5, called by ZLAQR0, performs a
*> single small-bulge multi-shift QR sweep.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTT
*> \verbatim
*> LDWV is the leading dimension of WV as declared in the
*> in the calling subroutine. LDWV.GE.NV.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
+*> \par Contributors:
+* ==================
+*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
+*>
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
+*>
* =====================================================================
SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
$ H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV,
* ..
*
* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* Reference:
-*
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part I: Maintaining Well Focused Shifts, and
-* Level 3 Performance, SIAM Journal of Matrix Analysis,
-* volume 23, pages 929--947, 2002.
-*
-* ================================================================
* .. Parameters ..
COMPLEX*16 ZERO, ONE
PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ),
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQSB equilibrates a symmetric band matrix A using the scaling
*> factors in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQSP equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAQSY equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
* PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
* COMPLEX*16 Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAR1V computes the (scaled) r-th column of the inverse of
*> the sumbmatrix in rows B1 through BN of the tridiagonal matrix
*> (d) Computation of the (scaled) r-th column of the inverse using the
*> twisted factorization obtained by combining the top part of the
*> the stationary and the bottom part of the progressive transform.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (4*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE ZLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
$ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAR2V applies a vector of complex plane rotations with real cosines
*> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
*>
*> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
*> ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARCM( M, N, A, LDA, B, LDB, C, LDC, RWORK )
*
* COMPLEX*16 B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARCM performs a very simple matrix-matrix multiplication:
*> C := A * B,
*> where A is M by M and real; B is M by N and complex;
*> C is M by N and complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (2*M*N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARF applies a complex elementary reflector H to a complex M-by-N
*> matrix C, from either the left or the right. H is represented in the
*>
*> To apply H**H, supply conjg(tau) instead
*> tau.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
* T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARFB applies a complex block reflector H or its transpose H**H to a
*> complex M-by-N matrix C, from either the left or the right.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
*
* COMPLEX*16 X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARFG generates a complex elementary reflector H of order n, such
*> that
*> and H is taken to be the unit matrix.
*>
*> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is COMPLEX*16
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARFGP( N, ALPHA, X, INCX, TAU )
*
* COMPLEX*16 X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARFGP generates a complex elementary reflector H of order n, such
*> that
*>
*> If the elements of x are all zero and alpha is real, then tau = 0
*> and H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> TAU is COMPLEX*16
*> The value tau.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARFT forms the triangular factor T of a complex block reflector H
*> of order n, which is defined as a product of k elementary reflectors.
*> H(i) is stored in the i-th row of the array V, and
*>
*> H = I - V**H * T * V
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
*> ( 1 v3 )
*> ( 1 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARFX( SIDE, M, N, V, TAU, C, LDC, WORK )
*
* COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARFX applies a complex elementary reflector H to a complex m by n
*> matrix C, from either the left or the right. H is represented in the
*> If tau = 0, then H is taken to be the unit matrix
*>
*> This version uses inline code if H has order < 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> or (M) if SIDE = 'R'
*> WORK is not referenced if H has order < 11.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* COMPLEX*16 X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARGV generates a vector of complex plane rotations with real
*> cosines, determined by elements of the complex vectors x and y.
*> but differ from the BLAS1 routine ZROTG):
*> If y(i)=0, then c(i)=1 and s(i)=0.
*> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*>
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
*
* COMPLEX*16 X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARNV returns a vector of n random complex numbers from a uniform or
*> normal distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> X is COMPLEX*16 array, dimension (N)
*> The generated random numbers.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine DLARUV to generate random
*> real numbers from a uniform (0,1) distribution, in batches of up to
*> 128 using vectorisable code. The Box-Muller method is used to
*> transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARRV( N, VL, VU, D, L, PIVMIN,
* ISPLIT, M, DOL, DOU, MINRGP,
* COMPLEX*16 Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARRV computes the eigenvectors of the tridiagonal matrix
*> T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
*> The input eigenvalues should have been computed by DLARRE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 5: The Rayleigh Quotient Iteration failed to converge to
*> full accuracy in MAXITR steps.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA
+*
* =====================================================================
SUBROUTINE ZLARRV( N, VL, VU, D, L, PIVMIN,
$ ISPLIT, M, DOL, DOU, MINRGP,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARSCL2 ( M, N, D, X, LDX )
*
* DOUBLE PRECISION D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARSCL2 performs a reciprocal diagonal scaling on an vector:
*> x <-- inv(D) * x
*>
*> Eventually to be replaced by BLAS_zge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARTG( F, G, CS, SN, R )
*
* COMPLEX*16 F, G, R, SN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARTG generates a plane rotation so that
*>
*> F and G are unchanged on return.
*> If G=0, then CS=1 and SN=0.
*> If F=0, then CS=0 and SN is chosen so that R is real.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] F
*> \verbatim
*> R is COMPLEX*16
*> The nonzero component of the rotated vector.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*>
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARTV( N, X, INCX, Y, INCY, C, S, INCC )
*
* COMPLEX*16 S( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARTV applies a vector of complex plane rotations with real cosines
*> to elements of the complex vectors x and y. For i = 1,2,...,n
*>
*> ( x(i) ) := ( c(i) s(i) ) ( x(i) )
*> ( y(i) ) ( -conjg(s(i)) c(i) ) ( y(i) )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARZ applies a complex elementary reflector H to a complex
*> M-by-N matrix C, from either the left or the right. H is represented
*> tau.
*>
*> H is a product of k elementary reflectors as returned by ZTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
* LDV, T, LDT, C, LDC, WORK, LDWORK )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARZB applies a complex block reflector H or its transpose H**H
*> to a complex distributed M-by-N C from the left or the right.
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= max(1,N);
*> if SIDE = 'R', LDWORK >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARZT forms the triangular factor T of a complex block reflector
*> H of order > n, which is defined as a product of k elementary
*> H = I - V**H * T * V
*>
*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DIRECT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= K.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The shape of the matrix V and the storage of the vectors which define
*> the H(i) is best illustrated by the following example with n = 5 and
*> V = ( v1 v2 v3 )
*> ( v1 v2 v3 )
*> ( v1 v2 v3 )
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASCL multiplies the M by N complex matrix A by the real scalar
*> CTO/CFROM. This is done without over/underflow as long as the final
*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
*> A may be full, upper triangular, lower triangular, upper Hessenberg,
*> or banded.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> 0 - successful exit
*> <0 - if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASCL2 ( M, N, D, X, LDX )
*
* COMPLEX*16 X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASCL2 performs a diagonal scaling on a vector:
*> x <-- D * x
*>
*> Eventually to be replaced by BLAS_zge_diag_scale in the new BLAS
*> standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the vector X. LDX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASET initializes a 2-D array A to BETA on the diagonal and
*> ALPHA on the offdiagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASR applies a sequence of real plane rotations to a complex matrix
*> A, from either the left or the right.
*>
*> where R(k) appears in rows and columns k and z. The rotations are
*> performed without ever forming P(k) explicitly.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* COMPLEX*16 X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASSQ returns the values scl and ssq such that
*>
*> SCALE and SUMSQ are overwritten by scl and ssq respectively.
*>
*> The routine makes only one pass through the vector X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> On entry, the value sumsq in the equation above.
*> On exit, SUMSQ is overwritten with the value ssq .
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASWP( N, A, LDA, K1, K2, IPIV, INCX )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASWP performs a series of row interchanges on the matrix A.
*> One row interchange is initiated for each of rows K1 through K2 of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The increment between successive values of IPIV. If IPIV
*> is negative, the pivots are applied in reverse order.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> Modified by
*> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
* COMPLEX*16 A( LDA, * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLASYF computes a partial factorization of a complex symmetric matrix
*> A using the Bunch-Kaufman diagonal pivoting method. The partial
*> ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
*> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
*> A22 (if UPLO = 'L').
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAT2C( UPLO, N, A, LDA, SA, LDSA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAT2C converts a COMPLEX*16 triangular matrix, SA, to a COMPLEX
*> triangular matrix, A.
*> RMAX. If not the convertion is aborted and a flag is raised.
*>
*> This is an auxiliary routine so there is no argument checking.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> PRECISION overflow threshold, in this case, the content
*> of the UPLO part of SA in exit is unspecified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
* SCALE, CNORM, INFO )
* COMPLEX*16 AB( LDAB, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATBS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine ZTBSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, ZTBSV
*>
*> and we can safely call ZTBSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
* JPIV )
* COMPLEX*16 RHS( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATDF computes the contribution to the reciprocal Dif-estimate
*> by solving for x in Z * x = b, where b is chosen such that the norm
*> The factorization of Z returned by ZGETC2 has the form
*> Z = P * L * U * Q, where P and Q are permutation matrices. L is lower
*> triangular with unit diagonal elements and U is upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> The pivot indices; for 1 <= j <= N, column j of the
*> matrix has been interchanged with column JPIV(j).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
+*> \par Further Details:
+* =====================
+*>
+*> This routine is a further developed implementation of algorithm
+*> BSOLVE in [1] using complete pivoting in the LU factorization.
*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> This routine is a further developed implementation of algorithm
-*> BSOLVE in [1] using complete pivoting in the LU factorization.
+*
+*> \par References:
+* ================
*>
*> [1] Bo Kagstrom and Lars Westin,
*> Generalized Schur Methods with Condition Estimators for
*> Solving the Generalized Sylvester Equation, IEEE Transactions
*> on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
-*>
+*>\n
*> [2] Peter Poromaa,
*> On Efficient and Robust Estimators for the Separation
*> between two Regular Matrix Pairs with Applications in
*> Condition Estimation. Report UMINF-95.05, Department of
*> Computing Science, Umea University, S-901 87 Umea, Sweden,
*> 1995.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
$ JPIV )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATPS( UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE,
* CNORM, INFO )
* COMPLEX*16 AP( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATPS solves one of the triangular systems
*>
*> overflow, the Level 2 BLAS routine ZTPSV is called. If the matrix A
*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*> non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, ZTPSV
*>
*> and we can safely call ZTPSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
*> Hermitian tridiagonal form by a unitary similarity
*> matrix, of which the lower triangle is supplied.
*>
*> This is an auxiliary routine called by ZHETRD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDW is INTEGER
*> The leading dimension of the array W. LDW >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', the matrix Q is represented as a product of elementary
*> where d denotes a diagonal element of the reduced matrix, a denotes
*> an element of the original matrix that is unchanged, and vi denotes
*> an element of the vector defining H(i).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
* CNORM, INFO )
* COMPLEX*16 A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATRS solves one of the triangular systems
*>
*> unscaled problem will not cause overflow, the Level 2 BLAS routine
*> ZTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j),
*> then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A rough bound on x is computed; if that is less than overflow, ZTRSV
*>
*> and we can safely call ZTRSV if 1/M(n) and 1/G(n) are both greater
*> than max(underflow, 1/overflow).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATRZ( M, N, L, A, LDA, TAU, WORK )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
*> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means
*> of unitary transformations, where Z is an (M+L)-by-(M+L) unitary
*> matrix and, R and A1 are M-by-M upper triangular matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
* COMPLEX*16 C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine ZUNMRZ.
*>
*> C = [ C1, C2 ] m
*> 1 n-1
*> Then C is overwritten by C*P.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> (N) if SIDE = 'L'
*> (M) if SIDE = 'R'
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAUU2( UPLO, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAUU2 computes the product U * U**H or L**H * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the unblocked form of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAUUM( UPLO, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAUUM computes the product U * U**H or L**H * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> overwriting the factor L in A.
*>
*> This is the blocked form of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
* RWORK, INFO )
* COMPLEX*16 AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite band matrix using
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBEQU computes row and column scalings intended to equilibrate a
*> Hermitian positive definite band matrix A and reduce its condition
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B,
* LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite
*> and banded, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBSTF( UPLO, N, KD, AB, LDAB, INFO )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBSTF computes a split Cholesky factorization of a complex
*> Hermitian positive definite band matrix A.
*>
*> where U is upper triangular of order m = (n+kd)/2, and L is lower
*> triangular of order n-m.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> because the updated element a(i,i) was negative; the
*> matrix A is not positive definite.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*>
*> Array elements marked * are not used by the routine; s12**H denotes
*> conjg(s12); the diagonal elements of S are real.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular band matrix, with the same number of superdiagonals or
*> subdiagonals as A. The factored form of A is then used to solve the
*> system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBSVX( FACT, UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB,
* EQUED, S, B, LDB, X, LDX, RCOND, FERR, BERR,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
*> compute the solution to a complex system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBTF2 computes the Cholesky factorization of a complex Hermitian
*> positive definite band matrix A.
*> of U, and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite band matrix A.
*> A = U**H * U, if UPLO = 'U', or
*> A = L * L**H, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*>
*> Array elements marked * are not used by the routine.
-*>
-*> Contributed by
-*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
+*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
+*
* =====================================================================
SUBROUTINE ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite band matrix A using the Cholesky factorization
*> A = U**H *U or A = L*L**H computed by ZPBTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPFTRF( TRANSR, UPLO, N, A, INFO )
*
* .. Array Arguments ..
* COMPLEX*16 A( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPFTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPFTRI( TRANSR, UPLO, N, A, INFO )
*
* COMPLEX*16 A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPFTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by ZPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* COMPLEX*16 A( 0: * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPFTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A using the Cholesky factorization
*> A = U**H*U or A = L*L**H computed by ZPFTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
* INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite matrix using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOEQU computes row and column scalings intended to equilibrate a
*> Hermitian positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
*
* DOUBLE PRECISION S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOEQUB computes row and column scalings intended to equilibrate a
*> symmetric positive definite matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X,
* LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPORFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite,
*> and provides error bounds and backward error estimates for the
*> solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
* LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPORFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric positive
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOSV computes the solution to a complex system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
*> compute the solution to a complex system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
* S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
*> to compute the solution to a complex*16 system of linear equations
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what ZPOSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOTF2 computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A.
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the block version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOTRI( UPLO, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by ZPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A using the Cholesky factorization
*> A = U**H * U or A = L * L**H computed by ZPOTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
*
* COMPLEX*16 AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite packed matrix using
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPEQU computes row and column scalings intended to equilibrate a
*> Hermitian positive definite matrix A in packed storage and reduce
*> This choice of S puts the condition number of B within a factor N of
*> the smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR,
* BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPSV computes the solution to a complex system of linear equations
*> A * X = B,
*> where U is an upper triangular matrix and L is a lower triangular
*> matrix. The factored form of A is then used to solve the system of
*> equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, so the factorization could not be
*> completed, and the solution has not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPSVX( FACT, UPLO, N, NRHS, AP, AFP, EQUED, S, B, LDB,
* X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPSVX uses the Cholesky factorization A = U**H * U or A = L * L**H to
*> compute the solution to a complex system of linear equations
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(S) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPTRF computes the Cholesky factorization of a complex Hermitian
*> positive definite matrix A stored in packed format.
*> A = U**H * U, if UPLO = 'U', or
*> A = L * L**H, if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> positive definite, and the factorization could not be
*> completed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPTRI( UPLO, N, AP, INFO )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPTRI computes the inverse of a complex Hermitian positive definite
*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*> computed by ZPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, the (i,i) element of the factor U or L is
*> zero, and the inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPTRS solves a system of linear equations A*X = B with a Hermitian
*> positive definite matrix A in packed storage using the Cholesky
*> factorization A = U**H * U or A = L * L**H computed by ZPPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPSTF2 computes the Cholesky factorization with complete
*> pivoting of a complex Hermitian positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
* INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPSTRF computes the Cholesky factorization with complete
*> pivoting of a complex Hermitian positive semidefinite matrix A.
*>
*> This algorithm does not attempt to check that A is positive
*> semidefinite. This version of the algorithm calls level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> as returned in RANK, or is indefinite. See Section 7 of
*> LAPACK Working Note #161 for further information.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
*
* COMPLEX*16 E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTCON computes the reciprocal of the condition number (in the
*> 1-norm) of a complex Hermitian positive definite tridiagonal matrix
*> Norm(inv(A)) is computed by a direct method, and the reciprocal of
*> the condition number is computed as
*> RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The method used is described in Nicholas J. Higham, "Efficient
*> Algorithms for Computing the Condition Number of a Tridiagonal
*> Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* COMPLEX*16 Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric positive definite tridiagonal matrix by first factoring the
*> tridiagonal form, however, may preclude the possibility of obtaining
*> high relative accuracy in the small eigenvalues of the original
*> matrix, if these eigenvalues range over many orders of magnitude.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> if INFO = N+i, i off-diagonal elements of the
*> bidiagonal factor did not converge to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is Hermitian positive definite
*> and tridiagonal, and provides error bounds and backward error
*> estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTSV( N, NRHS, D, E, B, LDB, INFO )
*
* COMPLEX*16 B( LDB, * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTSV computes the solution to a complex system of linear equations
*> A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
*>
*> A is factored as A = L*D*L**H, and the factored form of A is then
*> used to solve the system of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> computed. The factorization has not been completed
*> unless i = N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
* RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTSVX uses the factorization A = L*D*L**H to compute the solution
*> to a complex system of linear equations A*X = B, where A is an
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTTRF( N, D, E, INFO )
*
* COMPLEX*16 E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
*> positive definite tridiagonal matrix A. The factorization may also
*> be regarded as having the form A = U**H *D*U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be completed, while if k = N, the factorization was
*> completed, but D(N) <= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
*
* COMPLEX*16 B( LDB, * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTTRS solves a tridiagonal system of the form
*> A * X = B
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
*
* COMPLEX*16 B( LDB, * ), E( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTTS2 solves a tridiagonal system of the form
*> A * X = B
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IUPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZROT( N, CX, INCX, CY, INCY, C, S )
*
* COMPLEX*16 CX( * ), CY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZROT applies a plane rotation, where the cos (C) is real and the
*> sin (S) is complex, and the vectors CX and CY are complex.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> [ -conjg(S) C ]
*> where C*C + S*CONJG(S) = 1.0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
*
* COMPLEX*16 AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex symmetric packed matrix A using the
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*
* COMPLEX*16 AP( * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
*
* COMPLEX*16 AP( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a complex scalar, x is an n element vector and A is an
*> n by n symmetric matrix, supplied in packed form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> not be set, they are assumed to be zero, and on exit they
*> are set to zero.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite
*> and packed, and provides error bounds and backward error estimates
*> for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, D is symmetric and block diagonal with 1-by-1
*> and 2-by-2 diagonal blocks. The factored form of A is then used to
*> solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, so the solution could not be
*> computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPSVX( FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X,
* LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
*> A = L*D*L**T to compute the solution to a complex system of linear
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERsolve
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The packed storage scheme is illustrated by the following example
*> Packed storage of the upper triangle of A:
*>
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPTRF computes the factorization of a complex symmetric matrix A
*> stored in packed format using the Bunch-Kaufman diagonal pivoting
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* COMPLEX*16 AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPTRI computes the inverse of a complex symmetric indefinite matrix
*> A in packed storage using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by ZSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPTRS solves a system of linear equations A*X = B with a complex
*> symmetric matrix A stored in packed format using the factorization
*> A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,
* LRWORK, IWORK, LIWORK, INFO )
* COMPLEX*16 WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*> It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none. See DLAED3 for details.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> working on the submatrix lying in rows and columns
*> INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Jeff Rutter, Computer Science Division, University of California
-*> at Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA
+*
* =====================================================================
SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,
$ LRWORK, IWORK, LIWORK, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
* COMPLEX*16 Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTEGR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> NaNs. Normal execution may create these exceptiona values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by DLARRE or
*> ZLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Inderjit Dhillon, IBM Almaden, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, LBNL/NERSC, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Inderjit Dhillon, IBM Almaden, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, LBNL/NERSC, USA \n
+*
* =====================================================================
SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
* IWORK, IFAIL, INFO )
* COMPLEX*16 Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTEIN computes the eigenvectors of a real symmetric tridiagonal
*> matrix T corresponding to specified eigenvalues, using inverse
*> transformation to the eigenvectors of a complex Hermitian matrix
*> which was reduced to tridiagonal form.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> > 0: if INFO = i, then i eigenvectors failed to converge
*> in MAXITS iterations. Their indices are stored in
*> array IFAIL.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> MAXITS INTEGER, default = 5
*> The maximum number of iterations performed.
*>
*> The number of iterations performed after norm growth
*> criterion is satisfied, should be at least 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
* COMPLEX*16 Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTEMR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> Since LAPACK drivers overwrite the matrix data with the eigenvectors,
*> ZSTEMR accepts complex workspace to facilitate interoperability
*> with ZUNMTR or ZUPMTR.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> the nonzero error code returned by DLARRE or
*> ZLARRV, respectively.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Beresford Parlett, University of California, Berkeley, USA
-*> Jim Demmel, University of California, Berkeley, USA
-*> Inderjit Dhillon, University of Texas, Austin, USA
-*> Osni Marques, LBNL/NERSC, USA
-*> Christof Voemel, University of California, Berkeley, USA
-*>
-*> \endverbatim
+*> \par Contributors:
+* ==================
*>
+*> Beresford Parlett, University of California, Berkeley, USA \n
+*> Jim Demmel, University of California, Berkeley, USA \n
+*> Inderjit Dhillon, University of Texas, Austin, USA \n
+*> Osni Marques, LBNL/NERSC, USA \n
+*> Christof Voemel, University of California, Berkeley, USA \n
+*
* =====================================================================
SUBROUTINE ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* COMPLEX*16 Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric tridiagonal matrix using the implicit QL or QR method.
*> The eigenvectors of a full or band complex Hermitian matrix can also
*> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
*> matrix to tridiagonal form.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> matrix which is unitarily similar to the original
*> matrix.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
* INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a complex symmetric matrix A using the factorization
*>
*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYCONV( UPLO, WAY, N, A, LDA, IPIV, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYCONV converts A given by ZHETRF into L and D or vice-versa.
*> Get nondiagonal elements of D (returned in workspace) and
*> apply or reverse permutation done in TRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
* DOUBLE PRECISION S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYEQUB computes row and column scalings intended to equilibrate a
*> symmetric matrix A and reduce its condition number
*> choice of S puts the condition number of B within a factor N of the
*> smallest possible condition number over all possible diagonal
*> scalings.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element is nonpositive.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16SYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par References:
+* ================
*>
-*> Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
-*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
-*> DOI 10.1023/B:NUMA.0000016606.32820.69
+*> Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n
+*> Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n
+*> DOI 10.1023/B:NUMA.0000016606.32820.69 \n
*> Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
*
* COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
*
* COMPLEX*16 A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYR performs the symmetric rank 1 operation
*>
*>
*> where alpha is a complex scalar, x is an n element vector and A is an
*> n by n symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> max( 1, N ).
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
* X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYRFS improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> provides error bounds and backward error estimates for the solution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> ITMAX is the maximum number of steps of iterative refinement.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
* S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
* $ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYRFSX improves the computed solution to a system of linear
*> equations when the coefficient matrix is symmetric indefinite, and
*> before calling this routine, as described by arguments EQUED and S
*> below. In this case, the solution and error bounds returned are
*> for the original unequilibrated system.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
* LWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYSV computes the solution to a complex system of linear equations
*> A * X = B,
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
*> used to solve the system of equations A * X = B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
* LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYSVX uses the diagonal pivoting factorization to compute the
*> solution to a complex system of linear equations A * X = B,
*>
*> Error bounds on the solution and a condition estimate are also
*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 4. Iterative refinement is applied to improve the computed solution
*> matrix and calculate error bounds and backward error estimates
*> for it.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] FACT
*> \verbatim
*> computed solution can be more accurate than the
*> value of RCOND would suggest.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
* EQUED, S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*> Purpose
-*> =======
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYSVXX uses the diagonal pivoting factorization to compute the
*> solution to a complex*16 system of linear equations A * X = B, where
*> errors or warnings, but we cannot make that claim for general
*> user-provided factorizations and equilibration factors if they
*> differ from what ZSYSVXX would itself produce.
+*> \endverbatim
+*
+*> \par Description:
+* =================
*>
-*> Description
-*> ===========
+*> \verbatim
*>
*> The following steps are performed:
*>
*> 6. If equilibration was used, the matrix X is premultiplied by
*> diag(R) so that it solves the original system before
*> equilibration.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> Some optional parameters are bundled in the PARAMS array. These
*> about all of the right-hand sides check ERR_BNDS_NORM or
*> ERR_BNDS_COMP.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYSWAPR( UPLO, N, A, LDA, I1, I2)
*
* .. Array Arguments ..
* COMPLEX*16 A( LDA, N )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYSWAPR applies an elementary permutation on the rows and the columns of
*> a symmetric matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> I2 is INTEGER
*> Index of the second row to swap
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTF2 computes the factorization of a complex symmetric matrix A
*> using the Bunch-Kaufman diagonal pivoting method:
*> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16SYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Further Details:
+* =====================
*>
-*> 09-29-06 - patch from
-*> Bobby Cheng, MathWorks
-*>
-*> Replace l.209 and l.377
-*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
-*> by
-*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
-*>
-*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
-*> Company
+*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
+*>
+*> 09-29-06 - patch from
+*> Bobby Cheng, MathWorks
*>
+*> Replace l.209 and l.377
+*> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*> by
+*> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
+*>
+*> 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
+*> Company
+*> \endverbatim
+*
* =====================================================================
SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTRF computes the factorization of a complex symmetric matrix A
*> using the Bunch-Kaufman diagonal pivoting method. The form of the
*> with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> This is the blocked version of the algorithm, calling Level 3 BLAS.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> exactly singular, and division by zero will occur if it
*> is used to solve a system of equations.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16SYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> If UPLO = 'U', then A = U*D*U**T, where
*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTRI computes the inverse of a complex symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> ZSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTRI2 computes the inverse of a COMPLEX*16 hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> ZSYTRF. ZSYTRI2 sets the LEADING DIMENSION of the workspace
*> before calling ZSYTRI2X that actually computes the inverse.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTRI2X computes the inverse of a complex symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> ZSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*> inverse could not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTRS solves a system of linear equations A*X = B with a complex
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by ZSYTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYTRS2 solves a system of linear equations A*X = B with a real
*> symmetric matrix A using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
* RWORK, INFO )
* COMPLEX*16 AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBCON estimates the reciprocal of the condition number of a
*> triangular band matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular band
*> The solution matrix X must be computed by ZTBTRS or some other
*> means before entering this routine. ZTBRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, INFO )
* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBTRS solves a triangular system of the form
*>
*>
*> where A is a triangular band matrix of order N, and B is an
*> N-by-NRHS matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
* B, LDB )
* COMPLEX*16 A( 0: * ), B( 0: LDB-1, 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Level 3 BLAS like routine for A in RFP Format.
*>
*> A is in Rectangular Full Packed (RFP) Format.
*>
*> The matrix X is overwritten on B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> max( 1, m ).
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
* COMPLEX*16 A( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTFTRI computes the inverse of a triangular matrix A stored in RFP
*> format.
*>
*> This is a Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* COMPLEX*16 AP( 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTFTTP copies a triangular matrix A from rectangular full packed
*> format (TF) to standard packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
* COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTFTTR copies a triangular matrix A from rectangular full packed
*> format (TF) to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
* ..
*
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGEVC computes some or all of the right and/or left eigenvectors of
*> a pair of complex matrices (S,P), where S and P are upper triangular.
*> If Q and Z are the unitary factors from the generalized Schur
*> factorization of a matrix pair (A,B), then Z*X and Q*Y
*> are the matrices of right and left eigenvectors of (A,B).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, J1, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
*> in an upper triangular matrix pair (A, B) by an unitary equivalence
*> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
*> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> from generalized Schur form; the problem is ill-
*> conditioned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
-*>
-*> Based on contributions by
-*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
-*> Umea University, S-901 87 Umea, Sweden.
+*> \par Further Details:
+* =====================
*>
*> In the current code both weak and strong stability tests are
*> performed. The user can omit the strong stability test by changing
*> the internal logical parameter WANDS to .FALSE.. See ref. [2] for
*> details.
+*
+*> \par Contributors:
+* ==================
+*>
+*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
+*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
+*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report UMINF-94.04,
*> Sweden, 1994. Also as LAPACK Working Note 87. To appear in
*> Numerical Algorithms, 1996.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, J1, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, IFST, ILST, INFO )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGEXC reorders the generalized Schur decomposition of a complex
*> matrix pair (A,B), using an unitary equivalence transformation
*>
*> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
*> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> and ILST points to the first row of the current
*> position of the block being moved.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16GEcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
+*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report
*> UMINF - 94.04, Department of Computing Science, Umea University,
*> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
*> To appear in Numerical Algorithms, 1996.
-*>
+*> \n
*> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO )
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB,
* ALPHA, BETA, Q, LDQ, Z, LDZ, M, PL, PR, DIF,
* $ BETA( * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGSEN reorders the generalized Schur decomposition of a complex
*> matrix pair (A, B) (in terms of an unitary equivalence trans-
*> and norms of "projections" onto left and right eigenspaces w.r.t.
*> the selected cluster in the (1,1)-block.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> (A, B) may have been partially reordered.
*> If requested, 0 is returned in DIF(*), PL and PR.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> ZTGSEN first collects the selected eigenvalues by computing unitary
*> based estimate DIF is not wanted (see ZLATDF), then the parameter
*> IDIFJB (see below) should be changed from 3 to 4 (routine ZLATDF
*> (IJOB = 2 will be used)). See ZTGSYL for more details.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> References
-*> ==========
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
-*>
+*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report
*> UMINF - 94.04, Department of Computing Science, Umea University,
*> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
*> To appear in Numerical Algorithms, 1996.
-*>
+*> \n
*> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB,
$ ALPHA, BETA, Q, LDQ, Z, LDZ, M, PL, PR, DIF,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
* $ U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGSJA computes the generalized singular value decomposition (GSVD)
*> of two complex upper triangular (or trapezoidal) matrices A and B.
*> The computation of the unitary transformation matrices U, V or Q
*> is optional. These matrices may either be formed explicitly, or they
*> may be postmultiplied into input matrices U1, V1, or Q1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1: the procedure does not converge after MAXIT cycles.
+*> \endverbatim
+*
+*> \par Internal Parameters:
+* =========================
*>
-*> Internal Parameters
-*> ===================
-*>
+*> \verbatim
*> MAXIT INTEGER
*> MAXIT specifies the total loops that the iterative procedure
*> may take. If after MAXIT cycles, the routine fails to
*> converge, we return INFO = 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> ZTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
*> C1**2 + S1**2 = I,
*>
*> and R1 is an L-by-L nonsingular upper triangular matrix.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK,
* $ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or eigenvectors of a matrix pair (A, B).
*>
*> (A, B) must be in generalized Schur canonical form, that is, A and
*> B are both upper triangular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: Successful exit
*> < 0: If INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of the i-th generalized
*> EPS * norm(A, B) / DIF(i).
*>
*> See ref. [2-3] for more details and further references.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
-*> References
-*> ==========
+*> \verbatim
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75.
*> To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
* $ D( LDD, * ), E( LDE, * ), F( LDF, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGSY2 solves the generalized Sylvester equation
*>
*> of an upper bound on the separation between to matrix pairs. Then
*> the input (A, D), (B, E) are sub-pencils of two matrix pairs in
*> ZTGSYL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> >0: The matrix pairs (A, D) and (B, E) have common or very
*> close eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16SYauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
-*>
-*> \endverbatim
-*>
+*
* =====================================================================
SUBROUTINE ZTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTGSYL solves the generalized Sylvester equation:
*>
*> reciprocal of the smallest singular value of Z.
*>
*> This is a level-3 BLAS algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> >0: (A, D) and (B, E) have common or very close
*> eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16SYcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
+*
+*> \par References:
+* ================
*>
*> [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
*> No 1, 1996.
-*>
+*> \n
*> [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
*> Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
*> Appl., 15(4):1045-1060, 1994.
-*>
+*> \n
*> [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
*> Condition Estimators for Solving the Generalized Sylvester
*> Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
*> July 1989, pp 745-751.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK,
* INFO )
* COMPLEX*16 AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPCON estimates the reciprocal of the condition number of a packed
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
* A, LDA, B, LDB, WORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPMQRT applies a complex orthogonal matrix Q obtained from a
*> "triangular-pentagonal" complex block reflector H to a general
*> complex matrix C, which consists of two blocks A and B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The columns of the pentagonal matrix V contain the elementary reflectors
*> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
*>
*> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
* INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPQRT computes a blocked QR factorization of a complex
*> "triangular-pentagonal" matrix C, which is composed of a
*> triangular block A and pentagonal block B, using the compact
*> WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
+*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> C = [ A ]
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = [T1 T2 ... TB].
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPQRT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPQRT2 computes a QR factorization of a complex "triangular-pentagonal"
*> matrix C, which is composed of a triangular block A and pentagonal block B,
*> using the compact WY representation for Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> where W**H is the conjugate transpose of W and T is the upper triangular
*> factor of the block reflector.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L,
* V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK )
* $ V( LDV, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPRFB applies a complex "triangular-pentagonal" block reflector H or its
*> conjugate transpose H**H to a complex matrix C, which is composed of two
*> blocks A and B, either from the left or right.
*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> If SIDE = 'L', LDWORK >= K;
*> if SIDE = 'R', LDWORK >= M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERauxiliary
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The matrix C is a composite matrix formed from blocks A and B.
*> If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
*>
*> If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* FERR, BERR, WORK, RWORK, INFO )
* COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular packed
*> The solution matrix X must be computed by ZTPTRS or some other
*> means before entering this routine. ZTPRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPTRI computes the inverse of a complex upper or lower triangular
*> matrix A stored in packed format.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> A triangular matrix A can be transferred to packed storage using one
*> 1 CONTINUE 1 CONTINUE
*> JC = JC + J JC = JC + N - J + 1
*> 2 CONTINUE 2 CONTINUE
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
*
* COMPLEX*16 AP( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPTRS solves a triangular system of the form
*>
*> where A is a triangular matrix of order N stored in packed format,
*> and B is an N-by-NRHS matrix. A check is made to verify that A is
*> nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the
*> solutions X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
*
* .. Array Arguments ..
* COMPLEX*16 AP( 0: * ), ARF( 0: * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPTTF copies a triangular matrix A from standard packed format (TP)
*> to rectangular full packed format (TF).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPTTR( UPLO, N, AP, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPTTR copies a triangular matrix A from standard packed format (TP)
*> to standard full format (TR).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
* RWORK, INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRCON estimates the reciprocal of the condition number of a
*> triangular matrix A, in either the 1-norm or the infinity-norm.
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NORM
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, MM, M, WORK, RWORK, INFO )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTREVC computes some or all of the right and/or left eigenvectors of
*> a complex upper triangular matrix T.
*> input matrix. If Q is the unitary factor that reduces a matrix A to
*> Schur form T, then Q*X and Q*Y are the matrices of right and left
*> eigenvectors of A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The algorithm used in this program is basically backward (forward)
*> Each eigenvector is normalized so that the element of largest
*> magnitude has magnitude 1; here the magnitude of a complex number
*> (x,y) is taken to be |x| + |y|.
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
* COMPLEX*16 Q( LDQ, * ), T( LDT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTREXC reorders the Schur factorization of a complex matrix
*> A = Q*T*Q**H, so that the diagonal element of T with row index IFST
*> The Schur form T is reordered by a unitary similarity transformation
*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
*> postmultplying it with Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, FERR, BERR, WORK, RWORK, INFO )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRRFS provides error bounds and backward error estimates for the
*> solution to a system of linear equations with a triangular
*> The solution matrix X must be computed by ZTRTRS or some other
*> means before entering this routine. ZTRRFS does not do iterative
*> refinement because doing so cannot improve the backward error.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, W, M, S,
* SEP, WORK, LWORK, INFO )
* COMPLEX*16 Q( LDQ, * ), T( LDT, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRSEN reorders the Schur factorization of a complex matrix
*> A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in
*>
*> Optionally the routine computes the reciprocal condition numbers of
*> the cluster of eigenvalues and/or the invariant subspace.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> ZTRSEN first collects the selected eigenvalues by computing a unitary
*> error in the computed right invariant subspace is
*>
*> EPS * norm(T) / SEP
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
* LDVR, S, SEP, MM, M, WORK, LDWORK, RWORK,
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRSNA estimates reciprocal condition numbers for specified
*> eigenvalues and/or right eigenvectors of a complex upper triangular
*> matrix T (or of any matrix Q*T*Q**H with Q unitary).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The reciprocal of the condition number of an eigenvalue lambda is
*> is given by
*>
*> EPS * norm(T) / SEP(i)
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
* LDC, SCALE, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRSYL solves the complex Sylvester matrix equation:
*>
*> M-by-M and B is N-by-N; the right hand side C and the solution X are
*> M-by-N; and scale is an output scale factor, set <= 1 to avoid
*> overflow in X.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANA
*> \verbatim
*> values were used to solve the equation (but the matrices
*> A and B are unchanged).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRTI2 computes the inverse of a complex upper or lower triangular
*> matrix.
*>
*> This is the Level 2 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRTRI computes the inverse of a complex upper or lower triangular
*> matrix A.
*>
*> This is the Level 3 BLAS version of the algorithm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
* INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRTRS solves a triangular system of the form
*>
*>
*> where A is a triangular matrix of order N, and B is an N-by-NRHS
*> matrix. A check is made to verify that A is nonsingular.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> indicating that the matrix is singular and the solutions
*> X have not been computed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
* COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRTTF copies a triangular matrix A from standard full format (TR)
*> to rectangular full packed format (TF) .
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> We first consider Standard Packed Format when N is even.
*> 03 13 23 33 11 33 11 21 31 41 51
*> -- -- -- -- -- -- -- -- --
*> 04 14 24 34 44 43 44 22 32 42 52
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRTTP( UPLO, N, A, LDA, AP, INFO )
*
* COMPLEX*16 A( LDA, * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRTTP copies a triangular matrix A from full format (TR) to standard
*> packed format (TP).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine ZTZRZF.
*>
*>
*> where Z is an N-by-N unitary matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
*> to upper triangular form by means of unitary transformations.
*>
*> where Z is an N-by-N unitary matrix and R is an M-by-M upper
*> triangular matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
*>
*> The factorization is obtained by Householder's method. The kth
*> transformation matrix, Z( k ), which is used to introduce zeros into
*> Z is given by
*>
*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*>
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
* $ X21( LDX21, * ), X22( LDX22, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
*> partitioned unitary matrix X:
*>
*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
*> implicitly by angles THETA, PHI.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The bidiagonal blocks B11, B12, B21, and B22 are represented
*> P1, P2, Q1, and Q2 are represented as products of elementary
*> reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
*> using ZUNGQR and ZUNGLQ.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*>
-*> \endverbatim
-*>
* =====================================================================
SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
* SIGNS, M, P, Q, X11, LDX11, X12,
* $ * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNCSD computes the CS decomposition of an M-by-M partitioned
*> unitary matrix X:
*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
*> which R = MIN(P,M-P,Q,M-Q).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: ZBBCSD did not converge. See the description of RWORK
*> above for details.
-*>
-*> Reference
-*> =========
+*> \endverbatim
+*
+*> \par References:
+* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
-*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
*> which is defined as the last n columns of a product of k elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by ZGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
*> which is defined as the first n columns of a product of k elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by ZGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGBR generates one of the complex unitary matrices Q or P**H
*> determined by ZGEBRD when reducing a complex matrix A to bidiagonal
*> rows of P**H, where n >= m >= k;
*> if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
*> an N-by-N matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGHR generates a complex unitary matrix Q which is defined as the
*> product of IHI-ILO elementary reflectors of order N, as returned by
*> ZGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
*> which is defined as the first m rows of a product of k elementary
*> Q = H(k)**H . . . H(2)**H H(1)**H
*>
*> as returned by ZGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
*> which is defined as the first M rows of a product of K elementary
*> Q = H(k)**H . . . H(2)**H H(1)**H
*>
*> as returned by ZGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit;
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
*> which is defined as the last N columns of a product of K elementary
*> Q = H(k) . . . H(2) H(1)
*>
*> as returned by ZGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
*> which is defined as the first N columns of a product of K elementary
*> Q = H(1) H(2) . . . H(k)
*>
*> as returned by ZGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
*> which is defined as the last m rows of a product of k elementary
*> Q = H(1)**H H(2)**H . . . H(k)**H
*>
*> as returned by ZGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,
*> which is defined as the last M rows of a product of K elementary
*> Q = H(1)**H H(2)**H . . . H(k)**H
*>
*> as returned by ZGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNGTR generates a complex unitary matrix Q which is defined as the
*> product of n-1 elementary reflectors of order N, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNM2L overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNM2R overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by ZGEQRF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
*> with
*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
*> if k < nq, P = G(1) G(2) . . . G(k);
*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] VECT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
* LDC, WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMHR overwrites the general complex M-by-N matrix C with
*>
*> IHI-ILO elementary reflectors, as returned by ZGEHRD:
*>
*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNML2 overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMLQ overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMQL overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMQR overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMR2 overwrites the general complex m-by-n matrix C with
*>
*>
*> as returned by ZGERQF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMR3 overwrites the general complex m by n matrix C with
*>
*>
*> as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMRQ overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by ZGERQF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMRZ overwrites the general complex M-by-N matrix C with
*>
*>
*> as returned by ZTZRZF. Q is of order M if SIDE = 'L' and of order N
*> if SIDE = 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16OTHERcomputational
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
-*> \verbatim
+*> \par Contributors:
+* ==================
*>
-*> Based on contributions by
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
*>
+*> \verbatim
*> \endverbatim
*>
* =====================================================================
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,
* WORK, LWORK, INFO )
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNMTR overwrites the general complex M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
* COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUPGTR generates a complex unitary matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> [TXT]</a>
*> \endhtmlonly
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
* INFO )
* COMPLEX*16 AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUPMTR overwrites the general complex M-by-N matrix C with
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALAHDG( IOUNIT, PATH )
*
* INTEGER IOUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALAHDG prints header information for the different test paths.
+*> \verbatim
*>
-*>\endverbatim
+*> ALAHDG prints header information for the different test paths.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IOUNIT
*> \verbatim
*> GSV: Generalized Singular Value Decomposition
*> CSD: CS Decomposition
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ALAREQ handles input for the LAPACK test program. It is called
*> to evaluate the input line which requested NMATS matrix types for
*> Read the next input line for NMATS matrix types
*> Set DOTYPE(I) = .TRUE. for each valid type I
*> endif
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output. NOUT >= 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALARQG( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ALARQG handles input for the LAPACK test program. It is called
*> to evaluate the input line which requested NMATS matrix types for
*> Read the next input line for NMATS matrix types
*> Set DOTYPE(I) = .TRUE. for each valid type I
*> endif
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output. NOUT >= 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALASMG( TYPE, NOUT, NFAIL, NRUN, NERRS )
*
* INTEGER NFAIL, NOUT, NRUN, NERRS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALASMG prints a summary of results from one of the -CHK- routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ALASMG prints a summary of results from one of the -CHK- routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> NERRS is INTEGER
*> The number of error messages recorded.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALASUM( TYPE, NOUT, NFAIL, NRUN, NERRS )
*
* INTEGER NFAIL, NOUT, NRUN, NERRS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALASUM prints a summary of results from one of the -CHK- routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ALASUM prints a summary of results from one of the -CHK- routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> NERRS is INTEGER
*> The number of error messages recorded.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALASVM( TYPE, NOUT, NFAIL, NRUN, NERRS )
*
* INTEGER NFAIL, NOUT, NRUN, NERRS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALASVM prints a summary of results from one of the -DRV- routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ALASVM prints a summary of results from one of the -DRV- routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> NERRS is INTEGER
*> The number of error messages recorded.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
* RWORK, RESID )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CBDT01 reconstructs a general matrix A from its bidiagonal form
*> A = Q * B * P'
*> The test ratio to test the reduction is
*> RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
*> where PT = P' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK,
* RESID )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CBDT02 tests the change of basis C = U' * B by computing the residual
*>
*>
*> where B and C are M by N matrices, U is an M by M orthogonal matrix,
*> and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CBDT03( UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK,
* RESID )
* COMPLEX U( LDU, * ), VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CBDT03 reconstructs a bidiagonal matrix B from its SVD:
*> S = U' * B * V
*> The test ratio to test the singular value decomposition is
*> RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS )
*> where VT = V' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
* NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKBB tests the reduction of a general complex rectangular band
*> matrix to real bidiagonal form.
*> (13) Rectangular matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
* ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
* $ X( LDX, * ), Y( LDX, * ), Z( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKBD checks the singular value decomposition (SVD) routines.
*>
*>
*> A subset of the full set of matrix types may be selected through
*> the logical array DOTYPE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKBK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKBK tests CGEBAK, a routine for backward transformation of
*> the computed right or left eigenvectors if the orginal matrix
*> was preprocessed by balance subroutine CGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKBL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKBL tests CGEBAL, a routine for balancing a general complex
*> matrix and isolating some of its eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKEC( THRESH, TSTERR, NIN, NOUT )
*
* REAL THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKEC tests eigen- condition estimation routines
*> CTRSYL, CTREXC, CTRSNA, CTRSEN
*> results to a threshold THRESH. In addition, CTRSNA and CTRSEN are
*> tested by reading in precomputed examples from a file (on input unit
*> NIN). Output is written to output unit NOUT.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM CCHKEE
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKEE tests the COMPLEX LAPACK subroutines for the matrix
*> eigenvalue problem. The test paths in this version are
*> precomputed examples, and LWORK = NMAX*(5*NMAX+20) in the parameter
*> statements below. For SVD, we assume NRHS may be as big as N. The
*> parameter NEED is set to 14 to allow for 14 N-by-N matrices for CGG.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_eig
*
-* =====================================================================
- PROGRAM CCHKEE
+* ===================================================================== PROGRAM CCHKEE
*
* -- LAPACK test routine (version 3.1.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
* $ WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKGG checks the nonsymmetric generalized eigenvalue problem
*> routines.
*>
*> (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKGK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKGK tests CGGBAK, a routine for backward balancing of
*> a matrix pair (A, B).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKGL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKGL tests CGGBAL, a routine for balancing a matrix pair (A, B).
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKGL tests CGGBAL, a routine for balancing a matrix pair (A, B).
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKHB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED,
* THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK,
* COMPLEX A( LDA, * ), U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKHB tests the reduction of a Hermitian band matrix to tridiagonal
*> from, used with the Hermitian eigenvalue problem.
*> (13) Hermitian matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
* $ WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKHS checks the nonsymmetric eigenvalue problem routines.
*>
*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1
*> (20) Same as (19), but multiplied by SQRT( overflow threshold )
*> (21) Same as (19), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES - INTEGER
*> KCONDS(j) Selects whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, AP, SD, SE, D1, D2, D3, D4, D5,
* $ V( LDU, * ), VP( * ), WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKST checks the Hermitian eigenvalue problem routines.
*>
*> (20) Same as (16), but multiplied by SQRT( underflow threshold )
*> (21) A diagonally dominant tridiagonal matrix with geometrically
*> spaced diagonal entries 1, ..., ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
* MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
* $ WORK( * ), X( * ), XF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCKCSD tests CUNCSD:
*> the CSD for an M-by-M unitary matrix X partitioned as
*> [ X11 X12; X21 X22 ]. X11 is P-by-Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If CLAROR returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCKGLM( NN, NVAL, MVAL, PVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCKGLM tests CGGGLM - subroutine for solving generalized linear
*> model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If CLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCKGQR( NM, MVAL, NP, PVAL, NN, NVAL, NMATS, ISEED,
* THRESH, NMAX, A, AF, AQ, AR, TAUA, B, BF, BZ,
* $ TAUB( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCKGQR tests
*> CGGQRF: GQR factorization for N-by-M matrix A and N-by-P matrix B,
*> CGGRQF: GRQ factorization for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If CLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCKGSV( NM, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, U, V, Q, ALPHA, BETA, R,
* $ R( * ), U( * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCKGSV tests CGGSVD:
*> the GSVD for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If CLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCKLSE( NN, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCKLSE tests CGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If CLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
* LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
* $ XF( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCSDTS tests CUNCSD, which, given an M-by-M partitioned unitary
*> matrix X,
*> [ 0 0 0 | I 0 0 ] [ D21 D22 ]
*> [ 0 S 0 | 0 C 0 ]
*> [ 0 0 I | 0 0 0 ]
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = ULPINV otherwise.
*> ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem driver CGGES.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRGEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRGEV checks the nonsymmetric generalized eigenvalue problem driver
*> routine CGGEV.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B,
* AI, BI, Z, Q, ALPHA, BETA, C, LDC, S, WORK,
* $ Z( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem expert driver CGGESX.
*> and DIF_l when testing the built-in test problems.
*>
*> Built-in Test Matrices
-*> ======================
+* ======================
*>
*> All built-in test matrices are the 2 by 2 block of triangular
*> matrices
*> | 1-d |
*> and matrix B are chosen as identity matrices (see SLATM5).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRGVX( NSIZE, THRESH, NIN, NOUT, A, LDA, B, AI, BI,
* ALPHA, BETA, VL, VR, ILO, IHI, LSCALE, RSCALE,
* $ VL( LDA, * ), VR( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRGVX checks the nonsymmetric generalized eigenvalue problem
*> expert driver CGGEVX.
*>
*> a, b, x and y will have all values independently of each other from
*> { sqrt(sqrt(ULP)), 0.1, 1, 10, 1/sqrt(sqrt(ULP)) }.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
* $ VTSAV( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVBD checks the singular value decomposition (SVD) driver CGESVD
*> and CGESDD.
*> on the diagonal.
*> (4) Same as (3), but multiplied by the underflow-threshold / ULP.
*> (5) Same as (3), but multiplied by the overflow-threshold * ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> If CLATMS, or CGESVD returns an error code, the
*> absolute value of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, HT, W, WT, VS, LDVS, RESULT,
* $ VS( LDVS, * ), W( * ), WORK( * ), WT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVES checks the nonsymmetric eigenvalue (Schur form) problem
*> driver CGEES.
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Select whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR, LDVR,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVEV checks the nonsymmetric eigenvalue problem driver CGEEV.
*>
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
* ..
* .. Array Arguments ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVGG checks the nonsymmetric generalized eigenvalue driver
*> routines.
*>
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVSG checks the complex Hermitian generalized eigenproblem
*> drivers.
*> (19) Same as (8), but with KA = 3 and KB = 1
*> (20) Same as (8), but with KA = 3 and KB = 2
*> (21) Same as (8), but with KA = 3 and KB = 3
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
* $ V( LDU, * ), WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVST checks the Hermitian eigenvalue problem drivers.
*>
*> with random signs.
*> (17) Same as (16), but multiplied by SQRT( overflow threshold )
*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS,
* $ WORK( * ), WT( * ), WTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver CGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVVX checks the nonsymmetric eigenvalue problem expert driver
*> CGEEVX.
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRBD( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CERRBD tests the error exits for CGEBRD, CUNGBR, CUNMBR, and CBDSQR.
+*> \verbatim
*>
-*>\endverbatim
+*> CERRBD tests the error exits for CGEBRD, CUNGBR, CUNMBR, and CBDSQR.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERREC( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERREC tests the error exits for the routines for eigen- condition
*> estimation for REAL matrices:
*> CTRSYL, CTREXC, CTRSNA and CTRSEN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRED( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRED tests the error exits for the eigenvalue driver routines for
*> REAL matrices:
*> CBD CGESVD compute SVD of an M-by-N matrix A
*> CGESDD compute SVD of an M-by-N matrix A(by divide and
*> conquer)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRGG( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRGG tests the error exits for CGGES, CGGESX, CGGEV, CGGEVX,
*> CGGGLM, CGGHRD, CGGLSE, CGGQRF, CGGRQF, CGGSVD, CGGSVP, CHGEQZ,
*> CTGEVC, CTGEXC, CTGSEN, CTGSJA, CTGSNA, CTGSYL and CUNCSD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRHS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRHS tests the error exits for CGEBAK, CGEBAL, CGEHRD, CUNGHR,
*> CUNMHR, CHSEQR, CHSEIN, and CTREVC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRST( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRST tests the error exits for CHETRD, CUNGTR, CUNMTR, CHPTRD,
*> CUNGTR, CUPMTR, CSTEQR, CSTEIN, CPTEQR, CHBTRD,
*> CHEEV, CHEEVX, CHEEVD, CHBEV, CHBEVX, CHBEVD,
*> CHPEV, CHPEVX, CHPEVD, and CSTEDC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET10( M, N, A, LDA, B, LDB, WORK, RWORK, RESULT )
*
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET10 compares two matrices A and B and computes the ratio
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT is REAL
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
* WORK, RWORK, RESULT )
* COMPLEX A( LDA, * ), E( LDE, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET22 does an eigenvector check.
*>
*> where E(j) is the j-th eigenvector, and m-norm is the max-norm of a
*> vector. The max-norm of a complex n-vector x in this case is the
*> maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
*> \endverbatim
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
* NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX.
*> If COMP = .FALSE., the first 8 of the following tests will be
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, CGEEVX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
* H, HT, W, WT, WTMP, VS, LDVS, VS1, RCDEIN,
* $ WORK( * ), WT( * ), WTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET24 checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver CGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, CGEESX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET35( RMAX, LMAX, NINFO, KNT, NIN )
*
* REAL RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET35 tests CTRSYL, a routine for solving the Sylvester matrix
*> equation
*>
*> norm(op(A)*X + ISGN*X*op(B) - scale*C) /
*> (EPS*max(norm(A),norm(B))*norm(X))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* REAL RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET36 tests CTREXC, a routine for reordering diagonal entries of a
*> matrix in complex Schur form. Thus, CLAEXC computes a unitary matrix
*> ILST.
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* REAL RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET37 tests CTRSNA, a routine for estimating condition numbers of
*> eigenvalues and/or right eigenvectors of a matrix.
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET38( RMAX, LMAX, NINFO, KNT, NIN )
*
* REAL RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET38 tests CTRSEN, a routine for estimating condition numbers of a
*> cluster of eigenvalues and/or its associated right invariant subspace
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
* RWORK, RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET51 generally checks a decomposition of the form
*>
*> If ITYPE=3, then:
*>
*> RESULT = | I - UU* | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> value is currently limited to 1/ulp, to avoid overflow.
*> Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET52( LEFT, N, A, LDA, B, LDB, E, LDE, ALPHA, BETA,
* WORK, RWORK, RESULT )
* $ BETA( * ), E( LDE, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET52 does an eigenvector check for the generalized eigenvalue
*> problem.
*>
*> RESULT(2) = max | M(v(i)) - 1 | / ( n ulp )
*> eigenvectors v(i)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LEFT
*> \verbatim
*> B E is likely to overflow, then RESULT(1:2) is set to
*> 10 / ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
* LDV, WORK, RESULT )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET54 checks a generalized decomposition of the form
*>
*> Specifically,
*>
*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The value RESULT, It is currently limited to 1/ulp, to
*> avoid overflow. Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF,
* X, U, WORK, LWORK, RWORK, RESULT )
* $ BF( LDB, * ), D( * ), DF( * ), U( * ),
* $ WORK( LWORK ), X( * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGLMTS tests CGGGLM - a subroutine for solving the generalized
*> linear model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT = -----------------------------------------
*> (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ TAUA( * ), TAUB( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGQRTS tests CGGQRF, which computes the GQR factorization of an
*> N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ TAUA( * ), TAUB( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGRQTS tests CGGRQF, which computes the GRQ factorization of an
*> M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGSVTS( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
* LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
* $ U( LDU, * ), V( LDV, * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGSVTS tests CGGSVD, which computes the GSVD of an M-by-N matrix A
*> and a P-by-N matrix B:
*> U'*A*Q = D1*R and V'*B*Q = D2*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(6) = 0 if ALPHA is in decreasing order;
*> = ULPINV otherwise.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHBT21( UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK,
* RWORK, RESULT )
* COMPLEX A( LDA, * ), U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHBT21 generally checks a decomposition of the form
*>
*> Specifically:
*>
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
* LDV, TAU, WORK, RWORK, RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHET21 generally checks a decomposition of the form
*>
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each
*> vector v(j) has its first j elements 0 and the remaining n-j elements
*> stored in V(j+1:n,j).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
* V, LDV, TAU, WORK, RWORK, RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHET22 generally checks a decomposition of the form
*>
*> Specifically, if ITYPE=1, then:
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC> RESULT(2) = | I - U'U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> ITYPE INTEGER
*> if LDU is at least N.
*> Modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
*
* CHARACTER*(*) SRNAMT
* INTEGER INFOT, NOUT
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*>\endverbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
* TAU, WORK, RWORK, RESULT )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPT21 generally checks a decomposition of the form
*>
*> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
*> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
*> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
* LWORK, RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHST01 tests the reduction of a general matrix A to upper Hessenberg
*> form: A = Q*H*Q'. Two test ratios are computed;
*>
*> In this version, ILO and IHI are not used, but they could be used
*> to save some work if this is desired.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARFY applies an elementary reflector, or Householder matrix, H,
*> to an n x n Hermitian matrix C, from both the left and the right.
*> where tau is a scalar and v is a vector.
*>
*> If tau is zero, then H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
*> transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATM4( ITYPE, N, NZ1, NZ2, RSIGN, AMAGN, RCOND,
* TRIANG, IDIST, ISEED, A, LDA )
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATM4 generates basic square matrices, which may later be
*> multiplied by others in order to produce test matrices. It is
*> according to the value of ITYPE, NZ1, NZ2, RSIGN, AMAGN, and RCOND.
*> It then fills in the upper triangle with random numbers, if TRIANG is
*> non-zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A. Must be at least 1 and at least N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION CLCTES( Z, D )
*
* COMPLEX D, Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLCTES returns .TRUE. if the eigenvalue Z/D is to be selected
*> (specifically, in this subroutine, if the real part of the
*>
*> It is used by the test routine CDRGES to test whether the driver
*> routine CGGES succesfully sorts eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] Z
*> \verbatim
*> D is COMPLEX
*> The denominator part of a complex eigenvalue Z/D.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION CLCTSX( ALPHA, BETA )
*
* COMPLEX ALPHA, BETA
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This function is used to determine what eigenvalues will be
*> selected. If this is part of the test driver CDRGSX, do not
*> change the code UNLESS you are testing input examples and not
*> using the built-in examples.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ALPHA
*> \verbatim
*> parameters to decide whether the pair (ALPHA, BETA) is
*> selected.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLSETS( M, P, N, A, AF, LDA, B, BF, LDB, C, CF,
* D, DF, X, WORK, LWORK, RWORK, RESULT )
* $ BF( LDB, * ), C( * ), D( * ), CF( * ),
* $ DF( * ), WORK( LWORK ), X( * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLSETS tests CGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( A*x - c )/ norm(A)*norm(X)*EPS
*> RESULT(2) = norm( B*x - d )/ norm(B)*norm(X)*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* COMPLEX A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
* WORK, RWORK, RESULT )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSGT01 checks a decomposition of the form
*>
*> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
*>
*> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT is REAL array, dimension (1)
*> The test ratio as described above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION CSLECT( Z )
*
* COMPLEX Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSLECT returns .TRUE. if the eigenvalue Z is to be selected,
*> otherwise it returns .FALSE.
*> zero, and .FALSE. otherwise.
*> If SELOPT is at least 1, CSLECT returns SELVAL(SELOPT) and adds 1
*> to SELOPT, cycling back to 1 at SELMAX.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] Z
*> \verbatim
*> Z is COMPLEX
*> The eigenvalue Z.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
* RESULT )
* COMPLEX U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTT21 checks a decomposition of the form
*>
*> RESULT(1) = | A - U S U* | / ( |A| n ulp )
*>
*> RESULT(2) = | I - UU* | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> values are currently limited to 1/ulp, to avoid overflow.
*> RESULT(1) is always modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* LDWORK, RWORK, RESULT )
* COMPLEX U( LDU, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSTT22 checks a set of M eigenvalues and eigenvectors,
*>
*> RESULT(1) = | U* A U - S | / ( |A| m ulp )
*>
*> RESULT(2) = | I - U*U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK,
* RESID )
* COMPLEX U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNT01 checks that the matrix U is unitary by computing the ratio
*>
*> where EPS is the machine precision. ROWCOL is used only if m = n;
*> if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
*> assumed to be 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ROWCOL
*> \verbatim
*> RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
*> RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CUNT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
* RWORK, RESULT, INFO )
* COMPLEX U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CUNT03 compares two unitary matrices U and V to see if their
*> corresponding rows or columns span the same spaces. The rows are
*>
*> where abs(S) = 1 (chosen to minimize the expression), U(i) is the
*> i-th row (column) of U, and V(i) is the i-th row (column) of V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RC
*> \verbatim
*> 0 indicates a successful exit
*> -k indicates the k-th parameter had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
* RESID )
* $ Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DBDT01 reconstructs a general matrix A from its bidiagonal form
*> A = Q * B * P'
*> The test ratio to test the reduction is
*> RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
*> where PT = P' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
*
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DBDT02 tests the change of basis C = U' * B by computing the residual
*>
*>
*> where B and C are M by N matrices, U is an M by M orthogonal matrix,
*> and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DBDT03( UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK,
* RESID )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DBDT03 reconstructs a bidiagonal matrix B from its SVD:
*> S = U' * B * V
*> The test ratio to test the singular value decomposition is
*> RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS )
*> where VT = V' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
* NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
* $ Q( LDQ, * ), RESULT( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKBB tests the reduction of a general real rectangular band
*> matrix to bidiagonal form.
*> (13) Rectangular matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
* ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
* $ Y( LDX, * ), Z( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKBD checks the singular value decomposition (SVD) routines.
*>
*>
*> A subset of the full set of matrix types may be selected through
*> the logical array DOTYPE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKBK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKBK tests DGEBAK, a routine for backward transformation of
*> the computed right or left eigenvectors if the orginal matrix
*> was preprocessed by balance subroutine DGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKBL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKBL tests DGEBAL, a routine for balancing a general real
*> matrix and isolating some of its eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKEC( THRESH, TSTERR, NIN, NOUT )
*
* DOUBLE PRECISION THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKEC tests eigen- condition estimation routines
*> DLALN2, DLASY2, DLANV2, DLAQTR, DLAEXC,
*> results to a threshold THRESH. In addition, DTREXC, DTRSNA and DTRSEN
*> are tested by reading in precomputed examples from a file (on input
*> unit NIN). Output is written to output unit NOUT.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DCHKEE
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKEE tests the DOUBLE PRECISION LAPACK subroutines for the matrix
*> eigenvalue problem. The test paths in this version are
*> precomputed examples, and LWORK = NMAX*(5*NMAX+5)+1 in the parameter
*> statements below. For SVD, we assume NRHS may be as big as N. The
*> parameter NEED is set to 14 to allow for 14 N-by-N matrices for DGG.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_eig
*
-* =====================================================================
- PROGRAM DCHKEE
+* ===================================================================== PROGRAM DCHKEE
*
* -- LAPACK test routine (version 3.3.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
* $ Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKGG checks the nonsymmetric generalized eigenvalue problem
*> routines.
*>
*> (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKGK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKGK tests DGGBAK, a routine for backward balancing of
*> a matrix pair (A, B).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKGL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKGL tests DGGBAL, a routine for balancing a matrix pair (A, B).
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKGL tests DGGBAL, a routine for balancing a matrix pair (A, B).
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1,
* $ WR3( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKHS checks the nonsymmetric eigenvalue problem routines.
*>
*> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
*> (20) Same as (19), but multiplied by SQRT( overflow threshold )
*> (21) Same as (19), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES - INTEGER
*> KCONDS(j) Selects whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKSB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED,
* THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK,
* $ U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKSB tests the reduction of a symmetric band matrix to tridiagonal
*> form, used with the symmetric eigenvalue problem.
*> (13) Symmetric matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, AP, SD, SE, D1, D2, D3, D4, D5,
* $ WA3( * ), WORK( * ), WR( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKST checks the symmetric eigenvalue problem routines.
*>
*> (20) Same as (16), but multiplied by SQRT( underflow threshold )
*> (21) A diagonally dominant tridiagonal matrix with geometrically
*> spaced diagonal entries 1, ..., ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
* MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
* $ WORK( * ), X( * ), XF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCKCSD tests DORCSD:
*> the CSD for an M-by-M orthogonal matrix X partitioned as
*> [ X11 X12; X21 X22 ]. X11 is P-by-Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If DLAROR returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCKGLM( NN, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCKGLM tests DGGGLM - subroutine for solving generalized linear
*> model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If DLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCKGQR( NM, MVAL, NP, PVAL, NN, NVAL, NMATS, ISEED,
* THRESH, NMAX, A, AF, AQ, AR, TAUA, B, BF, BZ,
* $ RWORK( * ), TAUA( * ), TAUB( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCKGQR tests
*> DGGQRF: GQR factorization for N-by-M matrix A and N-by-P matrix B,
*> DGGRQF: GRQ factorization for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If DLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCKGSV( NM, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, U, V, Q, ALPHA, BETA, R,
* $ V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCKGSV tests DGGSVD:
*> the GSVD for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If DLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCKLSE( NN, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCKLSE tests DGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If DLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
* LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
* $ XF( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCSDTS tests DORCSD, which, given an M-by-M partitioned orthogonal
*> matrix X,
*> [ 0 0 0 | I 0 0 ] [ D21 D22 ]
*> [ 0 S 0 | 0 C 0 ]
*> [ 0 0 I | 0 0 0 ]
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = ULPINV otherwise.
*> ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR,
* $ WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem driver DGGES.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRGEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRGEV checks the nonsymmetric generalized eigenvalue problem driver
*> routine DGGEV.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B, AI,
* BI, Z, Q, ALPHAR, ALPHAI, BETA, C, LDC, S,
* $ WORK( * ), Z( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem expert driver DGGESX.
*> and DIF_l when testing the built-in test problems.
*>
*> Built-in Test Matrices
-*> ======================
+* ======================
*>
*> All built-in test matrices are the 2 by 2 block of triangular
*> matrices
*> | 1-d |
*> and matrix B are chosen as identity matrices (see DLATM5).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRGVX( NSIZE, THRESH, NIN, NOUT, A, LDA, B, AI, BI,
* ALPHAR, ALPHAI, BETA, VL, VR, ILO, IHI, LSCALE,
* $ VL( LDA, * ), VR( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRGVX checks the nonsymmetric generalized eigenvalue problem
*> expert driver DGGEVX.
*>
*> a, b, x and y will have all values independently of each other from
*> { sqrt(sqrt(ULP)), 0.1, 1, 10, 1/sqrt(sqrt(ULP)) }.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
* $ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVBD checks the singular value decomposition (SVD) drivers
*> DGESVD, DGESDD, DGESVJ, and DGEJSV.
*> on the diagonal.
*> (4) Same as (3), but multiplied by the underflow-threshold / ULP.
*> (5) Same as (3), but multiplied by the overflow-threshold * ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> If DLATMS, or DGESVD returns an error code, the
*> absolute value of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
* $ WORK( * ), WR( * ), WRT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVES checks the nonsymmetric eigenvalue (Schur form) problem
*> driver DGEES.
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL,
* $ WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVEV checks the nonsymmetric eigenvalue problem driver DGEEV.
*>
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
* $ VR( LDQ, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVGG checks the nonsymmetric generalized eigenvalue driver
*> routines.
*>
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
* $ RESULT( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVSG checks the real symmetric generalized eigenproblem
*> drivers.
*> (19) Same as (8), but with KA = 3 and KB = 1
*> (20) Same as (8), but with KA = 3 and KB = 2
*> (21) Same as (8), but with KA = 3 and KB = 3
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, D1, D2, D3, D4, EVEIGS, WA1,
* $ WA3( * ), WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVST checks the symmetric eigenvalue problem drivers.
*>
*> with random signs.
*> (17) Same as (16), but multiplied by SQRT( overflow threshold )
*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> 95= | I - U U' | / ( n ulp ) DSBEVR('L','V','V', ... )
*> 96= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVR('L','N','V', ... )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT,
* $ WR( * ), WRT( * ), WRTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver DGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
* $ WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVVX checks the nonsymmetric eigenvalue problem expert driver
*> DGEEVX.
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRBD( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRBD tests the error exits for DGEBRD, DORGBR, DORMBR, DBDSQR and
*> DBDSDC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERREC( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERREC tests the error exits for the routines for eigen- condition
*> estimation for DOUBLE PRECISION matrices:
*> DTRSYL, STREXC, STRSNA and STRSEN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRED( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRED tests the error exits for the eigenvalue driver routines for
*> DOUBLE PRECISION matrices:
*> DGESDD compute SVD of an M-by-N matrix A (by divide and
*> conquer)
*> DGEJSV compute SVD of an M-by-N matrix A where M >= N
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRGG( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRGG tests the error exits for DGGES, DGGESX, DGGEV, DGGEVX,
*> DGGGLM, DGGHRD, DGGLSE, DGGQRF, DGGRQF, DGGSVD, DGGSVP, DHGEQZ,
*> DORCSD, DTGEVC, DTGEXC, DTGSEN, DTGSJA, DTGSNA, and DTGSYL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRHS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRHS tests the error exits for DGEBAK, SGEBAL, SGEHRD, DORGHR,
*> DORMHR, DHSEQR, SHSEIN, and DTREVC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRST( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRST tests the error exits for DSYTRD, DORGTR, DORMTR, DSPTRD,
*> DOPGTR, DOPMTR, DSTEQR, SSTERF, SSTEBZ, SSTEIN, DPTEQR, DSBTRD,
*> DSYEV, SSYEVX, SSYEVD, DSBEV, SSBEVX, SSBEVD,
*> DSPEV, SSPEVX, SSPEVD, DSTEV, SSTEVX, SSTEVD, and SSTEDC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET10( M, N, A, LDA, B, LDB, WORK, RESULT )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET10 compares two matrices A and B and computes the ratio
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT is DOUBLE PRECISION
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, WR,
* WI, WORK, RESULT )
* $ WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET22 does an eigenvector check.
*>
*> To handle various schemes for storage of left eigenvectors, there are
*> options to use A-transpose instead of A, E-transpose instead of E,
*> and/or W-transpose instead of W.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> RESULT(1) = | A E - E W | / ( |A| |E| ulp )
*> RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N,
* A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR,
* $ WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX.
*> If COMP = .FALSE., the first 8 of the following tests will be
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, DGEEVX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
* H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS,
* $ WR( * ), WRT( * ), WRTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET24 checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver DGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, DGEESX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET31( RMAX, LMAX, NINFO, KNT )
*
* INTEGER NINFO( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET31 tests DLALN2, a routine for solving
*>
*> should be on the order of 1. Here, ulp is the machine precision.
*> Also, it is verified that SCALE is less than or equal to 1, and that
*> XNORM = infinity-norm(X).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET32( RMAX, LMAX, NINFO, KNT )
*
* DOUBLE PRECISION RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET32 tests DLASY2, a routine for solving
*>
*> should be on the order of 1. Here, ulp is the machine precision.
*> Also, it is verified that SCALE is less than or equal to 1, and
*> that XNORM = infinity-norm(X).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET33( RMAX, LMAX, NINFO, KNT )
*
* DOUBLE PRECISION RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET33 tests DLANV2, a routine for putting 2 by 2 blocks into
*> standard form. In other words, it computes a two by two rotation
*> 1) T21=0 (real eigenvalues), or
*> 2) T11=T22 and T21*T12<0 (complex conjugate eigenvalues).
*> We also verify that the residual is small.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET34( RMAX, LMAX, NINFO, KNT )
*
* INTEGER NINFO( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET34 tests DLAEXC, a routine for swapping adjacent blocks (either
*> 1 by 1 or 2 by 2) on the diagonal of a matrix in real Schur form.
*>
*> The test code verifies these last last assertions, as well as that
*> the residual in the above equation is small.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET35( RMAX, LMAX, NINFO, KNT )
*
* DOUBLE PRECISION RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET35 tests DTRSYL, a routine for solving the Sylvester matrix
*> equation
*>
*> norm(op(A)*X + ISGN*X*op(B) - scale*C) /
*> (EPS*max(norm(A),norm(B))*norm(X))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* INTEGER NINFO( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET36 tests DTREXC, a routine for moving blocks (either 1 by 1 or
*> 2 by 2) on the diagonal of a matrix in real Schur form. Thus, DLAEXC
*> ILST (within +-1).
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* DOUBLE PRECISION RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET37 tests DTRSNA, a routine for estimating condition numbers of
*> eigenvalues and/or right eigenvectors of a matrix.
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET38( RMAX, LMAX, NINFO, KNT, NIN )
*
* DOUBLE PRECISION RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET38 tests DTRSEN, a routine for estimating condition numbers of a
*> cluster of eigenvalues and/or its associated right invariant subspace
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET39( RMAX, LMAX, NINFO, KNT )
*
* DOUBLE PRECISION RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET39 tests DLAQTR, a routine for solving the real or
*> special complex quasi upper triangular system
*>
*> (The (||T||+||B||)*smlnum/ulp term accounts for possible
*> (gradual or nongradual) underflow in x1 and x2.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
* RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET51 generally checks a decomposition of the form
*>
*> If ITYPE=3, then:
*>
*> RESULT = | I - UU' | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> value is currently limited to 1/ulp, to avoid overflow.
*> Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET52( LEFT, N, A, LDA, B, LDB, E, LDE, ALPHAR,
* ALPHAI, BETA, WORK, RESULT )
* $ RESULT( 2 ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET52 does an eigenvector check for the generalized eigenvalue
*> problem.
*>
*> RESULT(2) = max | M(v(j)) - 1 | / ( n ulp )
*> eigenvectors v(j)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LEFT
*> \verbatim
*> B E is likely to overflow, then RESULT(1:2) is set to
*> 10 / ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET53( A, LDA, B, LDB, SCALE, WR, WI, RESULT, INFO )
*
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET53 checks the generalized eigenvalues computed by DLAG2.
*>
*>
*> If these tests are not passed, then s and w are scaled and
*> tested anyway, if this is possible.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> =3: same as INFO=2, but s and w could not be scaled so
*> as to compute the test.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
* LDV, WORK, RESULT )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET54 checks a generalized decomposition of the form
*>
*> Specifically,
*>
*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The value RESULT, It is currently limited to 1/ulp, to
*> avoid overflow. Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF, X, U,
* WORK, LWORK, RWORK, RESULT )
* ..
* .. Array Arguments ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGLMTS tests DGGGLM - a subroutine for solving the generalized
*> linear model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT = -----------------------------------------
*> (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ WORK( LWORK ), Z( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGQRTS tests DGGQRF, which computes the GQR factorization of an
*> N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ WORK( LWORK ), Z( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGRQTS tests DGGRQF, which computes the GRQ factorization of an
*> M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGSVTS( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
* LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGSVTS tests DGGSVD, which computes the GSVD of an M-by-N matrix A
*> and a P-by-N matrix B:
*> U'*A*Q = D1*R and V'*B*Q = D2*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(6) = 0 if ALPHA is in decreasing order;
*> = ULPINV otherwise.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
* LWORK, RESULT )
* $ RESULT( 2 ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DHST01 tests the reduction of a general matrix A to upper Hessenberg
*> form: A = Q*H*Q'. Two test ratios are computed;
*>
*> In this version, ILO and IHI are not used and are assumed to be 1 and
*> N, respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAFTS( TYPE, M, N, IMAT, NTESTS, RESULT, ISEED,
* THRESH, IOUNIT, IE )
* DOUBLE PRECISION RESULT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAFTS tests the result vector against the threshold value to
*> see which tests for this matrix type failed to pass the threshold.
*> Output is to the file given by unit IOUNIT.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> TYPE - CHARACTER*3
*> failed to pass the threshold so far.
*> Updated on exit if any of the ratios in RESULT also fail.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAHD2( IOUNIT, PATH )
*
* INTEGER IOUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DLAHD2 prints header information for the different test paths.
+*> \verbatim
*>
-*>\endverbatim
+*> DLAHD2 prints header information for the different test paths.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IOUNIT
*> \verbatim
*> These paths also are supplied in double precision (replace
*> leading S by D and leading C by Z in path names).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARFY applies an elementary reflector, or Householder matrix, H,
*> to an n x n symmetric matrix C, from both the left and the right.
*> where tau is a scalar and v is a vector.
*>
*> If tau is zero, then H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A or A' (transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLASUM( TYPE, IOUNIT, IE, NRUN )
*
* INTEGER IE, IOUNIT, NRUN
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DLASUM prints a summary of the results from one of the test routines.
+*> \verbatim
*>
-*>\endverbatim
+*> DLASUM prints a summary of the results from one of the test routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATB9( PATH, IMAT, M, P, N, TYPE, KLA, KUA, KLB, KUB,
* ANORM, BNORM, MODEA, MODEB, CNDNMA, CNDNMB,
* DOUBLE PRECISION ANORM, BNORM, CNDNMA, CNDNMB
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATB9 sets parameters for the matrix generator based on the type of
*> matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATM4( ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND,
* TRIANG, IDIST, ISEED, A, LDA )
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM4 generates basic square matrices, which may later be
*> multiplied by others in order to produce test matrices. It is
*> according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND.
*> It then fills in the upper triangle with random numbers, if TRIANG is
*> non-zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A. Must be at least 1 and at least N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION DLCTES( ZR, ZI, D )
*
* DOUBLE PRECISION D, ZI, ZR
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLCTES returns .TRUE. if the eigenvalue (ZR/D) + sqrt(-1)*(ZI/D)
*> is to be selected (specifically, in this subroutine, if the real
*>
*> It is used by the test routine DDRGES to test whether the driver
*> routine DGGES succesfully sorts eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ZR
*> \verbatim
*> The denominator part of a complex eigenvalue
*> (ZR/D) + i*(ZI/D).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION DLCTSX( AR, AI, BETA )
*
* DOUBLE PRECISION AI, AR, BETA
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This function is used to determine what eigenvalues will be
*> selected. If this is part of the test driver DDRGSX, do not
*> change the code UNLESS you are testing input examples and not
*> using the built-in examples.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] AR
*> \verbatim
*> The denominator part of a complex eigenvalue
*> (AR/BETA) + i*(AI/BETA).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLSETS( M, P, N, A, AF, LDA, B, BF, LDB, C, CF, D, DF,
* X, WORK, LWORK, RWORK, RESULT )
* ..
* .. Array Arguments ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLSETS tests DGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( A*x - c )/ norm(A)*norm(X)*EPS
*> RESULT(2) = norm( B*x - d )/ norm(B)*norm(X)*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RESID )
*
* DOUBLE PRECISION U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORT01 checks that the matrix U is orthogonal by computing the ratio
*>
*> where EPS is the machine precision. ROWCOL is used only if m = n;
*> if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
*> assumed to be 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ROWCOL
*> \verbatim
*> RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
*> RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
* RESULT, INFO )
* DOUBLE PRECISION U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DORT03 compares two orthogonal matrices U and V to see if their
*> corresponding rows or columns span the same spaces. The rows are
*>
*> where S is +-1 (chosen to minimize the expression), U(i) is the i-th
*> row (column) of U, and V(i) is the i-th row (column) of V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RC
*> \verbatim
*> 0 indicates a successful exit
*> -k indicates the k-th parameter had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSBT21( UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK,
* RESULT )
* $ U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSBT21 generally checks a decomposition of the form
*>
*> Specifically:
*>
*> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
* WORK, RESULT )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDGT01 checks a decomposition of the form
*>
*> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
*>
*> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (1)
*> The test ratio as described above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION DSLECT( ZR, ZI )
*
* DOUBLE PRECISION ZI, ZR
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSLECT returns .TRUE. if the eigenvalue ZR+sqrt(-1)*ZI is to be
*> selected, and otherwise it returns .FALSE.
*> and .FALSE. otherwise.
*> If SELOPT is at least 1, DSLECT returns SELVAL(SELOPT) and adds 1
*> to SELOPT, cycling back to 1 at SELMAX.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ZR
*> \verbatim
*> ZI is DOUBLE PRECISION
*> The imaginary part of a complex eigenvalue ZR + i*ZI.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
* TAU, WORK, RESULT )
* $ U( LDU, * ), VP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPT21 generally checks a decomposition of the form
*>
*> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
*> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
*> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTECH( N, A, B, EIG, TOL, WORK, INFO )
*
* DOUBLE PRECISION A( * ), B( * ), EIG( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Let T be the tridiagonal matrix with diagonal entries A(1) ,...,
*> A(N) and offdiagonal entries B(1) ,..., B(N-1)). DSTECH checks to
*> eigenvalue. If each interval contains the correct number of
*> eigenvalues, INFO = 0 is returned, otherwise INFO is the index of
*> the first eigenvalue in the first bad interval.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> >0 if the interval containing the INFO-th eigenvalue
*> contains the incorrect number of eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTECT( N, A, B, SHIFT, NUM )
*
* DOUBLE PRECISION A( * ), B( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTECT counts the number NUM of eigenvalues of a tridiagonal
*> matrix T which are less than or equal to SHIFT. T has
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The number of eigenvalues of T less than or equal
*> to SHIFT.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* RESULT )
* $ SE( * ), U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTT21 checks a decomposition of the form
*>
*> RESULT(1) = | A - U S U' | / ( |A| n ulp )
*>
*> RESULT(2) = | I - UU' | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> values are currently limited to 1/ulp, to avoid overflow.
*> RESULT(1) is always modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* LDWORK, RESULT )
* $ SE( * ), U( LDU, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSTT22 checks a set of M eigenvalues and eigenvectors,
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp )
*>
*> RESULT(2) = | I - U'U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSVDCH( N, S, E, SVD, TOL, INFO )
*
* DOUBLE PRECISION E( * ), S( * ), SVD( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSVDCH checks to see if SVD(1) ,..., SVD(N) are accurate singular
*> values of the bidiagonal matrix B with diagonal entries
*> contains the correct number of singular values, INFO = 0 is returned,
*> otherwise INFO is the index of the first singular value in the first
*> bad interval.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> >0 if the interval containing the INFO-th singular value
*> contains the incorrect number of singular values.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSVDCT( N, S, E, SHIFT, NUM )
*
* DOUBLE PRECISION E( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSVDCT counts the number NUM of eigenvalues of a 2*N by 2*N
*> tridiagonal matrix T which are less than or equal to SHIFT. T is
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford University,
*> July 21, 1966
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> NUM is INTEGER
*> The number of eigenvalues of T less than or equal to SHIFT.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DSXT1( IJOB, D1, N1, D2, N2, ABSTOL,
* ULP, UNFL )
* DOUBLE PRECISION D1( * ), D2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSXT1 computes the difference between a set of eigenvalues.
*> The result is returned as the function value.
*> IJOB = 2: Computes max { min | D1(i)-D2(j) | /
*> i j
*> ( ABSTOL + |D1(i)|*ULP ) }
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> The smallest positive number whose reciprocal does not
*> overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYT21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
* LDV, TAU, WORK, RESULT )
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYT21 generally checks a decomposition of the form
*>
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)' and each
*> vector v(j) has its first j elements 0 and the remaining n-j elements
*> stored in V(j+1:n,j).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYT22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
* V, LDV, TAU, WORK, RESULT )
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYT22 generally checks a decomposition of the form
*>
*> Specifically, if ITYPE=1, then:
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC> RESULT(2) = | I - U'U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> ITYPE INTEGER
*> if LDU is at least N.
*> Modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3,
* N4 )
* INTEGER ISPEC, N1, N2, N3, N4
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ILAENV returns problem-dependent parameters for the local
*> environment. See ISPEC for a description of the parameters.
*> the integer array IPARMS in the common block CLAENV and the value
*> with index ISPEC is copied to ILAENV. This version of ILAENV is
*> to be used in conjunction with XLAENV in TESTING and TIMING.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> >= 0: the value of the parameter specified by ISPEC
*> < 0: if ILAENV = -k, the k-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_eig
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The following conventions have been used when calling ILAENV from the
*>
*> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
*> IF( NB.LE.1 ) NB = MAX( 1, N )
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
* RESID )
* $ Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SBDT01 reconstructs a general matrix A from its bidiagonal form
*> A = Q * B * P'
*> The test ratio to test the reduction is
*> RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
*> where PT = P' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
*
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SBDT02 tests the change of basis C = U' * B by computing the residual
*>
*>
*> where B and C are M by N matrices, U is an M by M orthogonal matrix,
*> and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SBDT03( UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK,
* RESID )
* $ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SBDT03 reconstructs a bidiagonal matrix B from its SVD:
*> S = U' * B * V
*> The test ratio to test the singular value decomposition is
*> RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS )
*> where VT = V' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
* NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
* $ Q( LDQ, * ), RESULT( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKBB tests the reduction of a general real rectangular band
*> matrix to bidiagonal form.
*> (13) Rectangular matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
* ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
* $ Y( LDX, * ), Z( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKBD checks the singular value decomposition (SVD) routines.
*>
*>
*> A subset of the full set of matrix types may be selected through
*> the logical array DOTYPE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKBK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKBK tests SGEBAK, a routine for backward transformation of
*> the computed right or left eigenvectors if the orginal matrix
*> was preprocessed by balance subroutine SGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKBL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKBL tests SGEBAL, a routine for balancing a general real
*> matrix and isolating some of its eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKEC( THRESH, TSTERR, NIN, NOUT )
*
* REAL THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKEC tests eigen- condition estimation routines
*> SLALN2, SLASY2, SLANV2, SLAQTR, SLAEXC,
*> results to a threshold THRESH. In addition, STREXC, STRSNA and STRSEN
*> are tested by reading in precomputed examples from a file (on input
*> unit NIN). Output is written to output unit NOUT.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM SCHKEE
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKEE tests the REAL LAPACK subroutines for the matrix
*> eigenvalue problem. The test paths in this version are
*> precomputed examples, and LWORK = NMAX*(5*NMAX+5)+1 in the parameter
*> statements below. For SVD, we assume NRHS may be as big as N. The
*> parameter NEED is set to 14 to allow for 14 N-by-N matrices for SGG.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_eig
*
-* =====================================================================
- PROGRAM SCHKEE
+* ===================================================================== PROGRAM SCHKEE
*
* -- LAPACK test routine (version 3.1.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
* $ Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKGG checks the nonsymmetric generalized eigenvalue problem
*> routines.
*>
*> (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKGK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKGK tests SGGBAK, a routine for backward balancing of
*> a matrix pair (A, B).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKGL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKGL tests SGGBAL, a routine for balancing a matrix pair (A, B).
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKGL tests SGGBAL, a routine for balancing a matrix pair (A, B).
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1,
* $ WR3( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKHS checks the nonsymmetric eigenvalue problem routines.
*>
*> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
*> (20) Same as (19), but multiplied by SQRT( overflow threshold )
*> (21) Same as (19), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES - INTEGER
*> KCONDS(j) Selects whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKSB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED,
* THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK,
* $ U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKSB tests the reduction of a symmetric band matrix to tridiagonal
*> form, used with the symmetric eigenvalue problem.
*> (13) Symmetric matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, AP, SD, SE, D1, D2, D3, D4, D5,
* $ WA3( * ), WORK( * ), WR( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKST checks the symmetric eigenvalue problem routines.
*>
*> (20) Same as (16), but multiplied by SQRT( underflow threshold )
*> (21) A diagonally dominant tridiagonal matrix with geometrically
*> spaced diagonal entries 1, ..., ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
* MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
* $ WORK( * ), X( * ), XF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCKCSD tests SORCSD:
*> the CSD for an M-by-M orthogonal matrix X partitioned as
*> [ X11 X12; X21 X22 ]. X11 is P-by-Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If SLAROR returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCKGLM( NN, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCKGLM tests SGGGLM - subroutine for solving generalized linear
*> model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If SLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCKGQR( NM, MVAL, NP, PVAL, NN, NVAL, NMATS, ISEED,
* THRESH, NMAX, A, AF, AQ, AR, TAUA, B, BF, BZ,
* $ RWORK( * ), TAUA( * ), TAUB( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCKGQR tests
*> SGGQRF: GQR factorization for N-by-M matrix A and N-by-P matrix B,
*> SGGRQF: GRQ factorization for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If SLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCKGSV( NM, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, U, V, Q, ALPHA, BETA, R,
* $ V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCKGSV tests SGGSVD:
*> the GSVD for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If SLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCKLSE( NN, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCKLSE tests SGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If SLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
* LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
* $ XF( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCSDTS tests SORCSD, which, given an M-by-M partitioned orthogonal
*> matrix X,
*> [ 0 0 0 | I 0 0 ] [ D21 D22 ]
*> [ 0 S 0 | 0 C 0 ]
*> [ 0 0 I | 0 0 0 ]
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = ULPINV otherwise.
*> ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR,
* $ WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem driver SGGES.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRGEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRGEV checks the nonsymmetric generalized eigenvalue problem driver
*> routine SGGEV.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B,
* AI, BI, Z, Q, ALPHAR, ALPHAI, BETA, C, LDC, S,
* $ WORK( * ), Z( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem expert driver SGGESX.
*> and DIF_l when testing the built-in test problems.
*>
*> Built-in Test Matrices
-*> ======================
+* ======================
*>
*> All built-in test matrices are the 2 by 2 block of triangular
*> matrices
*> | 1-d |
*> and matrix B are chosen as identity matrices (see SLATM5).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRGVX( NSIZE, THRESH, NIN, NOUT, A, LDA, B, AI, BI,
* ALPHAR, ALPHAI, BETA, VL, VR, ILO, IHI, LSCALE,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRGVX checks the nonsymmetric generalized eigenvalue problem
*> expert driver SGGEVX.
*>
*> a, b, x and y will have all values independently of each other from
*> { sqrt(sqrt(ULP)), 0.1, 1, 10, 1/sqrt(sqrt(ULP)) }.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
* $ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVBD checks the singular value decomposition (SVD) drivers
*> SGESVD, SGESDD, SGESVJ, and SGEJSV.
*> on the diagonal.
*> (4) Same as (3), but multiplied by the underflow-threshold / ULP.
*> (5) Same as (3), but multiplied by the overflow-threshold * ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> If SLATMS, or SGESVD returns an error code, the
*> absolute value of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
* $ WORK( * ), WR( * ), WRT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVES checks the nonsymmetric eigenvalue (Schur form) problem
*> driver SGEES.
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL,
* $ WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVEV checks the nonsymmetric eigenvalue problem driver SGEEV.
*>
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
* $ VR( LDQ, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVGG checks the nonsymmetric generalized eigenvalue driver
*> routines.
*>
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
* $ RESULT( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVSG checks the real symmetric generalized eigenproblem
*> drivers.
*> (19) Same as (8), but with KA = 3 and KB = 1
*> (20) Same as (8), but with KA = 3 and KB = 2
*> (21) Same as (8), but with KA = 3 and KB = 3
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, D1, D2, D3, D4, EVEIGS, WA1,
* $ WA3( * ), WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVST checks the symmetric eigenvalue problem drivers.
*>
*> with random signs.
*> (17) Same as (16), but multiplied by SQRT( overflow threshold )
*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> 95= | I - U U' | / ( n ulp ) SSBEVR('L','V','V', ... )
*> 96= |D(with Z) - D(w/o Z)| / (|D| ulp) SSBEVR('L','N','V', ... )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT,
* $ WR( * ), WRT( * ), WRTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver SGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
* $ WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVVX checks the nonsymmetric eigenvalue problem expert driver
*> SGEEVX.
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRBD( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRBD tests the error exits for SGEBRD, SORGBR, SORMBR, SBDSQR and
*> SBDSDC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERREC( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERREC tests the error exits for the routines for eigen- condition
*> estimation for REAL matrices:
*> STRSYL, STREXC, STRSNA and STRSEN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRED( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRED tests the error exits for the eigenvalue driver routines for
*> REAL matrices:
*> SGESDD compute SVD of an M-by-N matrix A (by divide and
*> conquer)
*> SGEJSV compute SVD of an M-by-N matrix A where M >= N
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRGG( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRGG tests the error exits for SGGES, SGGESX, SGGEV, SGGEVX,
*> SGGGLM, SGGHRD, SGGLSE, SGGQRF, SGGRQF, SGGSVD, SGGSVP, SHGEQZ,
*> SORCSD, STGEVC, STGEXC, STGSEN, STGSJA, STGSNA, and STGSYL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRHS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRHS tests the error exits for SGEBAK, SGEBAL, SGEHRD, SORGHR,
*> SORMHR, SHSEQR, SHSEIN, and STREVC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRST( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRST tests the error exits for SSYTRD, SORGTR, SORMTR, SSPTRD,
*> SOPGTR, SOPMTR, SSTEQR, SSTERF, SSTEBZ, SSTEIN, SPTEQR, SSBTRD,
*> SSYEV, SSYEVX, SSYEVD, SSBEV, SSBEVX, SSBEVD,
*> SSPEV, SSPEVX, SSPEVD, SSTEV, SSTEVX, SSTEVD, and SSTEDC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET10( M, N, A, LDA, B, LDB, WORK, RESULT )
*
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET10 compares two matrices A and B and computes the ratio
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT is REAL
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, WR,
* WI, WORK, RESULT )
* $ WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET22 does an eigenvector check.
*>
*> To handle various schemes for storage of left eigenvectors, there are
*> options to use A-transpose instead of A, E-transpose instead of E,
*> and/or W-transpose instead of W.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> RESULT(1) = | A E - E W | / ( |A| |E| ulp )
*> RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N,
* A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR,
* $ WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX.
*> If COMP = .FALSE., the first 8 of the following tests will be
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, SGEEVX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
* H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS,
* $ WR( * ), WRT( * ), WRTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET24 checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver SGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, SGEESX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET31( RMAX, LMAX, NINFO, KNT )
*
* INTEGER NINFO( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET31 tests SLALN2, a routine for solving
*>
*> should be on the order of 1. Here, ulp is the machine precision.
*> Also, it is verified that SCALE is less than or equal to 1, and that
*> XNORM = infinity-norm(X).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET32( RMAX, LMAX, NINFO, KNT )
*
* REAL RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET32 tests SLASY2, a routine for solving
*>
*> should be on the order of 1. Here, ulp is the machine precision.
*> Also, it is verified that SCALE is less than or equal to 1, and
*> that XNORM = infinity-norm(X).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET33( RMAX, LMAX, NINFO, KNT )
*
* REAL RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET33 tests SLANV2, a routine for putting 2 by 2 blocks into
*> standard form. In other words, it computes a two by two rotation
*> 1) T21=0 (real eigenvalues), or
*> 2) T11=T22 and T21*T12<0 (complex conjugate eigenvalues).
*> We also verify that the residual is small.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET34( RMAX, LMAX, NINFO, KNT )
*
* INTEGER NINFO( 2 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET34 tests SLAEXC, a routine for swapping adjacent blocks (either
*> 1 by 1 or 2 by 2) on the diagonal of a matrix in real Schur form.
*>
*> The test code verifies these last last assertions, as well as that
*> the residual in the above equation is small.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET35( RMAX, LMAX, NINFO, KNT )
*
* REAL RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET35 tests STRSYL, a routine for solving the Sylvester matrix
*> equation
*>
*> norm(op(A)*X + ISGN*X*op(B) - scale*C) /
*> (EPS*max(norm(A),norm(B))*norm(X))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* INTEGER NINFO( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET36 tests STREXC, a routine for moving blocks (either 1 by 1 or
*> 2 by 2) on the diagonal of a matrix in real Schur form. Thus, SLAEXC
*> ILST (within +-1).
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* REAL RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET37 tests STRSNA, a routine for estimating condition numbers of
*> eigenvalues and/or right eigenvectors of a matrix.
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET38( RMAX, LMAX, NINFO, KNT, NIN )
*
* REAL RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET38 tests STRSEN, a routine for estimating condition numbers of a
*> cluster of eigenvalues and/or its associated right invariant subspace
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET39( RMAX, LMAX, NINFO, KNT )
*
* REAL RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET39 tests SLAQTR, a routine for solving the real or
*> special complex quasi upper triangular system
*>
*> (The (||T||+||B||)*smlnum/ulp term accounts for possible
*> (gradual or nongradual) underflow in x1 and x2.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
* RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET51 generally checks a decomposition of the form
*>
*> If ITYPE=3, then:
*>
*> RESULT = | I - UU' | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> value is currently limited to 1/ulp, to avoid overflow.
*> Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET52( LEFT, N, A, LDA, B, LDB, E, LDE, ALPHAR,
* ALPHAI, BETA, WORK, RESULT )
* $ RESULT( 2 ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET52 does an eigenvector check for the generalized eigenvalue
*> problem.
*>
*> RESULT(2) = max | M(v(j)) - 1 | / ( n ulp )
*> eigenvectors v(j)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LEFT
*> \verbatim
*> B E is likely to overflow, then RESULT(1:2) is set to
*> 10 / ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET53( A, LDA, B, LDB, SCALE, WR, WI, RESULT, INFO )
*
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET53 checks the generalized eigenvalues computed by SLAG2.
*>
*>
*> If these tests are not passed, then s and w are scaled and
*> tested anyway, if this is possible.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] A
*> \verbatim
*> =3: same as INFO=2, but s and w could not be scaled so
*> as to compute the test.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
* LDV, WORK, RESULT )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET54 checks a generalized decomposition of the form
*>
*> Specifically,
*>
*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The value RESULT, It is currently limited to 1/ulp, to
*> avoid overflow. Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF,
* X, U, WORK, LWORK, RWORK, RESULT )
* $ BF( LDB, * ), RWORK( * ), D( * ), DF( * ),
* $ U( * ), WORK( LWORK ), X( * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGLMTS tests SGGGLM - a subroutine for solving the generalized
*> linear model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT = -----------------------------------------
*> (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ RWORK( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGQRTS tests SGGQRF, which computes the GQR factorization of an
*> N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ RESULT( 4 ), RWORK( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGRQTS tests SGGRQF, which computes the GRQ factorization of an
*> M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGSVTS( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
* LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGSVTS tests SGGSVD, which computes the GSVD of an M-by-N matrix A
*> and a P-by-N matrix B:
*> U'*A*Q = D1*R and V'*B*Q = D2*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(6) = 0 if ALPHA is in decreasing order;
*> = ULPINV otherwise.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
* LWORK, RESULT )
* $ RESULT( 2 ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SHST01 tests the reduction of a general matrix A to upper Hessenberg
*> form: A = Q*H*Q'. Two test ratios are computed;
*>
*> In this version, ILO and IHI are not used and are assumed to be 1 and
*> N, respectively.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAFTS( TYPE, M, N, IMAT, NTESTS, RESULT, ISEED,
* THRESH, IOUNIT, IE )
* REAL RESULT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAFTS tests the result vector against the threshold value to
*> see which tests for this matrix type failed to pass the threshold.
*> Output is to the file given by unit IOUNIT.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> TYPE - CHARACTER*3
*> failed to pass the threshold so far.
*> Updated on exit if any of the ratios in RESULT also fail.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAHD2( IOUNIT, PATH )
*
* INTEGER IOUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SLAHD2 prints header information for the different test paths.
+*> \verbatim
*>
-*>\endverbatim
+*> SLAHD2 prints header information for the different test paths.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IOUNIT
*> \verbatim
*> These paths also are supplied in double precision (replace
*> leading S by D and leading C by Z in path names).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* REAL C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARFY applies an elementary reflector, or Householder matrix, H,
*> to an n x n symmetric matrix C, from both the left and the right.
*> where tau is a scalar and v is a vector.
*>
*> If tau is zero, then H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A or A' (transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLASUM( TYPE, IOUNIT, IE, NRUN )
*
*
* =====================================================================
*
-* Authors
-* =======
+* Authors:
+* ========
*
* \author Univ. of Tennessee
* \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATB9( PATH, IMAT, M, P, N, TYPE, KLA, KUA,
* KLB, KUB, ANORM, BNORM, MODEA, MODEB,
* REAL ANORM, BNORM, CNDNMA, CNDNMB
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATB9 sets parameters for the matrix generator based on the type of
*> matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATM4( ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND,
* TRIANG, IDIST, ISEED, A, LDA )
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM4 generates basic square matrices, which may later be
*> multiplied by others in order to produce test matrices. It is
*> according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND.
*> It then fills in the upper triangle with random numbers, if TRIANG is
*> non-zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A. Must be at least 1 and at least N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION SLCTES( ZR, ZI, D )
*
* REAL D, ZI, ZR
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLCTES returns .TRUE. if the eigenvalue (ZR/D) + sqrt(-1)*(ZI/D)
*> is to be selected (specifically, in this subroutine, if the real
*>
*> It is used by the test routine SDRGES to test whether the driver
*> routine SGGES succesfully sorts eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ZR
*> \verbatim
*> The denominator part of a complex eigenvalue
*> (ZR/D) + i*(ZI/D).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION SLCTSX( AR, AI, BETA )
*
* REAL AI, AR, BETA
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This function is used to determine what eigenvalues will be
*> selected. If this is part of the test driver SDRGSX, do not
*> change the code UNLESS you are testing input examples and not
*> using the built-in examples.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] AR
*> \verbatim
*> The denominator part of a complex eigenvalue
*> (AR/BETA) + i*(AI/BETA).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLSETS( M, P, N, A, AF, LDA, B, BF, LDB, C, CF,
* D, DF, X, WORK, LWORK, RWORK, RESULT )
* $ C( * ), D( * ), CF( * ), DF( * ),
* $ WORK( LWORK ), X( * )
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLSETS tests SGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( A*x - c )/ norm(A)*norm(X)*EPS
*> RESULT(2) = norm( B*x - d )/ norm(B)*norm(X)*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RESID )
*
* REAL U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORT01 checks that the matrix U is orthogonal by computing the ratio
*>
*> where EPS is the machine precision. ROWCOL is used only if m = n;
*> if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
*> assumed to be 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ROWCOL
*> \verbatim
*> RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
*> RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SORT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
* RESULT, INFO )
* REAL U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SORT03 compares two orthogonal matrices U and V to see if their
*> corresponding rows or columns span the same spaces. The rows are
*>
*> where S is +-1 (chosen to minimize the expression), U(i) is the i-th
*> row (column) of U, and V(i) is the i-th row (column) of V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RC
*> \verbatim
*> 0 indicates a successful exit
*> -k indicates the k-th parameter had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSBT21( UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK,
* RESULT )
* $ U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSBT21 generally checks a decomposition of the form
*>
*> Specifically:
*>
*> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
* WORK, RESULT )
* $ WORK( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSGT01 checks a decomposition of the form
*>
*> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
*>
*> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT is REAL array, dimension (1)
*> The test ratio as described above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION SSLECT( ZR, ZI )
*
* REAL ZI, ZR
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSLECT returns .TRUE. if the eigenvalue ZR+sqrt(-1)*ZI is to be
*> selected, and otherwise it returns .FALSE.
*> and .FALSE. otherwise.
*> If SELOPT is at least 1, SSLECT returns SELVAL(SELOPT) and adds 1
*> to SELOPT, cycling back to 1 at SELMAX.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ZR
*> \verbatim
*> ZI is REAL
*> The imaginary part of a complex eigenvalue ZR + i*ZI.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
* TAU, WORK, RESULT )
* $ U( LDU, * ), VP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPT21 generally checks a decomposition of the form
*>
*> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
*> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
*> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTECH( N, A, B, EIG, TOL, WORK, INFO )
*
* REAL A( * ), B( * ), EIG( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Let T be the tridiagonal matrix with diagonal entries A(1) ,...,
*> A(N) and offdiagonal entries B(1) ,..., B(N-1)). SSTECH checks to
*> eigenvalue. If each interval contains the correct number of
*> eigenvalues, INFO = 0 is returned, otherwise INFO is the index of
*> the first eigenvalue in the first bad interval.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> >0 if the interval containing the INFO-th eigenvalue
*> contains the incorrect number of eigenvalues.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTECT( N, A, B, SHIFT, NUM )
*
* REAL A( * ), B( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTECT counts the number NUM of eigenvalues of a tridiagonal
*> matrix T which are less than or equal to SHIFT. T has
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford
*> University, July 21, 1966
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The number of eigenvalues of T less than or equal
*> to SHIFT.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* RESULT )
* $ SE( * ), U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTT21 checks a decomposition of the form
*>
*> RESULT(1) = | A - U S U' | / ( |A| n ulp )
*>
*> RESULT(2) = | I - UU' | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> values are currently limited to 1/ulp, to avoid overflow.
*> RESULT(1) is always modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* LDWORK, RESULT )
* $ SE( * ), U( LDU, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSTT22 checks a set of M eigenvalues and eigenvectors,
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp )
*>
*> RESULT(2) = | I - U'U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSVDCH( N, S, E, SVD, TOL, INFO )
*
* REAL E( * ), S( * ), SVD( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSVDCH checks to see if SVD(1) ,..., SVD(N) are accurate singular
*> values of the bidiagonal matrix B with diagonal entries
*> contains the correct number of singular values, INFO = 0 is returned,
*> otherwise INFO is the index of the first singular value in the first
*> bad interval.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> >0 if the interval containing the INFO-th singular value
*> contains the incorrect number of singular values.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSVDCT( N, S, E, SHIFT, NUM )
*
* REAL E( * ), S( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSVDCT counts the number NUM of eigenvalues of a 2*N by 2*N
*> tridiagonal matrix T which are less than or equal to SHIFT. T is
*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
*> Matrix", Report CS41, Computer Science Dept., Stanford University,
*> July 21, 1966
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> NUM is INTEGER
*> The number of eigenvalues of T less than or equal to SHIFT.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SSXT1( IJOB, D1, N1, D2, N2, ABSTOL,
* ULP, UNFL )
* REAL D1( * ), D2( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSXT1 computes the difference between a set of eigenvalues.
*> The result is returned as the function value.
*> IJOB = 2: Computes max { min | D1(i)-D2(j) | /
*> i j
*> ( ABSTOL + |D1(i)|*ULP ) }
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IJOB
*> \verbatim
*> The smallest positive number whose reciprocal does not
*> overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYT21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
* LDV, TAU, WORK, RESULT )
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYT21 generally checks a decomposition of the form
*>
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)' and each
*> vector v(j) has its first j elements 0 and the remaining n-j elements
*> stored in V(j+1:n,j).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYT22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
* V, LDV, TAU, WORK, RESULT )
* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYT22 generally checks a decomposition of the form
*>
*> Specifically, if ITYPE=1, then:
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC> RESULT(2) = | I - U'U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> ITYPE INTEGER
*> if LDU is at least N.
*> Modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XERBLA( SRNAME, INFO )
*
* INTEGER INFO
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This is a special version of XERBLA to be used only as part of
*> the test program for testing error exits from the LAPACK routines.
*> Error messages are printed if INFO.NE.INFOT or if SRNAME.NE.SRNAMT,
*> where INFOT and SRNAMT are values stored in COMMON.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SRNAME
*> \verbatim
*> The error return code from the calling subroutine. INFO
*> should equal the COMMON variable INFOT.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_eig
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The following variables are passed via the common blocks INFOC and
*> SRNAME = SRNAMT, otherwise set to .FALSE.
*> LERR LOGICAL Set to .TRUE., indicating that XERBLA was called
*> SRNAMT CHARACTER*(*) Expected name of calling subroutine
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XLAENV( ISPEC, NVALUE )
*
* INTEGER ISPEC, NVALUE
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> XLAENV sets certain machine- and problem-dependent quantities
*> which will later be retrieved by ILAENV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> NVALUE is INTEGER
*> The value of the parameter specified by ISPEC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
* RWORK, RESID )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZBDT01 reconstructs a general matrix A from its bidiagonal form
*> A = Q * B * P'
*> The test ratio to test the reduction is
*> RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
*> where PT = P' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK,
* RESID )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZBDT02 tests the change of basis C = U' * B by computing the residual
*>
*>
*> where B and C are M by N matrices, U is an M by M orthogonal matrix,
*> and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZBDT03( UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK,
* RESID )
* COMPLEX*16 U( LDU, * ), VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZBDT03 reconstructs a bidiagonal matrix B from its SVD:
*> S = U' * B * V
*> The test ratio to test the singular value decomposition is
*> RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS )
*> where VT = V' and EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
* NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKBB tests the reduction of a general complex rectangular band
*> matrix to real bidiagonal form.
*> (13) Rectangular matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
* ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
* $ X( LDX, * ), Y( LDX, * ), Z( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKBD checks the singular value decomposition (SVD) routines.
*>
*>
*> A subset of the full set of matrix types may be selected through
*> the logical array DOTYPE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKBK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKBK tests ZGEBAK, a routine for backward transformation of
*> the computed right or left eigenvectors if the orginal matrix
*> was preprocessed by balance subroutine ZGEBAL.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKBL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKBL tests ZGEBAL, a routine for balancing a general complex
*> matrix and isolating some of its eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKEC( THRESH, TSTERR, NIN, NOUT )
*
* DOUBLE PRECISION THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKEC tests eigen- condition estimation routines
*> ZTRSYL, CTREXC, CTRSNA, CTRSEN
*> results to a threshold THRESH. In addition, ZTRSNA and CTRSEN are
*> tested by reading in precomputed examples from a file (on input unit
*> NIN). Output is written to output unit NOUT.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZCHKEE
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKEE tests the COMPLEX*16 LAPACK subroutines for the matrix
*> eigenvalue problem. The test paths in this version are
*> precomputed examples, and LWORK = NMAX*(5*NMAX+20) in the parameter
*> statements below. For SVD, we assume NRHS may be as big as N. The
*> parameter NEED is set to 14 to allow for 14 N-by-N matrices for ZGG.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_eig
*
-* =====================================================================
- PROGRAM ZCHKEE
+* ===================================================================== PROGRAM ZCHKEE
*
* -- LAPACK test routine (version 3.3.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
* $ WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKGG checks the nonsymmetric generalized eigenvalue problem
*> routines.
*>
*> (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKGK( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKGK tests ZGGBAK, a routine for backward balancing of
*> a matrix pair (A, B).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKGL( NIN, NOUT )
*
* INTEGER NIN, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKGL tests ZGGBAL, a routine for balancing a matrix pair (A, B).
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKGL tests ZGGBAL, a routine for balancing a matrix pair (A, B).
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NIN
*> \verbatim
*> NOUT is INTEGER
*> The logical unit number for output. NOUT > 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKHB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED,
* THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK,
* COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKHB tests the reduction of a Hermitian band matrix to tridiagonal
*> from, used with the Hermitian eigenvalue problem.
*> (13) Hermitian matrix with random entries chosen from (-1,1).
*> (14) Same as (13), but multiplied by SQRT( overflow threshold )
*> (15) Same as (13), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, W1,
* $ WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKHS checks the nonsymmetric eigenvalue problem routines.
*>
*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1
*> (20) Same as (19), but multiplied by SQRT( overflow threshold )
*> (21) Same as (19), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES - INTEGER
*> KCONDS(j) Selects whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, AP, SD, SE, D1, D2, D3, D4, D5,
* $ V( LDU, * ), VP( * ), WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKST checks the Hermitian eigenvalue problem routines.
*>
*> (20) Same as (16), but multiplied by SQRT( underflow threshold )
*> (21) A diagonally dominant tridiagonal matrix with geometrically
*> spaced diagonal entries 1, ..., ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
* MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
* $ WORK( * ), X( * ), XF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCKCSD tests ZUNCSD:
*> the CSD for an M-by-M unitary matrix X partitioned as
*> [ X11 X12; X21 X22 ]. X11 is P-by-Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If ZLAROR returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCKGLM( NN, NVAL, MVAL, PVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCKGLM tests ZGGGLM - subroutine for solving generalized linear
*> model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If ZLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCKGQR( NM, MVAL, NP, PVAL, NN, NVAL, NMATS, ISEED,
* THRESH, NMAX, A, AF, AQ, AR, TAUA, B, BF, BZ,
* $ TAUB( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCKGQR tests
*> ZGGQRF: GQR factorization for N-by-M matrix A and N-by-P matrix B,
*> ZGGRQF: GRQ factorization for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If ZLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCKGSV( NM, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, U, V, Q, ALPHA, BETA, R,
* $ R( * ), U( * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCKGSV tests ZGGSVD:
*> the GSVD for M-by-N matrix A and P-by-N matrix B.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NM
*> \verbatim
*> > 0 : If ZLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCKLSE( NN, MVAL, PVAL, NVAL, NMATS, ISEED, THRESH,
* NMAX, A, AF, B, BF, X, WORK, RWORK, NIN, NOUT,
* $ X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCKLSE tests ZGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NN
*> \verbatim
*> > 0 : If ZLATMS returns an error code, the absolute value
*> of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
* LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
* $ XF( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCSDTS tests ZUNCSD, which, given an M-by-M partitioned unitary
*> matrix X,
*> [ 0 0 0 | I 0 0 ] [ D21 D22 ]
*> [ 0 S 0 | 0 C 0 ]
*> [ 0 0 I | 0 0 0 ]
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = ULPINV otherwise.
*> ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem driver ZGGES.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRGEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRGEV checks the nonsymmetric generalized eigenvalue problem driver
*> routine ZGGEV.
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B, AI,
* BI, Z, Q, ALPHA, BETA, C, LDC, S, WORK, LWORK,
* $ Z( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem expert driver ZGGESX.
*> and DIF_l when testing the built-in test problems.
*>
*> Built-in Test Matrices
-*> ======================
+* ======================
*>
*> All built-in test matrices are the 2 by 2 block of triangular
*> matrices
*> | 1-d |
*> and matrix B are chosen as identity matrices (see DLATM5).
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRGVX( NSIZE, THRESH, NIN, NOUT, A, LDA, B, AI, BI,
* ALPHA, BETA, VL, VR, ILO, IHI, LSCALE, RSCALE,
* $ VL( LDA, * ), VR( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRGVX checks the nonsymmetric generalized eigenvalue problem
*> expert driver ZGGEVX.
*>
*> a, b, x and y will have all values independently of each other from
*> { sqrt(sqrt(ULP)), 0.1, 1, 10, 1/sqrt(sqrt(ULP)) }.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZE
*> \verbatim
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
* $ VTSAV( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD
*> and ZGESDD.
*> on the diagonal.
*> (4) Same as (3), but multiplied by the underflow-threshold / ULP.
*> (5) Same as (3), but multiplied by the overflow-threshold * ULP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> If ZLATMS, or ZGESVD returns an error code, the
*> absolute value of it is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, HT, W, WT, VS, LDVS, RESULT,
* $ VS( LDVS, * ), W( * ), WORK( * ), WT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVES checks the nonsymmetric eigenvalue (Schur form) problem
*> driver ZGEES.
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Select whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR, LDVR,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVEV checks the nonsymmetric eigenvalue problem driver ZGEEV.
*>
*> near the overflow threshold
*> (21) Same as (19), but multiplied by a constant
*> near the underflow threshold
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
* ..
* .. Array Arguments ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVGG checks the nonsymmetric generalized eigenvalue driver
*> routines.
*>
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVSG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, LDB, D, Z, LDZ, AB, BB, AP,
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVSG checks the complex Hermitian generalized eigenproblem
*> drivers.
*> (19) Same as (8), but with KA = 3 and KB = 1
*> (20) Same as (8), but with KA = 3 and KB = 2
*> (21) Same as (8), but with KA = 3 and KB = 3
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVST( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
* $ V( LDU, * ), WORK( * ), Z( LDU, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVST checks the Hermitian eigenvalue problem drivers.
*>
*> with random signs.
*> (17) Same as (16), but multiplied by SQRT( overflow threshold )
*> (18) Same as (16), but multiplied by SQRT( underflow threshold )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NSIZES INTEGER
*> KMAGN(j) The order of magnitude ( O(1),
*> O(overflow^(1/2) ), O(underflow^(1/2) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS,
* $ WORK( * ), WT( * ), WTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver ZGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVVX checks the nonsymmetric eigenvalue problem expert driver
*> ZGEEVX.
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> KCONDS(j) Selectw whether CONDS is to be 1 or
*> 1/sqrt(ulp). (0 means irrelevant.)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRBD( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZERRBD tests the error exits for ZGEBRD, ZUNGBR, ZUNMBR, and ZBDSQR.
+*> \verbatim
*>
-*>\endverbatim
+*> ZERRBD tests the error exits for ZGEBRD, ZUNGBR, ZUNMBR, and ZBDSQR.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERREC( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERREC tests the error exits for the routines for eigen- condition
*> estimation for DOUBLE PRECISION matrices:
*> ZTRSYL, CTREXC, CTRSNA and CTRSEN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRED( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRED tests the error exits for the eigenvalue driver routines for
*> DOUBLE PRECISION matrices:
*> ZBD ZGESVD compute SVD of an M-by-N matrix A
*> ZGESDD compute SVD of an M-by-N matrix A(by divide and
*> conquer)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRGG( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRGG tests the error exits for ZGGES, ZGGESX, ZGGEV, ZGGEVX,
*> ZGGGLM, ZGGHRD, ZGGLSE, ZGGQRF, ZGGRQF, ZGGSVD, ZGGSVP, ZHGEQZ,
*> ZTGEVC, ZTGEXC, ZTGSEN, ZTGSJA, ZTGSNA, ZTGSYL, and ZUNCSD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRHS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRHS tests the error exits for ZGEBAK, CGEBAL, CGEHRD, ZUNGHR,
*> ZUNMHR, ZHSEQR, CHSEIN, and ZTREVC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRST( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRST tests the error exits for ZHETRD, ZUNGTR, CUNMTR, ZHPTRD,
*> ZUNGTR, ZUPMTR, ZSTEQR, CSTEIN, ZPTEQR, ZHBTRD,
*> ZHEEV, CHEEVX, CHEEVD, ZHBEV, CHBEVX, CHBEVD,
*> ZHPEV, CHPEVX, CHPEVD, and ZSTEDC.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET10( M, N, A, LDA, B, LDB, WORK, RWORK, RESULT )
*
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET10 compares two matrices A and B and computes the ratio
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT is DOUBLE PRECISION
*> RESULT = norm( A - B ) / ( norm(A) * M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
* WORK, RWORK, RESULT )
* COMPLEX*16 A( LDA, * ), E( LDE, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET22 does an eigenvector check.
*>
*> where E(j) is the j-th eigenvector, and m-norm is the max-norm of a
*> vector. The max-norm of a complex n-vector x in this case is the
*> maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> RESULT(1) = | A E - E W | / ( |A| |E| ulp )
*> RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
* NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX.
*> If COMP = .FALSE., the first 8 of the following tests will be
*> of RCONDE, and takes errors in computing RCONDE into account,
*> so that the resulting quantity should be O(ULP). cond(RCONDE)
*> is essentially given by norm(A)/RCONDV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, ZGEEVX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
* H, HT, W, WT, WTMP, VS, LDVS, VS1, RCDEIN,
* $ WORK( * ), WT( * ), WTMP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET24 checks the nonsymmetric eigenvalue (Schur form) problem
*> expert driver ZGEESX.
*> number of RCONDV, and takes errors in computing RCONDV into
*> account, so that the resulting quantity should be O(ULP).
*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] COMP
*> \verbatim
*> If >0, ZGEESX returned an error code, the absolute
*> value of which is returned.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET35( RMAX, LMAX, NINFO, KNT, NIN )
*
* DOUBLE PRECISION RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET35 tests ZTRSYL, a routine for solving the Sylvester matrix
*> equation
*>
*> norm(op(A)*X + ISGN*X*op(B) - scale*C) /
*> (EPS*max(norm(A),norm(B))*norm(X))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* DOUBLE PRECISION RMAX
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET36 tests ZTREXC, a routine for reordering diagonal entries of a
*> matrix in complex Schur form. Thus, ZLAEXC computes a unitary matrix
*> ILST.
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET37( RMAX, LMAX, NINFO, KNT, NIN )
*
* DOUBLE PRECISION RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET37 tests ZTRSNA, a routine for estimating condition numbers of
*> eigenvalues and/or right eigenvectors of a matrix.
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET38( RMAX, LMAX, NINFO, KNT, NIN )
*
* DOUBLE PRECISION RMAX( 3 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET38 tests ZTRSEN, a routine for estimating condition numbers of a
*> cluster of eigenvalues and/or its associated right invariant subspace
*>
*> The test matrices are read from a file with logical unit number NIN.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[out] RMAX
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
* RWORK, RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET51 generally checks a decomposition of the form
*>
*> If ITYPE=3, then:
*>
*> RESULT = | I - UU* | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> value is currently limited to 1/ulp, to avoid overflow.
*> Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET52( LEFT, N, A, LDA, B, LDB, E, LDE, ALPHA, BETA,
* WORK, RWORK, RESULT )
* $ BETA( * ), E( LDE, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET52 does an eigenvector check for the generalized eigenvalue
*> problem.
*> RESULT(2) = max | M(v(i)) - 1 | / ( n ulp )
*> eigenvectors v(i)
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] LEFT
*> \verbatim
*> B E is likely to overflow, then RESULT(1:2) is set to
*> 10 / ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
* LDV, WORK, RESULT )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET54 checks a generalized decomposition of the form
*>
*> Specifically,
*>
*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The value RESULT, It is currently limited to 1/ulp, to
*> avoid overflow. Errors are flagged by RESULT=10/ulp.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF, X, U,
* WORK, LWORK, RWORK, RESULT )
* ..
* .. Array Arguments ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGLMTS tests ZGGGLM - a subroutine for solving the generalized
*> linear model problem.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT = -----------------------------------------
*> (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ WORK( LWORK ), Z( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGQRTS tests ZGGQRF, which computes the GQR factorization of an
*> N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
* $ WORK( LWORK ), Z( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGRQTS tests ZGGRQF, which computes the GRQ factorization of an
*> M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGSVTS( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
* LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
* $ U( LDU, * ), V( LDV, * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGSVTS tests ZGGSVD, which computes the GSVD of an M-by-N matrix A
*> and a P-by-N matrix B:
*> U'*A*Q = D1*R and V'*B*Q = D2*R.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(6) = 0 if ALPHA is in decreasing order;
*> = ULPINV otherwise.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHBT21( UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK,
* RWORK, RESULT )
* COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHBT21 generally checks a decomposition of the form
*>
*> Specifically:
*>
*> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHET21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
* LDV, TAU, WORK, RWORK, RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHET21 generally checks a decomposition of the form
*>
*> V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)C> and each
*> vector v(j) has its first j elements 0 and the remaining n-j elements
*> stored in V(j+1:n,j).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
* V, LDV, TAU, WORK, RWORK, RESULT )
* $ V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHET22 generally checks a decomposition of the form
*>
*> Specifically, if ITYPE=1, then:
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp ) *andC> RESULT(2) = | I - U'U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> ITYPE INTEGER
*> if LDU is at least N.
*> Modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
* TAU, WORK, RWORK, RESULT )
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPT21 generally checks a decomposition of the form
*>
*> and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
*> (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
*> in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT(1) is always modified. RESULT(2) is modified only
*> if ITYPE=1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
* LWORK, RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHST01 tests the reduction of a general matrix A to upper Hessenberg
*> form: A = Q*H*Q'. Two test ratios are computed;
*>
*> In this version, ILO and IHI are not used, but they could be used
*> to save some work if this is desired.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARFY applies an elementary reflector, or Householder matrix, H,
*> to an n x n Hermitian matrix C, from both the left and the right.
*> where tau is a scalar and v is a vector.
*>
*> If tau is zero, then H is taken to be the unit matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
*> transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATM4( ITYPE, N, NZ1, NZ2, RSIGN, AMAGN, RCOND,
* TRIANG, IDIST, ISEED, A, LDA )
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATM4 generates basic square matrices, which may later be
*> multiplied by others in order to produce test matrices. It is
*> according to the value of ITYPE, NZ1, NZ2, RSIGN, AMAGN, and RCOND.
*> It then fills in the upper triangle with random numbers, if TRIANG is
*> non-zero.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A. Must be at least 1 and at least N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION ZLCTES( Z, D )
*
* COMPLEX*16 D, Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLCTES returns .TRUE. if the eigenvalue Z/D is to be selected
*> (specifically, in this subroutine, if the real part of the
*>
*> It is used by the test routine ZDRGES to test whether the driver
*> routine ZGGES succesfully sorts eigenvalues.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] Z
*> \verbatim
*> D is COMPLEX*16
*> The denominator part of a complex eigenvalue Z/D.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION ZLCTSX( ALPHA, BETA )
*
* COMPLEX*16 ALPHA, BETA
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This function is used to determine what eigenvalues will be
*> selected. If this is part of the test driver ZDRGSX, do not
*> change the code UNLESS you are testing input examples and not
*> using the built-in examples.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ALPHA
*> \verbatim
*> parameters to decide whether the pair (ALPHA, BETA) is
*> selected.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLSETS( M, P, N, A, AF, LDA, B, BF, LDB, C, CF, D, DF,
* X, WORK, LWORK, RWORK, RESULT )
* ..
* .. Array Arguments ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLSETS tests ZGGLSE - a subroutine for solving linear equality
*> constrained least square problem (LSE).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( A*x - c )/ norm(A)*norm(X)*EPS
*> RESULT(2) = norm( B*x - d )/ norm(B)*norm(X)*EPS
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
* WORK, RWORK, RESULT )
* $ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDGT01 checks a decomposition of the form
*>
*> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
*>
*> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (1)
*> The test ratio as described above.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION ZSLECT( Z )
*
* COMPLEX*16 Z
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSLECT returns .TRUE. if the eigenvalue Z is to be selected,
*> otherwise it returns .FALSE.
*> zero, and .FALSE. otherwise.
*> If SELOPT is at least 1, ZSLECT returns SELVAL(SELOPT) and adds 1
*> to SELOPT, cycling back to 1 at SELMAX.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] Z
*> \verbatim
*> Z is COMPLEX*16
*> The eigenvalue Z.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
* RESULT )
* COMPLEX*16 U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTT21 checks a decomposition of the form
*>
*> RESULT(1) = | A - U S U* | / ( |A| n ulp )
*>
*> RESULT(2) = | I - UU* | / ( n ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> values are currently limited to 1/ulp, to avoid overflow.
*> RESULT(1) is always modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* LDWORK, RWORK, RESULT )
* COMPLEX*16 U( LDU, * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSTT22 checks a set of M eigenvalues and eigenvectors,
*>
*> RESULT(1) = | U* A U - S | / ( |A| m ulp )
*>
*> RESULT(2) = | I - U*U | / ( m ulp )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK,
* RESID )
* COMPLEX*16 U( LDU, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNT01 checks that the matrix U is unitary by computing the ratio
*>
*> where EPS is the machine precision. ROWCOL is used only if m = n;
*> if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
*> assumed to be 'R'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ROWCOL
*> \verbatim
*> RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
*> RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZUNT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
* RWORK, RESULT, INFO )
* COMPLEX*16 U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZUNT03 compares two unitary matrices U and V to see if their
*> corresponding rows or columns span the same spaces. The rows are
*>
*> where abs(S) = 1 (chosen to minimize the expression), U(i) is the
*> i-th row (column) of U, and V(i) is the i-th row (column) of V.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RC
*> \verbatim
*> 0 indicates a successful exit
*> -k indicates the k-th parameter had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALADHD( IOUNIT, PATH )
*
* INTEGER IOUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALADHD prints header information for the driver routines test paths.
+*> \verbatim
*>
-*>\endverbatim
+*> ALADHD prints header information for the driver routines test paths.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IOUNIT
*> \verbatim
*> The first character must be one of S, D, C, or Z (C or Z only
*> if complex).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALAERH( PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU,
* N5, IMAT, NFAIL, NERRS, NOUT )
* $ NFAIL, NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ALAERH is an error handler for the LAPACK routines. It prints the
*> header if this is the first error message and prints the error code
*> and form of recovery, if any. The character evaluations in this
*> routine may make it slow, but it should not be called once the LAPACK
*> routines are fully debugged.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NOUT is INTEGER
*> The unit number on which results are to be printed.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALAESM( PATH, OK, NOUT )
*
* INTEGER NOUT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALAESM prints a summary of results from one of the -ERR- routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ALAESM prints a summary of results from one of the -ERR- routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The unit number on which results are to be printed.
*> NOUT >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALAHD( IOUNIT, PATH )
*
* INTEGER IOUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALAHD prints header information for the different test paths.
+*> \verbatim
*>
-*>\endverbatim
+*> ALAHD prints header information for the different test paths.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IOUNIT
*> \verbatim
*> The first character must be one of S, D, C, or Z (C or Z only
*> if complex).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ALAREQ handles input for the LAPACK test program. It is called
*> to evaluate the input line which requested NMATS matrix types for
*> Read the next input line for NMATS matrix types
*> Set DOTYPE(I) = .TRUE. for each valid type I
*> endif
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output. NOUT >= 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALASUM( TYPE, NOUT, NFAIL, NRUN, NERRS )
*
* INTEGER NFAIL, NOUT, NRUN, NERRS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALASUM prints a summary of results from one of the -CHK- routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ALASUM prints a summary of results from one of the -CHK- routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> NERRS is INTEGER
*> The number of error messages recorded.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ALASVM( TYPE, NOUT, NFAIL, NRUN, NERRS )
*
* INTEGER NFAIL, NOUT, NRUN, NERRS
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ALASVM prints a summary of results from one of the -DRV- routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ALASVM prints a summary of results from one of the -DRV- routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> NERRS is INTEGER
*> The number of error messages recorded.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM CCHKAA
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKAA is the main test program for the COMPLEX linear equation
*> routines.
*> CTZ 3 List types on next line if 0 < NTYPES < 3
*> CLS 6 List types on next line if 0 < NTYPES < 6
*> CEQ
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NMAX INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_lin
*
-* =====================================================================
- PROGRAM CCHKAA
+* ===================================================================== PROGRAM CCHKAA
*
* -- LAPACK test routine (version 3.1.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKEQ( THRESH, NOUT )
*
* REAL THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKEQ tests CGEEQU, CGBEQU, CPOEQU, CPPEQU and CPBEQU
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKEQ tests CGEEQU, CGBEQU, CPOEQU, CPPEQU and CPBEQU
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKGB tests CGBTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKGB tests CGBTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKGE tests CGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKGE tests CGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKGT tests CGTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKGT tests CGTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKHE( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKHE tests CHETRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKHE tests CHETRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKHP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKHP tests CHPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKHP tests CHPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKLQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKLQ tests CGELQF, CUNGLQ and CUNMLQ.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKLQ tests CGELQF, CUNGLQ and CUNMLQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKPB tests CPBTRF, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKPB tests CPBTRF, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKPO tests CPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKPO tests CPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKPP tests CPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKPP tests CPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKPS( DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL,
* THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK,
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKPS tests CPSTRF.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKPS tests CPSTRF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, D, E, B, X, XACT, WORK, RWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKPT tests CPTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKPT tests CPTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* THRESH, A, COPYA, S, TAU, WORK, RWORK,
* COMPLEX A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKQ3 tests CGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKQ3 tests CGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKQL( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKQL tests CGEQLF, CUNGQL and CUNMQL.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKQL tests CGEQLF, CUNGQL and CUNMQL.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKQP( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, RWORK, IWORK,
* COMPLEX A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKQP tests CGEQPF.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKQP tests CGEQPF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKQR( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKQR tests CGEQRF, CUNGQR and CUNMQR.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKQR tests CGEQRF, CUNGQR and CUNMQR.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM CCHKRFP
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CCHKRFP is the main test program for the COMPLEX linear equation
*> routines with RFP storage format
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> MAXIN INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_lin
*
-* =====================================================================
- PROGRAM CCHKRFP
+* ===================================================================== PROGRAM CCHKRFP
*
* -- LAPACK test routine (version 3.2.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKRQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKRQ tests CGERQF, CUNGRQ and CUNMRQ.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKRQ tests CGERQF, CUNGRQ and CUNMRQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKSP tests CSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKSP tests CSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKSY( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKSY tests CSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKSY tests CSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKTB tests CTBTRS, -RFS, and -CON, and CLATBS.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKTB tests CTBTRS, -RFS, and -CON, and CLATBS.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKTP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKTP tests CTPTRI, -TRS, -RFS, and -CON, and CLATPS
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKTP tests CTPTRI, -TRS, -RFS, and -CON, and CLATPS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKTR tests CTRTRI, -TRS, -RFS, and -CON, and CLATRS
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKTR tests CTRTRI, -TRS, -RFS, and -CON, and CLATRS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, RWORK, NOUT )
* COMPLEX A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CCHKTZ tests CTZRQF and CTZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> CCHKTZ tests CTZRQF and CTZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVGB tests the driver routines CGBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVGB tests the driver routines CGBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVGB tests the driver routines CGBSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cdrvgb.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVGE tests the driver routines CGESV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVGE tests the driver routines CGESV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVGE tests the driver routines CGESV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cdrvge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
* B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVGT tests CGTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVGT tests CGTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVHE tests the driver routines CHESV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVHE tests the driver routines CHESV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVHE tests the driver routines CHESV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cdrvhe.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVHP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVHP tests the driver routines CHPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVHP tests the driver routines CHPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
* NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVLS tests the least squares driver routines CGELS, CGELSX, CGELSS,
*> CGELSY and CGELSD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVPB tests the driver routines CPBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVPB tests the driver routines CPBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVPO tests the driver routines CPOSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVPO tests the driver routines CPOSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVPO tests the driver routines CPOSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cdrvpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVPP tests the driver routines CPPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVPP tests the driver routines CPPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
* E, B, X, XACT, WORK, RWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVPT tests CPTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVPT tests CPTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVRF1( NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK )
*
* COMPLEX A( LDA, * ), ARF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVRF1 tests the LAPACK RFP routines:
*> CLANHF.F
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> WORK is COMPLEX array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVRF2( NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV )
*
* COMPLEX A( LDA, * ), ARF( * ), AP(*), ASAV( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVRF2 tests the LAPACK RFP convertion routines.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVRF2 tests the LAPACK RFP convertion routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> ASAV is COMPLEX6 array, dimension (LDA,NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
* + S_WORK_CLANGE, C_WORK_CGEQRF, TAU )
* COMPLEX C_WORK_CGEQRF( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVRF3 tests the LAPACK RFP routines:
*> CTFSM
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> TAU is COMPLEX array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVRF4( NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A,
* + LDA, S_WORK_CLANGE )
* + CRF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVRF4 tests the LAPACK RFP routines:
*> CHFRK
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> S_WORK_CLANGE is REAL array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
* + THRESH, A, ASAV, AFAC, AINV, B,
* REAL S_WORK_CPOT03( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVRFP tests the LAPACK RFP routines:
*> CPFTRF, CPFTRS, and CPFTRI.
*> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
*> Errors occur when INFO parameter is not as expected. Failures occur when
*> a test ratios is greater than THRES.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> S_WORK_CPOT03 is REAL array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVSP tests the driver routines CSPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVSP tests the driver routines CSPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CDRVSY tests the driver routines CSYSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> CDRVSY tests the driver routines CSYSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CDRVSY tests the driver routines CSYSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cdrvsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CEBCHVXX( THRESH, PATH )
*
* Purpose
* ======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \details \b Purpose:
+*> \verbatim
+*>
*> CEBCHVXX will run CGESVXX on a series of Hilbert matrices and then
*> compare the error bounds returned by CGESVXX to see if the returned
*> answer indeed falls within those bounds.
*> type used plus one, which is 24 for single precision.
*> NMAX should be 6 for single and 11 for double.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRGE tests the error exits for the COMPLEX routines
*> for general matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRGE tests the error exits for the COMPLEX routines
*> for general matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cerrge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRGT( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRGT tests the error exits for the COMPLEX tridiagonal
*> routines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRHE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRHE tests the error exits for the COMPLEX routines
*> for Hermitian indefinite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRHE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRHE tests the error exits for the COMPLEX routines
*> for Hermitian indefinite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cerrhe.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRLQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRLQ tests the error exits for the COMPLEX routines
*> that use the LQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRLS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRLS tests the error exits for the COMPLEX least squares
*> driver routines (CGELS, CGELSS, CGELSX, CGELSY, CGELSD).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRPO tests the error exits for the COMPLEX routines
*> for Hermitian positive definite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRPO tests the error exits for the COMPLEX routines
*> for Hermitian positive definite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cerrpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRPS( PATH, NUNIT )
*
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRPS tests the error exits for the COMPLEX routines
*> for CPSTRF..
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRQL( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRQL tests the error exits for the COMPLEX routines
*> that use the QL decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRQP( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CERRQP tests the error exits for CGEQPF and CGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> CERRQP tests the error exits for CGEQPF and CGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRQR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRQR tests the error exits for the COMPLEX routines
*> that use the QR decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRRFP( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRRFP tests the error exits for the COMPLEX driver routines
*> for solving linear systems of equations.
*> CDRVRFP tests the COMPLEX LAPACK RFP routines:
*> CTFSM, CTFTRI, CHFRK, CTFTTP, CTFTTR, CPFTRF, CPFTRS, CTPTTF,
*> CTPTTR, CTRTTF, and CTRTTP
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRRQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRRQ tests the error exits for the COMPLEX routines
*> that use the RQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRSY tests the error exits for the COMPLEX routines
*> for symmetric indefinite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRSY tests the error exits for the COMPLEX routines
*> for symmetric indefinite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise cerrsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRTR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CERRTR tests the error exits for the COMPLEX triangular routines.
+*> \verbatim
*>
-*>\endverbatim
+*> CERRTR tests the error exits for the COMPLEX triangular routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRTZ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CERRTZ tests the error exits for CTZRQF and CTZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> CERRTZ tests the error exits for CTZRQF and CTZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRVX tests the error exits for the COMPLEX driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CERRVX tests the error exits for the COMPLEX driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
* RESID )
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBT01 reconstructs a band matrix A from its L*U factorization and
*> computes the residual:
*>
*> The expression L*U - A is computed one column at a time, so A and
*> AFAC are not modified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
* LDB, RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBT02 computes the residual for a solution of a banded system of
*> equations A*x = b or A'*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by CGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION CGENND (M, N, A, LDA)
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CGENND tests that its argument has a real, non-negative diagonal.
+*> \verbatim
*>
-*>\endverbatim
+*> CGENND tests that its argument has a real, non-negative diagonal.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QL factorization
*> A = Q*L
*> computed by CGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by CGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the RQ factorization
*> A = R*Q
*> computed by CGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
* RESID )
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET01 reconstructs a matrix A from its L*U factorization and
*> computes the residual
*> norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
* RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET03 computes the residual for a general matrix times its inverse:
*> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
* COMPLEX X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET04 computes the difference between a computed solution and the
*> true solution to a system of linear equations.
*> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*> where RCOND is the reciprocal of the condition number and EPS is the
*> machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The maximum over the NRHS solution vectors of
*> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, CHKFERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGET07 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
* LDWORK, RWORK, RESID )
* $ DU2( * ), DUF( * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTT01 reconstructs a tridiagonal matrix A from its LU factorization
*> and computes the residual
*> norm(L*U - A) / ( norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> The scaled residual: norm(L*U - A) / (norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
* RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTT02 computes the residual for the solution to a tridiagonal
*> system of equations:
*> RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESID is REAL
*> norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CGTT05( TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CGTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHET01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
* RWORK, RESID )
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHET01 reconstructs a Hermitian indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the conjugate transpose of L, and U' is the conjugate transpose
*> of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
*
* End of CHKXER.
*
* END
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
-*>\endverbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* COMPLEX A( * ), AFAC( * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CHPT01 reconstructs a Hermitian indefinite packed matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the conjugate transpose of L, and U' is the conjugate transpose
*> of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAHILB(N, NRHS, A, LDA, X, LDX, B, LDB, WORK,
* INFO, PATH)
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> PATH is CHARACTER*3
*> The LAPACK path name.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAIPD( N, A, INDA, VINDA )
*
* COMPLEX A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAIPD sets the imaginary part of the diagonal elements of a complex
*> matrix A to a large value. This is used to test LAPACK routines for
*> complex Hermitian matrices, which are not supposed to access or use
*> the imaginary parts of the diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 1: packed upper triangular matrix
*> = -1: packed lower triangular matrix
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
* LDB )
* COMPLEX B( LDB, * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal
*> matrix A and stores the result in a matrix B. The operation has the
*> B := alpha * A * X + beta * B
*>
*> where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
*> transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* REAL ANORM, CNDNUM
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATB4 sets parameters for the matrix generator based on the type of
*> matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATB5( PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATB5 sets parameters for the matrix generator based on the type
*> of matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATSP( UPLO, N, X, ISEED )
*
* COMPLEX X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATSP generates a special test matrix for the complex symmetric
*> (indefinite) factorization for packed matrices. The pivot blocks of
*> 2x2 pivot block, diagonalizable
*> (cycle repeats)
*> A row interchange is required for each non-diagonalizable 2x2 block.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, the seed for the random number generator. The last
*> of the four integers must be odd. (modified on exit)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATSY( UPLO, N, X, LDX, ISEED )
*
* COMPLEX X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATSY generates a special test matrix for the complex symmetric
*> (indefinite) factorization. The pivot blocks of the generated matrix
*> 2x2 pivot block, diagonalizable
*> (cycle repeats)
*> A row interchange is required for each non-diagonalizable 2x2 block.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, the seed for the random number generator. The last
*> of the four integers must be odd. (modified on exit)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB,
* LDAB, B, WORK, RWORK, INFO )
* COMPLEX AB( LDAB, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATTB generates a triangular test matrix in 2-dimensional storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATTP( IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, B, WORK,
* RWORK, INFO )
* COMPLEX AP( * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATTP generates a triangular test matrix in packed storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array AP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B,
* WORK, RWORK, INFO )
* COMPLEX A( LDA, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATTR generates a triangular test matrix in 2-dimensional storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAVHE( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAVHE performs one of the matrix-vector operations
*> x := A*x or x := A^H*x,
*> (or L or L * D).
*> If TRANS = 'C' or 'c', CLAVHE multiplies either by U^H or D * U^H
*> (or L^H or D * L^H ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAVHP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
* INFO )
* COMPLEX A( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAVHP performs one of the matrix-vector operations
*> x := A*x or x := A^H*x,
*> (or L or L * D).
*> If TRANS = 'C' or 'c', CLAVHP multiplies either by U^H or D * U^H
*> (or L^H or D * L^H ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
* INFO )
* COMPLEX A( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAVSP performs one of the matrix-vector operations
*> x := A*x or x := A^T*x,
*> (or L or L * D).
*> If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
*> (or L^T or D * L^T ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
* COMPLEX A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAVSY performs one of the matrix-vector operations
*> x := A*x or x := A'*x,
*> (or L or L * D).
*> If TRANS = 'T' or 't', CLAVSY multiplies either by U' or D * U'
*> (or L' or D * L' ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
*> matrix A, and partially tests CUNGLQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> CLQT01 compares L with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLQT02 tests CUNGLQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
*> checks that the rows of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLQT03 tests CUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> CLQT03 compares the results of a call to CUNMLQ with the results of
*> forming Q explicitly by a call to CUNGLQ and then performing matrix
*> multiplication by a call to CGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
* RESID )
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBT01 reconstructs a Hermitian positive definite band matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBT02 computes the residual for a solution of a Hermitian banded
*> system of equations A*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPBT05( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
*
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOT01 reconstructs a Hermitian positive definite matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of L,
*> and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOT02 computes the residual for the solution of a Hermitian system
*> of linear equations A*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*>
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOT03 computes the residual for a Hermitian matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPOT05( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPOT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* COMPLEX A( * ), AFAC( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPT01 reconstructs a Hermitian positive definite packed matrix A
*> from its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX A( * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPT02 computes the residual in the solution of a Hermitian system
*> of linear equations A*x = b when packed storage is used for the
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
*>
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
* RESID )
* COMPLEX A( * ), AINV( * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPT03 computes the residual for a Hermitian packed matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPPT05( UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
* PIV, RWORK, RESID, RANK )
* INTEGER PIV( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPST01 reconstructs an Hermitian positive semidefinite matrix A
*> from its L or U factors and the permutation matrix P and computes
*> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of L,
*> and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RANK is INTEGER
*> number of nonzero singular values of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTT01( N, D, E, DF, EF, WORK, RESID )
*
* COMPLEX E( * ), EF( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
*> factorization and computes the residual
*> norm(L*D*L' - A) / ( n * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> norm(L*D*L' - A) / (n * norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID )
*
* COMPLEX B( LDB, * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTT02 computes the residual for the solution to a symmetric
*> tridiagonal system of equations:
*> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(B - A*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CPTT05( N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT,
* FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CPTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQLT01 tests CGEQLF, which computes the QL factorization of an m-by-n
*> matrix A, and partially tests CUNGQL which forms the m-by-m
*> orthogonal matrix Q.
*>
*> CQLT01 compares L with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQLT02 tests CUNGQL, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> columns of A; it compares L(m-n+1:m,n-k+1:n) with
*> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQLT03 tests CUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> CQLT03 compares the results of a call to CUNMQL with the results of
*> forming Q explicitly by a call to CUNGQL and then performing matrix
*> multiplication by a call to CGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
* WORK, LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQPT01 tests the QR-factorization with pivoting of a matrix A. The
*> array AF contains the (possibly partial) QR-factorization of A, where
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*N+N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT01 tests CGEQRF, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests CUNGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> CQRT01 compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT01P tests CGEQRFP, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests CUNGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> CQRT01P compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
*> and checks that the columns of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT03 tests CUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> CQRT03 compares the results of a call to CUNMQR with the results of
*> forming Q explicitly by a call to CUNGQR and then performing matrix
*> multiplication by a call to CGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT04(M,N,NB,RESULT)
*
* .. Return values ..
* REAL RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CQRT04 tests CGEQRT and CGEMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> CQRT04 tests CGEQRT and CGEMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT05(M,N,L,NB,RESULT)
*
* .. Return values ..
* REAL RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> CQRT05 tests CTPQRT and CTPMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> CQRT05 tests CTPQRT and CTPMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CQRT11( M, K, A, LDA, TAU, WORK, LWORK )
*
* COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT11 computes the test ratio
*>
*> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
*> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
*> in A(k+1:m,k).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*M + M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK,
* RWORK )
* COMPLEX A( LDA, * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> RWORK is REAL array, dimension (4*min(M,N))
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT13 generates a full-rank matrix that may be scaled to have large
*> or small norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> ISEED is integer array, dimension (4)
*> Seed for random number generator
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CQRT14( TRANS, M, N, NRHS, A, LDA, X,
* LDX, WORK, LWORK )
* COMPLEX A( LDA, * ), WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT14 checks whether X is in the row space of A or A'. It does so
*> by scaling both X and A such that their norms are in the range
*> (if TRANS = 'C') or an LQ factorization of [A',X]' (if TRANS = 'N'),
*> and returning the norm of the trailing triangle, scaled by
*> MAX(M,N,NRHS)*eps.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
*> if TRANS = 'C', LWORK >= (N+NRHS)*(M+2).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
* RANK, NORMA, NORMB, ISEED, WORK, LWORK )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT15 generates a matrix with full or deficient rank and of various
*> norms.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> length of work space required.
*> LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT16 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CQRT17( TRANS, IRESID, M, N, NRHS, A,
* LDA, X, LDX, B, LDB, C, WORK, LWORK )
* $ WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CQRT17 computes the ratio
*>
*>
*> alpha = ||B|| if IRESID = 1 (zero-residual problem)
*> alpha = ||R|| if IRESID = 2 (otherwise).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= NRHS*(M+N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
*> matrix A, and partially tests CUNGRQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> CRQT01 compares R with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CRQT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CRQT02 tests CUNGRQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> rows of A; it compares R(m-k+1:m,n-m+1:n) with
*> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> CRQT03 compares the results of a call to CUNMRQ with the results of
*> forming Q explicitly by a call to CUNGRQ and then performing matrix
*> multiplication by a call to CGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CRZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CRZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with CTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CRZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* COMPLEX AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CRZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by CTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> Length of WORK array. LWORK >= N*N+N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* COMPLEX A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* COMPLEX A( * ), AFAC( * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPT01 reconstructs a symmetric indefinite packed matrix A from its
*> diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
*> the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX A( * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPT02 computes the residual in the solution of a complex symmetric
*> system of linear equations A*x = b when packed storage is used for
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*>
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
* RESID )
* COMPLEX A( * ), AINV( * ), WORK( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSPT03 computes the residual for a complex symmetric packed matrix
*> times its inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
* RWORK, RESID )
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYT01 reconstructs a complex symmetric indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the transpose of L, and U' is the transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYT02 computes the residual for a solution to a complex symmetric
*> system of linear equations A*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*>
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CSYT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CSYT03 computes the residual for a complex symmetric matrix times
*> its inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
* LDX, B, LDB, WORK, RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b, A**T *x = b, or
*> the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBT03( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
* SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK,
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b
*> the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
* RWORK, RAT )
* COMPLEX AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTBT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by CTBCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID )
*
* COMPLEX AINVP( * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPT01 computes the residual for a triangular matrix A times its
*> inverse when A is stored in packed format:
*> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
* WORK, RWORK, RESID )
* COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b, A**T *x = b, or
*> the maximum over the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
* TSCAL, X, LDX, B, LDB, WORK, RESID )
* COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b,
*> is the maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
*
* COMPLEX AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTPT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of the triangular matrix A) and RCONDC, the estimate
*> computed by CTPCON. Information about the triangular matrix is used
*> if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
* RWORK, RESID )
* COMPLEX A( LDA, * ), AINV( LDAINV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRT01 computes the residual for a triangular matrix A times its
*> inverse:
*> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
* LDB, WORK, RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b, A**T *x = b,
*> hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
* CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b.
*> right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
* RAT )
* COMPLEX A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTRT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by CTRCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CTZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with CTZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION CTZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* COMPLEX AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CTZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by CTZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. Must be >= N*N+N
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DCHKAA
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKAA is the main test program for the DOUBLE PRECISION LAPACK
*> linear equation routines
*> DTZ 3 List types on next line if 0 < NTYPES < 3
*> DLS 6 List types on next line if 0 < NTYPES < 6
*> DEQ
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NMAX INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_lin
*
-* =====================================================================
- PROGRAM DCHKAA
+* ===================================================================== PROGRAM DCHKAA
*
* -- LAPACK test routine (version 3.1.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DCHKAB
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKAB is the test program for the DOUBLE PRECISION LAPACK
*> DSGESV/DSPOSV routine
*> T Put T to test the error exits
*> DGE 11 List types on next line if 0 < NTYPES < 11
*> DPO 9 List types on next line if 0 < NTYPES < 9
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NMAX INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_lin
*
-* =====================================================================
- PROGRAM DCHKAB
+* ===================================================================== PROGRAM DCHKAB
*
* -- LAPACK test routine (version 3.2.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKEQ( THRESH, NOUT )
*
* DOUBLE PRECISION THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKGB tests DGBTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKGB tests DGBTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKGT tests DGTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKGT tests DGTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKLQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKLQ tests DGELQF, DORGLQ and DORMLQ.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKLQ tests DGELQF, DORGLQ and DORMLQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKPB tests DPBTRF, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKPB tests DPBTRF, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKPP tests DPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKPP tests DPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKPS( DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL,
* THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK,
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKPS tests DPSTRF.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKPS tests DPSTRF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, D, E, B, X, XACT, WORK, RWORK, NOUT )
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* THRESH, A, COPYA, S, TAU, WORK, IWORK,
* $ TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKQ3 tests DGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKQ3 tests DGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKQL( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKQL tests DGEQLF, DORGQL and DORMQL.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKQL tests DGEQLF, DORGQL and DORMQL.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKQP( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, IWORK, NOUT )
* $ TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKQP tests DGEQPF.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKQP tests DGEQPF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKQR( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKQR tests DGEQRF, DORGQR and DORMQR.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKQR tests DGEQRF, DORGQR and DORMQR.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM DCHKRFP
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DCHKRFP is the main test program for the DOUBLE PRECISION linear
*> equation routines with RFP storage format
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> MAXIN INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_lin
*
-* =====================================================================
- PROGRAM DCHKRFP
+* ===================================================================== PROGRAM DCHKRFP
*
* -- LAPACK test routine (version 3.2.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKRQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKRQ tests DGERQF, DORGRQ and DORMRQ.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKRQ tests DGERQF, DORGRQ and DORMRQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKSY( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKSY tests DSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKSY tests DSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKTP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKTP tests DTPTRI, -TRS, -RFS, and -CON, and DLATPS
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKTP tests DTPTRI, -TRS, -RFS, and -CON, and DLATPS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, NOUT )
* $ TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DCHKTZ tests DTZRQF and STZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> DCHKTZ tests DTZRQF and STZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVAB( DOTYPE, NM, MVAL, NNS,
* NSVAL, THRESH, NMAX, A, AFAC, B,
* $ RWORK( * ), WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVAB tests DSGESV
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVAB tests DSGESV
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVAC( DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX,
* A, AFAC, B, X, WORK,
* $ RWORK( * ), WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVAC tests DSPOSV.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVAC tests DSPOSV.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVGB tests the driver routines DGBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVGB tests the driver routines DGBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVGB tests the driver routines DGBSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise ddrvgb.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVGE tests the driver routines DGESV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVGE tests the driver routines DGESV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVGE tests the driver routines DGESV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise ddrvge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
* B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVGT tests DGTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVGT tests DGTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
* NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
* $ COPYS( * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSX,
*> DGELSY and DGELSD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVPB tests the driver routines DPBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVPB tests the driver routines DPBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVPO tests the driver routines DPOSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVPO tests the driver routines DPOSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVPO tests the driver routines DPOSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise ddrvpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVPP tests the driver routines DPPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVPP tests the driver routines DPPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
* E, B, X, XACT, WORK, RWORK, NOUT )
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVPT tests DPTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVPT tests DPTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVRF1( NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK )
*
* DOUBLE PRECISION A( LDA, * ), ARF( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVRF1 tests the LAPACK RFP routines:
*> DLANSF
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVRF2( NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV )
*
* DOUBLE PRECISION A( LDA, * ), ARF( * ), AP(*), ASAV( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVRF2 tests the LAPACK RFP convertion routines.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVRF2 tests the LAPACK RFP convertion routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> ASAV is DOUBLE PRECISION array, dimension (LDA,NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
* + D_WORK_DLANGE, D_WORK_DGEQRF, TAU )
* + D_WORK_DLANGE( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVRF3 tests the LAPACK RFP routines:
*> DTFSM
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVRF4( NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A,
* + LDA, D_WORK_DLANGE )
* + CRF( * ), D_WORK_DLANGE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVRF4 tests the LAPACK RFP routines:
*> DSFRK
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
* + THRESH, A, ASAV, AFAC, AINV, B,
* DOUBLE PRECISION D_WORK_DPOT03( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVRFP tests the LAPACK RFP routines:
*> DPFTRF, DPFTRS, and DPFTRI.
*> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
*> Errors occur when INFO parameter is not as expected. Failures occur when
*> a test ratios is greater than THRES.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> D_WORK_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVSP tests the driver routines DSPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVSP tests the driver routines DSPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DDRVSY tests the driver routines DSYSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> DDRVSY tests the driver routines DSYSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DDRVSY tests the driver routines DSYSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise ddrvsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DEBCHVXX( THRESH, PATH )
*
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*> DEBCHVXX will run D**SVXX on a series of Hilbert matrices and then
*> compare the error bounds returned by D**SVXX to see if the returned
*> answer indeed falls within those bounds.
*> type used plus one, which is 24 for single precision.
*> NMAX should be 6 for single and 11 for double.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRAB( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DERRAB tests the error exits for DSGESV.
+*> \verbatim
*>
-*>\endverbatim
+*> DERRAB tests the error exits for DSGESV.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRAC( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DERRAC tests the error exits for DSPOSV.
+*> \verbatim
*>
-*>\endverbatim
+*> DERRAC tests the error exits for DSPOSV.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRGE tests the error exits for the DOUBLE PRECISION routines
*> for general matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRGE tests the error exits for the DOUBLE PRECISION routines
*> for general matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise derrge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRGT( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRGT tests the error exits for the DOUBLE PRECISION tridiagonal
*> routines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRLQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRLQ tests the error exits for the DOUBLE PRECISION routines
*> that use the LQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRLS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRLS tests the error exits for the DOUBLE PRECISION least squares
*> driver routines (DGELS, SGELSS, SGELSX, SGELSY, SGELSD).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRPO tests the error exits for the DOUBLE PRECISION routines
*> for symmetric positive definite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRPO tests the error exits for the DOUBLE PRECISION routines
*> for symmetric positive definite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise derrpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRPS( PATH, NUNIT )
*
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRPS tests the error exits for the DOUBLE PRECISION routines
*> for DPSTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRQL( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRQL tests the error exits for the DOUBLE PRECISION routines
*> that use the QL decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRQP( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DERRQP tests the error exits for DGEQPF and DGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> DERRQP tests the error exits for DGEQPF and DGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRQR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRQR tests the error exits for the DOUBLE PRECISION routines
*> that use the QR decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRRFP( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRRFP tests the error exits for the DOUBLE PRECISION driver routines
*> for solving linear systems of equations.
*> DDRVRFP tests the DOUBLE PRECISION LAPACK RFP routines:
*> DTFSM, DTFTRI, DSFRK, DTFTTP, DTFTTR, DPFTRF, DPFTRS, DTPTTF,
*> DTPTTR, DTRTTF, and DTRTTP
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRRQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRRQ tests the error exits for the DOUBLE PRECISION routines
*> that use the RQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRSY tests the error exits for the DOUBLE PRECISION routines
*> for symmetric indefinite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRSY tests the error exits for the DOUBLE PRECISION routines
*> for symmetric indefinite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise derrsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRTR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRTR tests the error exits for the DOUBLE PRECISION triangular
*> routines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRTZ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DERRTZ tests the error exits for DTZRQF and STZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> DERRTZ tests the error exits for DTZRQF and STZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRVX tests the error exits for the DOUBLE PRECISION driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DERRVX tests the error exits for the DOUBLE PRECISION driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
* RESID )
* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBT01 reconstructs a band matrix A from its L*U factorization and
*> computes the residual:
*>
*> The expression L*U - A is computed one column at a time, so A and
*> AFAC are not modified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
* LDB, RESID )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBT02 computes the residual for a solution of a banded system of
*> equations A*x = b or A'*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by DGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION DGENND (M, N, A, LDA)
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DGENND tests that its argument has a non-negative diagonal.
+*> \verbatim
*>
-*>\endverbatim
+*> DGENND tests that its argument has a non-negative diagonal.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QL factorization
*> A = Q*L
*> computed by DGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by DGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the RQ factorization
*> A = R*Q
*> computed by DGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
* RESID )
* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET01 reconstructs a matrix A from its L*U factorization and
*> computes the residual
*> norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
* RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET03 computes the residual for a general matrix times its inverse:
*> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
* DOUBLE PRECISION X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET04 computes the difference between a computed solution and the
*> true solution to a system of linear equations.
*> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*> where RCOND is the reciprocal of the condition number and EPS is the
*> machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The maximum over the NRHS solution vectors of
*> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DGET06( RCOND, RCONDC )
*
* DOUBLE PRECISION RCOND, RCONDC
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DGET06 computes a test ratio to compare two values for RCOND.
+*> \verbatim
*>
-*>\endverbatim
+*> DGET06 computes a test ratio to compare two values for RCOND.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> The reciprocal of the condition number of A, computed as
*> ( 1/norm(A) ) / norm(inv(A)).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, CHKFERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET07 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGET08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGET08 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
* LDWORK, RWORK, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTT01 reconstructs a tridiagonal matrix A from its LU factorization
*> and computes the residual
*> norm(L*U - A) / ( norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The scaled residual: norm(L*U - A) / (norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
* RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTT02 computes the residual for the solution to a tridiagonal
*> system of equations:
*> RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DGTT05( TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DGTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAHILB(N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
*
* DOUBLE PRECISION A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be not exact.
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAORD( JOB, N, X, INCX )
*
* DOUBLE PRECISION X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAORD sorts the elements of a vector x in increasing or decreasing
*> order.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive elements of X. INCX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAPTM( N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAPTM multiplies an N by NRHS matrix X by a symmetric tridiagonal
*> matrix A and stores the result in a matrix B. The operation has the
*> B := alpha * A * X + beta * B
*>
*> where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A or A' (transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* DOUBLE PRECISION ANORM, CNDNUM
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATB4 sets parameters for the matrix generator based on the type of
*> matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATB5( PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATB5 sets parameters for the matrix generator based on the type
*> of matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB,
* LDAB, B, WORK, INFO )
* DOUBLE PRECISION AB( LDAB, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATTB generates a triangular test matrix in 2-dimensional storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATTP( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, B, WORK,
* INFO )
* DOUBLE PRECISION A( * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATTP generates a triangular test matrix in packed storage.
*> IMAT and UPLO uniquely specify the properties of the test
*> matrix, which is returned in the array AP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B,
* WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATTR generates a triangular test matrix.
*> IMAT and UPLO uniquely specify the properties of the test
*> matrix, which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
* INFO )
* DOUBLE PRECISION A( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAVSP performs one of the matrix-vector operations
*> x := A*x or x := A'*x,
*> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
*> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAVSY performs one of the matrix-vector operations
*> x := A*x or x := A'*x,
*> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
*> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLQT01 tests DGELQF, which computes the LQ factorization of an m-by-n
*> matrix A, and partially tests DORGLQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> DLQT01 compares L with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
*> checks that the rows of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> DLQT03 compares the results of a call to DORMLQ with the results of
*> forming Q explicitly by a call to DORGLQ and then performing matrix
*> multiplication by a call to DGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
* RESID )
* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBT01 reconstructs a symmetric positive definite band matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBT02 computes the residual for a solution of a symmetric banded
*> system of equations A*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPBT05( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
*
* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOT01 reconstructs a symmetric positive definite matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
* RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOT02 computes the residual for the solution of a symmetric system
*> of linear equations A*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*>
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOT03 computes the residual for a symmetric matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOT05( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPOT06 computes the residual for a solution of a system of linear
*> equations A*x = b :
*> RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* DOUBLE PRECISION A( * ), AFAC( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPT01 reconstructs a symmetric positive definite packed matrix A
*> from its L*L' or U'*U factorization and computes the residual
*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
* RESID )
* DOUBLE PRECISION A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPT02 computes the residual in the solution of a symmetric system
*> of linear equations A*x = b when packed storage is used for the
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
*>
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
* RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPT03 computes the residual for a symmetric packed matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPPT05( UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
* PIV, RWORK, RESID, RANK )
* INTEGER PIV( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPST01 reconstructs a symmetric positive semidefinite matrix A
*> from its L or U factors and the permutation matrix P and computes
*> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
*> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RANK is INTEGER
*> number of nonzero singular values of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTT01( N, D, E, DF, EF, WORK, RESID )
*
* DOUBLE PRECISION D( * ), DF( * ), E( * ), EF( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
*> factorization and computes the residual
*> norm(L*D*L' - A) / ( n * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*D*L' - A) / (n * norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
*
* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTT02 computes the residual for the solution to a symmetric
*> tridiagonal system of equations:
*> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(B - A*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DPTT05( N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT,
* FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DPTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQLT01 tests DGEQLF, which computes the QL factorization of an m-by-n
*> matrix A, and partially tests DORGQL which forms the m-by-m
*> orthogonal matrix Q.
*>
*> DQLT01 compares L with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQLT02 tests DORGQL, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> columns of A; it compares L(m-n+1:m,n-k+1:n) with
*> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> DQLT03 compares the results of a call to DORMQL with the results of
*> forming Q explicitly by a call to DORGQL and then performing matrix
*> multiplication by a call to DGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
* WORK, LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQPT01 tests the QR-factorization with pivoting of a matrix A. The
*> array AF contains the (possibly partial) QR-factorization of A, where
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*N+N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT01 tests DGEQRF, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests DORGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> DQRT01 compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT01P tests DGEQRFP, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests DORGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> DQRT01P compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT02 tests DORGQR, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
*> and checks that the columns of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> DQRT03 compares the results of a call to DORMQR with the results of
*> forming Q explicitly by a call to DORGQR and then performing matrix
*> multiplication by a call to DGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT04(M,N,NB,RESULT)
*
* .. Return values ..
* DOUBLE PRECISION RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DQRT04 tests DGEQRT and DGEMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> DQRT04 tests DGEQRT and DGEMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT05(M,N,L,NB,RESULT)
*
* .. Return values ..
* DOUBLE PRECISION RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DQRT05 tests DTPQRT and DTPMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> DQRT05 tests DTPQRT and DTPMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DQRT11( M, K, A, LDA, TAU, WORK, LWORK )
*
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT11 computes the test ratio
*>
*> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
*> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
*> in A(k+1:m,k).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*M + M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DQRT12( M, N, A, LDA, S, WORK, LWORK )
*
* DOUBLE PRECISION A( LDA, * ), S( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) +
*> max(M,N), M*N+2*MIN( M, N )+4*N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT13 generates a full-rank matrix that may be scaled to have large
*> or small norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> ISEED is integer array, dimension (4)
*> Seed for random number generator
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DQRT14( TRANS, M, N, NRHS, A, LDA, X,
* LDX, WORK, LWORK )
* DOUBLE PRECISION A( LDA, * ), WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT14 checks whether X is in the row space of A or A'. It does so
*> by scaling both X and A such that their norms are in the range
*> (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'),
*> and returning the norm of the trailing triangle, scaled by
*> MAX(M,N,NRHS)*eps.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
*> if TRANS = 'T', LWORK >= (N+NRHS)*(M+2).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
* RANK, NORMA, NORMB, ISEED, WORK, LWORK )
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT15 generates a matrix with full or deficient rank and of various
*> norms.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> length of work space required.
*> LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT16 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DQRT17( TRANS, IRESID, M, N, NRHS, A,
* LDA, X, LDX, B, LDB, C, WORK, LWORK )
* $ WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DQRT17 computes the ratio
*>
*>
*> alpha = ||B|| if IRESID = 1 (zero-residual problem)
*> alpha = ||R|| if IRESID = 2 (otherwise).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= NRHS*(M+N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n
*> matrix A, and partially tests DORGRQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> DRQT01 compares R with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DRQT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DRQT02 tests DORGRQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> rows of A; it compares R(m-k+1:m,n-m+1:n) with
*> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DRQT03 tests DORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> DRQT03 compares the results of a call to DORMRQ with the results of
*> forming Q explicitly by a call to DORGRQ and then performing matrix
*> multiplication by a call to DGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DRZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DRZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with DTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m*nb.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DRZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* DOUBLE PRECISION AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DRZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by DTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. LWORK >= N*N+N*NB.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* DOUBLE PRECISION A( * ), AFAC( * ), C( LDC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSPT01 reconstructs a symmetric indefinite packed matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
* RWORK, RESID )
* $ RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DSYT01 reconstructs a symmetric indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
* LDX, B, LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b or A' *x = b when
*> the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBT03( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
* SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b or A'*x = s*b when A is a
*> over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
* WORK, RAT )
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTBT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by DTBCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
*
* DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPT01 computes the residual for a triangular matrix A times its
*> inverse when A is stored in packed format:
*> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
* WORK, RESID )
* DOUBLE PRECISION AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b or A'*x = b when
*> the maximum over the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
* TSCAL, X, LDX, B, LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b or A'*x = s*b when the triangular
*> the maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
*
* DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTPT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by DTPCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
* WORK, RESID )
* DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRT01 computes the residual for a triangular matrix A times its
*> inverse:
*> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
* LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b or A'*x = b.
*> number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
* CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b or A'*x = s*b.
*> maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
* RAT )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTRT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by DTRCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DTZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with DTZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DTZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* DOUBLE PRECISION AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DTZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by DTZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. Must be >= N*N+N
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ICOPY( N, SX, INCX, SY, INCY )
*
* INTEGER SX( * ), SY( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ICOPY copies an integer vector x to an integer vector y.
*> Uses unrolled loops for increments equal to 1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> INCY is INTEGER
*> The spacing between consecutive elements of SY.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3,
* N4 )
* INTEGER ISPEC, N1, N2, N3, N4
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ILAENV returns problem-dependent parameters for the local
*> environment. See ISPEC for a description of the parameters.
*> the integer array IPARMS in the common block CLAENV and the value
*> with index ISPEC is copied to ILAENV. This version of ILAENV is
*> to be used in conjunction with XLAENV in TESTING and TIMING.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> >= 0: the value of the parameter specified by ISPEC
*> < 0: if ILAENV = -k, the k-th argument had an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_lin
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The following conventions have been used when calling ILAENV from the
*>
*> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
*> IF( NB.LE.1 ) NB = MAX( 1, N )
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM SCHKAA
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKAA is the main test program for the REAL LAPACK
*> linear equation routines
*> STZ 3 List types on next line if 0 < NTYPES < 3
*> SLS 6 List types on next line if 0 < NTYPES < 6
*> SEQ
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NMAX INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_lin
*
-* =====================================================================
- PROGRAM SCHKAA
+* ===================================================================== PROGRAM SCHKAA
*
* -- LAPACK test routine (version 3.1.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKEQ( THRESH, NOUT )
*
* REAL THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKGB tests SGBTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKGB tests SGBTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKGE tests SGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKGE tests SGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKGT tests SGTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKGT tests SGTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKLQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKLQ tests SGELQF, SORGLQ and SORMLQ.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKLQ tests SGELQF, SORGLQ and SORMLQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKPB tests SPBTRF, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKPB tests SPBTRF, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKPO tests SPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKPO tests SPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKPP tests SPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKPP tests SPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKPS( DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL,
* THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK,
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKPS tests SPSTRF.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKPS tests SPSTRF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, D, E, B, X, XACT, WORK, RWORK, NOUT )
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKPT tests SPTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKPT tests SPTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* THRESH, A, COPYA, S, TAU, WORK, IWORK,
* $ TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKQ3 tests SGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKQ3 tests SGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKQL( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKQL tests SGEQLF, SORGQL and SORMQL.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKQL tests SGEQLF, SORGQL and SORMQL.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKQP( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, IWORK, NOUT )
* $ TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKQP tests SGEQPF.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKQP tests SGEQPF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKQR( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKQR tests SGEQRF, SORGQR and SORMQR.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKQR tests SGEQRF, SORGQR and SORMQR.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM SCHKRFP
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SCHKRFP is the main test program for the REAL linear
*> equation routines with RFP storage format
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> MAXIN INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup single_lin
*
-* =====================================================================
- PROGRAM SCHKRFP
+* ===================================================================== PROGRAM SCHKRFP
*
* -- LAPACK test routine (version 3.2.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKRQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKRQ tests SGERQF, SORGRQ and SORMRQ.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKRQ tests SGERQF, SORGRQ and SORMRQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKSP tests SSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKSP tests SSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKSY( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKSY tests SSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKSY tests SSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKTB tests STBTRS, -RFS, and -CON, and SLATBS.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKTB tests STBTRS, -RFS, and -CON, and SLATBS.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKTP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKTP tests STPTRI, -TRS, -RFS, and -CON, and SLATPS
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKTP tests STPTRI, -TRS, -RFS, and -CON, and SLATPS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKTR tests STRTRI, -TRS, -RFS, and -CON, and SLATRS
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKTR tests STRTRI, -TRS, -RFS, and -CON, and SLATRS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, NOUT )
* $ TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SCHKTZ tests STZRQF and STZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> SCHKTZ tests STZRQF and STZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVGB tests the driver routines SGBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVGB tests the driver routines SGBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVGB tests the driver routines SGBSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise sdrvgb.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVGE tests the driver routines SGESV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVGE tests the driver routines SGESV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVGE tests the driver routines SGESV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise sdrvge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
* B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVGT tests SGTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVGT tests SGTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
* NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
* $ COPYS( * ), S( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVLS tests the least squares driver routines SGELS, SGELSS, SGELSX,
*> SGELSY and SGELSD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVPB tests the driver routines SPBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVPB tests the driver routines SPBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVPO tests the driver routines SPOSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVPO tests the driver routines SPOSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVPO tests the driver routines SPOSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise sdrvpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVPP tests the driver routines SPPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVPP tests the driver routines SPPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
* E, B, X, XACT, WORK, RWORK, NOUT )
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVPT tests SPTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVPT tests SPTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVRF1( NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK )
*
* REAL A( LDA, * ), ARF( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVRF1 tests the LAPACK RFP routines:
*> SLANSF
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> WORK is REAL array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVRF2( NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV )
*
* REAL A( LDA, * ), ARF( * ), AP(*), ASAV( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVRF2 tests the LAPACK RFP convertion routines.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVRF2 tests the LAPACK RFP convertion routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> ASAV is REAL array, dimension (LDA,NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
* + S_WORK_SLANGE, S_WORK_SGEQRF, TAU )
* + S_WORK_SLANGE( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVRF3 tests the LAPACK RFP routines:
*> STFSM
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> TAU is REAL array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVRF4( NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A,
* + LDA, S_WORK_SLANGE )
* + CRF( * ), S_WORK_SLANGE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVRF4 tests the LAPACK RFP routines:
*> SSFRK
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> S_WORK_SLANGE is REAL array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
* + THRESH, A, ASAV, AFAC, AINV, B,
* REAL S_WORK_SPOT03( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVRFP tests the LAPACK RFP routines:
*> SPFTRF, SPFTRS, and SPFTRI.
*> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
*> Errors occur when INFO parameter is not as expected. Failures occur when
*> a test ratios is greater than THRES.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> S_WORK_SPOT03 is REAL array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVSP tests the driver routines SSPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVSP tests the driver routines SSPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SDRVSY tests the driver routines SSYSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> SDRVSY tests the driver routines SSYSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SDRVSY tests the driver routines SSYSV, -SVX, and -SVXX
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise sdrvsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SEBCHVXX( THRESH, PATH )
*
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
*> SEBCHVXX will run S**SVXX on a series of Hilbert matrices and then
*> compare the error bounds returned by SGESVXX to see if the returned
*> answer indeed falls within those bounds.
*> type used plus one, which is 24 for single precision.
*> NMAX should be 6 for single and 11 for double.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRGE tests the error exits for the REAL routines
*> for general matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRGE tests the error exits for the REAL routines
*> for general matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise serrge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRGT( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRGT tests the error exits for the REAL tridiagonal
*> routines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRLQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRLQ tests the error exits for the REAL routines
*> that use the LQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRLS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRLS tests the error exits for the REAL least squares
*> driver routines (SGELS, SGELSS, SGELSX, SGELSY, SGELSD).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRPO tests the error exits for the REAL routines
*> for symmetric positive definite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRPO tests the error exits for the REAL routines
*> for symmetric positive definite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise serrpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRPS( PATH, NUNIT )
*
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRPS tests the error exits for the REAL routines
*> for SPSTRF..
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRQL( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRQL tests the error exits for the REAL routines
*> that use the QL decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRQP( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SERRQP tests the error exits for SGEQPF and SGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> SERRQP tests the error exits for SGEQPF and SGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRQR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRQR tests the error exits for the REAL routines
*> that use the QR decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRRFP( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRRFP tests the error exits for the REAL driver routines
*> for solving linear systems of equations.
*> SDRVRFP tests the REAL LAPACK RFP routines:
*> STFSM, STFTRI, SSFRK, STFTTP, STFTTR, SPFTRF, SPFTRS, STPTTF,
*> STPTTR, STRTTF, and STRTTP
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRRQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRRQ tests the error exits for the REAL routines
*> that use the RQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRSY tests the error exits for the REAL routines
*> for symmetric indefinite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRSY tests the error exits for the REAL routines
*> for symmetric indefinite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise serrsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRTR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRTR tests the error exits for the REAL triangular
*> routines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRTZ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SERRTZ tests the error exits for STZRQF and STZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> SERRTZ tests the error exits for STZRQF and STZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRVX tests the error exits for the REAL driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SERRVX tests the error exits for the REAL driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
* RESID )
* REAL A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBT01 reconstructs a band matrix A from its L*U factorization and
*> computes the residual:
*>
*> The expression L*U - A is computed one column at a time, so A and
*> AFAC are not modified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
* LDB, RESID )
* REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBT02 computes the residual for a solution of a banded system of
*> equations A*x = b or A'*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by SGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION SGENND (M, N, A, LDA)
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SGENND tests that its argument has a non-negative diagonal.
+*> \verbatim
*>
-*>\endverbatim
+*> SGENND tests that its argument has a non-negative diagonal.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QL factorization
*> A = Q*L
*> computed by SGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by SGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the RQ factorization
*> A = R*Q
*> computed by SGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
* RESID )
* REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET01 reconstructs a matrix A from its L*U factorization and
*> computes the residual
*> norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is REAL
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
* RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET03 computes the residual for a general matrix times its inverse:
*> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
* REAL X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET04 computes the difference between a computed solution and the
*> true solution to a system of linear equations.
*> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*> where RCOND is the reciprocal of the condition number and EPS is the
*> machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The maximum over the NRHS solution vectors of
*> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SGET06( RCOND, RCONDC )
*
* REAL RCOND, RCONDC
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SGET06 computes a test ratio to compare two values for RCOND.
+*> \verbatim
*>
-*>\endverbatim
+*> SGET06 computes a test ratio to compare two values for RCOND.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> The reciprocal of the condition number of A, computed as
*> ( 1/norm(A) ) / norm(inv(A)).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, CHKFERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGET07 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
* LDWORK, RWORK, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTT01 reconstructs a tridiagonal matrix A from its LU factorization
*> and computes the residual
*> norm(L*U - A) / ( norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> The scaled residual: norm(L*U - A) / (norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
* RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTT02 computes the residual for the solution to a tridiagonal
*> system of equations:
*> RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESID is REAL
*> norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SGTT05( TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SGTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAHILB(N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
*
* REAL A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be not exact.
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAORD( JOB, N, X, INCX )
*
* REAL X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAORD sorts the elements of a vector x in increasing or decreasing
*> order.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] JOB
*> \verbatim
*> INCX is INTEGER
*> The spacing between successive elements of X. INCX >= 0.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAPTM( N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB )
*
* REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAPTM multiplies an N by NRHS matrix X by a symmetric tridiagonal
*> matrix A and stores the result in a matrix B. The operation has the
*> B := alpha * A * X + beta * B
*>
*> where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A or A' (transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* REAL ANORM, CNDNUM
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATB4 sets parameters for the matrix generator based on the type of
*> matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATB5( PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATB5 sets parameters for the matrix generator based on the type
*> of matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB,
* LDAB, B, WORK, INFO )
* REAL AB( LDAB, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATTB generates a triangular test matrix in 2-dimensional storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATTP( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, B, WORK,
* INFO )
* REAL A( * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATTP generates a triangular test matrix in packed storage.
*> IMAT and UPLO uniquely specify the properties of the test
*> matrix, which is returned in the array AP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B,
* WORK, INFO )
* REAL A( LDA, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATTR generates a triangular test matrix.
*> IMAT and UPLO uniquely specify the properties of the test
*> matrix, which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
* INFO )
* REAL A( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAVSP performs one of the matrix-vector operations
*> x := A*x or x := A'*x,
*> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
*> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
* REAL A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAVSY performs one of the matrix-vector operations
*> x := A*x or x := A'*x,
*> If TRANS = 'N', multiplies by U or U * D (or L or L * D)
*> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
*> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLQT01 tests SGELQF, which computes the LQ factorization of an m-by-n
*> matrix A, and partially tests SORGLQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> SLQT01 compares L with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLQT02 tests SORGLQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
*> checks that the rows of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLQT03 tests SORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> SLQT03 compares the results of a call to SORMLQ with the results of
*> forming Q explicitly by a call to SORGLQ and then performing matrix
*> multiplication by a call to SGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
* RESID )
* REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBT01 reconstructs a symmetric positive definite band matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBT02 computes the residual for a solution of a symmetric banded
*> system of equations A*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPBT05( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
*
* REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOT01 reconstructs a symmetric positive definite matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
* RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOT02 computes the residual for the solution of a symmetric system
*> of linear equations A*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*>
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOT03 computes the residual for a symmetric matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPOT05( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPOT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* REAL A( * ), AFAC( * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPT01 reconstructs a symmetric positive definite packed matrix A
*> from its L*L' or U'*U factorization and computes the residual
*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
* RESID )
* REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPT02 computes the residual in the solution of a symmetric system
*> of linear equations A*x = b when packed storage is used for the
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
*>
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
* RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPT03 computes the residual for a symmetric packed matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPPT05( UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
* PIV, RWORK, RESID, RANK )
* INTEGER PIV( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPST01 reconstructs a symmetric positive semidefinite matrix A
*> from its L or U factors and the permutation matrix P and computes
*> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
*> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RANK is INTEGER
*> number of nonzero singular values of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTT01( N, D, E, DF, EF, WORK, RESID )
*
* REAL D( * ), DF( * ), E( * ), EF( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
*> factorization and computes the residual
*> norm(L*D*L' - A) / ( n * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> norm(L*D*L' - A) / (n * norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
*
* REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTT02 computes the residual for the solution to a symmetric
*> tridiagonal system of equations:
*> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is REAL
*> norm(B - A*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SPTT05( N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT,
* FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SPTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQLT01 tests SGEQLF, which computes the QL factorization of an m-by-n
*> matrix A, and partially tests SORGQL which forms the m-by-m
*> orthogonal matrix Q.
*>
*> SQLT01 compares L with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQLT02 tests SORGQL, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> columns of A; it compares L(m-n+1:m,n-k+1:n) with
*> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQLT03 tests SORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> SQLT03 compares the results of a call to SORMQL with the results of
*> forming Q explicitly by a call to SORGQL and then performing matrix
*> multiplication by a call to SGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
* WORK, LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQPT01 tests the QR-factorization with pivoting of a matrix A. The
*> array AF contains the (possibly partial) QR-factorization of A, where
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*N+N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests SORGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> SQRT01 compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT01P tests SGEQRFP, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests SORGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> SQRT01P compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT02 tests SORGQR, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
*> and checks that the columns of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> SQRT03 compares the results of a call to SORMQR with the results of
*> forming Q explicitly by a call to SORGQR and then performing matrix
*> multiplication by a call to SGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT04(M,N,NB,RESULT)
*
* .. Return values ..
* REAL RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SQRT04 tests SGEQRT and SGEMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> SQRT04 tests SGEQRT and SGEMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT05(M,N,L,NB,RESULT)
*
* .. Return values ..
* REAL RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> SQRT05 tests STPQRT and STPMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> SQRT05 tests STPQRT and STPMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SQRT11( M, K, A, LDA, TAU, WORK, LWORK )
*
* REAL A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT11 computes the test ratio
*>
*> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
*> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
*> in A(k+1:m,k).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*M + M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SQRT12( M, N, A, LDA, S, WORK, LWORK )
*
* REAL A( LDA, * ), S( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) +
*> max(M,N), M*N+2*MIN( M, N )+4*N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* REAL A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT13 generates a full-rank matrix that may be scaled to have large
*> or small norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> ISEED is integer array, dimension (4)
*> Seed for random number generator
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SQRT14( TRANS, M, N, NRHS, A, LDA, X,
* LDX, WORK, LWORK )
* REAL A( LDA, * ), WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT14 checks whether X is in the row space of A or A'. It does so
*> by scaling both X and A such that their norms are in the range
*> (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'),
*> and returning the norm of the trailing triangle, scaled by
*> MAX(M,N,NRHS)*eps.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
*> if TRANS = 'T', LWORK >= (N+NRHS)*(M+2).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
* RANK, NORMA, NORMB, ISEED, WORK, LWORK )
* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT15 generates a matrix with full or deficient rank and of various
*> norms.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> length of work space required.
*> LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT16 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SQRT17( TRANS, IRESID, M, N, NRHS, A,
* LDA, X, LDX, B, LDB, C, WORK, LWORK )
* $ WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SQRT17 computes the ratio
*>
*>
*> alpha = ||B|| if IRESID = 1 (zero-residual problem)
*> alpha = ||R|| if IRESID = 2 (otherwise).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= NRHS*(M+N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SRQT01 tests SGERQF, which computes the RQ factorization of an m-by-n
*> matrix A, and partially tests SORGRQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> SRQT01 compares R with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SRQT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SRQT02 tests SORGRQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> rows of A; it compares R(m-k+1:m,n-m+1:n) with
*> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SRQT03 tests SORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> SRQT03 compares the results of a call to SORMRQ with the results of
*> forming Q explicitly by a call to SORGRQ and then performing matrix
*> multiplication by a call to SGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SRZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with STZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m*nb.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SRZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* REAL AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SRZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by STZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. LWORK >= N*N+N*NB.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* REAL A( * ), AFAC( * ), C( LDC, * ), RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSPT01 reconstructs a symmetric indefinite packed matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
* RWORK, RESID )
* $ RWORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SSYT01 reconstructs a symmetric indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
* LDX, B, LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b or A' *x = b when
*> the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBT03( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
* SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK,
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b or A'*x = s*b when A is a
*> over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
* WORK, RAT )
* REAL AB( LDAB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STBT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by STBCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
*
* REAL AINVP( * ), AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPT01 computes the residual for a triangular matrix A times its
*> inverse when A is stored in packed format:
*> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
* WORK, RESID )
* REAL AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b or A'*x = b when
*> the maximum over the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
* TSCAL, X, LDX, B, LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b or A'*x = s*b when the triangular
*> the maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
*
* REAL AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STPT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by STPCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
* WORK, RESID )
* REAL A( LDA, * ), AINV( LDAINV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRT01 computes the residual for a triangular matrix A times its
*> inverse:
*> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is REAL
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
* LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b or A'*x = b.
*> number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
* CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
* $ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b or A'*x = s*b.
*> maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE STRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
* RAT )
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STRT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by STRCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION STZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with STZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION STZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* REAL AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> STZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by STZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. Must be >= N*N+N
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XERBLA( SRNAME, INFO )
*
* INTEGER INFO
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> This is a special version of XERBLA to be used only as part of
*> the test program for testing error exits from the LAPACK routines.
*> Error messages are printed if INFO.NE.INFOT or if SRNAME.NE.SRNAMT,
*> where INFOT and SRNAMT are values stored in COMMON.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SRNAME
*> \verbatim
*> The error return code from the calling subroutine. INFO
*> should equal the COMMON variable INFOT.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup aux_eig
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> The following variables are passed via the common blocks INFOC and
*> SRNAME = SRNAMT, otherwise set to .FALSE.
*> LERR LOGICAL Set to .TRUE., indicating that XERBLA was called
*> SRNAMT CHARACTER*(*) Expected name of calling subroutine
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE XLAENV( ISPEC, NVALUE )
*
* INTEGER ISPEC, NVALUE
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> XLAENV sets certain machine- and problem-dependent quantities
*> which will later be retrieved by ILAENV.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] ISPEC
*> \verbatim
*> NVALUE is INTEGER
*> The value of the parameter specified by ISPEC.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZCHKAA
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKAA is the main test program for the COMPLEX*16 linear equation
*> routines.
*> ZTZ 3 List types on next line if 0 < NTYPES < 3
*> ZLS 6 List types on next line if 0 < NTYPES < 6
*> ZEQ
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NMAX INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_lin
*
-* =====================================================================
- PROGRAM ZCHKAA
+* ===================================================================== PROGRAM ZCHKAA
*
* -- LAPACK test routine (version 3.1.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZCHKAB
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKAB is the test program for the COMPLEX*16 LAPACK
*> ZCGESV/ZCPOSV routine
*> T Put T to test the error exits
*> DGE 11 List types on next line if 0 < NTYPES < 11
*> DPO 9 List types on next line if 0 < NTYPES < 9
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> NMAX INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_lin
*
-* =====================================================================
- PROGRAM ZCHKAB
+* ===================================================================== PROGRAM ZCHKAB
*
* -- LAPACK test routine (version 3.2.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKEQ( THRESH, NOUT )
*
* DOUBLE PRECISION THRESH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKEQ tests ZGEEQU, ZGBEQU, ZPOEQU, ZPPEQU and ZPBEQU
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKEQ tests ZGEEQU, ZGBEQU, ZPOEQU, ZPPEQU and ZPBEQU
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] THRESH
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKGB tests ZGBTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKGB tests ZGBTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKGE tests ZGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKGE tests ZGETRF, -TRI, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKGT tests ZGTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKGT tests ZGTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKHE( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKHE tests ZHETRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKHE tests ZHETRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKHP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKHP tests ZHPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKHP tests ZHPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKLQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKLQ tests ZGELQF, ZUNGLQ and CUNMLQ.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKLQ tests ZGELQF, ZUNGLQ and CUNMLQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKPB tests ZPBTRF, -TRS, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKPB tests ZPBTRF, -TRS, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKPO tests ZPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKPO tests ZPOTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKPP tests ZPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKPP tests ZPPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKPS( DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL,
* THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK,
* LOGICAL DOTYPE( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKPS tests ZPSTRF.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKPS tests ZPSTRF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* A, D, E, B, X, XACT, WORK, RWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKPT tests ZPTTRF, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKPT tests ZPTTRF, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* THRESH, A, COPYA, S, TAU, WORK, RWORK,
* COMPLEX*16 A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKQ3 tests ZGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKQ3 tests ZGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKQL( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKQL tests ZGEQLF, ZUNGQL and CUNMQL.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKQL tests ZGEQLF, ZUNGQL and CUNMQL.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKQP( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, RWORK, IWORK,
* COMPLEX*16 A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKQP tests ZGEQPF.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKQP tests ZGEQPF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKQR( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKQR tests ZGEQRF, ZUNGQR and CUNMQR.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKQR tests ZGEQRF, ZUNGQR and CUNMQR.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* PROGRAM ZCHKRFP
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZCHKRFP is the main test program for the COMPLEX*16 linear equation
*> routines with RFP storage format
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> MAXIN INTEGER
*> NOUT INTEGER
*> The unit number for output
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_lin
*
-* =====================================================================
- PROGRAM ZCHKRFP
+* ===================================================================== PROGRAM ZCHKRFP
*
* -- LAPACK test routine (version 3.2.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKRQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
* NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
* $ B( * ), TAU( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKRQ tests ZGERQF, ZUNGRQ and CUNMRQ.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKRQ tests ZGERQF, ZUNGRQ and CUNMRQ.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKSP tests ZSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKSP tests ZSPTRF, -TRI, -TRS, -RFS, and -CON
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKSY( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKSY tests ZSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKSY tests ZSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKTB tests ZTBTRS, -RFS, and -CON, and ZLATBS.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKTB tests ZTBTRS, -RFS, and -CON, and ZLATBS.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKTP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKTP tests ZTPTRI, -TRS, -RFS, and -CON, and ZLATPS
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKTP tests ZTPTRI, -TRS, -RFS, and -CON, and ZLATPS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKTR tests ZTRTRI, -TRS, -RFS, and -CON, and ZLATRS
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKTR tests ZTRTRI, -TRS, -RFS, and -CON, and ZLATRS
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZCHKTZ( DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A,
* COPYA, S, TAU, WORK, RWORK, NOUT )
* COMPLEX*16 A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZCHKTZ tests ZTZRQF and ZTZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> ZCHKTZ tests ZTZRQF and ZTZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVAB( DOTYPE, NM, MVAL, NNS,
* NSVAL, THRESH, NMAX, A, AFAC, B,
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVAB tests ZCGESV
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVAB tests ZCGESV
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVAC( DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX,
* A, AFAC, B, X, WORK,
* $ WORK( * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVAC tests ZCPOSV.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVAC tests ZCPOSV.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVGB tests the driver routines ZGBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVGB tests the driver routines ZGBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVGB tests the driver routines ZGBSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zdrvgb.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVGE tests the driver routines ZGESV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVGE tests the driver routines ZGESV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVGE tests the driver routines ZGESV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zdrvge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
* B, X, XACT, WORK, RWORK, IWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVGT tests ZGTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVGT tests ZGTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVHE tests the driver routines ZHESV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVHE tests the driver routines ZHESV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVHE tests the driver routines ZHESV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zdrvhe.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVHP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVHP tests the driver routines ZHPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVHP tests the driver routines ZHPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
* NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
* $ WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVLS tests the least squares driver routines ZGELS, CGELSX, CGELSS,
*> ZGELSY and CGELSD.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVPB tests the driver routines ZPBSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVPB tests the driver routines ZPBSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVPO tests the driver routines ZPOSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVPO tests the driver routines ZPOSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVPO tests the driver routines ZPOSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zdrvpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
* $ BSAV( * ), WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVPP tests the driver routines ZPPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVPP tests the driver routines ZPPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
* E, B, X, XACT, WORK, RWORK, NOUT )
* $ XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVPT tests ZPTSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVPT tests ZPTSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVRF1( NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK )
*
* COMPLEX*16 A( LDA, * ), ARF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVRF1 tests the LAPACK RFP routines:
*> ZLANHF.F
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVRF2( NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV )
*
* COMPLEX*16 A( LDA, * ), ARF( * ), AP(*), ASAV( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVRF2 tests the LAPACK RFP convertion routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVRF2 tests the LAPACK RFP convertion routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> ASAV is COMPLEX*16 array, dimension (LDA,NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
* + D_WORK_ZLANGE, Z_WORK_ZGEQRF, TAU )
* COMPLEX*16 Z_WORK_ZGEQRF( * ), TAU( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVRF3 tests the LAPACK RFP routines:
*> ZTFSM
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVRF4( NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A,
* + LDA, D_WORK_ZLANGE )
* + CRF( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVRF4 tests the LAPACK RFP routines:
*> ZHFRK
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> D_WORK_ZLANGE is DOUBLE PRECISION array, dimension (NMAX)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
* + THRESH, A, ASAV, AFAC, AINV, B,
* DOUBLE PRECISION D_WORK_ZPOT03( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVRFP tests the LAPACK RFP routines:
*> ZPFTRF, ZPFTRS, and ZPFTRI.
*> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
*> Errors occur when INFO parameter is not as expected. Failures occur when
*> a test ratios is greater than THRES.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NOUT
*> \verbatim
*> \verbatim
*> D_WORK_ZPOT03 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVSP tests the driver routines ZSPSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVSP tests the driver routines ZSPSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZDRVSY tests the driver routines ZSYSV and -SVX.
+*> \verbatim
*>
-*>\endverbatim
+*> ZDRVSY tests the driver routines ZSYSV and -SVX.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
* $ WORK( * ), X( * ), XACT( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZDRVSY tests the driver routines ZSYSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zdrvsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZEBCHVXX( THRESH, PATH )
*
* Purpose
* ======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \details \b Purpose:
+*> \verbatim
+*>
*> ZEBCHVXX will run Z**SVXX on a series of Hilbert matrices and then
*> compare the error bounds returned by Z**SVXX to see if the returned
*> answer indeed falls within those bounds.
*> type used plus one, which is 24 for single precision.
*> NMAX should be 6 for single and 11 for double.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRAB( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> DERRAB tests the error exits for ZCGESV.
+*> \verbatim
*>
-*>\endverbatim
+*> DERRAB tests the error exits for ZCGESV.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRAC( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZERRPX tests the error exits for ZCPOSV.
+*> \verbatim
*>
-*>\endverbatim
+*> ZERRPX tests the error exits for ZCPOSV.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRGE tests the error exits for the COMPLEX*16 routines
*> for general matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRGE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRGE tests the error exits for the COMPLEX*16 routines
*> for general matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zerrge.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRGT( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRGT tests the error exits for the COMPLEX*16 tridiagonal
*> routines.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRHE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRHE tests the error exits for the COMPLEX*16 routines
*> for Hermitian indefinite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRHE( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRHE tests the error exits for the COMPLEX*16 routines
*> for Hermitian indefinite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zerrhe.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRLQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRLQ tests the error exits for the COMPLEX*16 routines
*> that use the LQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRLS( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRLS tests the error exits for the COMPLEX*16 least squares
*> driver routines (ZGELS, CGELSS, CGELSX, CGELSY, CGELSD).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRPO tests the error exits for the COMPLEX*16 routines
*> for Hermitian positive definite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRPO( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRPO tests the error exits for the COMPLEX*16 routines
*> for Hermitian positive definite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zerrpo.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRPS( PATH, NUNIT )
*
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRPS tests the error exits for the COMPLEX routines
*> for ZPSTRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRQL( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRQL tests the error exits for the COMPLEX*16 routines
*> that use the QL decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRQP( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZERRQP tests the error exits for ZGEQPF and CGEQP3.
+*> \verbatim
*>
-*>\endverbatim
+*> ZERRQP tests the error exits for ZGEQPF and CGEQP3.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRQR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRQR tests the error exits for the COMPLEX*16 routines
*> that use the QR decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRRFP( NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRRFP tests the error exits for the COMPLEX*16 driver routines
*> for solving linear systems of equations.
*> ZDRVRFP tests the COMPLEX*16 LAPACK RFP routines:
*> ZTFSM, ZTFTRI, ZHFRK, ZTFTTP, ZTFTTR, ZPFTRF, ZPFTRS, ZTPTTF,
*> ZTPTTR, ZTRTTF, and ZTRTTP
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] NUNIT
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRRQ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRRQ tests the error exits for the COMPLEX*16 routines
*> that use the RQ decomposition of a general matrix.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRSY tests the error exits for the COMPLEX*16 routines
*> for symmetric indefinite matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRSY( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRSY tests the error exits for the COMPLEX*16 routines
*> for symmetric indefinite matrices.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zerrsy.f defines this subroutine.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRTR( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZERRTR tests the error exits for the COMPLEX*16 triangular routines.
+*> \verbatim
*>
-*>\endverbatim
+*> ZERRTR tests the error exits for the COMPLEX*16 triangular routines.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRTZ( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZERRTZ tests the error exits for ZTZRQF and ZTZRZF.
+*> \verbatim
*>
-*>\endverbatim
+*> ZERRTZ tests the error exits for ZTZRQF and ZTZRZF.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRVX tests the error exits for the COMPLEX*16 driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZERRVX( PATH, NUNIT )
*
* INTEGER NUNIT
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZERRVX tests the error exits for the COMPLEX*16 driver routines
*> for solving linear systems of equations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> NUNIT is INTEGER
*> The unit number for output.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
* RESID )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBT01 reconstructs a band matrix A from its L*U factorization and
*> computes the residual:
*>
*> The expression L*U - A is computed one column at a time, so A and
*> AFAC are not modified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
* LDB, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBT02 computes the residual for a solution of a banded system of
*> equations A*x = b or A'*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by ZGELQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* LOGICAL FUNCTION ZGENND (M, N, A, LDA)
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZGENND tests that its argument has a real, non-negative diagonal.
+*> \verbatim
*>
-*>\endverbatim
+*> ZGENND tests that its argument has a real, non-negative diagonal.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDA is INTEGER
*> Leading dimension of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QL factorization
*> A = Q*L
*> computed by ZGEQLF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by ZGEQRF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the RQ factorization
*> A = R*Q
*> computed by ZGERQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
* RESID )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET01 reconstructs a matrix A from its L*U factorization and
*> computes the residual
*> norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
* RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET03 computes the residual for a general matrix times its inverse:
*> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
* COMPLEX*16 X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET04 computes the difference between a computed solution and the
*> true solution to a system of linear equations.
*> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*> where RCOND is the reciprocal of the condition number and EPS is the
*> machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> The maximum over the NRHS solution vectors of
*> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, CHKFERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET07 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGET08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGET08 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
* LDWORK, RWORK, RESID )
* $ DU2( * ), DUF( * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTT01 reconstructs a tridiagonal matrix A from its LU factorization
*> and computes the residual
*> norm(L*U - A) / ( norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The scaled residual: norm(L*U - A) / (norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
* RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTT02 computes the residual for the solution to a tridiagonal
*> system of equations:
*> RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZGTT05( TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ X( LDX, * ), XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZGTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHET01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHET01 reconstructs a Hermitian indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the conjugate transpose of L, and U' is the conjugate transpose
*> of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the conjugate transpose of L, and U' is the conjugate transpose
*> of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAHILB(N, NRHS, A, LDA, X, LDX, B, LDB, WORK,
* INFO, PATH)
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> PATH is CHARACTER*3
*> The LAPACK path name.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAIPD( N, A, INDA, VINDA )
*
* COMPLEX*16 A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAIPD sets the imaginary part of the diagonal elements of a complex
*> matrix A to a large value. This is used to test LAPACK routines for
*> complex Hermitian matrices, which are not supposed to access or use
*> the imaginary parts of the diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 1: packed upper triangular matrix
*> = -1: packed lower triangular matrix
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
* LDB )
* COMPLEX*16 B( LDB, * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal
*> matrix A and stores the result in a matrix B. The operation has the
*> B := alpha * A * X + beta * B
*>
*> where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
* A, LDA, X, LDX, B, LDB, ISEED, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*> op( A ) * X = B,
*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
*> transpose of A).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* DOUBLE PRECISION ANORM, CNDNUM
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATB4 sets parameters for the matrix generator based on the type of
*> matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATB5( PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE,
* CNDNUM, DIST )
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATB5 sets parameters for the matrix generator based on the type
*> of matrix to be generated.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PATH
*> \verbatim
*> The type of distribution to be used by the random number
*> generator.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATSP( UPLO, N, X, ISEED )
*
* COMPLEX*16 X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATSP generates a special test matrix for the complex symmetric
*> (indefinite) factorization for packed matrices. The pivot blocks of
*> 2x2 pivot block, diagonalizable
*> (cycle repeats)
*> A row interchange is required for each non-diagonalizable 2x2 block.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, the seed for the random number generator. The last
*> of the four integers must be odd. (modified on exit)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATSY( UPLO, N, X, LDX, ISEED )
*
* COMPLEX*16 X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATSY generates a special test matrix for the complex symmetric
*> (indefinite) factorization. The pivot blocks of the generated matrix
*> 2x2 pivot block, diagonalizable
*> (cycle repeats)
*> A row interchange is required for each non-diagonalizable 2x2 block.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> On entry, the seed for the random number generator. The last
*> of the four integers must be odd. (modified on exit)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB,
* LDAB, B, WORK, RWORK, INFO )
* COMPLEX*16 AB( LDAB, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATTB generates a triangular test matrix in 2-dimensional storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATTP( IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, B, WORK,
* RWORK, INFO )
* COMPLEX*16 AP( * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATTP generates a triangular test matrix in packed storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array AP.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B,
* WORK, RWORK, INFO )
* COMPLEX*16 A( LDA, * ), B( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATTR generates a triangular test matrix in 2-dimensional storage.
*> IMAT and UPLO uniquely specify the properties of the test matrix,
*> which is returned in the array A.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IMAT
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAVHE( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAVHE performs one of the matrix-vector operations
*> x := A*x or x := A^H*x,
*> (or L or L * D).
*> If TRANS = 'C' or 'c', ZLAVHE multiplies either by U^H or D * U^H
*> (or L^H or D * L^H ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAVHP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
* INFO )
* COMPLEX*16 A( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAVHP performs one of the matrix-vector operations
*> x := A*x or x := A^H*x,
*> (or L or L * D).
*> If TRANS = 'C' or 'c', ZLAVHP multiplies either by U^H or D * U^H
*> (or L^H or D * L^H ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
* INFO )
* COMPLEX*16 A( * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAVSP performs one of the matrix-vector operations
*> x := A*x or x := A^T*x,
*> (or L or L * D).
*> If TRANS = 'C' or 'c', ZLAVSP multiplies either by U^T or D * U^T
*> (or L^T or D * L^T ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAVSY( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B,
* LDB, INFO )
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAVSY performs one of the matrix-vector operations
*> x := A*x or x := A'*x,
*> (or L or L * D).
*> If TRANS = 'T' or 't', ZLAVSY multiplies either by U' or D * U'
*> (or L' or D * L' ).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> A negative value, say -K, indicates that the K-th argument
*> has an illegal value.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n
*> matrix A, and partially tests ZUNGLQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> ZLQT01 compares L with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLQT02 tests ZUNGLQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
*> checks that the rows of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLQT03 tests ZUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> ZLQT03 compares the results of a call to ZUNMLQ with the results of
*> forming Q explicitly by a call to ZUNGLQ and then performing matrix
*> multiplication by a call to ZGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
* RESID )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBT01 reconstructs a Hermitian positive definite band matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBT02 computes the residual for a solution of a Hermitian banded
*> system of equations A*x = b:
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPBT05( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
*
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOT01 reconstructs a Hermitian positive definite matrix A from
*> its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of L,
*> and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOT02 computes the residual for the solution of a Hermitian system
*> of linear equations A*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*>
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOT03 computes the residual for a Hermitian matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOT05( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPOT06 computes the residual for a solution of a system of linear
*> equations A*x = b :
*> RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* COMPLEX*16 A( * ), AFAC( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPT01 reconstructs a Hermitian positive definite packed matrix A
*> from its L*L' or U'*U factorization and computes the residual
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX*16 A( * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPT02 computes the residual in the solution of a Hermitian system
*> of linear equations A*x = b when packed storage is used for the
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
*>
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
* RESID )
* COMPLEX*16 A( * ), AINV( * ), WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPT03 computes the residual for a Hermitian packed matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPPT05( UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT,
* LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
* PIV, RWORK, RESID, RANK )
* INTEGER PIV( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPST01 reconstructs an Hermitian positive semidefinite matrix A
*> from its L or U factors and the permutation matrix P and computes
*> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of L,
*> and U' is the conjugate transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RANK is INTEGER
*> number of nonzero singular values of A.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTT01( N, D, E, DF, EF, WORK, RESID )
*
* COMPLEX*16 E( * ), EF( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
*> factorization and computes the residual
*> norm(L*D*L' - A) / ( n * norm(A) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*D*L' - A) / (n * norm(A) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID )
*
* COMPLEX*16 B( LDB, * ), E( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTT02 computes the residual for the solution to a symmetric
*> tridiagonal system of equations:
*> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(B - A*X) / (norm(A) * norm(X) * EPS)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZPTT05( N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT,
* FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZPTT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQLT01 tests ZGEQLF, which computes the QL factorization of an m-by-n
*> matrix A, and partially tests ZUNGQL which forms the m-by-m
*> orthogonal matrix Q.
*>
*> ZQLT01 compares L with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQLT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQLT02 tests ZUNGQL, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> columns of A; it compares L(m-n+1:m,n-k+1:n) with
*> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQLT03 tests ZUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> ZQLT03 compares the results of a call to ZUNMQL with the results of
*> forming Q explicitly by a call to ZUNGQL and then performing matrix
*> multiplication by a call to ZGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
* WORK, LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQPT01 tests the QR-factorization with pivoting of a matrix A. The
*> array AF contains the (possibly partial) QR-factorization of A, where
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*N+N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT01 tests ZGEQRF, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests ZUNGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> ZQRT01 compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT01P tests ZGEQRFP, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests ZUNGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> ZQRT01P compares R with Q'*A, and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT02 tests ZUNGQR, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> the orthogonal matrix Q defined by the factorization of the first k
*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
*> and checks that the columns of Q are orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT03 tests ZUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> ZQRT03 compares the results of a call to ZUNMQR with the results of
*> forming Q explicitly by a call to ZUNGQR and then performing matrix
*> multiplication by a call to ZGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT04(M,N,NB,RESULT)
*
* .. Return values ..
* DOUBLE PRECISION RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZQRT04 tests ZGEQRT and ZGEMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> ZQRT04 tests ZGEQRT and ZGEMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT05(M,N,L,NB,RESULT)
*
* .. Return values ..
* DOUBLE PRECISION RESULT(6)
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
*>
-*> ZQRT05 tests ZTPQRT and ZTPMQRT.
+*> \verbatim
*>
-*>\endverbatim
+*> ZQRT05 tests ZTPQRT and ZTPMQRT.
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(5) = | C Q - C Q |
*> RESULT(6) = | C Q^H - C Q^H |
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZQRT11( M, K, A, LDA, TAU, WORK, LWORK )
*
* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT11 computes the test ratio
*>
*> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
*> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
*> in A(k+1:m,k).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*M + M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK,
* RWORK )
* COMPLEX*16 A( LDA, * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (2*min(M,N))
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT13 generates a full-rank matrix that may be scaled to have large
*> or small norm.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> ISEED is integer array, dimension (4)
*> Seed for random number generator
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZQRT14( TRANS, M, N, NRHS, A, LDA, X,
* LDX, WORK, LWORK )
* COMPLEX*16 A( LDA, * ), WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT14 checks whether X is in the row space of A or A'. It does so
*> by scaling both X and A such that their norms are in the range
*> (if TRANS = 'C') or an LQ factorization of [A',X]' (if TRANS = 'N'),
*> and returning the norm of the trailing triangle, scaled by
*> MAX(M,N,NRHS)*eps.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
*> if TRANS = 'C', LWORK >= (N+NRHS)*(M+2).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
* RANK, NORMA, NORMB, ISEED, WORK, LWORK )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT15 generates a matrix with full or deficient rank and of various
*> norms.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SCALE
*> \verbatim
*> length of work space required.
*> LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT16 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZQRT17( TRANS, IRESID, M, N, NRHS, A,
* LDA, X, LDX, B, LDB, C, WORK, LWORK )
* $ WORK( LWORK ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZQRT17 computes the ratio
*>
*>
*> alpha = ||B|| if IRESID = 1 (zero-residual problem)
*> alpha = ||R|| if IRESID = 2 (otherwise).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TRANS
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= NRHS*(M+N).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n
*> matrix A, and partially tests ZUNGRQ which forms the n-by-n
*> orthogonal matrix Q.
*>
*> ZRQT01 compares R with A*Q', and checks that Q is orthogonal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZRQT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> rows of A; it compares R(m-k+1:m,n-m+1:n) with
*> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
*> orthonormal.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> ZRQT03 compares the results of a call to ZUNMRQ with the results of
*> forming Q explicitly by a call to ZUNGRQ and then performing matrix
*> multiplication by a call to ZGEMM.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZRZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZRZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with ZTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZRZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZRZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by ZTZRZF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> Length of WORK array. LWORK >= N*N+N.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
* INCY )
* COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSBMV performs the matrix-vector operation
*>
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> UPLO - CHARACTER*1
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPT01 reconstructs a symmetric indefinite packed matrix A from its
*> diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
*> the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX*16 A( * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPT02 computes the residual in the solution of a complex symmetric
*> system of linear equations A*x = b when packed storage is used for
*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*>
*> where EPS is the machine precision.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
* RESID )
* COMPLEX*16 A( * ), AINV( * ), WORK( LDW, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSPT03 computes the residual for a complex symmetric packed matrix
*> times its inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYT01 reconstructs a complex symmetric indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the transpose of L, and U' is the transpose of U.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
* RESID )
* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYT02 computes the residual for a solution to a complex symmetric
*> system of linear equations A*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*>
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZSYT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
* $ WORK( LDWORK, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZSYT03 computes the residual for a complex symmetric matrix times
*> its inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
* LDX, B, LDB, WORK, RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b, A**T *x = b, or
*> the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBT03( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
* SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK,
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b
*> the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> = the maximum of BERR / ( NZ*EPS + (*) ), where
*> (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
*> and NZ = max. number of nonzeros in any row of A, plus 1
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( NZ*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
* RWORK, RAT )
* COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTBT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by ZTBCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID )
*
* COMPLEX*16 AINVP( * ), AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPT01 computes the residual for a triangular matrix A times its
*> inverse when A is stored in packed format:
*> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
* WORK, RWORK, RESID )
* COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b, A**T *x = b, or
*> the maximum over the number of right hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
* TSCAL, X, LDX, B, LDB, WORK, RESID )
* COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b,
*> is the maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
* XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
*
* COMPLEX*16 AP( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTPT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of the triangular matrix A) and RCONDC, the estimate
*> computed by ZTPCON. Information about the triangular matrix is used
*> if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
* RWORK, RESID )
* COMPLEX*16 A( LDA, * ), AINV( LDAINV, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRT01 computes the residual for a triangular matrix A times its
*> inverse:
*> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
* LDB, WORK, RWORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRT02 computes the residual for the computed solution to a
*> triangular system of linear equations A*x = b, A**T *x = b,
*> hand sides of
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
* CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
* $ X( LDX, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b.
*> right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
* LDX, XACT, LDXACT, FERR, BERR, RESLTS )
* $ XACT( LDXACT, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRT05 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations A*X = B, where A is a
*> RESLTS(2) = residual from the iterative refinement routine
*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] UPLO
*> \verbatim
*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
* RAT )
* COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTRT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by ZTRCON. Information about the triangular matrix A is
*> used if one estimate is zero and the other is non-zero to decide if
*> underflow in the estimate is justified.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] RCOND
*> \verbatim
*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
*> If RAT = 0, the two estimates are exactly the same.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZTZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
* $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with ZTZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION ZTZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
* COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZTZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by ZTZRQF.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. Must be >= N*N+N
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAGGE generates a complex general m by n matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with random unitary matrices:
*> A = U*D*V. The lower and upper bandwidths may then be reduced to
*> kl and ku by additional unitary transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAGHE generates a complex hermitian matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with a random unitary matrix:
*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
*> unitary transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAGSY generates a complex symmetric matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with a random unitary matrix:
*> A = U*D*U**T. The semi-bandwidth may then be reduced to k by
*> additional unitary transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK,
* INFO, PATH)
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> PATH is CHARACTER*3
*> The LAPACK path name.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* ..
*
* =====================================================================
-
* .. Local Scalars ..
INTEGER TM, TI, R
INTEGER M
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
*
* $ E( LDA, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Form the 2*M*N by 2*M*N matrix
*>
*> where In is the identity matrix of size n and X' is the transpose
*> of X. kron(X, Y) is the Kronecker product between the matrices X
*> and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of Z. ( LDZ >= 2*M*N )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARGE pre- and post-multiplies a complex general n by n matrix A
*> with a random unitary matrix: A = U*D*U'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX FUNCTION CLARND( IDIST, ISEED )
*
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLARND returns a random complex number from a uniform or normal
*> distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine SLARAN to generate a random
*> real number from a uniform (0,1) distribution. The Box-Muller method
*> is used to transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO )
*
* COMPLEX A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAROR pre- or post-multiplies an M by N matrix A by a random
*> unitary matrix U, overwriting A. A may optionally be
*> U is generated using the method of G.W. Stewart
*> ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ).
*> (BLAS-2 version)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> to M.
*> -6 if LDA is less than M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
* XRIGHT )
* COMPLEX A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLAROT applies a (Givens) rotation to two adjacent rows or
*> columns, where one element of the first and/or last column/row
*>
*> . . . . . .
*> A(1,i),LDA-1, XTOP, XBOTTM )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> LROWS - LOGICAL
*> (if LROWS=.FALSE.).
*> Read and modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* COMPLEX D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATM1 computes the entries of D(1..N) as specified by
*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. CLATM1 is called by CLATMR to generate
*> random test matrices for LAPACK programs.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] MODE
*> \verbatim
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4
*> -7 => if N negative
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX FUNCTION CLATM2( M, N, I, J, KL, KU, IDIST, ISEED, D,
* IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
* COMPLEX D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATM2 returns the (I,J) entry of a random matrix of dimension
*> (M, N) described by the other paramters. It is called by the
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX FUNCTION CLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
* COMPLEX D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATM3 returns the (ISUB,JSUB) entry of a random matrix of
*> dimension (M, N) described by the other paramters. (ISUB,JSUB)
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
* $ L( LDL, * ), R( LDR, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATM5 generates matrices involved in the Generalized Sylvester
*> equation:
*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] )
*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PRTYPE
*> \verbatim
*> blocks on the diagonal in B. Otherwise, QBLCKB is not
*> referenced. QBLCKB > 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
*> L, R specifies the right hand sides (C, F).
*>
*> PRTYPE = 5 special case common and/or close eigs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
* BETA, WX, WY, S, DIF )
* $ Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATM6 generates test matrices for the generalized eigenvalue
*> problem, their corresponding right and left eigenvector matrices,
*> 0 0 0 0 1, 0 0 0 0 1 , where
*>
*> a, b, x and y will have all values independently of each other.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> DIF is REAL array, dimension (N)
*> DIF(i) is the reciprocal condition number for eigenvector i.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATME( N, DIST, ISEED, D, MODE, COND, DMAX,
* RSIGN,
* COMPLEX A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATME generates random non-symmetric square matrices with
*> specified eigenvalues for testing LAPACK programs.
*>
*> (Note: since the matrix cannot be reduced beyond Hessenberg form,
*> no packing options are available.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> 4 => Error return from CLARGE
*> 5 => Zero singular value from SLATM1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
* COMPLEX A( LDA, * ), D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATMR generates random matrices of various types for testing
*> LAPACK programs.
*> in the order of the rows and/or columns, and otherwise
*> contain the same data. This consistency cannot be and
*> is not maintained with less than full bandwidth.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 5 => ANORM is positive, but matrix constructed prior to
*> attempting to scale it to have norm ANORM, is zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* KL, KU, PACK, A, LDA, WORK, INFO )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATMS generates random matrices with specified singular values
*> (or hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from CLAGGE, CLAGHE or CLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE CLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RANK, KL, KU, PACK, A, LDA, WORK, INFO )
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> CLATMT generates random matrices with specified singular values
*> (or hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from CLAGGE, CLAGHE or CLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGGE generates a real general m by n matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with random orthogonal matrices:
*> A = U*D*V. The lower and upper bandwidths may then be reduced to
*> kl and ku by additional orthogonal transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAGSY generates a real symmetric matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with a random orthogonal matrix:
*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
*> orthogonal transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
*
* DOUBLE PRECISION A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be not exact.
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* ..
*
* =====================================================================
-
* .. Local Scalars ..
INTEGER TM, TI, R
INTEGER M
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
*
* $ E( LDA, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Form the 2*M*N by 2*M*N matrix
*>
*> where In is the identity matrix of size n and X' is the transpose
*> of X. kron(X, Y) is the Kronecker product between the matrices X
*> and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of Z. ( LDZ >= 2*M*N )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLARAN( ISEED )
*
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARAN returns a random real number from a uniform (0,1)
*> distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] ISEED
*> \verbatim
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup list_temp
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine uses a multiplicative congruential method with modulus
*> 48-bit integers are stored in 4 integer array elements with 12 bits
*> per element. Hence the routine is portable across machines with
*> integers of 32 bits or more.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARGE pre- and post-multiplies a real general n by n matrix A
*> with a random orthogonal matrix: A = U*D*U'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLARND( IDIST, ISEED )
*
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLARND returns a random real number from a uniform or normal
*> distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine DLARAN to generate a random
*> real number from a uniform (0,1) distribution. The Box-Muller method
*> is used to transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO )
*
* DOUBLE PRECISION A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAROR pre- or post-multiplies an M by N matrix A by a random
*> orthogonal matrix U, overwriting A. A may optionally be initialized
*> to the identity matrix before multiplying by U. U is generated using
*> the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> = 1: if the random numbers generated by DLARND are bad.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
* XRIGHT )
* DOUBLE PRECISION A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLAROT applies a (Givens) rotation to two adjacent rows or
*> columns, where one element of the first and/or last column/row
*>
*> . . . . . .
*> A(1,i),LDA-1, XTOP, XBOTTM )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> LROWS - LOGICAL
*> (if LROWS=.FALSE.).
*> Read and modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* DOUBLE PRECISION D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM1 computes the entries of D(1..N) as specified by
*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. DLATM1 is called by SLATMR to generate
*> random test matrices for LAPACK programs.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] MODE
*> \verbatim
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
*> -7 => if N negative
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLATM2( M, N, I, J, KL, KU, IDIST,
* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
* DOUBLE PRECISION D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM2 returns the (I,J) entry of a random matrix of dimension
*> (M, N) described by the other paramters. It is called by the
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* DOUBLE PRECISION FUNCTION DLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
* DOUBLE PRECISION D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM3 returns the (ISUB,JSUB) entry of a random matrix of
*> dimension (M, N) described by the other paramters. (ISUB,JSUB)
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
* $ L( LDL, * ), R( LDR, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM5 generates matrices involved in the Generalized Sylvester
*> equation:
*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] )
*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PRTYPE
*> \verbatim
*> blocks on the diagonal in B. Otherwise, QBLCKB is not
*> referenced. QBLCKB > 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup double_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
*> L, R specifies the right hand sides (C, F).
*>
*> PRTYPE = 5 special case common and/or close eigs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
* BETA, WX, WY, S, DIF )
* $ X( LDX, * ), Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM6 generates test matrices for the generalized eigenvalue
*> problem, their corresponding right and left eigenvector matrices,
*> 0 0 0 0 1, 0 0 0 0 1 ,
*>
*> where a, b, x and y will have all values independently of each other.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> DIF is DOUBLE PRECISION array, dimension (N)
*> DIF(i) is the reciprocal condition number for eigenvector i.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
* RANK, INFO )
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATM7 computes the entries of D as specified by MODE
*> COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. DLATM7 is called by DLATMT to generate
*> random test matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> MODE - INTEGER
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
*> -7 => if N negative
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI,
* RSIGN,
* DOUBLE PRECISION A( LDA, * ), D( * ), DS( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATME generates random non-symmetric square matrices with
*> specified eigenvalues for testing LAPACK programs.
*>
*> (Note: since the matrix cannot be reduced beyond Hessenberg form,
*> no packing options are available.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> 4 => Error return from DLARGE
*> 5 => Zero singular value from DLATM1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
* DOUBLE PRECISION A( LDA, * ), D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATMR generates random matrices of various types for testing
*> LAPACK programs.
*> in the order of the rows and/or columns, and otherwise
*> contain the same data. This consistency cannot be and
*> is not maintained with less than full bandwidth.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 5 => ANORM is positive, but matrix constructed prior to
*> attempting to scale it to have norm ANORM, is zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* KL, KU, PACK, A, LDA, WORK, INFO )
* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATMS generates random matrices with specified singular values
*> (or symmetric/hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from DLAGGE or SLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE DLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RANK, KL, KU, PACK, A, LDA, WORK, INFO )
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> DLATMT generates random matrices with specified singular values
*> (or symmetric/hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from DLAGGE or DLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
*
* REAL A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGGE generates a real general m by n matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with random orthogonal matrices:
*> A = U*D*V. The lower and upper bandwidths may then be reduced to
*> kl and ku by additional orthogonal transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
*
* REAL A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAGSY generates a real symmetric matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with a random orthogonal matrix:
*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
*> orthogonal transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
*
* REAL A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N)
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> be not exact.
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* ..
*
* =====================================================================
-
* .. Local Scalars ..
INTEGER TM, TI, R
INTEGER M
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
*
* $ E( LDA, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Form the 2*M*N by 2*M*N matrix
*>
*> where In is the identity matrix of size n and X' is the transpose
*> of X. kron(X, Y) is the Kronecker product between the matrices X
*> and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of Z. ( LDZ >= 2*M*N )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLARAN( ISEED )
*
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARAN returns a random real number from a uniform (0,1)
*> distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in,out] ISEED
*> \verbatim
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup real_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine uses a multiplicative congruential method with modulus
*> 48-bit integers are stored in 4 integer array elements with 12 bits
*> per element. Hence the routine is portable across machines with
*> integers of 32 bits or more.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* REAL A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARGE pre- and post-multiplies a real general n by n matrix A
*> with a random orthogonal matrix: A = U*D*U'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLARND( IDIST, ISEED )
*
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLARND returns a random real number from a uniform or normal
*> distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup real_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine SLARAN to generate a random
*> real number from a uniform (0,1) distribution. The Box-Muller method
*> is used to transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO )
*
* REAL A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAROR pre- or post-multiplies an M by N matrix A by a random
*> orthogonal matrix U, overwriting A. A may optionally be initialized
*> to the identity matrix before multiplying by U. U is generated using
*> the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409).
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> < 0: if INFO = -k, the k-th argument had an illegal value
*> = 1: if the random numbers generated by SLARND are bad.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
* XRIGHT )
* REAL A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLAROT applies a (Givens) rotation to two adjacent rows or
*> columns, where one element of the first and/or last column/row
*>
*> . . . . . .
*> A(1,i),LDA-1, XTOP, XBOTTM )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> LROWS - LOGICAL
*> (if LROWS=.FALSE.).
*> Read and modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* REAL D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM1 computes the entries of D(1..N) as specified by
*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. SLATM1 is called by SLATMR to generate
*> random test matrices for LAPACK programs.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] MODE
*> \verbatim
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
*> -7 => if N negative
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLATM2( M, N, I, J, KL, KU, IDIST,
* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
* REAL D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM2 returns the (I,J) entry of a random matrix of dimension
*> (M, N) described by the other paramters. It is called by the
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* REAL FUNCTION SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
* REAL D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM3 returns the (ISUB,JSUB) entry of a random matrix of
*> dimension (M, N) described by the other paramters. (ISUB,JSUB)
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
* $ L( LDL, * ), R( LDR, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM5 generates matrices involved in the Generalized Sylvester
*> equation:
*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] )
*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PRTYPE
*> \verbatim
*> blocks on the diagonal in B. Otherwise, QBLCKB is not
*> referenced. QBLCKB > 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup real_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
*> L, R specifies the right hand sides (C, F).
*>
*> PRTYPE = 5 special case common and/or close eigs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
* BETA, WX, WY, S, DIF )
* $ X( LDX, * ), Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM6 generates test matrices for the generalized eigenvalue
*> problem, their corresponding right and left eigenvector matrices,
*> 0 0 0 0 1, 0 0 0 0 1 ,
*>
*> where a, b, x and y will have all values independently of each other.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> DIF is REAL array, dimension (N)
*> DIF(i) is the reciprocal condition number for eigenvector i.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
* RANK, INFO )
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATM7 computes the entries of D as specified by MODE
*> COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. SLATM7 is called by SLATMT to generate
*> random test matrices.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> MODE - INTEGER
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
*> -7 => if N negative
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI,
* RSIGN,
* REAL A( LDA, * ), D( * ), DS( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATME generates random non-symmetric square matrices with
*> specified eigenvalues for testing LAPACK programs.
*>
*> (Note: since the matrix cannot be reduced beyond Hessenberg form,
*> no packing options are available.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> 4 => Error return from SLARGE
*> 5 => Zero singular value from SLATM1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
* REAL A( LDA, * ), D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATMR generates random matrices of various types for testing
*> LAPACK programs.
*> in the order of the rows and/or columns, and otherwise
*> contain the same data. This consistency cannot be and
*> is not maintained with less than full bandwidth.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 5 => ANORM is positive, but matrix constructed prior to
*> attempting to scale it to have norm ANORM, is zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* KL, KU, PACK, A, LDA, WORK, INFO )
* REAL A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATMS generates random matrices with specified singular values
*> (or symmetric/hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from SLAGGE or SLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE SLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RANK, KL, KU, PACK, A, LDA, WORK, INFO )
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> SLATMT generates random matrices with specified singular values
*> (or symmetric/hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from SLAGGE or SLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAGGE generates a complex general m by n matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with random unitary matrices:
*> A = U*D*V. The lower and upper bandwidths may then be reduced to
*> kl and ku by additional unitary transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAGHE generates a complex hermitian matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with a random unitary matrix:
*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
*> unitary transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAGSY generates a complex symmetric matrix A, by pre- and post-
*> multiplying a real diagonal matrix D with a random unitary matrix:
*> A = U*D*U**T. The semi-bandwidth may then be reduced to k by
*> additional unitary transformations.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK,
* INFO, PATH)
* CHARACTER*3 PATH
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAHILB generates an N by N scaled Hilbert matrix in A along with
*> NRHS right-hand sides in B and solutions in X such that A*X=B.
*>
*> In single, the generated solution is exact for N <= 6 and has
*> small componentwise error for 7 <= N <= 11.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> PATH is CHARACTER*3
*> The LAPACK path name.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* ..
*
* =====================================================================
-
* .. Local Scalars ..
INTEGER TM, TI, R
INTEGER M
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
*
* $ E( LDA, * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> Form the 2*M*N by 2*M*N matrix
*>
*> where In is the identity matrix of size n and X' is the transpose
*> of X. kron(X, Y) is the Kronecker product between the matrices X
*> and Y.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of Z. ( LDZ >= 2*M*N )
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARGE pre- and post-multiplies a complex general n by n matrix A
*> with a random unitary matrix: A = U*D*U'.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX*16 FUNCTION ZLARND( IDIST, ISEED )
*
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLARND returns a random complex number from a uniform or normal
*> distribution.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] IDIST
*> \verbatim
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> This routine calls the auxiliary routine DLARAN to generate a random
*> real number from a uniform (0,1) distribution. The Box-Muller method
*> is used to transform numbers from a uniform to a normal distribution.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO )
*
* COMPLEX*16 A( LDA, * ), X( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAROR pre- or post-multiplies an M by N matrix A by a random
*> unitary matrix U, overwriting A. A may optionally be
*> U is generated using the method of G.W. Stewart
*> ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ).
*> (BLAS-2 version)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] SIDE
*> \verbatim
*> to M.
*> -6 if LDA is less than M.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
* XRIGHT )
* COMPLEX*16 A( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLAROT applies a (Givens) rotation to two adjacent rows or
*> columns, where one element of the first and/or last column/row
*>
*> . . . . . .
*> A(1,i),LDA-1, XTOP, XBOTTM )
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \verbatim
*> LROWS - LOGICAL
*> (if LROWS=.FALSE.).
*> Read and modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* COMPLEX*16 D( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATM1 computes the entries of D(1..N) as specified by
*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. ZLATM1 is called by CLATMR to generate
*> random test matrices for LAPACK programs.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] MODE
*> \verbatim
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4
*> -7 => if N negative
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX*16 FUNCTION ZLATM2( M, N, I, J, KL, KU, IDIST,
* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
* COMPLEX*16 D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATM2 returns the (I,J) entry of a random matrix of dimension
*> (M, N) described by the other paramters. It is called by the
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* COMPLEX*16 FUNCTION ZLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
* COMPLEX*16 D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of
*> dimension (M, N) described by the other paramters. (ISUB,JSUB)
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
* $ L( LDL, * ), R( LDR, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATM5 generates matrices involved in the Generalized Sylvester
*> equation:
*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] )
*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )
*>
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] PRTYPE
*> \verbatim
*> blocks on the diagonal in B. Otherwise, QBLCKB is not
*> referenced. QBLCKB > 1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*
*> \ingroup complex16_matgen
*
-*
-* Further Details
-* ===============
-*>\details \b Further \b Details
+*> \par Further Details:
+* =====================
+*>
*> \verbatim
*>
*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
*> L, R specifies the right hand sides (C, F).
*>
*> PRTYPE = 5 special case common and/or close eigs.
-*>
*> \endverbatim
*>
* =====================================================================
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
* BETA, WX, WY, S, DIF )
* $ Y( LDY, * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATM6 generates test matrices for the generalized eigenvalue
*> problem, their corresponding right and left eigenvector matrices,
*> 0 0 0 0 1, 0 0 0 0 1 , where
*>
*> a, b, x and y will have all values independently of each other.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] TYPE
*> \verbatim
*> DIF is DOUBLE PRECISION array, dimension (N)
*> DIF(i) is the reciprocal condition number for eigenvector i.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATME( N, DIST, ISEED, D, MODE, COND, DMAX,
* RSIGN,
* COMPLEX*16 A( LDA, * ), D( * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATME generates random non-symmetric square matrices with
*> specified eigenvalues for testing LAPACK programs.
*>
*> (Note: since the matrix cannot be reduced beyond Hessenberg form,
*> no packing options are available.)
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] N
*> \verbatim
*> 4 => Error return from ZLARGE
*> 5 => Zero singular value from DLATM1.
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
* COMPLEX*16 A( LDA, * ), D( * ), DL( * ), DR( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATMR generates random matrices of various types for testing
*> LAPACK programs.
*> in the order of the rows and/or columns, and otherwise
*> contain the same data. This consistency cannot be and
*> is not maintained with less than full bandwidth.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 5 => ANORM is positive, but matrix constructed prior to
*> attempting to scale it to have norm ANORM, is zero
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* KL, KU, PACK, A, LDA, WORK, INFO )
* COMPLEX*16 A( LDA, * ), WORK( * )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATMS generates random matrices with specified singular values
*> (or hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from ZLAGGE, CLAGHE or CLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
-* Definition
-* ==========
+* Definition:
+* ===========
*
* SUBROUTINE ZLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
* RANK, KL, KU, PACK, A, LDA, WORK, INFO )
* INTEGER ISEED( 4 )
* ..
*
-* Purpose
-* =======
*
-*>\details \b Purpose:
-*>\verbatim
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
*>
*> ZLATMT generates random matrices with specified singular values
*> (or hermitian with specified eigenvalues)
*> If Method B is chosen, and band format is specified, then the
*> matrix will be generated in the band format, so no repacking
*> will be necessary.
-*>
-*>\endverbatim
+*> \endverbatim
*
-* Arguments
-* =========
+* Arguments:
+* ==========
*
*> \param[in] M
*> \verbatim
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
*> 3 => Error return from ZLAGGE, ZLAGHE or ZLAGSY
*> \endverbatim
-*>
*
-* Authors
-* =======
+* Authors:
+* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
projects / platform / upstream / lapack.git / commitdiff