slaqtr.f slar1v.f slar2v.f ilaslr.f ilaslc.f
slarf.f slarfb.f slarfg.f slarfgp.f slarft.f slarfx.f slargv.f
slarrv.f slartv.f
- slarz.f slarzb.f slarzt.f slaswp.f slasy2.f slasyf.f slasyf_rook.f
+ slarz.f slarzb.f slarzt.f slaswp.f slasy2.f slasyf.f slasyf_rook.f slasyf_aasen.f
slatbs.f slatdf.f slatps.f slatrd.f slatrs.f slatrz.f
slauu2.f slauum.f sopgtr.f sopmtr.f sorg2l.f sorg2r.f
sorgbr.f sorghr.f sorgl2.f sorglq.f sorgql.f sorgqr.f sorgr2.f
ssygst.f ssygv.f ssygvd.f ssygvx.f ssyrfs.f ssysv.f ssysvx.f
ssytd2.f ssytf2.f ssytrd.f ssytrf.f ssytri.f ssytri2.f ssytri2x.f
ssyswapr.f ssytrs.f ssytrs2.f ssyconv.f
+ ssysv_aasen.f ssytrf_aasen.f ssytrs_aasen.f
ssytf2_rook.f ssytrf_rook.f ssytrs_rook.f
ssytri_rook.f ssycon_rook.f ssysv_rook.f
stbcon.f
chetf2.f chetrd.f
chetrf.f chetri.f chetri2.f chetri2x.f cheswapr.f
chetrs.f chetrs2.f
+ chesv_aasen.f chetrf_aasen.f chetrs_aasen.f
chetf2_rook.f chetrf_rook.f chetri_rook.f chetrs_rook.f checon_rook.f chesv_rook.f
chgeqz.f chpcon.f chpev.f chpevd.f
chpevx.f chpgst.f chpgv.f chpgvd.f chpgvx.f chprfs.f chpsv.f
clacgv.f clacon.f clacn2.f clacp2.f clacpy.f clacrm.f clacrt.f cladiv.f
claed0.f claed7.f claed8.f
claein.f claesy.f claev2.f clags2.f clagtm.f
- clahef.f clahef_rook.f clahqr.f
+ clahef.f clahef_rook.f clahef_aasen.f clahqr.f
clahr2.f claic1.f clals0.f clalsa.f clalsd.f clangb.f clange.f clangt.f
clanhb.f clanhe.f
clanhp.f clanhs.f clanht.f clansb.f clansp.f clansy.f clantb.f
dlaqtr.f dlar1v.f dlar2v.f iladlr.f iladlc.f
dlarf.f dlarfb.f dlarfg.f dlarfgp.f dlarft.f dlarfx.f dlargv.f
dlarrv.f dlartv.f
- dlarz.f dlarzb.f dlarzt.f dlaswp.f dlasy2.f dlasyf.f dlasyf_rook.f
+ dlarz.f dlarzb.f dlarzt.f dlaswp.f dlasy2.f dlasyf.f dlasyf_rook.f dlasyf_aasen.f
dlatbs.f dlatdf.f dlatps.f dlatrd.f dlatrs.f dlatrz.f dlauu2.f
dlauum.f dopgtr.f dopmtr.f dorg2l.f dorg2r.f
dorgbr.f dorghr.f dorgl2.f dorglq.f dorgql.f dorgqr.f dorgr2.f
dsysv.f dsysvx.f
dsytd2.f dsytf2.f dsytrd.f dsytrf.f dsytri.f dsytrs.f dsytrs2.f
dsytri2.f dsytri2x.f dsyswapr.f dsyconv.f
+ dsysv_aasen.f dsytrf_aasen.f dsytrs_aasen.f
dsytf2_rook.f dsytrf_rook.f dsytrs_rook.f
dsytri_rook.f dsycon_rook.f dsysv_rook.f
dtbcon.f
zhetf2.f zhetrd.f
zhetrf.f zhetri.f zhetri2.f zhetri2x.f zheswapr.f
zhetrs.f zhetrs2.f
+ zhesv_aasen.f zhetrf_aasen.f zhetrs_aasen.f
zhetf2_rook.f zhetrf_rook.f zhetri_rook.f zhetrs_rook.f zhecon_rook.f zhesv_rook.f
zhgeqz.f zhpcon.f zhpev.f zhpevd.f
zhpevx.f zhpgst.f zhpgv.f zhpgvd.f zhpgvx.f zhprfs.f zhpsv.f
zlacgv.f zlacon.f zlacn2.f zlacp2.f zlacpy.f zlacrm.f zlacrt.f zladiv.f
zlaed0.f zlaed7.f zlaed8.f
zlaein.f zlaesy.f zlaev2.f zlags2.f zlagtm.f
- zlahef.f zlahef_rook.f zlahqr.f
+ zlahef.f zlahef_rook.f zlahef_aasen.f zlahqr.f
zlahr2.f zlaic1.f zlals0.f zlalsa.f zlalsd.f zlangb.f zlange.f
zlangt.f zlanhb.f
zlanhe.f
ssytd2.o ssytf2.o ssytrd.o ssytrf.o ssytri.o ssytri2.o ssytri2x.o \
ssyswapr.o ssytrs.o ssytrs2.o ssyconv.o \
ssytf2_rook.o ssytrf_rook.o ssytrs_rook.o \
+ slasyf_aasen.o ssysv_aasen.o ssytrf_aasen.o ssytrs_aasen.o \
ssytri_rook.o ssycon_rook.o ssysv_rook.o \
stbcon.o \
stbrfs.o stbtrs.o stgevc.o stgex2.o stgexc.o stgsen.o \
chetrf.o chetri.o chetri2.o chetri2x.o cheswapr.o \
chetrs.o chetrs2.o \
chetf2_rook.o chetrf_rook.o chetri_rook.o chetrs_rook.o checon_rook.o chesv_rook.o \
+ chesv_aasen.o chetrf_aasen.o chetrs_aasen.o clahef_aasen.o\
chgeqz.o chpcon.o chpev.o chpevd.o \
chpevx.o chpgst.o chpgv.o chpgvd.o chpgvx.o chprfs.o chpsv.o \
chpsvx.o \
dsytd2.o dsytf2.o dsytrd.o dsytrf.o dsytri.o dsytri2.o dsytri2x.o \
dsyswapr.o dsytrs.o dsytrs2.o dsyconv.o \
dsytf2_rook.o dsytrf_rook.o dsytrs_rook.o \
+ dlasyf_aasen.o dsysv_aasen.o dsytrf_aasen.o dsytrs_aasen.o \
dsytri_rook.o dsycon_rook.o dsysv_rook.o \
dtbcon.o dtbrfs.o dtbtrs.o dtgevc.o dtgex2.o dtgexc.o dtgsen.o \
dtgsja.o dtgsna.o dtgsy2.o dtgsyl.o dtpcon.o dtprfs.o dtptri.o \
zhetrf.o zhetri.o zhetri2.o zhetri2x.o zheswapr.o \
zhetrs.o zhetrs2.o \
zhetf2_rook.o zhetrf_rook.o zhetri_rook.o zhetrs_rook.o zhecon_rook.o zhesv_rook.o \
+ zhesv_aasen.o zhetrf_aasen.o zhetrs_aasen.o zlahef_aasen.o \
zhgeqz.o zhpcon.o zhpev.o zhpevd.o \
zhpevx.o zhpgst.o zhpgv.o zhpgvd.o zhpgvx.o zhprfs.o zhpsv.o \
zhpsvx.o \
--- /dev/null
+*> \brief <b> CHESV_AASEN computes the solution to system of linear equations A * X = B for HE matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHESV_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chesv_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chesv_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chesv_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CHESV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CHESV_AASEN computes the solution to a complex system of linear equations
+*> A * X = B,
+*> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Aasen's algorithm is used to factor A as
+*> A = U * T * U**H, if UPLO = 'U', or
+*> A = L * T * L**H, if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is Hermitian and tridiagonal. The factored form
+*> of A is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (LDA,N)
+*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, if INFO = 0, the tridiagonal matrix T and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*T*U**H or A = L*T*L**H as computed by
+*> CHETRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= 1, and for best performance
+*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*> CHETRF.
+*> for LWORK < N, TRS will be done with Level BLAS 2
+*> for LWORK >= N, TRS will be done with Level BLAS 3
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexHEsolve
+*
+* @generated from zhesv_aasen.f, fortran z -> c, Mon Oct 3 01:48:05 2016
+*
+* =====================================================================
+ SUBROUTINE CHESV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+* -- LAPACK driver routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER LWKOPT, NB
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, CHETRF, CHETRS, CHETRS2
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ NB = ILAENV( 1, 'CHETRF_AASEN', UPLO, N, -1, -1, -1 )
+ LWKOPT = MAX( 3*N-2, (1+NB)*N )
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CHESV_AASEN ', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Compute the factorization A = U*T*U**H or A = L*T*L**H.
+*
+ CALL CHETRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+ IF( INFO.EQ.0 ) THEN
+*
+* Solve the system A*X = B, overwriting B with X.
+*
+ CALL CHETRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+ END IF
+*
+ WORK( 1 ) = LWKOPT
+*
+ RETURN
+*
+* End of CHESV_AASEN
+*
+ END
--- /dev/null
+*> \brief \b CHETRF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETRF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrf_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrf_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrf_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CHETRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), WORK( * )
+* ..
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CHETRF_AASEN computes the factorization of a real hermitian matrix A
+*> using the Aasen's algorithm. The form of the factorization is
+*>
+*> A = U*T*U**T or A = L*T*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is a hermitian tridiagonal matrix.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (LDA,N)
+*> On entry, the hermitian matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the tridiagonal matrix is stored in the diagonals
+*> and the subdiagonals of A just below (or above) the diagonals,
+*> and L is stored below (or above) the subdiaonals, when UPLO
+*> is 'L' (or 'U').
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= 2*N. For optimum performance
+*> LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYcomputational
+*
+* @generated from zhetrf_aasen.f, fortran z -> c, Sun Oct 2 22:29:10 2016
+*
+* =====================================================================
+ SUBROUTINE CHETRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = (0.0E+0, 0.0E+0), ONE = (1.0E+0, 0.0E+0) )
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER J, LWKOPT, IINFO
+ INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
+ COMPLEX ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC REAL, CONJG, MAX
+* ..
+* .. Executable Statements ..
+*
+* Determine the block size
+*
+ NB = ILAENV( 1, 'CHETRF', UPLO, N, -1, -1, -1 )
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( LWORK.LT.( 2*N ) .AND. .NOT.LQUERY ) THEN
+ INFO = -7
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ LWKOPT = (NB+1)*N
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CHETRF_AASEN', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Quick return
+*
+ IF ( N.EQ.0 ) THEN
+ RETURN
+ ENDIF
+ IPIV( 1 ) = 1
+ IF ( N.EQ.1 ) THEN
+ A( 1, 1 ) = REAL( A( 1, 1 ) )
+ IF ( A( 1, 1 ).EQ.ZERO ) THEN
+ INFO = 1
+ END IF
+ RETURN
+ END IF
+*
+* Adjubst block size based on the workspace size
+*
+ IF( LWORK.LT.((1+NB)*N) ) THEN
+ NB = ( LWORK-N ) / N
+ END IF
+*
+ IF( UPPER ) THEN
+*
+* .....................................................
+* Factorize A as L*D*L**T using the upper triangle of A
+* .....................................................
+*
+* copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
+*
+ CALL CCOPY( N, A( 1, 1 ), LDA, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by CLAHEF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 10 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J + 1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL CLAHEF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( MAX(1, J), J+1 ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ),
+ $ IINFO )
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL CSWAP( J1-K1-2, A( 1, J2 ), 1,
+ $ A( 1, IPIV(J2) ), 1 )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* the row A(J1-1, J2-1:N) stores U(J1, J2+1:N) and
+* WORK stores the current block of the auxiriarly matrix H
+*
+ IF( J.LT.N ) THEN
+*
+* if the first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = CONJG( A( J, J+1 ) )
+ A( J, J+1 ) = ONE
+ CALL CCOPY( N-J, A( J-1, J+1 ), LDA,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL CSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=0 and K2=1 for the first panel,
+* and K1=1 and K2=0 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with CGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL CGEMM( 'Conjugate transpose', 'Transpose',
+ $ 1, MJ, JB+1,
+ $ -ONE, A( J1-K2, J3 ), LDA,
+ $ WORK( (J3-J1+1)+K1*N ), N,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block row with CGEMM
+*
+ CALL CGEMM( 'Conjugate transpose', 'Transpose',
+ $ NJ, N-J3+1, JB+1,
+ $ -ONE, A( J1-K2, J2 ), LDA,
+ $ WORK( (J3-J1+1)+K1*N ), N,
+ $ ONE, A( J2, J3 ), LDA )
+ END DO
+*
+* Recover T( J, J+1 )
+*
+ A( J, J+1 ) = CONJG( ALPHA )
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL CCOPY( N-J, A( J+1, J+1 ), LDA, WORK( 1 ), 1 )
+ END IF
+ GO TO 10
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+* copy first column A(1:N, 1) into H(1:N, 1)
+* (stored in WORK(1:N))
+*
+ CALL CCOPY( N, A( 1, 1 ), 1, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by CLAHEF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 11 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J+1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL CLAHEF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( J+1, MAX(1, J) ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ), IINFO)
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL CSWAP( J1-K1-2, A( J2, 1 ), LDA,
+ $ A( IPIV(J2), 1 ), LDA )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* A(J2+1, J1-1) stores L(J2+1, J1) and
+* WORK(J2+1, 1) stores H(J2+1, 1)
+*
+ IF( J.LT.N ) THEN
+*
+* if the first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = CONJG( A( J+1, J ) )
+ A( J+1, J ) = ONE
+ CALL CCOPY( N-J, A( J+1, J-1 ), 1,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL CSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=0 and K2=1 for the first panel,
+* and K1=1 and K2=0 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with CGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL CGEMM( 'No transpose', 'Conjugate transpose',
+ $ MJ, 1, JB+1,
+ $ -ONE, WORK( (J3-J1+1)+K1*N ), N,
+ $ A( J3, J1-K2 ), LDA,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block column with CGEMM
+*
+ CALL CGEMM( 'No transpose', 'Conjugate transpose',
+ $ N-J3+1, NJ, JB+1,
+ $ -ONE, WORK( (J3-J1+1)+K1*N ), N,
+ $ A( J2, J1-K2 ), LDA,
+ $ ONE, A( J3, J2 ), LDA )
+ END DO
+*
+* Recover T( J+1, J )
+*
+ A( J+1, J ) = CONJG( ALPHA )
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL CCOPY( N-J, A( J+1, J+1 ), 1, WORK( 1 ), 1 )
+ END IF
+ GO TO 11
+ END IF
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of CHETRF_AASEN
+*
+ END
--- /dev/null
+*> \brief \b CHETRS_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETRS_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrs_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrs_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrs_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CHETRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CHETRS_AASEN solves a system of linear equations A*X = B with a real
+*> hermitian matrix A using the factorization A = U*T*U**T or
+*> A = L*T*L**T computed by CHETRF_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*T*U**T;
+*> = 'L': Lower triangular, form is A = L*T*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (LDA,N)
+*> Details of factors computed by CHETRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges as computed by CHETRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] WORK
+*> \verbatim
+*> WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER, LWORK >= 3*N-2.
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYcomputational
+*
+* @generated from zhetrs_aasen.f, fortran z -> c, Fri Sep 23 00:09:52 2016
+*
+* =====================================================================
+ SUBROUTINE CHETRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, LWORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+ COMPLEX ONE
+ PARAMETER ( ONE = 1.0E+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER K, KP
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL CGTSV, CSWAP, CTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.(3*N-2) ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CHETRS_AASEN', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*T*U**T.
+*
+* P**T * B
+*
+ K = 1
+ DO WHILE ( K.LE.N )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K + 1
+ END DO
+*
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL CTRSM('L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (U \P**T * B) ]
+*
+ CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL CLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1)
+ CALL CLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1)
+ CALL CLACGV( N-1, WORK( 1 ), 1 )
+ END IF
+ CALL CGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+ $ INFO)
+*
+* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
+*
+ CALL CTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B(2, 1), LDB)
+*
+* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*
+ K = N
+ DO WHILE ( K.GE.1 )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K - 1
+ END DO
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*T*L**T.
+*
+* Pivot, P**T * B
+*
+ K = 1
+ DO WHILE ( K.LE.N )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K + 1
+ END DO
+*
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
+*
+ CALL CTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1), LDA,
+ $ B(2, 1), LDB)
+*
+* Compute T \ B -> B [ T \ (L \P**T * B) ]
+*
+ CALL CLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1)
+ CALL CLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1)
+ CALL CLACGV( N-1, WORK( 2*N ), 1 )
+ END IF
+ CALL CGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+ $ INFO)
+*
+* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
+*
+ CALL CTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+ K = N
+ DO WHILE ( K.GE.1 )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K - 1
+ END DO
+*
+ END IF
+*
+ RETURN
+*
+* End of CHETRS_AASEN
+*
+ END
--- /dev/null
+*> \brief \b CLAHEF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CLAHEF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clahef_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clahef_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clahef_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CLAHEF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+* H, LDH, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER J1, M, NB, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLATRF_AASEN factorizes a panel of a real hermitian matrix A using
+*> the Aasen's algorithm. The panel consists of a set of NB rows of A
+*> when UPLO is U, or a set of NB columns when UPLO is L.
+*>
+*> In order to factorize the panel, the Aasen's algorithm requires the
+*> last row, or column, of the previous panel. The first row, or column,
+*> of A is set to be the first row, or column, of an identity matrix,
+*> which is used to factorize the first panel.
+*>
+*> The resulting J-th row of U, or J-th column of L, is stored in the
+*> (J-1)-th row, or column, of A (without the unit diatonals), while
+*> the diagonal and subdiagonal of A are overwritten by those of T.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] J1
+*> \verbatim
+*> J1 is INTEGER
+*> The location of the first row, or column, of the panel
+*> within the submatrix of A, passed to this routine, e.g.,
+*> when called by CHETRF_AASEN, for the first panel, J1 is 1,
+*> while for the remaining panels, J1 is 2.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The dimension of the submatrix. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The dimension of the panel to be facotorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (LDA,M) for
+*> the first panel, while dimension (LDA,M+1) for the
+*> remaining panels.
+*>
+*> On entry, A contains the last row, or column, of
+*> the previous panel, and the trailing submatrix of A
+*> to be factorized, except for the first panel, only
+*> the panel is passed.
+*>
+*> On exit, the leading panel is factorized.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the row and column interchanges,
+*> the row and column k were interchanged with the row and
+*> column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is COMPLEX workspace, dimension (LDH,NB).
+*>
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the workspace H. LDH >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX workspace, dimension (M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complexSYcomputational
+*
+* @generated from zlahef_aasen.f, fortran z -> c, Sun Oct 2 22:41:33 2016
+*
+* =====================================================================
+ SUBROUTINE CLAHEF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+ $ H, LDH, WORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER M, NB, J1, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = (0.0E+0, 0.0E+0), ONE = (1.0E+0, 0.0E+0) )
+*
+* .. Local Scalars ..
+ INTEGER J, K, K1, I1, I2
+ COMPLEX PIV, ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ICAMAX, ILAENV
+ EXTERNAL LSAME, ILAENV, ICAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC REAL, CONJG, MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ J = 1
+*
+* K1 is the first column of the panel to be factorized
+* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks
+*
+ K1 = (2-J1)+1
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+*
+* .....................................................
+* Factorize A as U**T*D*U using the upper triangle of A
+* .....................................................
+*
+ 10 CONTINUE
+ IF ( J.GT.MIN(M, NB) )
+ $ GO TO 20
+*
+* K is the column to be factorized
+* when being called from CHETRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J),
+* where H(J:N, J) has been initialized to be A(J, J:N)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL CLACGV( J-K1, A( 1, J ), 1 )
+ CALL CGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( 1, J ), 1,
+ $ ONE, H( J, J ), 1 )
+ CALL CLACGV( J-K1, A( 1, J ), 1 )
+ END IF
+*
+* Copy H(i:n, i) into WORK
+*
+ CALL CCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J),
+* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N)
+*
+ ALPHA = -CONJG( A( K-1, J ) )
+ CALL CAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( K, J ) = REAL( WORK( 1 ) )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L(J, (J+1):N)
+* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( K, J )
+ CALL CAXPY( M-J, ALPHA, A( K-1, J+1 ), LDA,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = ICAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply hermitian pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1, I1+1:N) with A(I1+1:N, I2)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL CSWAP( I2-I1-1, A( J1+I1-1, I1+1 ), LDA,
+ $ A( J1+I1, I2 ), 1 )
+ CALL CLACGV( I2-I1, A( J1+I1-1, I1+1 ), LDA )
+ CALL CLACGV( I2-I1-1, A( J1+I1, I2 ), 1 )
+*
+* Swap A(I1, I2+1:N) with A(I2, I2+1:N)
+*
+ CALL CSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+ $ A( J1+I2-1, I2+1 ), LDA )
+*
+* Swap A(I1, I1) with A(I2,I2)
+*
+ PIV = A( I1+J1-1, I1 )
+ A( J1+I1-1, I1 ) = A( J1+I2-1, I2 )
+ A( J1+I2-1, I2 ) = PIV
+*
+* Swap H(I1, 1:J1) with H(I2, 1:J1)
+*
+ CALL CSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL CSWAP( I1-K1+1, A( 1, I1 ), 1,
+ $ A( 1, I2 ), 1 )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J, J+1) = T(J, J+1)
+*
+ A( K, J+1 ) = WORK( 2 )
+ IF( (A( K, J ).EQ.ZERO ) .AND.
+ $ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN
+ IF(INFO .EQ. 0) THEN
+ INFO = J
+ END IF
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J:N, J),
+*
+ CALL CCOPY( M-J, A( K+1, J+1 ), LDA,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( K, J+1 ).NE.ZERO ) THEN
+ ALPHA = ONE / A( K, J+1 )
+ CALL CCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+ CALL CSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+ ELSE
+ CALL CLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+ $ A( K, J+2 ), LDA)
+ END IF
+ ELSE
+ IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 10
+ 20 CONTINUE
+*
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+ 30 CONTINUE
+ IF( J.GT.MIN( M, NB ) )
+ $ GO TO 40
+*
+* K is the column to be factorized
+* when being called from CHETRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T,
+* where H(J:N, J) has been initialized to be A(J:N, J)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL CLACGV( J-K1, A( J, 1 ), LDA )
+ CALL CGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( J, 1 ), LDA,
+ $ ONE, H( J, J ), 1 )
+ CALL CLACGV( J-K1, A( J, 1 ), LDA )
+ END IF
+*
+* Copy H(J:N, J) into WORK
+*
+ CALL CCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J),
+* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1)
+*
+ ALPHA = -CONJG( A( J, K-1 ) )
+ CALL CAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( J, K ) = REAL( WORK( 1 ) )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L((J+1):N, J)
+* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( J, K )
+ CALL CAXPY( M-J, ALPHA, A( J+1, K-1 ), 1,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = ICAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply hermitian pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1+1:N, I1) with A(I2, I1+1:N)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL CSWAP( I2-I1-1, A( I1+1, J1+I1-1 ), 1,
+ $ A( I2, J1+I1 ), LDA )
+ CALL CLACGV( I2-I1, A( I1+1, J1+I1-1 ), 1 )
+ CALL CLACGV( I2-I1-1, A( I2, J1+I1 ), LDA )
+*
+* Swap A(I2+1:N, I1) with A(I2+1:N, I2)
+*
+ CALL CSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+ $ A( I2+1, J1+I2-1 ), 1 )
+*
+* Swap A(I1, I1) with A(I2, I2)
+*
+ PIV = A( I1, J1+I1-1 )
+ A( I1, J1+I1-1 ) = A( I2, J1+I2-1 )
+ A( I2, J1+I2-1 ) = PIV
+*
+* Swap H(I1, I1:J1) with H(I2, I2:J1)
+*
+ CALL CSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL CSWAP( I1-K1+1, A( I1, 1 ), LDA,
+ $ A( I2, 1 ), LDA )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J+1, J) = T(J+1, J)
+*
+ A( J+1, K ) = WORK( 2 )
+ IF( (A( J, K ).EQ.ZERO) .AND.
+ $ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN
+ IF (INFO .EQ. 0)
+ $ INFO = J
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J+1:N, J),
+*
+ CALL CCOPY( M-J, A( J+1, K+1 ), 1,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( J+1, K ).NE.ZERO ) THEN
+ ALPHA = ONE / A( J+1, K )
+ CALL CCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+ CALL CSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+ ELSE
+ CALL CLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+ $ A( J+2, K ), LDA )
+ END IF
+ ELSE
+ IF( (A( J, K ).EQ.ZERO) .AND. (J.EQ.M)
+ $ .AND. (INFO.EQ.0) ) INFO = J
+ END IF
+ J = J + 1
+ GO TO 30
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of CLAHEF_AASEN
+*
+ END
--- /dev/null
+*> \brief \b DLASYF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLASYF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLASYF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+* H, LDH, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER J1, M, NB, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLATRF_AASEN factorizes a panel of a real symmetric matrix A using
+*> the Aasen's algorithm. The panel consists of a set of NB rows of A
+*> when UPLO is U, or a set of NB columns when UPLO is L.
+*>
+*> In order to factorize the panel, the Aasen's algorithm requires the
+*> last row, or column, of the previous panel. The first row, or column,
+*> of A is set to be the first row, or column, of an identity matrix,
+*> which is used to factorize the first panel.
+*>
+*> The resulting J-th row of U, or J-th column of L, is stored in the
+*> (J-1)-th row, or column, of A (without the unit diatonals), while
+*> the diagonal and subdiagonal of A are overwritten by those of T.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] J1
+*> \verbatim
+*> J1 is INTEGER
+*> The location of the first row, or column, of the panel
+*> within the submatrix of A, passed to this routine, e.g.,
+*> when called by DSYTRF_AASEN, for the first panel, J1 is 1,
+*> while for the remaining panels, J1 is 2.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The dimension of the submatrix. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The dimension of the panel to be facotorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,M) for
+*> the first panel, while dimension (LDA,M+1) for the
+*> remaining panels.
+*>
+*> On entry, A contains the last row, or column, of
+*> the previous panel, and the trailing submatrix of A
+*> to be factorized, except for the first panel, only
+*> the panel is passed.
+*>
+*> On exit, the leading panel is factorized.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the row and column interchanges,
+*> the row and column k were interchanged with the row and
+*> column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is DOUBLE PRECISION workspace, dimension (LDH,NB).
+*>
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the workspace H. LDH >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION workspace, dimension (M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup doubleSYcomputational
+*
+* @precisions fortran d -> s
+*
+* =====================================================================
+ SUBROUTINE DLASYF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+ $ H, LDH, WORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER M, NB, J1, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ DOUBLE PRECISION A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+*
+* .. Local Scalars ..
+ INTEGER J, K, K1, I1, I2
+ DOUBLE PRECISION PIV, ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER IDAMAX, ILAENV
+ EXTERNAL LSAME, ILAENV, IDAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ J = 1
+*
+* K1 is the first column of the panel to be factorized
+* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks
+*
+ K1 = (2-J1)+1
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+*
+* .....................................................
+* Factorize A as U**T*D*U using the upper triangle of A
+* .....................................................
+*
+ 10 CONTINUE
+ IF ( J.GT.MIN(M, NB) )
+ $ GO TO 20
+*
+* K is the column to be factorized
+* when being called from DSYTRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J),
+* where H(J:N, J) has been initialized to be A(J, J:N)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL DGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( 1, J ), 1,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(i:n, i) into WORK
+*
+ CALL DCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J),
+* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N)
+*
+ ALPHA = -A( K-1, J )
+ CALL DAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( K, J ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L(J, (J+1):N)
+* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( K, J )
+ CALL DAXPY( M-J, ALPHA, A( K-1, J+1 ), LDA,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = IDAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1, I1+1:N) with A(I1+1:N, I2)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL DSWAP( I2-I1-1, A( J1+I1-1, I1+1 ), LDA,
+ $ A( J1+I1, I2 ), 1 )
+*
+* Swap A(I1, I2+1:N) with A(I2, I2+1:N)
+*
+ CALL DSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+ $ A( J1+I2-1, I2+1 ), LDA )
+*
+* Swap A(I1, I1) with A(I2,I2)
+*
+ PIV = A( I1+J1-1, I1 )
+ A( J1+I1-1, I1 ) = A( J1+I2-1, I2 )
+ A( J1+I2-1, I2 ) = PIV
+*
+* Swap H(I1, 1:J1) with H(I2, 1:J1)
+*
+ CALL DSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL DSWAP( I1-K1+1, A( 1, I1 ), 1,
+ $ A( 1, I2 ), 1 )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J, J+1) = T(J, J+1)
+*
+ A( K, J+1 ) = WORK( 2 )
+ IF( (A( K, J ).EQ.ZERO ) .AND.
+ $ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN
+ IF(INFO .EQ. 0) THEN
+ INFO = J
+ ENDIF
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J:N, J),
+*
+ CALL DCOPY( M-J, A( K+1, J+1 ), LDA,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( K, J+1 ).NE.ZERO ) THEN
+ ALPHA = ONE / A( K, J+1 )
+ CALL DCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+ CALL DSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+ ELSE
+ CALL DLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+ $ A( K, J+2 ), LDA)
+ END IF
+ ELSE
+ IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 10
+ 20 CONTINUE
+*
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+ 30 CONTINUE
+ IF( J.GT.MIN( M, NB ) )
+ $ GO TO 40
+*
+* K is the column to be factorized
+* when being called from DSYTRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T,
+* where H(J:N, J) has been initialized to be A(J:N, J)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL DGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( J, 1 ), LDA,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(J:N, J) into WORK
+*
+ CALL DCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J),
+* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1)
+*
+ ALPHA = -A( J, K-1 )
+ CALL DAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( J, K ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L((J+1):N, J)
+* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( J, K )
+ CALL DAXPY( M-J, ALPHA, A( J+1, K-1 ), 1,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = IDAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1+1:N, I1) with A(I2, I1+1:N)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL DSWAP( I2-I1-1, A( I1+1, J1+I1-1 ), 1,
+ $ A( I2, J1+I1 ), LDA )
+*
+* Swap A(I2+1:N, I1) with A(I2+1:N, I2)
+*
+ CALL DSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+ $ A( I2+1, J1+I2-1 ), 1 )
+*
+* Swap A(I1, I1) with A(I2, I2)
+*
+ PIV = A( I1, J1+I1-1 )
+ A( I1, J1+I1-1 ) = A( I2, J1+I2-1 )
+ A( I2, J1+I2-1 ) = PIV
+*
+* Swap H(I1, I1:J1) with H(I2, I2:J1)
+*
+ CALL DSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL DSWAP( I1-K1+1, A( I1, 1 ), LDA,
+ $ A( I2, 1 ), LDA )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J+1, J) = T(J+1, J)
+*
+ A( J+1, K ) = WORK( 2 )
+ IF( (A( J, K ).EQ.ZERO) .AND.
+ $ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN
+ IF (INFO .EQ. 0)
+ $ INFO = J
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J+1:N, J),
+*
+ CALL DCOPY( M-J, A( J+1, K+1 ), 1,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( J+1, K ).NE.ZERO ) THEN
+ ALPHA = ONE / A( J+1, K )
+ CALL DCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+ CALL DSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+ ELSE
+ CALL DLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+ $ A( J+2, K ), LDA )
+ END IF
+ ELSE
+ IF( (A( J, K ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 30
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of DLASYF_AASEN
+*
+ END
--- /dev/null
+*> \brief <b> DSYSV_AASEN computes the solution to system of linear equations A * X = B for SY matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYSV_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsysv_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsysv_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsysv_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYSV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSYSV computes the solution to a real system of linear equations
+*> A * X = B,
+*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Aasen's algorithm is used to factor A as
+*> A = U * T * U**T, if UPLO = 'U', or
+*> A = L * T * L**T, if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is symmetric tridiagonal. The factored
+*> form of A is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, if INFO = 0, the tridiagonal matrix T and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*T*U**T or A = L*T*L**T as computed by
+*> DSYTRF.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= MAX(2*N, 3*N-2), and for
+*> the best performance, LWORK >= max(1,N*NB), where NB is
+*> the optimal blocksize for DSYTRF_AASEN.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup doubleSYsolve
+*
+* @precisions fortran d -> s
+*
+* =====================================================================
+ SUBROUTINE DSYSV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+* -- LAPACK driver routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER LWKOPT, NB
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL ILAENV, LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, DSYTRF, DSYTRS, DSYTRS2
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ NB = ILAENV( 1, 'DSYTRF_AASEN', UPLO, N, -1, -1, -1 )
+ LWKOPT = MAX( 3*N-2, (1+NB)*N )
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DSYSV_AASEN ', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Compute the factorization A = U*T*U**T or A = L*T*L**T.
+*
+ CALL DSYTRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+ IF( INFO.EQ.0 ) THEN
+*
+* Solve the system A*X = B, overwriting B with X.
+*
+ CALL DSYTRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+ END IF
+*
+ WORK( 1 ) = LWKOPT
+*
+ RETURN
+*
+* End of DSYSV_AASEN
+*
+ END
--- /dev/null
+*> \brief \b DSYTRF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYTRF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrf_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrf_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrf_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYTRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * ), WORK( * )
+* ..
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSYTRF_AASEN computes the factorization of a real symmetric matrix A
+*> using the Aasen's algorithm. The form of the factorization is
+*>
+*> A = U*T*U**T or A = L*T*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is a symmetric tridiagonal matrix.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the tridiagonal matrix is stored in the diagonals
+*> and the subdiagonals of A just below (or above) the diagonals,
+*> and L is stored below (or above) the subdiaonals, when UPLO
+*> is 'L' (or 'U').
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >=2*N. For optimum performance
+*> LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup doubleSYcomputational
+*
+* @precisions fortran d -> s
+*
+* =====================================================================
+ SUBROUTINE DSYTRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ DOUBLE PRECISION A( LDA, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER J, LWKOPT, IINFO
+ INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
+ DOUBLE PRECISION ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Determine the block size
+*
+ NB = ILAENV( 1, 'DSYTRF', UPLO, N, -1, -1, -1 )
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( LWORK.LT.( 2*N ) .AND. .NOT.LQUERY ) THEN
+ INFO = -7
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ LWKOPT = (NB+1)*N
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DSYTRF_AASEN', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Quick return
+*
+ IF ( N.EQ.0 ) THEN
+ RETURN
+ ENDIF
+ IPIV( 1 ) = 1
+ IF ( N.EQ.1 ) THEN
+ IF ( A( 1, 1 ).EQ.ZERO ) THEN
+ INFO = 1
+ END IF
+ RETURN
+ END IF
+*
+* Adjubst block size based on the workspace size
+*
+ IF( LWORK.LT.((1+NB)*N) ) THEN
+ NB = ( LWORK-N ) / N
+ END IF
+*
+ IF( UPPER ) THEN
+*
+* .....................................................
+* Factorize A as L*D*L**T using the upper triangle of A
+* .....................................................
+*
+* Copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
+*
+ CALL DCOPY( N, A( 1, 1 ), LDA, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by DLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 10 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J + 1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL DLASYF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( MAX(1, J), J+1 ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ),
+ $ IINFO )
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL DSWAP( J1-K1-2, A( 1, J2 ), 1,
+ $ A( 1, IPIV(J2) ), 1 )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* the row A(J1-1, J2-1:N) stores U(J1, J2+1:N) and
+* WORK stores the current block of the auxiriarly matrix H
+*
+ IF( J.LT.N ) THEN
+*
+* If first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J, J+1 )
+ A( J, J+1 ) = ONE
+ CALL DCOPY( N-J, A( J-1, J+1 ), LDA,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL DSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with DGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL DGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J1-K2, J3 ), 1,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block row with DGEMM
+*
+ CALL DGEMM( 'Transpose', 'Transpose',
+ $ NJ, N-J3+1, JB+1,
+ $ -ONE, A( J1-K2, J2 ), LDA,
+ $ WORK( J3-J1+1+K1*N ), N,
+ $ ONE, A( J2, J3 ), LDA )
+ END DO
+*
+* Recover T( J, J+1 )
+*
+ A( J, J+1 ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL DCOPY( N-J, A( J+1, J+1 ), LDA, WORK( 1 ), 1 )
+ END IF
+ GO TO 10
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+* copy first column A(1:N, 1) into H(1:N, 1)
+* (stored in WORK(1:N))
+*
+ CALL DCOPY( N, A( 1, 1 ), 1, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by DLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 11 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J+1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL DLASYF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( J+1, MAX(1, J) ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ), IINFO)
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL DSWAP( J1-K1-2, A( J2, 1 ), LDA,
+ $ A( IPIV(J2), 1 ), LDA )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* A(J2+1, J1-1) stores L(J2+1, J1) and
+* WORK(J2+1, 1) stores H(J2+1, 1)
+*
+ IF( J.LT.N ) THEN
+*
+* if first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J+1, J )
+ A( J+1, J ) = ONE
+ CALL DCOPY( N-J, A( J+1, J-1 ), 1,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL DSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with DGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL DGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J3, J1-K2 ), LDA,
+ $ ONE, A( J3, J3 ), 1 )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block in J2-th block column with DGEMM
+*
+ CALL DGEMM( 'No transpose', 'Transpose',
+ $ N-J3+1, NJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J2, J1-K2 ), LDA,
+ $ ONE, A( J3, J2 ), LDA )
+ END DO
+*
+* Recover T( J+1, J )
+*
+ A( J+1, J ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL DCOPY( N-J, A( J+1, J+1 ), 1, WORK( 1 ), 1 )
+ END IF
+ GO TO 11
+ END IF
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of DSYTRF_AASEN
+*
+ END
--- /dev/null
+*> \brief \b DSYTRS_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYTRS_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYTRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSYTRS_AASEN solves a system of linear equations A*X = B with a real
+*> symmetric matrix A using the factorization A = U*T*U**T or
+*> A = L*T*L**T computed by DSYTRF_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*T*U**T;
+*> = 'L': Lower triangular, form is A = L*T*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> Details of factors computed by DSYTRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges as computed by DSYTRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] WORK
+*> \verbatim
+*> WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER, LWORK >= 3*N-2.
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup doubleSYcomputational
+*
+* @precisions fortran d -> s
+*
+* =====================================================================
+ SUBROUTINE DSYTRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, LWORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+ DOUBLE PRECISION ONE
+ PARAMETER ( ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER K, KP
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL DGTSV, DSWAP, DTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.(3*N-2) ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DSYTRS_AASEN', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*T*U**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (U \P**T * B) ]
+*
+ CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
+ IF( N.GT.1 ) THEN
+ CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
+ CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1 )
+ END IF
+ CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB,
+ $ INFO )
+*
+* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
+*
+ CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*T*L**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
+*
+ CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (L \P**T * B) ]
+*
+ CALL DLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 )
+ CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1 )
+ END IF
+ CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
+ $ INFO)
+*
+* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
+*
+ CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ END IF
+*
+ RETURN
+*
+* End of DSYTRS_AASEN
+*
+ END
--- /dev/null
+*> \brief \b SLASYF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download SLASYF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasyf_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasyf_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasyf_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SLASYF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+* H, LDH, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER J1, M, NB, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* REAL A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLATRF_AASEN factorizes a panel of a real symmetric matrix A using
+*> the Aasen's algorithm. The panel consists of a set of NB rows of A
+*> when UPLO is U, or a set of NB columns when UPLO is L.
+*>
+*> In order to factorize the panel, the Aasen's algorithm requires the
+*> last row, or column, of the previous panel. The first row, or column,
+*> of A is set to be the first row, or column, of an identity matrix,
+*> which is used to factorize the first panel.
+*>
+*> The resulting J-th row of U, or J-th column of L, is stored in the
+*> (J-1)-th row, or column, of A (without the unit diatonals), while
+*> the diagonal and subdiagonal of A are overwritten by those of T.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] J1
+*> \verbatim
+*> J1 is INTEGER
+*> The location of the first row, or column, of the panel
+*> within the submatrix of A, passed to this routine, e.g.,
+*> when called by SSYTRF_AASEN, for the first panel, J1 is 1,
+*> while for the remaining panels, J1 is 2.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The dimension of the submatrix. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The dimension of the panel to be facotorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,M) for
+*> the first panel, while dimension (LDA,M+1) for the
+*> remaining panels.
+*>
+*> On entry, A contains the last row, or column, of
+*> the previous panel, and the trailing submatrix of A
+*> to be factorized, except for the first panel, only
+*> the panel is passed.
+*>
+*> On exit, the leading panel is factorized.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the row and column interchanges,
+*> the row and column k were interchanged with the row and
+*> column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is REAL workspace, dimension (LDH,NB).
+*>
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the workspace H. LDH >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL workspace, dimension (M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup realSYcomputational
+*
+* @generated from dlasyf_aasen.f, fortran d -> s, Sun Oct 2 22:57:56 2016
+*
+* =====================================================================
+ SUBROUTINE SLASYF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+ $ H, LDH, WORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER M, NB, J1, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ REAL A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+*
+* .. Local Scalars ..
+ INTEGER J, K, K1, I1, I2
+ REAL PIV, ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ISAMAX, ILAENV
+ EXTERNAL LSAME, ILAENV, ISAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ J = 1
+*
+* K1 is the first column of the panel to be factorized
+* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks
+*
+ K1 = (2-J1)+1
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+*
+* .....................................................
+* Factorize A as U**T*D*U using the upper triangle of A
+* .....................................................
+*
+ 10 CONTINUE
+ IF ( J.GT.MIN(M, NB) )
+ $ GO TO 20
+*
+* K is the column to be factorized
+* when being called from SSYTRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J),
+* where H(J:N, J) has been initialized to be A(J, J:N)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL SGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( 1, J ), 1,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(i:n, i) into WORK
+*
+ CALL SCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J),
+* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N)
+*
+ ALPHA = -A( K-1, J )
+ CALL SAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( K, J ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L(J, (J+1):N)
+* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( K, J )
+ CALL SAXPY( M-J, ALPHA, A( K-1, J+1 ), LDA,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = ISAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1, I1+1:N) with A(I1+1:N, I2)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL SSWAP( I2-I1-1, A( J1+I1-1, I1+1 ), LDA,
+ $ A( J1+I1, I2 ), 1 )
+*
+* Swap A(I1, I2+1:N) with A(I2, I2+1:N)
+*
+ CALL SSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+ $ A( J1+I2-1, I2+1 ), LDA )
+*
+* Swap A(I1, I1) with A(I2,I2)
+*
+ PIV = A( I1+J1-1, I1 )
+ A( J1+I1-1, I1 ) = A( J1+I2-1, I2 )
+ A( J1+I2-1, I2 ) = PIV
+*
+* Swap H(I1, 1:J1) with H(I2, 1:J1)
+*
+ CALL SSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL SSWAP( I1-K1+1, A( 1, I1 ), 1,
+ $ A( 1, I2 ), 1 )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J, J+1) = T(J, J+1)
+*
+ A( K, J+1 ) = WORK( 2 )
+ IF( (A( K, J ).EQ.ZERO ) .AND.
+ $ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN
+ IF(INFO .EQ. 0) THEN
+ INFO = J
+ ENDIF
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J:N, J),
+*
+ CALL SCOPY( M-J, A( K+1, J+1 ), LDA,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( K, J+1 ).NE.ZERO ) THEN
+ ALPHA = ONE / A( K, J+1 )
+ CALL SCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+ CALL SSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+ ELSE
+ CALL SLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+ $ A( K, J+2 ), LDA)
+ END IF
+ ELSE
+ IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 10
+ 20 CONTINUE
+*
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+ 30 CONTINUE
+ IF( J.GT.MIN( M, NB ) )
+ $ GO TO 40
+*
+* K is the column to be factorized
+* when being called from SSYTRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T,
+* where H(J:N, J) has been initialized to be A(J:N, J)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL SGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( J, 1 ), LDA,
+ $ ONE, H( J, J ), 1 )
+ END IF
+*
+* Copy H(J:N, J) into WORK
+*
+ CALL SCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J),
+* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1)
+*
+ ALPHA = -A( J, K-1 )
+ CALL SAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( J, K ) = WORK( 1 )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L((J+1):N, J)
+* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( J, K )
+ CALL SAXPY( M-J, ALPHA, A( J+1, K-1 ), 1,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = ISAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply symmetric pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1+1:N, I1) with A(I2, I1+1:N)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL SSWAP( I2-I1-1, A( I1+1, J1+I1-1 ), 1,
+ $ A( I2, J1+I1 ), LDA )
+*
+* Swap A(I2+1:N, I1) with A(I2+1:N, I2)
+*
+ CALL SSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+ $ A( I2+1, J1+I2-1 ), 1 )
+*
+* Swap A(I1, I1) with A(I2, I2)
+*
+ PIV = A( I1, J1+I1-1 )
+ A( I1, J1+I1-1 ) = A( I2, J1+I2-1 )
+ A( I2, J1+I2-1 ) = PIV
+*
+* Swap H(I1, I1:J1) with H(I2, I2:J1)
+*
+ CALL SSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL SSWAP( I1-K1+1, A( I1, 1 ), LDA,
+ $ A( I2, 1 ), LDA )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J+1, J) = T(J+1, J)
+*
+ A( J+1, K ) = WORK( 2 )
+ IF( (A( J, K ).EQ.ZERO) .AND.
+ $ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN
+ IF (INFO .EQ. 0)
+ $ INFO = J
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J+1:N, J),
+*
+ CALL SCOPY( M-J, A( J+1, K+1 ), 1,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( J+1, K ).NE.ZERO ) THEN
+ ALPHA = ONE / A( J+1, K )
+ CALL SCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+ CALL SSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+ ELSE
+ CALL SLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+ $ A( J+2, K ), LDA )
+ END IF
+ ELSE
+ IF( (A( J, K ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 30
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of SLASYF_AASEN
+*
+ END
--- /dev/null
+*> \brief <b> SSYSV_AASEN computes the solution to system of linear equations A * X = B for SY matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download SSYSV_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssysv_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssysv_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssysv_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SSYSV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* REAL A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SSYSV computes the solution to a real system of linear equations
+*> A * X = B,
+*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Aasen's algorithm is used to factor A as
+*> A = U * T * U**T, if UPLO = 'U', or
+*> A = L * T * L**T, if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is symmetric tridiagonal. The factored
+*> form of A is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, if INFO = 0, the tridiagonal matrix T and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*T*U**T or A = L*T*L**T as computed by
+*> SSYTRF.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is REAL array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= MAX(2*N, 3*N-2), and for
+*> the best performance, LWORK >= max(1,N*NB), where NB is
+*> the optimal blocksize for SSYTRF_AASEN.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup realSYsolve
+*
+* @generated from dsysv_aasen.f, fortran d -> s, Mon Oct 3 01:04:05 2016
+*
+* =====================================================================
+ SUBROUTINE SSYSV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+* -- LAPACK driver routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ REAL A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER LWKOPT
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, SSYTRF, SSYTRS, SSYTRS2
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ CALL SSYTRF( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
+ LWKOPT = WORK(1)
+ LWKOPT = MAX( 3*N-2, LWKOPT )
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'SSYSV_AASEN', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Compute the factorization A = U*T*U**T or A = L*T*L**T.
+*
+ CALL SSYTRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+ IF( INFO.EQ.0 ) THEN
+*
+* Solve the system A*X = B, overwriting B with X.
+*
+ CALL SSYTRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+ END IF
+*
+ WORK( 1 ) = LWKOPT
+*
+ RETURN
+*
+* End of SSYSV_AASEN
+*
+ END
--- /dev/null
+*> \brief \b SSYTRF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download SSYTRF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrf_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrf_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrf_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SSYTRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* REAL A( LDA, * ), WORK( * )
+* ..
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SSYTRF_AASEN computes the factorization of a real symmetric matrix A
+*> using the Aasen's algorithm. The form of the factorization is
+*>
+*> A = U*T*U**T or A = L*T*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is a symmetric tridiagonal matrix.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the tridiagonal matrix is stored in the diagonals
+*> and the subdiagonals of A just below (or above) the diagonals,
+*> and L is stored below (or above) the subdiaonals, when UPLO
+*> is 'L' (or 'U').
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >=2*N. For optimum performance
+*> LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup realSYcomputational
+*
+* @generated from dsytrf_aasen.f, fortran d -> s, Sun Oct 2 22:27:17 2016
+*
+* =====================================================================
+ SUBROUTINE SSYTRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ REAL A( LDA, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER J, LWKOPT, IINFO
+ INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
+ REAL ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Determine the block size
+*
+ NB = ILAENV( 1, 'SSYTRF', UPLO, N, -1, -1, -1 )
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( LWORK.LT.( 2*N ) .AND. .NOT.LQUERY ) THEN
+ INFO = -7
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ LWKOPT = (NB+1)*N
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'SSYTRF_AASEN', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Quick return
+*
+ IF ( N.EQ.0 ) THEN
+ RETURN
+ ENDIF
+ IPIV( 1 ) = 1
+ IF ( N.EQ.1 ) THEN
+ IF ( A( 1, 1 ).EQ.ZERO ) THEN
+ INFO = 1
+ END IF
+ RETURN
+ END IF
+*
+* Adjubst block size based on the workspace size
+*
+ IF( LWORK.LT.((1+NB)*N) ) THEN
+ NB = ( LWORK-N ) / N
+ END IF
+*
+ IF( UPPER ) THEN
+*
+* .....................................................
+* Factorize A as L*D*L**T using the upper triangle of A
+* .....................................................
+*
+* Copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
+*
+ CALL SCOPY( N, A( 1, 1 ), LDA, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by SLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 10 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J + 1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL SLASYF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( MAX(1, J), J+1 ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ),
+ $ IINFO )
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL SSWAP( J1-K1-2, A( 1, J2 ), 1,
+ $ A( 1, IPIV(J2) ), 1 )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* the row A(J1-1, J2-1:N) stores U(J1, J2+1:N) and
+* WORK stores the current block of the auxiriarly matrix H
+*
+ IF( J.LT.N ) THEN
+*
+* If first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J, J+1 )
+ A( J, J+1 ) = ONE
+ CALL SCOPY( N-J, A( J-1, J+1 ), LDA,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL SSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with SGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL SGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J1-K2, J3 ), 1,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block row with SGEMM
+*
+ CALL SGEMM( 'Transpose', 'Transpose',
+ $ NJ, N-J3+1, JB+1,
+ $ -ONE, A( J1-K2, J2 ), LDA,
+ $ WORK( J3-J1+1+K1*N ), N,
+ $ ONE, A( J2, J3 ), LDA )
+ END DO
+*
+* Recover T( J, J+1 )
+*
+ A( J, J+1 ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL SCOPY( N-J, A( J+1, J+1 ), LDA, WORK( 1 ), 1 )
+ END IF
+ GO TO 10
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+* copy first column A(1:N, 1) into H(1:N, 1)
+* (stored in WORK(1:N))
+*
+ CALL SCOPY( N, A( 1, 1 ), 1, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by SLASYF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 11 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J+1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL SLASYF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( J+1, MAX(1, J) ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ), IINFO)
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL SSWAP( J1-K1-2, A( J2, 1 ), LDA,
+ $ A( IPIV(J2), 1 ), LDA )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* A(J2+1, J1-1) stores L(J2+1, J1) and
+* WORK(J2+1, 1) stores H(J2+1, 1)
+*
+ IF( J.LT.N ) THEN
+*
+* if first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = A( J+1, J )
+ A( J+1, J ) = ONE
+ CALL SCOPY( N-J, A( J+1, J-1 ), 1,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL SSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 and K2= 0 for the first panel,
+* while K1=0 and K2=1 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with SGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL SGEMV( 'No transpose', MJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J3, J1-K2 ), LDA,
+ $ ONE, A( J3, J3 ), 1 )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block in J2-th block column with SGEMM
+*
+ CALL SGEMM( 'No transpose', 'Transpose',
+ $ N-J3+1, NJ, JB+1,
+ $ -ONE, WORK( J3-J1+1+K1*N ), N,
+ $ A( J2, J1-K2 ), LDA,
+ $ ONE, A( J3, J2 ), LDA )
+ END DO
+*
+* Recover T( J+1, J )
+*
+ A( J+1, J ) = ALPHA
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL SCOPY( N-J, A( J+1, J+1 ), 1, WORK( 1 ), 1 )
+ END IF
+ GO TO 11
+ END IF
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of SSYTRF_AASEN
+*
+ END
--- /dev/null
+*> \brief \b SSYTRS_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download SSYTRS_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrs_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrs_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrs_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SSYTRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* REAL A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SSYTRS_AASEN solves a system of linear equations A*X = B with a real
+*> symmetric matrix A using the factorization A = U*T*U**T or
+*> A = L*T*L**T computed by SSYTRF_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*T*U**T;
+*> = 'L': Lower triangular, form is A = L*T*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> Details of factors computed by SSYTRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges as computed by SSYTRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is REAL array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] WORK
+*> \verbatim
+*> WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER, LWORK >= 3*N-2.
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup realSYcomputational
+*
+* @generated from dsytrs_aasen.f, fortran d -> s, Wed Sep 21 16:39:24 2016
+*
+* =====================================================================
+ SUBROUTINE SSYTRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, LWORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ REAL A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+ REAL ONE
+ PARAMETER ( ONE = 1.0E+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER K, KP
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL SGTSV, SSWAP, STRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.(3*N-2) ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'SSYTRS_AASEN', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*T*U**T.
+*
+* Pivot, P**T * B
+*
+ K = 1
+ DO WHILE ( K.LE.N )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K + 1
+ END DO
+*
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL STRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (U \P**T * B) ]
+*
+ CALL SLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL SLACPY( 'F', 1, N-1, A(1, 2), LDA+1, WORK(1), 1)
+ CALL SLACPY( 'F', 1, N-1, A(1, 2), LDA+1, WORK(2*N), 1)
+ END IF
+ CALL SGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+ $ INFO)
+*
+*
+* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
+*
+ CALL STRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B(2, 1), LDB)
+*
+* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*
+ K = N
+ DO WHILE ( K.GE.1 )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K - 1
+ END DO
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*T*L**T.
+*
+* Pivot, P**T * B
+*
+ K = 1
+ DO WHILE ( K.LE.N )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K + 1
+ END DO
+*
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
+*
+ CALL STRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1), LDA,
+ $ B(2, 1), LDB)
+*
+* Compute T \ B -> B [ T \ (L \P**T * B) ]
+*
+ CALL SLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL SLACPY( 'F', 1, N-1, A(2, 1), LDA+1, WORK(1), 1)
+ CALL SLACPY( 'F', 1, N-1, A(2, 1), LDA+1, WORK(2*N), 1)
+ END IF
+ CALL SGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+ $ INFO)
+*
+* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
+*
+ CALL STRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+ K = N
+ DO WHILE ( K.GE.1 )
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K - 1
+ END DO
+*
+ END IF
+*
+ RETURN
+*
+* End of SSYTRS_AASEN
+*
+ END
--- /dev/null
+*> \brief <b> ZHESV_AASEN computes the solution to system of linear equations A * X = B for HE matrices</b>
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHESV_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHESV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHESV_AASEN computes the solution to a complex system of linear equations
+*> A * X = B,
+*> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Aasen's algorithm is used to factor A as
+*> A = U * T * U**H, if UPLO = 'U', or
+*> A = L * T * L**H, if UPLO = 'L',
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is Hermitian and tridiagonal. The factored form
+*> of A is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of linear equations, i.e., the order of the
+*> matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, if INFO = 0, the tridiagonal matrix T and the
+*> multipliers used to obtain the factor U or L from the
+*> factorization A = U*T*U**H or A = L*T*L**H as computed by
+*> ZHETRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> On entry, the N-by-NRHS right hand side matrix B.
+*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= 1, and for best performance
+*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*> ZHETRF.
+*> for LWORK < N, TRS will be done with Level BLAS 2
+*> for LWORK >= N, TRS will be done with Level BLAS 3
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, so the solution could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16HEsolve
+*
+* @precisions fortran z -> c
+*
+* =====================================================================
+ SUBROUTINE ZHESV_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+* -- LAPACK driver routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, LDB, LWORK, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER LWKOPT, NB
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
+ INFO = -10
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ NB = ILAENV( 1, 'ZHETRF_AASEN', UPLO, N, -1, -1, -1 )
+ LWKOPT = MAX( 3*N-2, (1+NB)*N )
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZHESV_AASEN ', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Compute the factorization A = U*T*U**H or A = L*T*L**H.
+*
+ CALL ZHETRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+ IF( INFO.EQ.0 ) THEN
+*
+* Solve the system A*X = B, overwriting B with X.
+*
+ CALL ZHETRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+ $ LWORK, INFO )
+*
+ END IF
+*
+ WORK( 1 ) = LWKOPT
+*
+ RETURN
+*
+* End of ZHESV_AASEN
+*
+ END
--- /dev/null
+*> \brief \b ZHETRF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHETRF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrf_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrf_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrf_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHETRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), WORK( * )
+* ..
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHETRF_AASEN computes the factorization of a real hermitian matrix A
+*> using the Aasen's algorithm. The form of the factorization is
+*>
+*> A = U*T*U**T or A = L*T*L**T
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, and T is a hermitian tridiagonal matrix.
+*>
+*> This is the blocked version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the hermitian matrix A. If UPLO = 'U', the leading
+*> N-by-N upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading N-by-N lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the tridiagonal matrix is stored in the diagonals
+*> and the subdiagonals of A just below (or above) the diagonals,
+*> and L is stored below (or above) the subdiaonals, when UPLO
+*> is 'L' (or 'U').
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> On exit, it contains the details of the interchanges, i.e.,
+*> the row and column k of A were interchanged with the
+*> row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The length of WORK. LWORK >= 2*N. For optimum performance
+*> LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYcomputational
+*
+* @precisions fortran z -> c
+*
+* =====================================================================
+ SUBROUTINE ZHETRF_AASEN( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, LDA, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = (0.0D+0, 0.0D+0), ONE = (1.0D+0, 0.0D+0) )
+*
+* .. Local Scalars ..
+ LOGICAL LQUERY, UPPER
+ INTEGER J, LWKOPT, IINFO
+ INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
+ COMPLEX*16 ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER ILAENV
+ EXTERNAL LSAME, ILAENV
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE, DCONJG, MAX
+* ..
+* .. Executable Statements ..
+*
+* Determine the block size
+*
+ NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ LQUERY = ( LWORK.EQ.-1 )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ ELSE IF( LWORK.LT.( 2*N ) .AND. .NOT.LQUERY ) THEN
+ INFO = -7
+ END IF
+*
+ IF( INFO.EQ.0 ) THEN
+ LWKOPT = (NB+1)*N
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZHETRF_AASEN', -INFO )
+ RETURN
+ ELSE IF( LQUERY ) THEN
+ RETURN
+ END IF
+*
+* Quick return
+*
+ IF ( N.EQ.0 ) THEN
+ RETURN
+ ENDIF
+ IPIV( 1 ) = 1
+ IF ( N.EQ.1 ) THEN
+ A( 1, 1 ) = DBLE( A( 1, 1 ) )
+ IF ( A( 1, 1 ).EQ.ZERO ) THEN
+ INFO = 1
+ END IF
+ RETURN
+ END IF
+*
+* Adjubst block size based on the workspace size
+*
+ IF( LWORK.LT.((1+NB)*N) ) THEN
+ NB = ( LWORK-N ) / N
+ END IF
+*
+ IF( UPPER ) THEN
+*
+* .....................................................
+* Factorize A as L*D*L**T using the upper triangle of A
+* .....................................................
+*
+* copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
+*
+ CALL ZCOPY( N, A( 1, 1 ), LDA, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by ZLAHEF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 10 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J + 1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL ZLAHEF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( MAX(1, J), J+1 ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ),
+ $ IINFO )
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL ZSWAP( J1-K1-2, A( 1, J2 ), 1,
+ $ A( 1, IPIV(J2) ), 1 )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* the row A(J1-1, J2-1:N) stores U(J1, J2+1:N) and
+* WORK stores the current block of the auxiriarly matrix H
+*
+ IF( J.LT.N ) THEN
+*
+* if the first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = DCONJG( A( J, J+1 ) )
+ A( J, J+1 ) = ONE
+ CALL ZCOPY( N-J, A( J-1, J+1 ), LDA,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL ZSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=0 and K2=1 for the first panel,
+* and K1=1 and K2=0 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with ZGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL ZGEMM( 'Conjugate transpose', 'Transpose',
+ $ 1, MJ, JB+1,
+ $ -ONE, A( J1-K2, J3 ), LDA,
+ $ WORK( (J3-J1+1)+K1*N ), N,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block row with ZGEMM
+*
+ CALL ZGEMM( 'Conjugate transpose', 'Transpose',
+ $ NJ, N-J3+1, JB+1,
+ $ -ONE, A( J1-K2, J2 ), LDA,
+ $ WORK( (J3-J1+1)+K1*N ), N,
+ $ ONE, A( J2, J3 ), LDA )
+ END DO
+*
+* Recover T( J, J+1 )
+*
+ A( J, J+1 ) = DCONJG( ALPHA )
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL ZCOPY( N-J, A( J+1, J+1 ), LDA, WORK( 1 ), 1 )
+ END IF
+ GO TO 10
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+* copy first column A(1:N, 1) into H(1:N, 1)
+* (stored in WORK(1:N))
+*
+ CALL ZCOPY( N, A( 1, 1 ), 1, WORK( 1 ), 1 )
+*
+* J is the main loop index, increasing from 1 to N in steps of
+* JB, where JB is the number of columns factorized by ZLAHEF;
+* JB is either NB, or N-J+1 for the last block
+*
+ J = 0
+ 11 CONTINUE
+ IF( J.GE.N )
+ $ GO TO 20
+*
+* each step of the main loop
+* J is the last column of the previous panel
+* J1 is the first column of the current panel
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=1 for the first panel, and
+* K1=0 for the rest
+*
+ J1 = J+1
+ JB = MIN( N-J1+1, NB )
+ K1 = MAX(1, J)-J
+*
+* Panel factorization
+*
+ CALL ZLAHEF_AASEN( UPLO, 2-K1, N-J, JB,
+ $ A( J+1, MAX(1, J) ), LDA,
+ $ IPIV( J+1 ), WORK, N, WORK( N*NB+1 ), IINFO)
+ IF( (IINFO.GT.0) .AND. (INFO.EQ.0) ) THEN
+ INFO = IINFO+J
+ ENDIF
+*
+* Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*
+ DO J2 = J+2, MIN(N, J+JB+1)
+ IPIV( J2 ) = IPIV( J2 ) + J
+ IF( (J2.NE.IPIV(J2)) .AND. ((J1-K1).GT.2) ) THEN
+ CALL ZSWAP( J1-K1-2, A( J2, 1 ), LDA,
+ $ A( IPIV(J2), 1 ), LDA )
+ END IF
+ END DO
+ J = J + JB
+*
+* Trailing submatrix update, where
+* A(J2+1, J1-1) stores L(J2+1, J1) and
+* WORK(J2+1, 1) stores H(J2+1, 1)
+*
+ IF( J.LT.N ) THEN
+*
+* if the first panel and JB=1 (NB=1), then nothing to do
+*
+ IF( J1.GT.1 .OR. JB.GT.1 ) THEN
+*
+* Merge rank-1 update with BLAS-3 update
+*
+ ALPHA = DCONJG( A( J+1, J ) )
+ A( J+1, J ) = ONE
+ CALL ZCOPY( N-J, A( J+1, J-1 ), 1,
+ $ WORK( (J+1-J1+1)+JB*N ), 1 )
+ CALL ZSCAL( N-J, ALPHA, WORK( (J+1-J1+1)+JB*N ), 1 )
+*
+* K1 identifies if the previous column of the panel has been
+* explicitly stored, e.g., K1=0 and K2=1 for the first panel,
+* and K1=1 and K2=0 for the rest
+*
+ IF( J1.GT.1 ) THEN
+*
+* Not first panel
+*
+ K2 = 1
+ ELSE
+*
+* First panel
+*
+ K2 = 0
+*
+* First update skips the first column
+*
+ JB = JB - 1
+ END IF
+*
+ DO J2 = J+1, N, NB
+ NJ = MIN( NB, N-J2+1 )
+*
+* Update (J2, J2) diagonal block with ZGEMV
+*
+ J3 = J2
+ DO MJ = NJ-1, 1, -1
+ CALL ZGEMM( 'No transpose', 'Conjugate transpose',
+ $ MJ, 1, JB+1,
+ $ -ONE, WORK( (J3-J1+1)+K1*N ), N,
+ $ A( J3, J1-K2 ), LDA,
+ $ ONE, A( J3, J3 ), LDA )
+ J3 = J3 + 1
+ END DO
+*
+* Update off-diagonal block of J2-th block column with ZGEMM
+*
+ CALL ZGEMM( 'No transpose', 'Conjugate transpose',
+ $ N-J3+1, NJ, JB+1,
+ $ -ONE, WORK( (J3-J1+1)+K1*N ), N,
+ $ A( J2, J1-K2 ), LDA,
+ $ ONE, A( J3, J2 ), LDA )
+ END DO
+*
+* Recover T( J+1, J )
+*
+ A( J+1, J ) = DCONJG( ALPHA )
+ END IF
+*
+* WORK(J+1, 1) stores H(J+1, 1)
+*
+ CALL ZCOPY( N-J, A( J+1, J+1 ), 1, WORK( 1 ), 1 )
+ END IF
+ GO TO 11
+ END IF
+*
+ 20 CONTINUE
+ RETURN
+*
+* End of ZHETRF_AASEN
+*
+ END
--- /dev/null
+*> \brief \b ZHETRS_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHETRS_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrs_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrs_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrs_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHETRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+* WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHETRS_AASEN solves a system of linear equations A*X = B with a real
+*> hermitian matrix A using the factorization A = U*T*U**T or
+*> A = L*T*L**T computed by ZHETRF_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*T*U**T;
+*> = 'L': Lower triangular, form is A = L*T*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand sides, i.e., the number of columns
+*> of the matrix B. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> Details of factors computed by ZHETRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges as computed by ZHETRF_AASEN.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> On entry, the right hand side matrix B.
+*> On exit, the solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] WORK
+*> \verbatim
+*> WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER, LWORK >= 3*N-2.
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYcomputational
+*
+* @precisions fortran z -> c
+*
+* =====================================================================
+ SUBROUTINE ZHETRS_AASEN( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
+ $ WORK, LWORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER N, NRHS, LDA, LDB, LWORK, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+* =====================================================================
+*
+ COMPLEX*16 ONE
+ PARAMETER ( ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER K, KP
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL ZGTSV, ZSWAP, ZTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LWORK.LT.(3*N-2) ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZHETRS_AASEN', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*T*U**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
+*
+ CALL ZTRSM('L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Compute T \ B -> B [ T \ (U \P**T * B) ]
+*
+ CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1)
+ CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1)
+ CALL ZLACGV( N-1, WORK( 1 ), 1 )
+ END IF
+ CALL ZGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+ $ INFO)
+*
+* Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
+*
+ CALL ZTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
+ $ B(2, 1), LDB)
+*
+* Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*T*L**T.
+*
+* Pivot, P**T * B
+*
+ DO K = 1, N
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
+*
+ CALL ZTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B(2, 1), LDB)
+*
+* Compute T \ B -> B [ T \ (L \P**T * B) ]
+*
+ CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+ IF( N.GT.1 ) THEN
+ CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1)
+ CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1)
+ CALL ZLACGV( N-1, WORK( 2*N ), 1 )
+ END IF
+ CALL ZGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+ $ INFO)
+*
+* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
+*
+ CALL ZTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
+ $ B( 2, 1 ), LDB)
+*
+* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+ DO K = N, 1, -1
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ END DO
+*
+ END IF
+*
+ RETURN
+*
+* End of ZHETRS_AASEN
+*
+ END
--- /dev/null
+*> \brief \b ZLAHEF_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLAHEF_AASEN + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahef_aasen.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahef_aasen.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahef_aasen.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZLAHEF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+* H, LDH, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER J1, M, NB, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLATRF_AASEN factorizes a panel of a real hermitian matrix A using
+*> the Aasen's algorithm. The panel consists of a set of NB rows of A
+*> when UPLO is U, or a set of NB columns when UPLO is L.
+*>
+*> In order to factorize the panel, the Aasen's algorithm requires the
+*> last row, or column, of the previous panel. The first row, or column,
+*> of A is set to be the first row, or column, of an identity matrix,
+*> which is used to factorize the first panel.
+*>
+*> The resulting J-th row of U, or J-th column of L, is stored in the
+*> (J-1)-th row, or column, of A (without the unit diatonals), while
+*> the diagonal and subdiagonal of A are overwritten by those of T.
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] J1
+*> \verbatim
+*> J1 is INTEGER
+*> The location of the first row, or column, of the panel
+*> within the submatrix of A, passed to this routine, e.g.,
+*> when called by ZHETRF_AASEN, for the first panel, J1 is 1,
+*> while for the remaining panels, J1 is 2.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The dimension of the submatrix. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The dimension of the panel to be facotorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,M) for
+*> the first panel, while dimension (LDA,M+1) for the
+*> remaining panels.
+*>
+*> On entry, A contains the last row, or column, of
+*> the previous panel, and the trailing submatrix of A
+*> to be factorized, except for the first panel, only
+*> the panel is passed.
+*>
+*> On exit, the leading panel is factorized.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the row and column interchanges,
+*> the row and column k were interchanged with the row and
+*> column IPIV(k).
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is COMPLEX*16 workspace, dimension (LDH,NB).
+*>
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the workspace H. LDH >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 workspace, dimension (M).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16SYcomputational
+*
+* @precisions fortran z -> c
+*
+* =====================================================================
+ SUBROUTINE ZLAHEF_AASEN( UPLO, J1, M, NB, A, LDA, IPIV,
+ $ H, LDH, WORK, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER M, NB, J1, LDA, LDH, INFO
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), H( LDH, * ), WORK( * )
+* ..
+*
+* =====================================================================
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = (0.0D+0, 0.0D+0), ONE = (1.0D+0, 0.0D+0) )
+*
+* .. Local Scalars ..
+ INTEGER J, K, K1, I1, I2
+ COMPLEX*16 PIV, ALPHA
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ INTEGER IZAMAX, ILAENV
+ EXTERNAL LSAME, ILAENV, IZAMAX
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE, DCONJG, MAX
+* ..
+* .. Executable Statements ..
+*
+ INFO = 0
+ J = 1
+*
+* K1 is the first column of the panel to be factorized
+* i.e., K1 is 2 for the first block column, and 1 for the rest of the blocks
+*
+ K1 = (2-J1)+1
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+*
+* .....................................................
+* Factorize A as U**T*D*U using the upper triangle of A
+* .....................................................
+*
+ 10 CONTINUE
+ IF ( J.GT.MIN(M, NB) )
+ $ GO TO 20
+*
+* K is the column to be factorized
+* when being called from ZHETRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J, J:N) - H(J:N, 1:(J-1)) * L(J1:(J-1), J),
+* where H(J:N, J) has been initialized to be A(J, J:N)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL ZLACGV( J-K1, A( 1, J ), 1 )
+ CALL ZGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( 1, J ), 1,
+ $ ONE, H( J, J ), 1 )
+ CALL ZLACGV( J-K1, A( 1, J ), 1 )
+ END IF
+*
+* Copy H(i:n, i) into WORK
+*
+ CALL ZCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J-1, J:N) * T(J-1,J),
+* where A(J-1, J) stores T(J-1, J) and A(J-2, J:N) stores U(J-1, J:N)
+*
+ ALPHA = -DCONJG( A( K-1, J ) )
+ CALL ZAXPY( M-J+1, ALPHA, A( K-2, J ), LDA, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( K, J ) = DBLE( WORK( 1 ) )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L(J, (J+1):N)
+* where A(J, J) stores T(J, J) and A(J-1, (J+1):N) stores U(J, (J+1):N)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( K, J )
+ CALL ZAXPY( M-J, ALPHA, A( K-1, J+1 ), LDA,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = IZAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply hermitian pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1, I1+1:N) with A(I1+1:N, I2)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL ZSWAP( I2-I1-1, A( J1+I1-1, I1+1 ), LDA,
+ $ A( J1+I1, I2 ), 1 )
+ CALL ZLACGV( I2-I1, A( J1+I1-1, I1+1 ), LDA )
+ CALL ZLACGV( I2-I1-1, A( J1+I1, I2 ), 1 )
+*
+* Swap A(I1, I2+1:N) with A(I2, I2+1:N)
+*
+ CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+ $ A( J1+I2-1, I2+1 ), LDA )
+*
+* Swap A(I1, I1) with A(I2,I2)
+*
+ PIV = A( I1+J1-1, I1 )
+ A( J1+I1-1, I1 ) = A( J1+I2-1, I2 )
+ A( J1+I2-1, I2 ) = PIV
+*
+* Swap H(I1, 1:J1) with H(I2, 1:J1)
+*
+ CALL ZSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL ZSWAP( I1-K1+1, A( 1, I1 ), 1,
+ $ A( 1, I2 ), 1 )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J, J+1) = T(J, J+1)
+*
+ A( K, J+1 ) = WORK( 2 )
+ IF( (A( K, J ).EQ.ZERO ) .AND.
+ $ ( (J.EQ.M) .OR. (A( K, J+1 ).EQ.ZERO))) THEN
+ IF(INFO .EQ. 0) THEN
+ INFO = J
+ END IF
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J:N, J),
+*
+ CALL ZCOPY( M-J, A( K+1, J+1 ), LDA,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( K, J+1 ).NE.ZERO ) THEN
+ ALPHA = ONE / A( K, J+1 )
+ CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+ CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+ ELSE
+ CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+ $ A( K, J+2 ), LDA)
+ END IF
+ ELSE
+ IF( (A( K, J ).EQ.ZERO) .AND. (INFO.EQ.0) ) THEN
+ INFO = J
+ END IF
+ END IF
+ J = J + 1
+ GO TO 10
+ 20 CONTINUE
+*
+ ELSE
+*
+* .....................................................
+* Factorize A as L*D*L**T using the lower triangle of A
+* .....................................................
+*
+ 30 CONTINUE
+ IF( J.GT.MIN( M, NB ) )
+ $ GO TO 40
+*
+* K is the column to be factorized
+* when being called from ZHETRF_AASEN,
+* > for the first block column, J1 is 1, hence J1+J-1 is J,
+* > for the rest of the columns, J1 is 2, and J1+J-1 is J+1,
+*
+ K = J1+J-1
+*
+* H(J:N, J) := A(J:N, J) - H(J:N, 1:(J-1)) * L(J, J1:(J-1))^T,
+* where H(J:N, J) has been initialized to be A(J:N, J)
+*
+ IF( K.GT.2 ) THEN
+*
+* K is the column to be factorized
+* > for the first block column, K is J, skipping the first two
+* columns
+* > for the rest of the columns, K is J+1, skipping only the
+* first column
+*
+ CALL ZLACGV( J-K1, A( J, 1 ), LDA )
+ CALL ZGEMV( 'No transpose', M-J+1, J-K1,
+ $ -ONE, H( J, K1 ), LDH,
+ $ A( J, 1 ), LDA,
+ $ ONE, H( J, J ), 1 )
+ CALL ZLACGV( J-K1, A( J, 1 ), LDA )
+ END IF
+*
+* Copy H(J:N, J) into WORK
+*
+ CALL ZCOPY( M-J+1, H( J, J ), 1, WORK( 1 ), 1 )
+*
+ IF( J.GT.K1 ) THEN
+*
+* Compute WORK := WORK - L(J:N, J-1) * T(J-1,J),
+* where A(J-1, J) = T(J-1, J) and A(J, J-2) = L(J, J-1)
+*
+ ALPHA = -DCONJG( A( J, K-1 ) )
+ CALL ZAXPY( M-J+1, ALPHA, A( J, K-2 ), 1, WORK( 1 ), 1 )
+ END IF
+*
+* Set A(J, J) = T(J, J)
+*
+ A( J, K ) = DBLE( WORK( 1 ) )
+*
+ IF( J.LT.M ) THEN
+*
+* Compute WORK(2:N) = T(J, J) L((J+1):N, J)
+* where A(J, J) = T(J, J) and A((J+1):N, J-1) = L((J+1):N, J)
+*
+ IF( (J1+J-1).GT.1 ) THEN
+ ALPHA = -A( J, K )
+ CALL ZAXPY( M-J, ALPHA, A( J+1, K-1 ), 1,
+ $ WORK( 2 ), 1 )
+ ENDIF
+*
+* Find max(|WORK(2:n)|)
+*
+ I2 = IZAMAX( M-J, WORK( 2 ), 1 ) + 1
+ PIV = WORK( I2 )
+*
+* Apply hermitian pivot
+*
+ IF( (I2.NE.2) .AND. (PIV.NE.0) ) THEN
+*
+* Swap WORK(I1) and WORK(I2)
+*
+ I1 = 2
+ WORK( I2 ) = WORK( I1 )
+ WORK( I1 ) = PIV
+*
+* Swap A(I1+1:N, I1) with A(I2, I1+1:N)
+*
+ I1 = I1+J-1
+ I2 = I2+J-1
+ CALL ZSWAP( I2-I1-1, A( I1+1, J1+I1-1 ), 1,
+ $ A( I2, J1+I1 ), LDA )
+ CALL ZLACGV( I2-I1, A( I1+1, J1+I1-1 ), 1 )
+ CALL ZLACGV( I2-I1-1, A( I2, J1+I1 ), LDA )
+*
+* Swap A(I2+1:N, I1) with A(I2+1:N, I2)
+*
+ CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+ $ A( I2+1, J1+I2-1 ), 1 )
+*
+* Swap A(I1, I1) with A(I2, I2)
+*
+ PIV = A( I1, J1+I1-1 )
+ A( I1, J1+I1-1 ) = A( I2, J1+I2-1 )
+ A( I2, J1+I2-1 ) = PIV
+*
+* Swap H(I1, I1:J1) with H(I2, I2:J1)
+*
+ CALL ZSWAP( I1-1, H( I1, 1 ), LDH, H( I2, 1 ), LDH )
+ IPIV( I1 ) = I2
+*
+ IF( I1.GT.(K1-1) ) THEN
+*
+* Swap L(1:I1-1, I1) with L(1:I1-1, I2),
+* skipping the first column
+*
+ CALL ZSWAP( I1-K1+1, A( I1, 1 ), LDA,
+ $ A( I2, 1 ), LDA )
+ END IF
+ ELSE
+ IPIV( J+1 ) = J+1
+ ENDIF
+*
+* Set A(J+1, J) = T(J+1, J)
+*
+ A( J+1, K ) = WORK( 2 )
+ IF( (A( J, K ).EQ.ZERO) .AND.
+ $ ( (J.EQ.M) .OR. (A( J+1, K ).EQ.ZERO)) ) THEN
+ IF (INFO .EQ. 0)
+ $ INFO = J
+ END IF
+*
+ IF( J.LT.NB ) THEN
+*
+* Copy A(J+1:N, J+1) into H(J+1:N, J),
+*
+ CALL ZCOPY( M-J, A( J+1, K+1 ), 1,
+ $ H( J+1, J+1 ), 1 )
+ END IF
+*
+* Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
+* where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
+*
+ IF( A( J+1, K ).NE.ZERO ) THEN
+ ALPHA = ONE / A( J+1, K )
+ CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+ CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+ ELSE
+ CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+ $ A( J+2, K ), LDA )
+ END IF
+ ELSE
+ IF( (A( J, K ).EQ.ZERO) .AND. (J.EQ.M)
+ $ .AND. (INFO.EQ.0) ) INFO = J
+ END IF
+ J = J + 1
+ GO TO 30
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of ZLAHEF_AASEN
+*
+ END
schkeq.f schkgb.f schkge.f schkgt.f
schklq.f schkpb.f schkpo.f schkps.f schkpp.f
schkpt.f schkq3.f schkql.f schkqr.f schkrq.f
- schksp.f schksy.f schksy_rook.f schktb.f schktp.f schktr.f
+ schksp.f schksy.f schksy_rook.f schksy_aasen.f schktb.f schktp.f schktr.f
schktz.f
sdrvgt.f sdrvls.f sdrvpb.f
- sdrvpp.f sdrvpt.f sdrvsp.f sdrvsy.f sdrvsy_rook.f
+ sdrvpp.f sdrvpt.f sdrvsp.f sdrvsy.f sdrvsy_rook.f sdrvsy_aasen.f
serrgt.f serrlq.f serrls.f
serrpo.f serrps.f serrql.f serrqp.f serrqr.f
serrrq.f serrsy.f serrtr.f serrtz.f serrvx.f
sqrt01.f sqrt01p.f sqrt02.f sqrt03.f sqrt11.f sqrt12.f
sqrt13.f sqrt14.f sqrt15.f sqrt16.f sqrt17.f
srqt01.f srqt02.f srqt03.f srzt01.f srzt02.f
- sspt01.f ssyt01.f ssyt01_rook.f
+ sspt01.f ssyt01.f ssyt01_rook.f ssyt01_aasen.f
stbt02.f stbt03.f stbt05.f stbt06.f stpt01.f
stpt02.f stpt03.f stpt05.f stpt06.f strt01.f
strt02.f strt03.f strt05.f strt06.f
set(CLINTST cchkaa.f
cchkeq.f cchkgb.f cchkge.f cchkgt.f
- cchkhe.f cchkhe_rook.f cchkhp.f cchklq.f cchkpb.f
+ cchkhe.f cchkhe_rook.f cchkhe_aasen.f cchkhp.f cchklq.f cchkpb.f
cchkpo.f cchkps.f cchkpp.f cchkpt.f cchkq3.f cchkql.f
cchkqr.f cchkrq.f cchksp.f cchksy.f cchksy_rook.f cchktb.f
cchktp.f cchktr.f cchktz.f
- cdrvgt.f cdrvhe.f cdrvhe_rook.f cdrvhp.f
+ cdrvgt.f cdrvhe.f cdrvhe_rook.f cdrvhe_aasen.f cdrvhp.f
cdrvls.f cdrvpb.f cdrvpp.f cdrvpt.f
cdrvsp.f cdrvsy.f cdrvsy_rook.f
cerrgt.f cerrhe.f cerrlq.f
cgbt01.f cgbt02.f cgbt05.f cgelqs.f cgeqls.f cgeqrs.f
cgerqs.f cget01.f cget02.f
cget03.f cget04.f cget07.f cgtt01.f cgtt02.f
- cgtt05.f chet01.f chet01_rook.f chpt01.f claipd.f claptm.f clarhs.f clatb4.f clatb5.f
+ cgtt05.f chet01.f chet01_rook.f chet01_aasen.f chpt01.f claipd.f claptm.f clarhs.f clatb4.f clatb5.f
clatsp.f clatsy.f clattb.f clattp.f clattr.f
clavhe.f clavhe_rook.f clavhp.f clavsp.f clavsy.f clavsy_rook.f clqt01.f
clqt02.f clqt03.f cpbt01.f cpbt02.f cpbt05.f
dchkeq.f dchkgb.f dchkge.f dchkgt.f
dchklq.f dchkpb.f dchkpo.f dchkps.f dchkpp.f
dchkpt.f dchkq3.f dchkql.f dchkqr.f dchkrq.f
- dchksp.f dchksy.f dchksy_rook.f dchktb.f dchktp.f dchktr.f
+ dchksp.f dchksy.f dchksy_rook.f dchksy_aasen.f dchktb.f dchktp.f dchktr.f
dchktz.f
ddrvgt.f ddrvls.f ddrvpb.f
- ddrvpp.f ddrvpt.f ddrvsp.f ddrvsy.f ddrvsy_rook.f
+ ddrvpp.f ddrvpt.f ddrvsp.f ddrvsy.f ddrvsy_rook.f ddrvsy_aasen.f
derrgt.f derrlq.f derrls.f
derrps.f derrql.f derrqp.f derrqr.f
derrrq.f derrsy.f derrtr.f derrtz.f derrvx.f
dqrt01.f dqrt01p.f dqrt02.f dqrt03.f dqrt11.f dqrt12.f
dqrt13.f dqrt14.f dqrt15.f dqrt16.f dqrt17.f
drqt01.f drqt02.f drqt03.f drzt01.f drzt02.f
- dspt01.f dsyt01.f dsyt01_rook.f
+ dspt01.f dsyt01.f dsyt01_rook.f dsyt01_aasen.f
dtbt02.f dtbt03.f dtbt05.f dtbt06.f dtpt01.f
dtpt02.f dtpt03.f dtpt05.f dtpt06.f dtrt01.f
dtrt02.f dtrt03.f dtrt05.f dtrt06.f
set(ZLINTST zchkaa.f
zchkeq.f zchkgb.f zchkge.f zchkgt.f
- zchkhe.f zchkhe_rook.f zchkhp.f zchklq.f zchkpb.f
+ zchkhe.f zchkhe_rook.f zchkhe_aasen.f zchkhp.f zchklq.f zchkpb.f
zchkpo.f zchkps.f zchkpp.f zchkpt.f zchkq3.f zchkql.f
zchkqr.f zchkrq.f zchksp.f zchksy.f zchksy_rook.f zchktb.f
zchktp.f zchktr.f zchktz.f
- zdrvgt.f zdrvhe.f zdrvhe_rook.f zdrvhp.f
+ zdrvgt.f zdrvhe.f zdrvhe_rook.f zdrvhe_aasen.f zdrvhp.f
zdrvls.f zdrvpb.f zdrvpp.f zdrvpt.f
zdrvsp.f zdrvsy.f zdrvsy_rook.f
zerrgt.f zerrhe.f zerrlq.f
zgbt01.f zgbt02.f zgbt05.f zgelqs.f zgeqls.f zgeqrs.f
zgerqs.f zget01.f zget02.f
zget03.f zget04.f zget07.f zgtt01.f zgtt02.f
- zgtt05.f zhet01.f zhet01.f zhet01_rook.f zhpt01.f zlaipd.f zlaptm.f zlarhs.f zlatb4.f zlatb5.f
+ zgtt05.f zhet01.f zhet01.f zhet01_rook.f zhet01_aasen.f zhpt01.f zlaipd.f zlaptm.f zlarhs.f zlatb4.f zlatb5.f
zlatsp.f zlatsy.f zlattb.f zlattp.f zlattr.f
zlavhe.f zlavhe_rook.f zlavhp.f zlavsp.f zlavsy.f zlavsy_rook.f zlqt01.f
zlqt02.f zlqt03.f zpbt01.f zpbt02.f zpbt05.f
schkeq.o schkgb.o schkge.o schkgt.o \
schklq.o schkpb.o schkpo.o schkps.o schkpp.o \
schkpt.o schkq3.o schkql.o schkqr.o schkrq.o \
- schksp.o schksy.o schksy_rook.o schktb.o schktp.o schktr.o \
+ schksp.o schksy.o schksy_rook.o schksy_aasen.o schktb.o schktp.o schktr.o \
schktz.o \
sdrvgt.o sdrvls.o sdrvpb.o \
- sdrvpp.o sdrvpt.o sdrvsp.o sdrvsy_rook.o\
+ sdrvpp.o sdrvpt.o sdrvsp.o sdrvsy_rook.o sdrvsy_aasen.o\
serrgt.o serrlq.o serrls.o \
serrps.o serrql.o serrqp.o serrqr.o \
serrrq.o serrtr.o serrtz.o \
sqrt01.o sqrt01p.o sqrt02.o sqrt03.o sqrt11.o sqrt12.o \
sqrt13.o sqrt14.o sqrt15.o sqrt16.o sqrt17.o \
srqt01.o srqt02.o srqt03.o srzt01.o srzt02.o \
- sspt01.o ssyt01.o ssyt01_rook.o \
+ sspt01.o ssyt01.o ssyt01_rook.o ssyt01_aasen.o\
stbt02.o stbt03.o stbt05.o stbt06.o stpt01.o \
stpt02.o stpt03.o stpt05.o stpt06.o strt01.o \
strt02.o strt03.o strt05.o strt06.o \
CLINTST = cchkaa.o \
cchkeq.o cchkgb.o cchkge.o cchkgt.o \
- cchkhe.o cchkhe_rook.o cchkhp.o cchklq.o cchkpb.o \
+ cchkhe.o cchkhe_rook.o cchkhe_aasen.o cchkhp.o cchklq.o cchkpb.o \
cchkpo.o cchkps.o cchkpp.o cchkpt.o cchkq3.o cchkql.o \
cchkqr.o cchkrq.o cchksp.o cchksy.o cchksy_rook.o cchktb.o \
cchktp.o cchktr.o cchktz.o \
- cdrvgt.o cdrvhe_rook.o cdrvhp.o \
+ cdrvgt.o cdrvhe_rook.o cdrvhe_aasen.o cdrvhp.o \
cdrvls.o cdrvpb.o cdrvpp.o cdrvpt.o \
cdrvsp.o cdrvsy_rook.o \
cerrgt.o cerrlq.o \
cgbt01.o cgbt02.o cgbt05.o cgelqs.o cgeqls.o cgeqrs.o \
cgerqs.o cget01.o cget02.o \
cget03.o cget04.o cget07.o cgtt01.o cgtt02.o \
- cgtt05.o chet01.o chet01_rook.o chpt01.o claipd.o claptm.o clarhs.o clatb4.o clatb5.o \
+ cgtt05.o chet01.o chet01_rook.o chet01_aasen.o chpt01.o claipd.o claptm.o clarhs.o clatb4.o clatb5.o \
clatsp.o clatsy.o clattb.o clattp.o clattr.o \
clavhe.o clavhe_rook.o clavhp.o clavsp.o clavsy.o clavsy_rook.o clqt01.o \
clqt02.o clqt03.o cpbt01.o cpbt02.o cpbt05.o \
dchkeq.o dchkgb.o dchkge.o dchkgt.o \
dchklq.o dchkpb.o dchkpo.o dchkps.o dchkpp.o \
dchkpt.o dchkq3.o dchkql.o dchkqr.o dchkrq.o \
- dchksp.o dchksy.o dchksy_rook.o dchktb.o dchktp.o dchktr.o \
+ dchksp.o dchksy.o dchksy_rook.o dchksy_aasen.o dchktb.o dchktp.o dchktr.o \
dchktz.o \
ddrvgt.o ddrvls.o ddrvpb.o \
- ddrvpp.o ddrvpt.o ddrvsp.o ddrvsy_rook.o \
+ ddrvpp.o ddrvpt.o ddrvsp.o ddrvsy_rook.o ddrvsy_aasen.o\
derrgt.o derrlq.o derrls.o \
derrps.o derrql.o derrqp.o derrqr.o \
derrrq.o derrtr.o derrtz.o \
dqrt01.o dqrt01p.o dqrt02.o dqrt03.o dqrt11.o dqrt12.o \
dqrt13.o dqrt14.o dqrt15.o dqrt16.o dqrt17.o \
drqt01.o drqt02.o drqt03.o drzt01.o drzt02.o \
- dspt01.o dsyt01.o dsyt01_rook.o \
+ dspt01.o dsyt01.o dsyt01_rook.o dsyt01_aasen.o\
dtbt02.o dtbt03.o dtbt05.o dtbt06.o dtpt01.o \
dtpt02.o dtpt03.o dtpt05.o dtpt06.o dtrt01.o \
dtrt02.o dtrt03.o dtrt05.o dtrt06.o \
ZLINTST = zchkaa.o \
zchkeq.o zchkgb.o zchkge.o zchkgt.o \
- zchkhe.o zchkhe_rook.o zchkhp.o zchklq.o zchkpb.o \
+ zchkhe.o zchkhe_rook.o zchkhe_aasen.o zchkhp.o zchklq.o zchkpb.o \
zchkpo.o zchkps.o zchkpp.o zchkpt.o zchkq3.o zchkql.o \
zchkqr.o zchkrq.o zchksp.o zchksy.o zchksy_rook.o zchktb.o \
zchktp.o zchktr.o zchktz.o \
- zdrvgt.o zdrvhe_rook.o zdrvhp.o \
+ zdrvgt.o zdrvhe_rook.o zdrvhe_aasen.o zdrvhp.o \
zdrvls.o zdrvpb.o zdrvpp.o zdrvpt.o \
zdrvsp.o zdrvsy_rook.o \
zerrgt.o zerrlq.o \
zgbt01.o zgbt02.o zgbt05.o zgelqs.o zgeqls.o zgeqrs.o \
zgerqs.o zget01.o zget02.o \
zget03.o zget04.o zget07.o zgtt01.o zgtt02.o \
- zgtt05.o zhet01.o zhet01_rook.o zhpt01.o zlaipd.o zlaptm.o zlarhs.o zlatb4.o zlatb5.o \
+ zgtt05.o zhet01.o zhet01_rook.o zhet01_aasen.o zhpt01.o zlaipd.o zlaptm.o zlarhs.o zlatb4.o zlatb5.o \
zlatsp.o zlatsy.o zlattb.o zlattp.o zlattr.o \
zlavhe.o zlavhe_rook.o zlavhp.o zlavsp.o zlavsy.o zlavsy_rook.o zlqt01.o \
zlqt02.o zlqt03.o zpbt01.o zpbt02.o zpbt05.o \
*> with "rook" (bounded Bunch-Kaufman) pivoting
*> _SP: Symmetric indefinite packed,
*> with partial (Bunch-Kaufman) pivoting
+*> _HA: (complex) Hermitian ,
+*> Assen Algorithm
*> _HE: (complex) Hermitian indefinite,
*> with partial (Bunch-Kaufman) pivoting
*> _HR: (complex) Hermitian indefinite,
WRITE( IOUNIT, FMT = 9979 )3
WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
- ELSE IF( LSAMEN( 2, P2, 'HE' ) .OR. LSAMEN( 2, P2, 'HP' ) ) THEN
+ ELSE IF( LSAMEN( 2, P2, 'HA' ) ) THEN
+*
+* HA: Hermitian
+* Aasen algorithm
+ WRITE( IOUNIT, FMT = 9971 )PATH, 'Hermitian'
+*
+ WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
+ WRITE( IOUNIT, FMT = 9983 )
+*
+ WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
+ WRITE( IOUNIT, FMT = 9974 )1
+ WRITE( IOUNIT, FMT = 9980 )2
+ WRITE( IOUNIT, FMT = 9979 )3
+ WRITE( IOUNIT, FMT = 9977 )4
+ WRITE( IOUNIT, FMT = 9978 )5
+ WRITE( IOUNIT, FMT = 9976 )6
+ WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
+
+
+ ELSE IF( LSAMEN( 2, P2, 'HE' ) .OR.
+ $ LSAMEN( 2, P2, 'HP' ) ) THEN
*
* HE: Hermitian indefinite full
* with partial (Bunch-Kaufman) pivoting algorithm
$ ' positive definite band matrices' )
9993 FORMAT( / 1X, A3, ' drivers: ', A9,
$ ' positive definite tridiagonal' )
+ 9971 FORMAT( / 1X, A3, ' drivers: ', A9, ' indefinite matrices',
+ $ ', "Aasen" Algorithm' )
9992 FORMAT( / 1X, A3, ' drivers: ', A9, ' indefinite matrices',
$ ', "rook" (bounded Bunch-Kaufman) pivoting' )
9991 FORMAT( / 1X, A3, ' drivers: ', A9,
ELSE IF( LSAMEN( 2, P2, 'SY' )
$ .OR. LSAMEN( 2, P2, 'SR' )
$ .OR. LSAMEN( 2, P2, 'HE' )
+ $ .OR. LSAMEN( 2, P2, 'HA' )
$ .OR. LSAMEN( 2, P2, 'HR' ) ) THEN
*
* xSY: symmetric indefinite matrices
* with rook (bounded Bunch-Kaufman) pivoting;
* xHE: Hermitian indefinite matrices
* with partial (Bunch-Kaufman) pivoting.
+* xHA: Hermitian matrices
+* Aasen Algorithm
* xHR: Hermitian indefinite matrices
* with rook (bounded Bunch-Kaufman) pivoting;
*
*> with "rook" (bounded Bunch-Kaufman) pivoting
*> _SP: Symmetric indefinite packed,
*> with partial (Bunch-Kaufman) pivoting
+*> _HA: (complex) Hermitian ,
+*> with Aasen Algorithm
*> _HE: (complex) Hermitian indefinite,
*> with partial (Bunch-Kaufman) pivoting
*> _HR: Symmetric indefinite,
WRITE( IOUNIT, FMT = 9955 )8
WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
+ ELSE IF( LSAMEN( 2, P2, 'HA' ) ) THEN
+*
+* HA: Hermitian,
+* with Assen Algorithm
+*
+ WRITE( IOUNIT, FMT = 9992 )PATH, 'Hermitian'
+*
+ WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
+ WRITE( IOUNIT, FMT = 9972 )
+*
+ WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
+ WRITE( IOUNIT, FMT = 9953 )1
+ WRITE( IOUNIT, FMT = 9961 )2
+ WRITE( IOUNIT, FMT = 9960 )3
+ WRITE( IOUNIT, FMT = 9960 )4
+ WRITE( IOUNIT, FMT = 9959 )5
+ WRITE( IOUNIT, FMT = 9958 )6
+ WRITE( IOUNIT, FMT = 9956 )7
+ WRITE( IOUNIT, FMT = 9957 )8
+ WRITE( IOUNIT, FMT = 9955 )9
+ WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
+*
ELSE IF( LSAMEN( 2, P2, 'HE' ) ) THEN
*
* HE: Hermitian indefinite full,
*> CPT 12 List types on next line if 0 < NTYPES < 12
*> CHE 10 List types on next line if 0 < NTYPES < 10
*> CHR 10 List types on next line if 0 < NTYPES < 10
+*> CHA 10 List types on next line if 0 < NTYPES < 10
*> CHP 10 List types on next line if 0 < NTYPES < 10
*> CSY 11 List types on next line if 0 < NTYPES < 11
*> CSR 11 List types on next line if 0 < NTYPES < 11
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
-*> \date November 2015
+*> \date November 2016
*
*> \ingroup complex_lin
*
* =====================================================================
PROGRAM CCHKAA
*
-* -- LAPACK test routine (version 3.6.0) --
+* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2015
+* November 2016
*
* =====================================================================
*
WRITE( NOUT, FMT = 9988 )PATH
END IF
*
+ ELSE IF( LSAMEN( 2, C2, 'HA' ) ) THEN
+*
+* HA: Hermitian matrices,
+* Aasen Algorithm
+*
+ NTYPES = 10
+ CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
+*
+ IF( TSTCHK ) THEN
+ CALL CCHKHE_AASEN( DOTYPE, NN, NVAL, NNB2, NBVAL2, NNS,
+ $ NSVAL, THRESH, TSTERR, LDA,
+ $ A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9989 )PATH
+ END IF
+*
+ IF( TSTDRV ) THEN
+ CALL CDRVHE_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ LDA, A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9988 )PATH
+ END IF
+*
ELSE IF( LSAMEN( 2, C2, 'HR' ) ) THEN
*
* HR: Hermitian indefinite matrices,
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
-
*
ELSE IF( LSAMEN( 2, C2, 'RQ' ) ) THEN
*
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
-
*
ELSE IF( LSAMEN( 2, C2, 'LS' ) ) THEN
*
--- /dev/null
+*> \brief \b CCHKHE_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CCHKHE_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
+* XACT, WORK, RWORK, IWORK, NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NN, NNB, NNS, NOUT
+* REAL THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+* REAL RWORK( * )
+* COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CCHKHE_AASEN tests CHETRF_AASEN, -TRS_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NNB
+*> \verbatim
+*> NNB is INTEGER
+*> The number of values of NB contained in the vector NBVAL.
+*> \endverbatim
+*>
+*> \param[in] NBVAL
+*> \verbatim
+*> NBVAL is INTEGER array, dimension (NBVAL)
+*> The values of the blocksize NB.
+*> \endverbatim
+*>
+*> \param[in] NNS
+*> \verbatim
+*> NNS is INTEGER
+*> The number of values of NRHS contained in the vector NSVAL.
+*> \endverbatim
+*>
+*> \param[in] NSVAL
+*> \verbatim
+*> NSVAL is INTEGER array, dimension (NNS)
+*> The values of the number of right hand sides NRHS.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is REAL
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is COMPLEX array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is COMPLEX array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is COMPLEX array, dimension (NMAX*NSMAX)
+*> where NSMAX is the largest entry in NSVAL.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is COMPLEX array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is COMPLEX array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX array, dimension (NMAX*max(3,NSMAX))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is REAL array, dimension (max(NMAX,2*NSMAX))
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup complex_lin
+*
+* =====================================================================
+ SUBROUTINE CCHKHE_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+ $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
+ $ X, XACT, WORK, RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NMAX, NN, NNB, NNS, NOUT
+ REAL THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+ REAL RWORK( * )
+ COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ZERO
+ PARAMETER ( ZERO = 0.0E+0 )
+ COMPLEX CZERO
+ PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
+ INTEGER NTYPES
+ PARAMETER ( NTYPES = 10 )
+ INTEGER NTESTS
+ PARAMETER ( NTESTS = 9 )
+* ..
+* .. Local Scalars ..
+ LOGICAL TRFCON, ZEROT
+ CHARACTER DIST, TYPE, UPLO, XTYPE
+ CHARACTER*3 PATH, MATPATH
+ INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
+ $ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
+ $ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
+ REAL ANORM, CNDNUM, RCOND, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ REAL RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ REAL DGET06, CLANHE
+ EXTERNAL DGET06, CLANHE
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, CERRHE, CGET04,
+ $ ZHECON, CHERFS, CHET01, CHETRF_AASEN, ZHETRI2,
+ $ CHETRS_AASEN, CLACPY, CLAIPD, CLARHS, CLATB4,
+ $ CLATMS, CPOT02, ZPOT03, ZPOT05
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC REAL, IMAG, MAX, MIN
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Complex precision'
+ PATH( 2: 3 ) = 'HA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Complex precision'
+ MATPATH( 2: 3 ) = 'HE'
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL CERRHE( PATH, NOUT )
+ INFOT = 0
+*
+* Set the minimum block size for which the block routine should
+* be used, which will be later returned by ILAENV
+*
+ CALL XLAENV( 2, 2 )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ IF( N .GT. NMAX ) THEN
+ NFAIL = NFAIL + 1
+ WRITE(NOUT, 9995) 'M ', N, NMAX
+ GO TO 180
+ END IF
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ IZERO = 0
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Set up parameters with CLATB4 for the matrix generator
+* based on the type of matrix to be generated.
+*
+ CALL CLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU,
+ $ ANORM, MODE, CNDNUM, DIST )
+*
+* Generate a matrix with CLATMS.
+*
+ SRNAMT = 'CLATMS'
+ CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from CLATMS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+*
+* Skip all tests for this generated matrix
+*
+ GO TO 160
+ END IF
+*
+* For types 3-6, zero one or more rows and columns of
+* the matrix to test that INFO is returned correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = CZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = CZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = CZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = CZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = CZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = CZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+* End generate test matrix A.
+*
+*
+* Set the imaginary part of the diagonals.
+*
+ CALL CLAIPD( N, A, LDA+1, 0 )
+*
+* Do for each value of NB in NBVAL
+*
+ DO 150 INB = 1, NNB
+*
+* Set the optimal blocksize, which will be later
+* returned by ILAENV.
+*
+ NB = NBVAL( INB )
+ CALL XLAENV( 1, NB )
+*
+* Copy the test matrix A into matrix AFAC which
+* will be factorized in place. This is needed to
+* preserve the test matrix A for subsequent tests.
+*
+ CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+*
+* Compute the L*D*L**T or U*D*U**T factorization of the
+* matrix. IWORK stores details of the interchanges and
+* the block structure of D. AINV is a work array for
+* block factorization, LWORK is the length of AINV.
+*
+ LWORK = ( NB+1 )*LDA
+ SRNAMT = 'CHETRF_AASEN'
+ CALL CHETRF_AASEN( UPLO, N, AFAC, LDA, IWORK, AINV,
+ $ LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from CHETRF and handle error.
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'CHETRF_AASEN', INFO, K, UPLO,
+ $ N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
+ $ NOUT )
+ END IF
+*
+* Set the condition estimate flag if the INFO is not 0.
+*
+ IF( INFO.NE.0 ) THEN
+ TRFCON = .TRUE.
+ ELSE
+ TRFCON = .FALSE.
+ END IF
+*
+*+ TEST 1
+* Reconstruct matrix from factors and compute residual.
+*
+ CALL CHET01_AASEN( UPLO, N, A, LDA, AFAC, LDA, IWORK,
+ $ AINV, LDA, RWORK, RESULT( 1 ) )
+ NT = 1
+*
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
+ $ RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+*
+* Do only the condition estimate if INFO is not 0.
+*
+ IF( TRFCON ) THEN
+ RCONDC = ZERO
+ GO TO 140
+ END IF
+*
+* Do for each value of NRHS in NSVAL.
+*
+ DO 130 IRHS = 1, NNS
+ NRHS = NSVAL( IRHS )
+*
+*+ TEST 3 (Using TRS)
+* Solve and compute residual for A * X = B.
+*
+* Choose a set of NRHS random solution vectors
+* stored in XACT and set up the right hand side B
+*
+ SRNAMT = 'CLARHS'
+ CALL CLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
+ $ KL, KU, NRHS, A, LDA, XACT, LDA,
+ $ B, LDA, ISEED, INFO )
+ CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+ SRNAMT = 'CHETRS_AASEN'
+ LWORK = 3*N-2
+ CALL CHETRS_AASEN( UPLO, N, NRHS, AFAC, LDA, IWORK,
+ $ X, LDA, WORK, LWORK, INFO )
+*
+* Check error code from CHETRS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'CHETRS_AASEN', INFO, 0,
+ $ UPLO, N, N, -1, -1, NRHS, IMAT,
+ $ NFAIL, NERRS, NOUT )
+ END IF
+*
+ CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+*
+* Compute the residual for the solution
+*
+ CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 120 K = 2, 2
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
+ $ IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 120 CONTINUE
+ NRUN = NRUN + 1
+*
+* End do for each value of NRHS in NSVAL.
+*
+ 130 CONTINUE
+ 140 CONTINUE
+ 150 CONTINUE
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
+ $ I2, ', test ', I2, ', ratio =', G12.5 )
+ 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
+ $ I2, ', test(', I2, ') =', G12.5 )
+ 9995 FORMAT( ' Invalid input value: ', A4, '=', I6, '; must be <=',
+ $ I6 )
+ RETURN
+*
+* End of CCHKHE_AASEN
+*
+ END
--- /dev/null
+*> \brief \b CDRVHE_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CDRVHE_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
+* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
+* NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NMAX, NN, NOUT, NRHS
+* REAL THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NVAL( * )
+* REAL RWORK( * )
+* COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CDRVHE_AASEN tests the driver routine CHESV_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand side vectors to be generated for
+*> each linear system.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is REAL
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is COMPLEX array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is COMPLEX array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is COMPLEX array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is COMPLEX array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is COMPLEX array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is REAL array, dimension (NMAX+2*NRHS)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex_lin
+*
+* =====================================================================
+ SUBROUTINE CDRVHE_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
+ $ RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NMAX, NN, NOUT, NRHS
+ REAL THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NVAL( * )
+ REAL RWORK( * )
+ COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+ INTEGER NTYPES, NTESTS
+ PARAMETER ( NTYPES = 10, NTESTS = 3 )
+ INTEGER NFACT
+ PARAMETER ( NFACT = 2 )
+* ..
+* .. Local Scalars ..
+ LOGICAL ZEROT
+ CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
+ CHARACTER*3 MATPATH, PATH
+ INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
+ $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
+ $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
+ REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER FACTS( NFACT ), UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ REAL RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ REAL CLANHE, SGET06
+ EXTERNAL CLANHE, SGET06
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, CERRVX,
+ $ CGET04, CLACPY, CLARHS, CLATB4, CLATMS,
+ $ CHESV_AASEN, CHET01_AASEN, CPOT02,
+ $ CHETRF_AASEN
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX, MAX, MIN
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Complex precision'
+ PATH( 2: 3 ) = 'HA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Complex precision'
+ MATPATH( 2: 3 ) = 'HE'
+*
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+ LWORK = MAX( 2*NMAX, NMAX*NRHS )
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL CERRVX( PATH, NOUT )
+ INFOT = 0
+*
+* Set the block size and minimum block size for testing.
+*
+ NB = 1
+ NBMIN = 2
+ CALL XLAENV( 1, NB )
+ CALL XLAENV( 2, NBMIN )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Begin generate the test matrix A.
+*
+* Set up parameters with CLATB4 for the matrix generator
+* based on the type of matrix to be generated.
+*
+ CALL CLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
+ $ MODE, CNDNUM, DIST )
+*
+* Generate a matrix with CLATMS.
+*
+ SRNAMT = 'CLATMS'
+ CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
+ $ WORK, INFO )
+*
+* Check error code from CLATMS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N,
+ $ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
+ GO TO 160
+ END IF
+*
+* For types 3-6, zero one or more rows and columns of
+* the matrix to test that INFO is returned correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = ZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = ZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IOFF = 0
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = ZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the first IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = ZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+* End generate the test matrix A.
+*
+*
+ DO 150 IFACT = 1, NFACT
+*
+* Do first for FACT = 'F', then for other values.
+*
+ FACT = FACTS( IFACT )
+*
+* Compute the condition number for comparison with
+* the value returned by CHESVX.
+*
+ IF( ZEROT ) THEN
+ IF( IFACT.EQ.1 )
+ $ GO TO 150
+ RCONDC = ZERO
+*
+ ELSE IF( IFACT.EQ.1 ) THEN
+*
+* Compute the 1-norm of A.
+*
+ ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
+*
+* Factor the matrix A.
+*
+c CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+c SRNAMT = 'CHETRF_AASEN'
+c CALL CHETRF_AASEN( UPLO, N, AFAC, LDA, IWORK,
+c $ WORK, LWORK, INFO )
+*
+* Compute inv(A) and take its norm.
+*
+c CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
+c LWORK = (N+NB+1)*(NB+3)
+c SRNAMT = 'CHETRI2'
+c CALL CHETRI2( UPLO, N, AINV, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+c AINVNM = CLANHE( '1', UPLO, N, AINV, LDA, RWORK )
+*
+* Compute the 1-norm condition number of A.
+*
+c IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
+c RCONDC = ONE
+c ELSE
+c RCONDC = ( ONE / ANORM ) / AINVNM
+c END IF
+ END IF
+*
+* Form an exact solution and set the right hand side.
+*
+ SRNAMT = 'CLARHS'
+ CALL CLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
+ $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
+ $ INFO )
+ XTYPE = 'C'
+*
+* --- Test CHESV_AASEN ---
+*
+ IF( IFACT.EQ.2 ) THEN
+ CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+ CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+* Factor the matrix and solve the system using CHESV_AASEN.
+*
+ SRNAMT = 'CHESV_AASEN '
+ CALL CHESV_AASEN( UPLO, N, NRHS, AFAC, LDA, IWORK,
+ $ X, LDA, WORK, LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from CHESV_AASEN .
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'CHESV_AASEN', INFO, K,
+ $ UPLO, N, N, -1, -1, NRHS,
+ $ IMAT, NFAIL, NERRS, NOUT )
+ GO TO 120
+ ELSE IF( INFO.NE.0 ) THEN
+ GO TO 120
+ END IF
+*
+* Reconstruct matrix from factors and compute
+* residual.
+*
+ CALL CHET01_AASEN( UPLO, N, A, LDA, AFAC, LDA,
+ $ IWORK, AINV, LDA, RWORK,
+ $ RESULT( 1 ) )
+*
+* Compute residual of the computed solution.
+*
+ CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+ CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+* Check solution from generated exact solution.
+*
+ CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
+ $ RESULT( 3 ) )
+ NT = 3
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALADHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )'CHESV_AASEN ',
+ $ UPLO, N, IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+ 120 CONTINUE
+ END IF
+*
+ 150 CONTINUE
+*
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
+ $ ', test ', I2, ', ratio =', G12.5 )
+ RETURN
+*
+* End of CDRVHE_AASEN
+*
+ END
$ CHESV, CHESV_ROOK, CHESVX, CHKXER, CHPSV,
$ CHPSVX, CPBSV, CPBSVX, CPOSV, CPOSVX, CPPSV,
$ CPPSVX, CPTSV, CPTSVX, CSPSV, CSPSVX, CSYSV,
- $ CSYSV_ROOK, CSYSVX
+ $ CSYSV_AASEN, CSYSV_ROOK, CSYSVX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
$ RCOND, R1, R2, W, 3, RW, INFO )
CALL CHKXER( 'CHESVX', INFOT, NOUT, LERR, OK )
*
+ ELSE IF( LSAMEN( 2, C2, 'HA' ) ) THEN
+*
+* CHESV_AASEN
+*
+ SRNAMT = 'CHESV_AASEN'
+ INFOT = 1
+ CALL CHESV_AASEN( '/', 0, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'CHESV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHESV_AASEN( 'U', -1, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'CHESV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHESV_AASEN( 'U', 0, -1, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'CHESV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CHESV_AASEN( 'U', 2, 0, A, 2, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'CHESV_AASEN', INFOT, NOUT, LERR, OK )
+*
+
ELSE IF( LSAMEN( 2, C2, 'HR' ) ) THEN
*
* CHESV_ROOK
--- /dev/null
+*> \brief \b CHET01_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CHET01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV,
+* C, LDC, RWORK, RESID )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER LDA, LDAFAC, LDC, N
+* COMPLEX RESID
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+* $ RWORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CHET01_AASEN reconstructs a hermitian 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
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> hermitian matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows and columns of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is COMPLEX array, dimension (LDA,N)
+*> The original hermitian matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N)
+*> \endverbatim
+*>
+*> \param[in] AFAC
+*> \verbatim
+*> AFAC is COMPLEX array, dimension (LDAFAC,N)
+*> The factored form of the matrix A. AFAC contains the block
+*> diagonal matrix D and the multipliers used to obtain the
+*> factor L or U from the block L*D*L' or U*D*U' factorization
+*> as computed by CHETRF.
+*> \endverbatim
+*>
+*> \param[in] LDAFAC
+*> \verbatim
+*> LDAFAC is INTEGER
+*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> The pivot indices from CHETRF.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is COMPLEX array, dimension (LDC,N)
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the array C. LDC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is COMPLEX array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] RESID
+*> \verbatim
+*> RESID is COMPLEX
+*> 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:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup complex_lin
+*
+* =====================================================================
+ SUBROUTINE CHET01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
+ $ LDC, RWORK, RESID )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER LDA, LDAFAC, LDC, N
+ REAL RESID
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+ $ RWORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ COMPLEX CZERO, CONE
+ PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
+ $ CONE = ( 1.0E+0, 0.0E+0 ) )
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ REAL ANORM, EPS
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ REAL SLAMCH, CLANHE
+ EXTERNAL LSAME, SLAMCH, CLANHE
+* ..
+* .. External Subroutines ..
+ EXTERNAL CLASET, CLAVHE
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE
+* ..
+* .. Executable Statements ..
+*
+* Quick exit if N = 0.
+*
+ IF( N.LE.0 ) THEN
+ RESID = ZERO
+ RETURN
+ END IF
+*
+* Determine EPS and the norm of A.
+*
+ EPS = SLAMCH( 'Epsilon' )
+ ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
+*
+* Initialize C to the tridiagonal matrix T.
+*
+ CALL CLASET( 'Full', N, N, CZERO, CZERO, C, LDC )
+ CALL CLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
+ IF( N.GT.1 ) THEN
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL CLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL CLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ CALL CLACGV( N-1, C( 2, 1 ), LDC+1 )
+ ELSE
+ CALL CLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL CLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ CALL CLACGV( N-1, C( 1, 2 ), LDC+1 )
+ ENDIF
+ ENDIF
+*
+* Call CTRMM to form the product U' * D (or L * D ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL CTRMM( 'Left', UPLO, 'Conjugate transpose', 'Unit', N-1,
+ $ N, CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
+ ELSE
+ CALL CTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
+ $ CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
+ END IF
+*
+* Call CTRMM again to multiply by U (or L ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL CTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
+ $ CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
+ ELSE
+ CALL CTRMM( 'Right', UPLO, 'Conjugate transpose', 'Unit', N,
+ $ N-1, CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
+ END IF
+*
+* Apply hermitian pivots
+*
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL CSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
+ END DO
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL CSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
+ END DO
+*
+*
+* Compute the difference C - A .
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ DO J = 1, N
+ DO I = 1, J
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ ELSE
+ DO J = 1, N
+ DO I = J, N
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ END IF
+*
+* Compute norm( C - A ) / ( N * norm(A) * EPS )
+*
+ RESID = CLANHE( '1', UPLO, N, C, LDC, RWORK )
+*
+ IF( ANORM.LE.ZERO ) THEN
+ IF( RESID.NE.ZERO )
+ $ RESID = ONE / EPS
+ ELSE
+ RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
+ END IF
+*
+ RETURN
+*
+* End of CHET01_AASEN
+*
+ END
*> DPP 9 List types on next line if 0 < NTYPES < 9
*> DPB 8 List types on next line if 0 < NTYPES < 8
*> DPT 12 List types on next line if 0 < NTYPES < 12
+*> DSA 10 List types on next line if 0 < NTYPES < 10
*> DSY 10 List types on next line if 0 < NTYPES < 10
*> DSR 10 List types on next line if 0 < NTYPES < 10
*> DSP 10 List types on next line if 0 < NTYPES < 10
WRITE( NOUT, FMT = 9988 )PATH
END IF
*
+ ELSE IF( LSAMEN( 2, C2, 'SA' ) ) THEN
+*
+* SY: symmetric indefinite matrices,
+* with partial (Aasen's) pivoting algorithm
+*
+ NTYPES = 10
+ CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
+*
+ IF( TSTCHK ) THEN
+ CALL DCHKSY_AASEN( DOTYPE, NN, NVAL, NNB2, NBVAL2, NNS,
+ $ NSVAL, THRESH, TSTERR, LDA,
+ $ A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9989 )PATH
+ END IF
+*
+ IF( TSTDRV ) THEN
+ CALL DDRVSY_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ LDA, A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9988 )PATH
+ END IF
+*
+*
ELSE IF( LSAMEN( 2, C2, 'SP' ) ) THEN
*
* SP: symmetric indefinite packed matrices,
--- /dev/null
+*> \brief \b DCHKSY_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DCHKSY_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
+* XACT, WORK, RWORK, IWORK, NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NMAX, NN, NNB, NNS, NOUT
+* DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+* DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DCHKSY_AASEN tests DSYTRF_AASEN, -TRS_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NNB
+*> \verbatim
+*> NNB is INTEGER
+*> The number of values of NB contained in the vector NBVAL.
+*> \endverbatim
+*>
+*> \param[in] NBVAL
+*> \verbatim
+*> NBVAL is INTEGER array, dimension (NBVAL)
+*> The values of the blocksize NB.
+*> \endverbatim
+*>
+*> \param[in] NNS
+*> \verbatim
+*> NNS is INTEGER
+*> The number of values of NRHS contained in the vector NSVAL.
+*> \endverbatim
+*>
+*> \param[in] NSVAL
+*> \verbatim
+*> NSVAL is INTEGER array, dimension (NNS)
+*> The values of the number of right hand sides NRHS.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is DOUBLE PRECISION
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
+*> where NSMAX is the largest entry in NSVAL.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (2*NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup double_lin
+*
+* =====================================================================
+ SUBROUTINE DCHKSY_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+ $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
+ $ X, XACT, WORK, RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NN, NNB, NNS, NMAX, NOUT
+ DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+ DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+ INTEGER NTYPES
+ PARAMETER ( NTYPES = 10 )
+ INTEGER NTESTS
+ PARAMETER ( NTESTS = 9 )
+* ..
+* .. Local Scalars ..
+ LOGICAL TRFCON, ZEROT
+ CHARACTER DIST, TYPE, UPLO, XTYPE
+ CHARACTER*3 PATH, MATPATH
+ INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
+ $ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
+ $ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
+ DOUBLE PRECISION ANORM, CNDNUM, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ DOUBLE PRECISION RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ DOUBLE PRECISION DGET06, DLANSY
+ EXTERNAL DGET06, DLANSY
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALAERH, ALAHD, ALASUM, DERRSY, DGET04, DLACPY,
+ $ DLARHS, DLATB4, DLATMS, DPOT02, DPOT03, DPOT05,
+ $ DSYCON, DSYRFS, DSYT01, DSYTRF_AASEN,
+ $ DSYTRI2, DSYTRS_AASEN, XLAENV
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Double precision'
+ PATH( 2: 3 ) = 'SA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Double precision'
+ MATPATH( 2: 3 ) = 'SY'
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL DERRSY( PATH, NOUT )
+ INFOT = 0
+*
+* Set the minimum block size for which the block routine should
+* be used, which will be later returned by ILAENV
+*
+ CALL XLAENV( 2, 2 )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ IF( N .GT. NMAX ) THEN
+ NFAIL = NFAIL + 1
+ WRITE(NOUT, 9995) 'M ', N, NMAX
+ GO TO 180
+ END IF
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ IZERO = 0
+*
+* Do for each value of matrix type IMAT
+*
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Begin generate the test matrix A.
+*
+*
+* Set up parameters with DLATB4 for the matrix generator
+* based on the type of matrix to be generated.
+*
+ CALL DLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU,
+ $ ANORM, MODE, CNDNUM, DIST )
+*
+* Generate a matrix with DLATMS.
+*
+ SRNAMT = 'DLATMS'
+ CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from DLATMS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+*
+* Skip all tests for this generated matrix
+*
+ GO TO 160
+ END IF
+*
+* For matrix types 3-6, zero one or more rows and
+* columns of the matrix to test that INFO is returned
+* correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = ZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = ZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = ZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = ZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+* End generate the test matrix A.
+*
+* Do for each value of NB in NBVAL
+*
+ DO 150 INB = 1, NNB
+*
+* Set the optimal blocksize, which will be later
+* returned by ILAENV.
+*
+ NB = NBVAL( INB )
+ CALL XLAENV( 1, NB )
+*
+* Copy the test matrix A into matrix AFAC which
+* will be factorized in place. This is needed to
+* preserve the test matrix A for subsequent tests.
+*
+ CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+*
+* Compute the L*D*L**T or U*D*U**T factorization of the
+* matrix. IWORK stores details of the interchanges and
+* the block structure of D. AINV is a work array for
+* block factorization, LWORK is the length of AINV.
+*
+ SRNAMT = 'DSYTRF_AASEN'
+ LWORK = N*NB + N
+ CALL DSYTRF_AASEN( UPLO, N, AFAC, LDA, IWORK, AINV,
+ $ LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from DSYTRF and handle error.
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'DSYTRF_AASEN', INFO, K, UPLO,
+ $ N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
+ $ NOUT )
+ END IF
+*
+* Set the condition estimate flag if the INFO is not 0.
+*
+ IF( INFO.NE.0 ) THEN
+ TRFCON = .TRUE.
+ ELSE
+ TRFCON = .FALSE.
+ END IF
+*
+*+ TEST 1
+* Reconstruct matrix from factors and compute residual.
+*
+ CALL DSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDA, IWORK,
+ $ AINV, LDA, RWORK, RESULT( 1 ) )
+ NT = 1
+*
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
+ $ RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+*
+* Do only the condition estimate if INFO is not 0.
+*
+ IF( TRFCON ) THEN
+ RCONDC = ZERO
+ GO TO 140
+ END IF
+*
+* Do for each value of NRHS in NSVAL.
+*
+ DO 130 IRHS = 1, NNS
+ NRHS = NSVAL( IRHS )
+*
+*+ TEST 3 ( Using TRS)
+* Solve and compute residual for A * X = B.
+*
+* Choose a set of NRHS random solution vectors
+* stored in XACT and set up the right hand side B
+*
+ SRNAMT = 'DLARHS'
+ CALL DLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
+ $ KL, KU, NRHS, A, LDA, XACT, LDA,
+ $ B, LDA, ISEED, INFO )
+ CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+ SRNAMT = 'DSYTRS_AASEN'
+ LWORK = 3*N-2
+ CALL DSYTRS_AASEN( UPLO, N, NRHS, AFAC, LDA,
+ $ IWORK, X, LDA, WORK, LWORK,
+ $ INFO )
+*
+* Check error code from DSYTRS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'DSYTRS_AASEN', INFO, 0,
+ $ UPLO, N, N, -1, -1, NRHS, IMAT,
+ $ NFAIL, NERRS, NOUT )
+ END IF
+*
+ CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+*
+* Compute the residual for the solution
+*
+ CALL DPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 120 K = 2, 2
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
+ $ IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 120 CONTINUE
+ NRUN = NRUN + 1
+*
+* End do for each value of NRHS in NSVAL.
+*
+ 130 CONTINUE
+ 140 CONTINUE
+ 150 CONTINUE
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
+ $ I2, ', test ', I2, ', ratio =', G12.5 )
+ 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
+ $ I2, ', test(', I2, ') =', G12.5 )
+ 9995 FORMAT( ' Invalid input value: ', A4, '=', I6, '; must be <=',
+ $ I6 )
+ RETURN
+*
+* End of DCHKSY_AASEN
+*
+ END
--- /dev/null
+*> \brief \b DDRVSY_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DDRVSY_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
+* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
+* NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NMAX, NN, NOUT, NRHS
+* DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NVAL( * )
+* DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DDRVSY_AASEN tests the driver routine DSYSV_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand side vectors to be generated for
+*> each linear system.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is DOUBLE PRECISION
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (2*NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup double_lin
+*
+* =====================================================================
+ SUBROUTINE DDRVSY_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
+ $ RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NMAX, NN, NOUT, NRHS
+ DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NVAL( * )
+ DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE, ZERO
+ PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+ INTEGER NTYPES, NTESTS
+ PARAMETER ( NTYPES = 10, NTESTS = 3 )
+ INTEGER NFACT
+ PARAMETER ( NFACT = 2 )
+* ..
+* .. Local Scalars ..
+ LOGICAL ZEROT
+ CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
+ CHARACTER*3 MATPATH, PATH
+ INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
+ $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
+ $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
+ DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCOND, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER FACTS( NFACT ), UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ DOUBLE PRECISION RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ DOUBLE PRECISION DGET06, DLANSY
+ EXTERNAL DGET06, DLANSY
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALADHD, ALAERH, ALASVM, DERRVX, DGET04, DLACPY,
+ $ DLARHS, DLASET, DLATB4, DLATMS, DPOT02, DPOT05,
+ $ DSYSV_AASEN, DSYT01_AASEN, DSYTRF_AASEN, XLAENV
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Double precision'
+ PATH( 2: 3 ) = 'SA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Double precision'
+ MATPATH( 2: 3 ) = 'SY'
+*
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+ LWORK = MAX( 2*NMAX, NMAX*NRHS )
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL DERRVX( PATH, NOUT )
+ INFOT = 0
+*
+* Set the block size and minimum block size for testing.
+*
+ NB = 1
+ NBMIN = 2
+ CALL XLAENV( 1, NB )
+ CALL XLAENV( 2, NBMIN )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Set up parameters with DLATB4 and generate a test matrix
+* with DLATMS.
+*
+ CALL DLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
+ $ MODE, CNDNUM, DIST )
+*
+ SRNAMT = 'DLATMS'
+ CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from DLATMS.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+ GO TO 160
+ END IF
+*
+* For types 3-6, zero one or more rows and columns of the
+* matrix to test that INFO is returned correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = ZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = ZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IOFF = 0
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = ZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = ZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+ DO 150 IFACT = 1, NFACT
+*
+* Do first for FACT = 'F', then for other values.
+*
+ FACT = FACTS( IFACT )
+*
+* Compute the condition number for comparison with
+* the value returned by DSYSVX.
+*
+ IF( ZEROT ) THEN
+ IF( IFACT.EQ.1 )
+ $ GO TO 150
+ RCONDC = ZERO
+*
+ ELSE IF( IFACT.EQ.1 ) THEN
+*
+* Compute the 1-norm of A.
+*
+ ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
+*
+* Factor the matrix A.
+*
+c CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+c CALL DSYTRF( UPLO, N, AFAC, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+*
+* Compute inv(A) and take its norm.
+*
+c CALL DLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
+c LWORK = (N+NB+1)*(NB+3)
+c SRNAMT = 'DSYTRI2'
+c CALL DSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+c AINVNM = DLANSY( '1', UPLO, N, AINV, LDA, RWORK )
+*
+* Compute the 1-norm condition number of A.
+*
+c IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
+c RCONDC = ONE
+c ELSE
+c RCONDC = ( ONE / ANORM ) / AINVNM
+c END IF
+ END IF
+*
+* Form an exact solution and set the right hand side.
+*
+ SRNAMT = 'DLARHS'
+ CALL DLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
+ $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
+ $ INFO )
+ XTYPE = 'C'
+*
+* --- Test DSYSV_AASEN ---
+*
+ IF( IFACT.EQ.2 ) THEN
+ CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+ CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+* Factor the matrix and solve the system using DSYSV_AASEN.
+*
+ SRNAMT = 'DSYSV_AASEN'
+ CALL DSYSV_AASEN( UPLO, N, NRHS, AFAC, LDA, IWORK,
+ $ X, LDA, WORK, LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from DSYSV_AASEN .
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'DSYSV_AASEN ', INFO, K,
+ $ UPLO, N, N, -1, -1, NRHS,
+ $ IMAT, NFAIL, NERRS, NOUT )
+ GO TO 120
+ ELSE IF( INFO.NE.0 ) THEN
+ GO TO 120
+ END IF
+*
+* Reconstruct matrix from factors and compute
+* residual.
+*
+ CALL DSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDA,
+ $ IWORK, AINV, LDA, RWORK,
+ $ RESULT( 1 ) )
+*
+* Compute residual of the computed solution.
+*
+ CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+ CALL DPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+* Check solution from generated exact solution.
+*
+ CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
+ $ RESULT( 3 ) )
+ NT = 3
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALADHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )'DSYSV_AASEN ',
+ $ UPLO, N, IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+ 120 CONTINUE
+ END IF
+*
+ 150 CONTINUE
+*
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
+ $ ', test ', I2, ', ratio =', G12.5 )
+ RETURN
+*
+* End of DDRVSY_AASEN
+*
+ END
EXTERNAL CHKXER, DGBSV, DGBSVX, DGESV, DGESVX, DGTSV,
$ DGTSVX, DPBSV, DPBSVX, DPOSV, DPOSVX, DPPSV,
$ DPPSVX, DPTSV, DPTSVX, DSPSV, DSPSVX, DSYSV,
- $ DSYSV_ROOK, DSYSVX
+ $ DSYSV_AASEN, DSYSV_ROOK, DSYSVX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
$ RCOND, R1, R2, W, 3, IW, INFO )
CALL CHKXER( 'DSYSVX', INFOT, NOUT, LERR, OK )
*
+ ELSE IF( LSAMEN( 2, C2, 'SA' ) ) THEN
+*
+* DSYSV_AASEN
+*
+ SRNAMT = 'DSYSV_AASEN'
+ INFOT = 1
+ CALL DSYSV_AASEN( '/', 0, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'DSYSV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYSV_AASEN( 'U', -1, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'DSYSV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYSV_AASEN( 'U', 0, -1, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'DSYSV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DSYSV_AASEN( 'U', 2, 0, A, 2, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'DSYSV_AASEN', INFOT, NOUT, LERR, OK )
+*
+
ELSE IF( LSAMEN( 2, C2, 'SR' ) ) THEN
*
* DSYSV_ROOK
--- /dev/null
+*> \brief \b DSYT01
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
+* RWORK, RESID )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER LDA, LDAFAC, LDC, N
+* DOUBLE PRECISION RESID
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+* $ RWORK( * )
+* ..
+*
+*
+*> \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
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> symmetric matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows and columns of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> The original symmetric matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N)
+*> \endverbatim
+*>
+*> \param[in] AFAC
+*> \verbatim
+*> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
+*> The factored form of the matrix A. AFAC contains the block
+*> diagonal matrix D and the multipliers used to obtain the
+*> factor L or U from the block L*D*L' or U*D*U' factorization
+*> as computed by DSYTRF.
+*> \endverbatim
+*>
+*> \param[in] LDAFAC
+*> \verbatim
+*> LDAFAC is INTEGER
+*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> The pivot indices from DSYTRF.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is DOUBLE PRECISION array, dimension (LDC,N)
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the array C. LDC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] RESID
+*> \verbatim
+*> RESID is DOUBLE PRECISION
+*> 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:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+* @precisions fortran d -> s
+*
+*> \ingroup double_lin
+*
+* =====================================================================
+ SUBROUTINE DSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
+ $ LDC, RWORK, RESID )
+*
+* -- LAPACK test routine (version 3.5.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER LDA, LDAFAC, LDC, N
+ DOUBLE PRECISION RESID
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+ $ RWORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ DOUBLE PRECISION ANORM, EPS
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ DOUBLE PRECISION DLAMCH, DLANSY
+ EXTERNAL LSAME, DLAMCH, DLANSY
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLASET, DLAVSY
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE
+* ..
+* .. Executable Statements ..
+*
+* Quick exit if N = 0.
+*
+ IF( N.LE.0 ) THEN
+ RESID = ZERO
+ RETURN
+ END IF
+*
+* Determine EPS and the norm of A.
+*
+ EPS = DLAMCH( 'Epsilon' )
+ ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
+*
+* Initialize C to the tridiagonal matrix T.
+*
+ CALL DLASET( 'Full', N, N, ZERO, ZERO, C, LDC )
+ CALL DLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
+ IF( N.GT.1 ) THEN
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL DLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL DLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ ELSE
+ CALL DLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL DLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ ENDIF
+ ENDIF
+*
+* Call DTRMM to form the product U' * D (or L * D ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL DTRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N,
+ $ ONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
+ ELSE
+ CALL DTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
+ $ ONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
+ END IF
+*
+* Call DTRMM again to multiply by U (or L ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL DTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
+ $ ONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
+ ELSE
+ CALL DTRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1,
+ $ ONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
+ END IF
+*
+* Apply symmetric pivots
+*
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL DSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
+ END DO
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL DSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
+ END DO
+*
+*
+* Compute the difference C - A .
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ DO J = 1, N
+ DO I = 1, J
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ ELSE
+ DO J = 1, N
+ DO I = J, N
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ END IF
+*
+* Compute norm( C - A ) / ( N * norm(A) * EPS )
+*
+ RESID = DLANSY( '1', UPLO, N, C, LDC, RWORK )
+*
+ IF( ANORM.LE.ZERO ) THEN
+ IF( RESID.NE.ZERO )
+ $ RESID = ONE / EPS
+ ELSE
+ RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
+ END IF
+*
+ RETURN
+*
+* End of DSYT01
+*
+ END
WRITE( NOUT, FMT = 9988 )PATH
END IF
*
+ ELSE IF( LSAMEN( 2, C2, 'SA' ) ) THEN
+*
+* SY: symmetric indefinite matrices,
+* with partial (Aasen's) pivoting algorithm
+*
+ NTYPES = 10
+ CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
+*
+ IF( TSTCHK ) THEN
+ CALL SCHKSY_AASEN( DOTYPE, NN, NVAL, NNB2, NBVAL2, NNS,
+ $ NSVAL, THRESH, TSTERR, LDA,
+ $ A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9989 )PATH
+ END IF
+*
+ IF( TSTDRV ) THEN
+ CALL SDRVSY_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ LDA, A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9988 )PATH
+ END IF
+*
ELSE IF( LSAMEN( 2, C2, 'SP' ) ) THEN
*
* SP: symmetric indefinite packed matrices,
--- /dev/null
+*> \brief \b SCHKSY_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SCHKSY_AAEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
+* XACT, WORK, RWORK, IWORK, NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NMAX, NN, NNB, NNS, NOUT
+* REAL THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+* REAL A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SCHKSY_AASEN tests SSYTRF_AASEN, -TRS_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NNB
+*> \verbatim
+*> NNB is INTEGER
+*> The number of values of NB contained in the vector NBVAL.
+*> \endverbatim
+*>
+*> \param[in] NBVAL
+*> \verbatim
+*> NBVAL is INTEGER array, dimension (NBVAL)
+*> The values of the blocksize NB.
+*> \endverbatim
+*>
+*> \param[in] NNS
+*> \verbatim
+*> NNS is INTEGER
+*> The number of values of NRHS contained in the vector NSVAL.
+*> \endverbatim
+*>
+*> \param[in] NSVAL
+*> \verbatim
+*> NSVAL is INTEGER array, dimension (NNS)
+*> The values of the number of right hand sides NRHS.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is REAL
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is REAL array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is REAL array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is REAL array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is REAL array, dimension (NMAX*NSMAX)
+*> where NSMAX is the largest entry in NSVAL.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is REAL array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is REAL array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (NMAX*max(3,NSMAX))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is REAL array, dimension (max(NMAX,2*NSMAX))
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (2*NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup real_lin
+*
+* =====================================================================
+ SUBROUTINE SCHKSY_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+ $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
+ $ X, XACT, WORK, RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NN, NNB, NNS, NMAX, NOUT
+ REAL THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+ REAL A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ZERO
+ PARAMETER ( ZERO = 0.0E+0 )
+ INTEGER NTYPES
+ PARAMETER ( NTYPES = 10 )
+ INTEGER NTESTS
+ PARAMETER ( NTESTS = 9 )
+* ..
+* .. Local Scalars ..
+ LOGICAL TRFCON, ZEROT
+ CHARACTER DIST, TYPE, UPLO, XTYPE
+ CHARACTER*3 PATH, MATPATH
+ INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
+ $ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
+ $ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
+ REAL ANORM, CNDNUM, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ REAL RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ REAL DGET06, SLANSY
+ EXTERNAL DGET06, SLANSY
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALAERH, ALAHD, ALASUM, SERRSY, SGET04, SLACPY,
+ $ SLARHS, SLATB4, SLATMS, SPOT02, DPOT03, DPOT05,
+ $ DSYCON, SSYRFS, SSYT01_AASEN, SSYTRF_AASEN,
+ $ DSYTRI2, SSYTRS_AASEN, XLAENV
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Single precision'
+ PATH( 2: 3 ) = 'SA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Single precision'
+ MATPATH( 2: 3 ) = 'SY'
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL SERRSY( PATH, NOUT )
+ INFOT = 0
+*
+* Set the minimum block size for which the block routine should
+* be used, which will be later returned by ILAENV
+*
+ CALL XLAENV( 2, 2 )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ IF( N .GT. NMAX ) THEN
+ NFAIL = NFAIL + 1
+ WRITE(NOUT, 9995) 'M ', N, NMAX
+ GO TO 180
+ END IF
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ IZERO = 0
+*
+* Do for each value of matrix type IMAT
+*
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Begin generate the test matrix A.
+*
+*
+* Set up parameters with SLATB4 for the matrix generator
+* based on the type of matrix to be generated.
+*
+ CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU,
+ $ ANORM, MODE, CNDNUM, DIST )
+*
+* Generate a matrix with SLATMS.
+*
+ SRNAMT = 'SLATMS'
+ CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from SLATMS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+*
+* Skip all tests for this generated matrix
+*
+ GO TO 160
+ END IF
+*
+* For matrix types 3-6, zero one or more rows and
+* columns of the matrix to test that INFO is returned
+* correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = ZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = ZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = ZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = ZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+* End generate the test matrix A.
+*
+* Do for each value of NB in NBVAL
+*
+ DO 150 INB = 1, NNB
+*
+* Set the optimal blocksize, which will be later
+* returned by ILAENV.
+*
+ NB = NBVAL( INB )
+ CALL XLAENV( 1, NB )
+*
+* Copy the test matrix A into matrix AFAC which
+* will be factorized in place. This is needed to
+* preserve the test matrix A for subsequent tests.
+*
+ CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+*
+* Compute the L*D*L**T or U*D*U**T factorization of the
+* matrix. IWORK stores details of the interchanges and
+* the block structure of D. AINV is a work array for
+* block factorization, LWORK is the length of AINV.
+*
+ SRNAMT = 'SSYTRF_AASEN'
+ LWORK = N*NB + N
+ CALL SSYTRF_AASEN( UPLO, N, AFAC, LDA, IWORK, AINV,
+ $ LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from SSYTRF and handle error.
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'SSYTRF_AASEN', INFO, K, UPLO,
+ $ N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
+ $ NOUT )
+ END IF
+*
+* Set the condition estimate flag if the INFO is not 0.
+*
+ IF( INFO.NE.0 ) THEN
+ TRFCON = .TRUE.
+ ELSE
+ TRFCON = .FALSE.
+ END IF
+*
+*+ TEST 1
+* Reconstruct matrix from factors and compute residual.
+*
+ CALL SSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDA, IWORK,
+ $ AINV, LDA, RWORK, RESULT( 1 ) )
+ NT = 1
+*
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
+ $ RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+*
+* Do only the condition estimate if INFO is not 0.
+*
+ IF( TRFCON ) THEN
+ RCONDC = ZERO
+ GO TO 140
+ END IF
+*
+* Do for each value of NRHS in NSVAL.
+*
+ DO 130 IRHS = 1, NNS
+ NRHS = NSVAL( IRHS )
+*
+*+ TEST 3 ( Using TRS)
+* Solve and compute residual for A * X = B.
+*
+* Choose a set of NRHS random solution vectors
+* stored in XACT and set up the right hand side B
+*
+ SRNAMT = 'SLARHS'
+ CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
+ $ KL, KU, NRHS, A, LDA, XACT, LDA,
+ $ B, LDA, ISEED, INFO )
+ CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+ SRNAMT = 'SSYTRS_AASEN'
+ LWORK = 3*N-2
+ CALL SSYTRS_AASEN( UPLO, N, NRHS, AFAC, LDA,
+ $ IWORK, X, LDA, WORK, LWORK,
+ $ INFO )
+*
+* Check error code from SSYTRS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'SSYTRS_AASEN', INFO, 0,
+ $ UPLO, N, N, -1, -1, NRHS, IMAT,
+ $ NFAIL, NERRS, NOUT )
+ END IF
+*
+ CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+*
+* Compute the residual for the solution
+*
+ CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 120 K = 2, 2
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
+ $ IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 120 CONTINUE
+ NRUN = NRUN + 1
+*
+* End do for each value of NRHS in NSVAL.
+*
+ 130 CONTINUE
+ 140 CONTINUE
+ 150 CONTINUE
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
+ $ I2, ', test ', I2, ', ratio =', G12.5 )
+ 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
+ $ I2, ', test(', I2, ') =', G12.5 )
+ 9995 FORMAT( ' Invalid input value: ', A4, '=', I6, '; must be <=',
+ $ I6 )
+ RETURN
+*
+* End of SCHKSY_AASEN
+*
+ END
--- /dev/null
+*> \brief \b SDRVSY_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SDRVSY_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
+* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
+* NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NMAX, NN, NOUT, NRHS
+* REAL THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NVAL( * )
+* REAL A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SDRVSY_AASEN tests the driver routine SSYSV_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand side vectors to be generated for
+*> each linear system.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is REAL
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is REAL array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is REAL array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is REAL array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is REAL array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is REAL array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is REAL array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (NMAX*max(2,NRHS))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is REAL array, dimension (NMAX+2*NRHS)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (2*NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup real_lin
+*
+* =====================================================================
+ SUBROUTINE SDRVSY_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
+ $ RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NMAX, NN, NOUT, NRHS
+ REAL THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NVAL( * )
+ REAL A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ RWORK( * ), WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+ INTEGER NTYPES, NTESTS
+ PARAMETER ( NTYPES = 10, NTESTS = 3 )
+ INTEGER NFACT
+ PARAMETER ( NFACT = 2 )
+* ..
+* .. Local Scalars ..
+ LOGICAL ZEROT
+ CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
+ CHARACTER*3 MATPATH, PATH
+ INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
+ $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
+ $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
+ REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER FACTS( NFACT ), UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ REAL RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ REAL DGET06, SLANSY
+ EXTERNAL DGET06, SLANSY
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY,
+ $ SLARHS, SLASET, SLATB4, SLATMS, SPOT02, DPOT05,
+ $ SSYSV_AASEN, SSYT01_AASEN, SSYTRF_AASEN, XLAENV
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Single precision'
+ PATH( 2: 3 ) = 'SA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Single precision'
+ MATPATH( 2: 3 ) = 'SY'
+*
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+ LWORK = MAX( 2*NMAX, NMAX*NRHS )
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL SERRVX( PATH, NOUT )
+ INFOT = 0
+*
+* Set the block size and minimum block size for testing.
+*
+ NB = 1
+ NBMIN = 2
+ CALL XLAENV( 1, NB )
+ CALL XLAENV( 2, NBMIN )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Set up parameters with SLATB4 and generate a test matrix
+* with SLATMS.
+*
+ CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
+ $ MODE, CNDNUM, DIST )
+*
+ SRNAMT = 'SLATMS'
+ CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from SLATMS.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+ GO TO 160
+ END IF
+*
+* For types 3-6, zero one or more rows and columns of the
+* matrix to test that INFO is returned correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = ZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = ZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IOFF = 0
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = ZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = ZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+ DO 150 IFACT = 1, NFACT
+*
+* Do first for FACT = 'F', then for other values.
+*
+ FACT = FACTS( IFACT )
+*
+* Compute the condition number for comparison with
+* the value returned by SSYSVX.
+*
+ IF( ZEROT ) THEN
+ IF( IFACT.EQ.1 )
+ $ GO TO 150
+ RCONDC = ZERO
+*
+ ELSE IF( IFACT.EQ.1 ) THEN
+*
+* Compute the 1-norm of A.
+*
+ ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
+*
+* Factor the matrix A.
+*
+c CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+c CALL SSYTRF( UPLO, N, AFAC, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+*
+* Compute inv(A) and take its norm.
+*
+c CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
+c LWORK = (N+NB+1)*(NB+3)
+c SRNAMT = 'DSYTRI2'
+c CALL DSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+c AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, RWORK )
+*
+* Compute the 1-norm condition number of A.
+*
+c IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
+c RCONDC = ONE
+c ELSE
+c RCONDC = ( ONE / ANORM ) / AINVNM
+c END IF
+ END IF
+*
+* Form an exact solution and set the right hand side.
+*
+ SRNAMT = 'SLARHS'
+ CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
+ $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
+ $ INFO )
+ XTYPE = 'C'
+*
+* --- Test SSYSV_AASEN ---
+*
+ IF( IFACT.EQ.2 ) THEN
+ CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+ CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+* Factor the matrix and solve the system using SSYSV_AASEN.
+*
+ SRNAMT = 'SSYSV_AASEN'
+ CALL SSYSV_AASEN( UPLO, N, NRHS, AFAC, LDA, IWORK,
+ $ X, LDA, WORK, LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from SSYSV_AASEN .
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'SSYSV_AASEN ', INFO, K,
+ $ UPLO, N, N, -1, -1, NRHS,
+ $ IMAT, NFAIL, NERRS, NOUT )
+ GO TO 120
+ ELSE IF( INFO.NE.0 ) THEN
+ GO TO 120
+ END IF
+*
+* Reconstruct matrix from factors and compute
+* residual.
+*
+ CALL SSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDA,
+ $ IWORK, AINV, LDA, RWORK,
+ $ RESULT( 1 ) )
+*
+* Compute residual of the computed solution.
+*
+ CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+ CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+* Check solution from generated exact solution.
+*
+ CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
+ $ RESULT( 3 ) )
+ NT = 3
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALADHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )'SSYSV_AASEN ',
+ $ UPLO, N, IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+ 120 CONTINUE
+ END IF
+*
+ 150 CONTINUE
+*
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
+ $ ', test ', I2, ', ratio =', G12.5 )
+ RETURN
+*
+* End of SDRVSY_AASEN
+*
+ END
EXTERNAL CHKXER, SGBSV, SGBSVX, SGESV, SGESVX, SGTSV,
$ SGTSVX, SPBSV, SPBSVX, SPOSV, SPOSVX, SPPSV,
$ SPPSVX, SPTSV, SPTSVX, SSPSV, SSPSVX, SSYSV,
- $ SSYSV_ROOK, SSYSVX
+ $ SSYSV_AASEN, SSYSV_ROOK, SSYSVX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
$ RCOND, R1, R2, W, 3, IW, INFO )
CALL CHKXER( 'SSYSVX', INFOT, NOUT, LERR, OK )
*
+ ELSE IF( LSAMEN( 2, C2, 'SA' ) ) THEN
+*
+* SSYSV_AASEN
+*
+ SRNAMT = 'SSYSV_AASEN'
+ INFOT = 1
+ CALL SSYSV_AASEN( '/', 0, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'SSYSV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYSV_AASEN( 'U', -1, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'SSYSV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYSV_AASEN( 'U', 0, -1, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'SSYSV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SSYSV_AASEN( 'U', 2, 0, A, 2, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'SSYSV_AASEN', INFOT, NOUT, LERR, OK )
+*
ELSE IF( LSAMEN( 2, C2, 'SR' ) ) THEN
*
* SSYSV_ROOK
--- /dev/null
+*> \brief \b SSYT01_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV,
+* C, LDC, RWORK, RESID )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER LDA, LDAFAC, LDC, N
+* REAL RESID
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+* $ RWORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SSYT01_AASEN 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
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> symmetric matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows and columns of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> The original symmetric matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N)
+*> \endverbatim
+*>
+*> \param[in] AFAC
+*> \verbatim
+*> AFAC is REAL array, dimension (LDAFAC,N)
+*> The factored form of the matrix A. AFAC contains the block
+*> diagonal matrix D and the multipliers used to obtain the
+*> factor L or U from the block L*D*L' or U*D*U' factorization
+*> as computed by SSYTRF.
+*> \endverbatim
+*>
+*> \param[in] LDAFAC
+*> \verbatim
+*> LDAFAC is INTEGER
+*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> The pivot indices from SSYTRF.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is REAL array, dimension (LDC,N)
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the array C. LDC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is REAL array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] RESID
+*> \verbatim
+*> RESID is REAL
+*> 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:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup real_lin
+*
+* =====================================================================
+ SUBROUTINE SSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
+ $ LDC, RWORK, RESID )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER LDA, LDAFAC, LDC, N
+ REAL RESID
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+ $ RWORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ REAL ANORM, EPS
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ REAL SLAMCH, SLANSY
+ EXTERNAL LSAME, SLAMCH, SLANSY
+* ..
+* .. External Subroutines ..
+ EXTERNAL SLASET, SLAVSY
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE
+* ..
+* .. Executable Statements ..
+*
+* Quick exit if N = 0.
+*
+ IF( N.LE.0 ) THEN
+ RESID = ZERO
+ RETURN
+ END IF
+*
+* Determine EPS and the norm of A.
+*
+ EPS = SLAMCH( 'Epsilon' )
+ ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
+*
+* Initialize C to the tridiagonal matrix T.
+*
+ CALL SLASET( 'Full', N, N, ZERO, ZERO, C, LDC )
+ CALL SLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
+ IF( N.GT.1 ) THEN
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL SLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL SLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ ELSE
+ CALL SLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL SLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ ENDIF
+ ENDIF
+*
+* Call STRMM to form the product U' * D (or L * D ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL STRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N,
+ $ ONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
+ ELSE
+ CALL STRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
+ $ ONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
+ END IF
+*
+* Call STRMM again to multiply by U (or L ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL STRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
+ $ ONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
+ ELSE
+ CALL STRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1,
+ $ ONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
+ END IF
+*
+* Apply symmetric pivots
+*
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL SSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
+ END DO
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL SSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
+ END DO
+*
+*
+* Compute the difference C - A .
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ DO J = 1, N
+ DO I = 1, J
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ ELSE
+ DO J = 1, N
+ DO I = J, N
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ END IF
+*
+* Compute norm( C - A ) / ( N * norm(A) * EPS )
+*
+ RESID = SLANSY( '1', UPLO, N, C, LDC, RWORK )
+*
+ IF( ANORM.LE.ZERO ) THEN
+ IF( RESID.NE.ZERO )
+ $ RESID = ONE / EPS
+ ELSE
+ RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
+ END IF
+*
+ RETURN
+*
+* End of SSYT01_AASEN
+*
+ END
*> ZPB 8 List types on next line if 0 < NTYPES < 8
*> ZPT 12 List types on next line if 0 < NTYPES < 12
*> ZHE 10 List types on next line if 0 < NTYPES < 10
+*> ZHA 10 List types on next line if 0 < NTYPES < 10
*> ZHR 10 List types on next line if 0 < NTYPES < 10
*> ZHP 10 List types on next line if 0 < NTYPES < 10
*> ZSY 11 List types on next line if 0 < NTYPES < 11
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
-*> \date November 2015
+*> \date November 2016
*
*> \ingroup complex16_lin
*
* =====================================================================
PROGRAM ZCHKAA
*
-* -- LAPACK test routine (version 3.6.0) --
+* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2015
+* November 2016
*
* =====================================================================
*
WRITE( NOUT, FMT = 9988 )PATH
END IF
*
+ ELSE IF( LSAMEN( 2, C2, 'HA' ) ) THEN
+*
+* HA: Hermitian indefinite matrices,
+* with partial (Aasen's) pivoting algorithm
+*
+ NTYPES = 10
+ CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
+*
+ IF( TSTCHK ) THEN
+ CALL ZCHKHE_AASEN( DOTYPE, NN, NVAL, NNB2, NBVAL2, NNS,
+ $ NSVAL, THRESH, TSTERR, LDA,
+ $ A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9989 )PATH
+ END IF
+*
+ IF( TSTDRV ) THEN
+ CALL ZDRVHE_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ LDA, A( 1, 1 ), A( 1, 2 ), A( 1, 3 ),
+ $ B( 1, 1 ), B( 1, 2 ), B( 1, 3 ),
+ $ WORK, RWORK, IWORK, NOUT )
+ ELSE
+ WRITE( NOUT, FMT = 9988 )PATH
+ END IF
+*
ELSE IF( LSAMEN( 2, C2, 'HR' ) ) THEN
*
* HR: Hermitian indefinite matrices,
--- /dev/null
+*> \brief \b ZCHKHE_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZCHKHE_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
+* XACT, WORK, RWORK, IWORK, NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NN, NNB, NNS, NOUT
+* DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZCHKHE_AASEN tests ZHETRF_AASEN, -TRS_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NNB
+*> \verbatim
+*> NNB is INTEGER
+*> The number of values of NB contained in the vector NBVAL.
+*> \endverbatim
+*>
+*> \param[in] NBVAL
+*> \verbatim
+*> NBVAL is INTEGER array, dimension (NBVAL)
+*> The values of the blocksize NB.
+*> \endverbatim
+*>
+*> \param[in] NNS
+*> \verbatim
+*> NNS is INTEGER
+*> The number of values of NRHS contained in the vector NSVAL.
+*> \endverbatim
+*>
+*> \param[in] NSVAL
+*> \verbatim
+*> NSVAL is INTEGER array, dimension (NNS)
+*> The values of the number of right hand sides NRHS.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is DOUBLE PRECISION
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (NMAX*NSMAX)
+*> where NSMAX is the largest entry in NSVAL.
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup complex16_lin
+*
+* =====================================================================
+ SUBROUTINE ZCHKHE_AASEN( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
+ $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
+ $ X, XACT, WORK, RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+ IMPLICIT NONE
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NMAX, NN, NNB, NNS, NOUT
+ DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
+ DOUBLE PRECISION RWORK( * )
+ COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D+0 )
+ COMPLEX*16 CZERO
+ PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
+ INTEGER NTYPES
+ PARAMETER ( NTYPES = 10 )
+ INTEGER NTESTS
+ PARAMETER ( NTESTS = 9 )
+* ..
+* .. Local Scalars ..
+ LOGICAL TRFCON, ZEROT
+ CHARACTER DIST, TYPE, UPLO, XTYPE
+ CHARACTER*3 PATH, MATPATH
+ INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
+ $ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
+ $ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
+ DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ DOUBLE PRECISION RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ DOUBLE PRECISION DGET06, ZLANHE
+ EXTERNAL DGET06, ZLANHE
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, ZERRHE, ZGET04,
+ $ ZHECON, ZHERFS, ZHET01, ZHETRF_AASEN, ZHETRI2,
+ $ ZHETRS_AASEN, ZLACPY, ZLAIPD, ZLARHS, ZLATB4,
+ $ ZLATMS, ZPOT02, ZPOT03, ZPOT05
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Zomplex precision'
+ PATH( 2: 3 ) = 'HA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Zomplex precision'
+ MATPATH( 2: 3 ) = 'HE'
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL ZERRHE( PATH, NOUT )
+ INFOT = 0
+*
+* Set the minimum block size for which the block routine should
+* be used, which will be later returned by ILAENV
+*
+ CALL XLAENV( 2, 2 )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ IF( N .GT. NMAX ) THEN
+ NFAIL = NFAIL + 1
+ WRITE(NOUT, 9995) 'M ', N, NMAX
+ GO TO 180
+ END IF
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ IZERO = 0
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Set up parameters with ZLATB4 for the matrix generator
+* based on the type of matrix to be generated.
+*
+ CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU,
+ $ ANORM, MODE, CNDNUM, DIST )
+*
+* Generate a matrix with ZLATMS.
+*
+ SRNAMT = 'ZLATMS'
+ CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from ZLATMS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+*
+* Skip all tests for this generated matrix
+*
+ GO TO 160
+ END IF
+*
+* For types 3-6, zero one or more rows and columns of
+* the matrix to test that INFO is returned correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = CZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = CZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = CZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = CZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = CZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ IOFF = 0
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = CZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+* End generate test matrix A.
+*
+*
+* Set the imaginary part of the diagonals.
+*
+ CALL ZLAIPD( N, A, LDA+1, 0 )
+*
+* Do for each value of NB in NBVAL
+*
+ DO 150 INB = 1, NNB
+*
+* Set the optimal blocksize, which will be later
+* returned by ILAENV.
+*
+ NB = NBVAL( INB )
+ CALL XLAENV( 1, NB )
+*
+* Copy the test matrix A into matrix AFAC which
+* will be factorized in place. This is needed to
+* preserve the test matrix A for subsequent tests.
+*
+ CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+*
+* Compute the L*D*L**T or U*D*U**T factorization of the
+* matrix. IWORK stores details of the interchanges and
+* the block structure of D. AINV is a work array for
+* block factorization, LWORK is the length of AINV.
+*
+ LWORK = ( NB+1 )*LDA
+ SRNAMT = 'ZHETRF_AASEN'
+ CALL ZHETRF_AASEN( UPLO, N, AFAC, LDA, IWORK, AINV,
+ $ LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from ZHETRF and handle error.
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'ZHETRF_AASEN', INFO, K, UPLO,
+ $ N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
+ $ NOUT )
+ END IF
+*
+* Set the condition estimate flag if the INFO is not 0.
+*
+ IF( INFO.NE.0 ) THEN
+ TRFCON = .TRUE.
+ ELSE
+ TRFCON = .FALSE.
+ END IF
+*
+*+ TEST 1
+* Reconstruct matrix from factors and compute residual.
+*
+ CALL ZHET01_AASEN( UPLO, N, A, LDA, AFAC, LDA, IWORK,
+ $ AINV, LDA, RWORK, RESULT( 1 ) )
+ NT = 1
+*
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
+ $ RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+*
+* Do only the condition estimate if INFO is not 0.
+*
+ IF( TRFCON ) THEN
+ RCONDC = ZERO
+ GO TO 140
+ END IF
+*
+* Do for each value of NRHS in NSVAL.
+*
+ DO 130 IRHS = 1, NNS
+ NRHS = NSVAL( IRHS )
+*
+*+ TEST 3 (Using TRS)
+* Solve and compute residual for A * X = B.
+*
+* Choose a set of NRHS random solution vectors
+* stored in XACT and set up the right hand side B
+*
+ SRNAMT = 'ZLARHS'
+ CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
+ $ KL, KU, NRHS, A, LDA, XACT, LDA,
+ $ B, LDA, ISEED, INFO )
+ CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+ SRNAMT = 'ZHETRS_AASEN'
+ LWORK = 3*N-2
+ CALL ZHETRS_AASEN( UPLO, N, NRHS, AFAC, LDA, IWORK,
+ $ X, LDA, WORK, LWORK, INFO )
+*
+* Check error code from ZHETRS and handle error.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'ZHETRS', INFO, 0, UPLO, N,
+ $ N, -1, -1, NRHS, IMAT, NFAIL,
+ $ NERRS, NOUT )
+ END IF
+*
+ CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+*
+* Compute the residual for the solution
+*
+ CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 120 K = 2, 2
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALAHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
+ $ IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 120 CONTINUE
+ NRUN = NRUN + 1
+*
+* End do for each value of NRHS in NSVAL.
+*
+ 130 CONTINUE
+ 140 CONTINUE
+ 150 CONTINUE
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
+ $ I2, ', test ', I2, ', ratio =', G12.5 )
+ 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
+ $ I2, ', test(', I2, ') =', G12.5 )
+c 9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
+c $ ', test(', I2, ') =', G12.5 )
+ 9995 FORMAT( ' Invalid input value: ', A4, '=', I6, '; must be <=',
+ $ I6 )
+ RETURN
+*
+* End of ZCHKHE_AASEN
+*
+ END
--- /dev/null
+*> \brief \b ZDRVHE_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZDRVHE_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
+* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
+* NOUT )
+*
+* .. Scalar Arguments ..
+* LOGICAL TSTERR
+* INTEGER NMAX, NN, NOUT, NRHS
+* DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+* LOGICAL DOTYPE( * )
+* INTEGER IWORK( * ), NVAL( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
+* $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZDRVHE_AASEN tests the driver routine ZHESV_AASEN.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] DOTYPE
+*> \verbatim
+*> DOTYPE is LOGICAL array, dimension (NTYPES)
+*> The matrix types to be used for testing. Matrices of type j
+*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
+*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
+*> \endverbatim
+*>
+*> \param[in] NN
+*> \verbatim
+*> NN is INTEGER
+*> The number of values of N contained in the vector NVAL.
+*> \endverbatim
+*>
+*> \param[in] NVAL
+*> \verbatim
+*> NVAL is INTEGER array, dimension (NN)
+*> The values of the matrix dimension N.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*> NRHS is INTEGER
+*> The number of right hand side vectors to be generated for
+*> each linear system.
+*> \endverbatim
+*>
+*> \param[in] THRESH
+*> \verbatim
+*> THRESH is DOUBLE PRECISION
+*> The threshold value for the test ratios. A result is
+*> included in the output file if RESULT >= THRESH. To have
+*> every test ratio printed, use THRESH = 0.
+*> \endverbatim
+*>
+*> \param[in] TSTERR
+*> \verbatim
+*> TSTERR is LOGICAL
+*> Flag that indicates whether error exits are to be tested.
+*> \endverbatim
+*>
+*> \param[in] NMAX
+*> \verbatim
+*> NMAX is INTEGER
+*> The maximum value permitted for N, used in dimensioning the
+*> work arrays.
+*> \endverbatim
+*>
+*> \param[out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AFAC
+*> \verbatim
+*> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] AINV
+*> \verbatim
+*> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
+*> \endverbatim
+*>
+*> \param[out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is COMPLEX*16 array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] XACT
+*> \verbatim
+*> XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (NMAX)
+*> \endverbatim
+*>
+*> \param[in] NOUT
+*> \verbatim
+*> NOUT is INTEGER
+*> The unit number for output.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*> \ingroup complex16_lin
+*
+* =====================================================================
+ SUBROUTINE ZDRVHE_AASEN( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
+ $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
+ $ RWORK, IWORK, NOUT )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ LOGICAL TSTERR
+ INTEGER NMAX, NN, NOUT, NRHS
+ DOUBLE PRECISION THRESH
+* ..
+* .. Array Arguments ..
+ LOGICAL DOTYPE( * )
+ INTEGER IWORK( * ), NVAL( * )
+ DOUBLE PRECISION RWORK( * )
+ COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
+ $ WORK( * ), X( * ), XACT( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE, ZERO
+ PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+ INTEGER NTYPES, NTESTS
+ PARAMETER ( NTYPES = 10, NTESTS = 3 )
+ INTEGER NFACT
+ PARAMETER ( NFACT = 2 )
+* ..
+* .. Local Scalars ..
+ LOGICAL ZEROT
+ CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
+ CHARACTER*3 MATPATH, PATH
+ INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
+ $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
+ $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
+ DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCOND, RCONDC
+* ..
+* .. Local Arrays ..
+ CHARACTER FACTS( NFACT ), UPLOS( 2 )
+ INTEGER ISEED( 4 ), ISEEDY( 4 )
+ DOUBLE PRECISION RESULT( NTESTS )
+* ..
+* .. External Functions ..
+ DOUBLE PRECISION DGET06, ZLANHE
+ EXTERNAL DGET06, ZLANHE
+* ..
+* .. External Subroutines ..
+ EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
+ $ ZHESV_AASEN, ZHET01_AASEN, ZHETRF_AASEN,
+ $ ZHETRI2, ZLACPY, ZLAIPD, ZLARHS, ZLATB4, ZLATMS,
+ $ ZPOT02
+* ..
+* .. Scalars in Common ..
+ LOGICAL LERR, OK
+ CHARACTER*32 SRNAMT
+ INTEGER INFOT, NUNIT
+* ..
+* .. Common blocks ..
+ COMMON / INFOC / INFOT, NUNIT, OK, LERR
+ COMMON / SRNAMC / SRNAMT
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX, MAX, MIN
+* ..
+* .. Data statements ..
+ DATA ISEEDY / 1988, 1989, 1990, 1991 /
+ DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
+* ..
+* .. Executable Statements ..
+*
+* Initialize constants and the random number seed.
+*
+* Test path
+*
+ PATH( 1: 1 ) = 'Zomplex precision'
+ PATH( 2: 3 ) = 'HA'
+*
+* Path to generate matrices
+*
+ MATPATH( 1: 1 ) = 'Zomplex precision'
+ MATPATH( 2: 3 ) = 'HE'
+*
+ NRUN = 0
+ NFAIL = 0
+ NERRS = 0
+ DO 10 I = 1, 4
+ ISEED( I ) = ISEEDY( I )
+ 10 CONTINUE
+ LWORK = MAX( 2*NMAX, NMAX*NRHS )
+*
+* Test the error exits
+*
+ IF( TSTERR )
+ $ CALL ZERRVX( PATH, NOUT )
+ INFOT = 0
+*
+* Set the block size and minimum block size for testing.
+*
+ NB = 1
+ NBMIN = 2
+ CALL XLAENV( 1, NB )
+ CALL XLAENV( 2, NBMIN )
+*
+* Do for each value of N in NVAL
+*
+ DO 180 IN = 1, NN
+ N = NVAL( IN )
+ LDA = MAX( N, 1 )
+ XTYPE = 'N'
+ NIMAT = NTYPES
+ IF( N.LE.0 )
+ $ NIMAT = 1
+*
+ DO 170 IMAT = 1, NIMAT
+*
+* Do the tests only if DOTYPE( IMAT ) is true.
+*
+ IF( .NOT.DOTYPE( IMAT ) )
+ $ GO TO 170
+*
+* Skip types 3, 4, 5, or 6 if the matrix size is too small.
+*
+ ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
+ IF( ZEROT .AND. N.LT.IMAT-2 )
+ $ GO TO 170
+*
+* Do first for UPLO = 'U', then for UPLO = 'L'
+*
+ DO 160 IUPLO = 1, 2
+ UPLO = UPLOS( IUPLO )
+*
+* Begin generate the test matrix A.
+*
+* Set up parameters with ZLATB4 and generate a test matrix
+* with ZLATMS.
+*
+ CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
+ $ MODE, CNDNUM, DIST )
+*
+ SRNAMT = 'ZLATMS'
+ CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
+ $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
+ $ INFO )
+*
+* Check error code from ZLATMS.
+*
+ IF( INFO.NE.0 ) THEN
+ CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
+ $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
+ GO TO 160
+ END IF
+*
+* For types 3-6, zero one or more rows and columns of the
+* matrix to test that INFO is returned correctly.
+*
+ IF( ZEROT ) THEN
+ IF( IMAT.EQ.3 ) THEN
+ IZERO = 1
+ ELSE IF( IMAT.EQ.4 ) THEN
+ IZERO = N
+ ELSE
+ IZERO = N / 2 + 1
+ END IF
+*
+ IF( IMAT.LT.6 ) THEN
+*
+* Set row and column IZERO to zero.
+*
+ IF( IUPLO.EQ.1 ) THEN
+ IOFF = ( IZERO-1 )*LDA
+ DO 20 I = 1, IZERO - 1
+ A( IOFF+I ) = ZERO
+ 20 CONTINUE
+ IOFF = IOFF + IZERO
+ DO 30 I = IZERO, N
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 30 CONTINUE
+ ELSE
+ IOFF = IZERO
+ DO 40 I = 1, IZERO - 1
+ A( IOFF ) = ZERO
+ IOFF = IOFF + LDA
+ 40 CONTINUE
+ IOFF = IOFF - IZERO
+ DO 50 I = IZERO, N
+ A( IOFF+I ) = ZERO
+ 50 CONTINUE
+ END IF
+ ELSE
+ IOFF = 0
+ IF( IUPLO.EQ.1 ) THEN
+*
+* Set the first IZERO rows and columns to zero.
+*
+ DO 70 J = 1, N
+ I2 = MIN( J, IZERO )
+ DO 60 I = 1, I2
+ A( IOFF+I ) = ZERO
+ 60 CONTINUE
+ IOFF = IOFF + LDA
+ 70 CONTINUE
+ IZERO = 1
+ ELSE
+*
+* Set the last IZERO rows and columns to zero.
+*
+ DO 90 J = 1, N
+ I1 = MAX( J, IZERO )
+ DO 80 I = I1, N
+ A( IOFF+I ) = ZERO
+ 80 CONTINUE
+ IOFF = IOFF + LDA
+ 90 CONTINUE
+ END IF
+ END IF
+ ELSE
+ IZERO = 0
+ END IF
+*
+* Set the imaginary part of the diagonals.
+*
+ CALL ZLAIPD( N, A, LDA+1, 0 )
+*
+ DO 150 IFACT = 1, NFACT
+*
+* Do first for FACT = 'F', then for other values.
+*
+ FACT = FACTS( IFACT )
+*
+* Compute the condition number for comparison with
+* the value returned by ZHESVX.
+*
+ IF( ZEROT ) THEN
+ IF( IFACT.EQ.1 )
+ $ GO TO 150
+ RCONDC = ZERO
+*
+ ELSE IF( IFACT.EQ.1 ) THEN
+*
+* Compute the 1-norm of A.
+*
+ ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
+*
+* Factor the matrix A.
+*
+c CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+c CALL ZHETRF( UPLO, N, AFAC, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+*
+* Compute inv(A) and take its norm.
+*
+c CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
+c LWORK = (N+NB+1)*(NB+3)
+c CALL ZHETRI2( UPLO, N, AINV, LDA, IWORK, WORK,
+c $ LWORK, INFO )
+c AINVNM = ZLANHE( '1', UPLO, N, AINV, LDA, RWORK )
+*
+* Compute the 1-norm condition number of A.
+*
+c IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
+c RCONDC = ONE
+c ELSE
+c RCONDC = ( ONE / ANORM ) / AINVNM
+c END IF
+ END IF
+*
+* Form an exact solution and set the right hand side.
+*
+ SRNAMT = 'ZLARHS'
+ CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
+ $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
+ $ INFO )
+ XTYPE = 'C'
+*
+* --- Test ZHESV_AASEN ---
+*
+ IF( IFACT.EQ.2 ) THEN
+ CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
+ CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
+*
+* Factor the matrix and solve the system using ZHESV.
+*
+ SRNAMT = 'ZHESV_AASEN '
+ CALL ZHESV_AASEN( UPLO, N, NRHS, AFAC, LDA, IWORK,
+ $ X, LDA, WORK, LWORK, INFO )
+*
+* Adjust the expected value of INFO to account for
+* pivoting.
+*
+ IF( IZERO.GT.0 ) THEN
+ J = 1
+ K = IZERO
+ 100 CONTINUE
+ IF( J.EQ.K ) THEN
+ K = IWORK( J )
+ ELSE IF( IWORK( J ).EQ.K ) THEN
+ K = J
+ END IF
+ IF( J.LT.K ) THEN
+ J = J + 1
+ GO TO 100
+ END IF
+ ELSE
+ K = 0
+ END IF
+*
+* Check error code from ZHESV .
+*
+ IF( INFO.NE.K ) THEN
+ CALL ALAERH( PATH, 'ZHESV_AASEN', INFO, K, UPLO, N,
+ $ N, -1, -1, NRHS, IMAT, NFAIL,
+ $ NERRS, NOUT )
+ GO TO 120
+ ELSE IF( INFO.NE.0 ) THEN
+ GO TO 120
+ END IF
+*
+* Reconstruct matrix from factors and compute
+* residual.
+*
+ CALL ZHET01_AASEN( UPLO, N, A, LDA, AFAC, LDA,
+ $ IWORK, AINV, LDA, RWORK,
+ $ RESULT( 1 ) )
+*
+* Compute residual of the computed solution.
+*
+ CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
+ CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
+ $ LDA, RWORK, RESULT( 2 ) )
+*
+* Check solution from generated exact solution.
+*
+ CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
+ $ RESULT( 3 ) )
+ NT = 3
+*
+* Print information about the tests that did not pass
+* the threshold.
+*
+ DO 110 K = 1, NT
+ IF( RESULT( K ).GE.THRESH ) THEN
+ IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
+ $ CALL ALADHD( NOUT, PATH )
+ WRITE( NOUT, FMT = 9999 )'ZHESV_AASEN', UPLO, N,
+ $ IMAT, K, RESULT( K )
+ NFAIL = NFAIL + 1
+ END IF
+ 110 CONTINUE
+ NRUN = NRUN + NT
+ 120 CONTINUE
+ END IF
+*
+ 150 CONTINUE
+*
+ 160 CONTINUE
+ 170 CONTINUE
+ 180 CONTINUE
+*
+* Print a summary of the results.
+*
+ CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
+*
+ 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
+ $ ', test ', I2, ', ratio =', G12.5 )
+ RETURN
+*
+* End of ZDRVHE_AASEN
+*
+ END
$ ZGTSVX, ZHESV, ZHESV_ROOK, ZHESVX, ZHPSV,
$ ZHPSVX, ZPBSV, ZPBSVX, ZPOSV, ZPOSVX, ZPPSV,
$ ZPPSVX, ZPTSV, ZPTSVX, ZSPSV, ZSPSVX, ZSYSV,
- $ ZSYSV_ROOK, ZSYSVX
+ $ ZSYSV_AASEN, ZSYSV_ROOK, ZSYSVX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
$ RCOND, R1, R2, W, 3, RW, INFO )
CALL CHKXER( 'ZHESVX', INFOT, NOUT, LERR, OK )
*
+ ELSE IF( LSAMEN( 2, C2, 'HA' ) ) THEN
+*
+* ZHESV_AASEN
+*
+ SRNAMT = 'ZHESV_AASEN'
+ INFOT = 1
+ CALL ZHESV_AASEN( '/', 0, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'ZHESV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHESV_AASEN( 'U', -1, 0, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'ZHESV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHESV_AASEN( 'U', 0, -1, A, 1, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'ZHESV_AASEN', INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZHESV_AASEN( 'U', 2, 0, A, 2, IP, B, 1, W, 1, INFO )
+ CALL CHKXER( 'ZHESV_AASEN', INFOT, NOUT, LERR, OK )
+*
+
ELSE IF( LSAMEN( 2, C2, 'HR' ) ) THEN
*
* ZHESV_ROOK
--- /dev/null
+*> \brief \b ZHET01_AASEN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHET01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV,
+* C, LDC, RWORK, RESID )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER LDA, LDAFAC, LDC, N
+* COMPLEX*16 RESID
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+* $ RWORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHET01_AASEN reconstructs a hermitian 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
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> hermitian matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows and columns of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> The original hermitian matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N)
+*> \endverbatim
+*>
+*> \param[in] AFAC
+*> \verbatim
+*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
+*> The factored form of the matrix A. AFAC contains the block
+*> diagonal matrix D and the multipliers used to obtain the
+*> factor L or U from the block L*D*L' or U*D*U' factorization
+*> as computed by ZHETRF.
+*> \endverbatim
+*>
+*> \param[in] LDAFAC
+*> \verbatim
+*> LDAFAC is INTEGER
+*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> The pivot indices from ZHETRF.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is COMPLEX*16 array, dimension (LDC,N)
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the array C. LDC >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is COMPLEX*16 array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] RESID
+*> \verbatim
+*> RESID is COMPLEX*16
+*> 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:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2016
+*
+*
+*> \ingroup complex16_lin
+*
+* =====================================================================
+ SUBROUTINE ZHET01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
+ $ LDC, RWORK, RESID )
+*
+* -- LAPACK test routine (version 3.7.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2016
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER LDA, LDAFAC, LDC, N
+ DOUBLE PRECISION RESID
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
+ $ RWORK( * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ COMPLEX*16 CZERO, CONE
+ PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
+ $ CONE = ( 1.0D+0, 0.0D+0 ) )
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ DOUBLE PRECISION ANORM, EPS
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ DOUBLE PRECISION DLAMCH, ZLANHE
+ EXTERNAL LSAME, DLAMCH, ZLANHE
+* ..
+* .. External Subroutines ..
+ EXTERNAL ZLASET, ZLAVHE
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE
+* ..
+* .. Executable Statements ..
+*
+* Quick exit if N = 0.
+*
+ IF( N.LE.0 ) THEN
+ RESID = ZERO
+ RETURN
+ END IF
+*
+* Determine EPS and the norm of A.
+*
+ EPS = DLAMCH( 'Epsilon' )
+ ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
+*
+* Initialize C to the tridiagonal matrix T.
+*
+ CALL ZLASET( 'Full', N, N, CZERO, CZERO, C, LDC )
+ CALL ZLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
+ IF( N.GT.1 ) THEN
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ CALL ZLACGV( N-1, C( 2, 1 ), LDC+1 )
+ ELSE
+ CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
+ $ LDC+1 )
+ CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
+ $ LDC+1 )
+ CALL ZLACGV( N-1, C( 1, 2 ), LDC+1 )
+ ENDIF
+ ENDIF
+*
+* Call ZTRMM to form the product U' * D (or L * D ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose', 'Unit', N-1,
+ $ N, CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
+ ELSE
+ CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
+ $ CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
+ END IF
+*
+* Call ZTRMM again to multiply by U (or L ).
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
+ $ CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
+ ELSE
+ CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose', 'Unit', N,
+ $ N-1, CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
+ END IF
+*
+* Apply hermitian pivots
+*
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL ZSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
+ END DO
+ DO J = N, 1, -1
+ I = IPIV( J )
+ IF( I.NE.J )
+ $ CALL ZSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
+ END DO
+*
+*
+* Compute the difference C - A .
+*
+ IF( LSAME( UPLO, 'U' ) ) THEN
+ DO J = 1, N
+ DO I = 1, J
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ ELSE
+ DO J = 1, N
+ DO I = J, N
+ C( I, J ) = C( I, J ) - A( I, J )
+ END DO
+ END DO
+ END IF
+*
+* Compute norm( C - A ) / ( N * norm(A) * EPS )
+*
+ RESID = ZLANHE( '1', UPLO, N, C, LDC, RWORK )
+*
+ IF( ANORM.LE.ZERO ) THEN
+ IF( RESID.NE.ZERO )
+ $ RESID = ONE / EPS
+ ELSE
+ RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
+ END IF
+*
+ RETURN
+*
+* End of ZHET01_AASEN
+*
+ END
CPT 12 List types on next line if 0 < NTYPES < 12
CHE 10 List types on next line if 0 < NTYPES < 10
CHR 10 List types on next line if 0 < NTYPES < 10
+CHA 10 List types on next line if 0 < NTYPES < 10
CHP 10 List types on next line if 0 < NTYPES < 10
CSY 11 List types on next line if 0 < NTYPES < 11
CSR 11 List types on next line if 0 < NTYPES < 11
DPP 9 List types on next line if 0 < NTYPES < 9
DPB 8 List types on next line if 0 < NTYPES < 8
DPT 12 List types on next line if 0 < NTYPES < 12
+DSA 10 List types on next line if 0 < NTYPES < 10
DSY 10 List types on next line if 0 < NTYPES < 10
DSR 10 List types on next line if 0 < NTYPES < 10
DSP 10 List types on next line if 0 < NTYPES < 10
SPP 9 List types on next line if 0 < NTYPES < 9
SPB 8 List types on next line if 0 < NTYPES < 8
SPT 12 List types on next line if 0 < NTYPES < 12
+SSA 10 List types on next line if 0 < NTYPES < 10
SSY 10 List types on next line if 0 < NTYPES < 10
SSR 10 List types on next line if 0 < NTYPES < 10
SSP 10 List types on next line if 0 < NTYPES < 10
ZPP 9 List types on next line if 0 < NTYPES < 9
ZPB 8 List types on next line if 0 < NTYPES < 8
ZPT 12 List types on next line if 0 < NTYPES < 12
+ZHA 10 List types on next line if 0 < NTYPES < 10
ZHE 10 List types on next line if 0 < NTYPES < 10
ZHR 10 List types on next line if 0 < NTYPES < 10
ZHP 10 List types on next line if 0 < NTYPES < 10
projects / platform / upstream / lapack.git / commitdiff