../INSTALL/dlamch.o ../INSTALL/dsecnd_$(TIMER).o
SLASRC = \
- sbdsvdx.o \
+ sbdsvdx.o spotrf2.o \
sgbbrd.o sgbcon.o sgbequ.o sgbrfs.o sgbsv.o \
sgbsvx.o sgbtf2.o sgbtrf.o sgbtrs.o sgebak.o sgebal.o sgebd2.o \
sgebrd.o sgecon.o sgeequ.o sgees.o sgeesx.o sgeev.o sgeevx.o \
endif
CLASRC = \
+ cpotrf2.o \
cbdsqr.o cgbbrd.o cgbcon.o cgbequ.o cgbrfs.o cgbsv.o cgbsvx.o \
cgbtf2.o cgbtrf.o cgbtrs.o cgebak.o cgebal.o cgebd2.o cgebrd.o \
cgecon.o cgeequ.o cgees.o cgeesx.o cgeev.o cgeevx.o \
ZCLASRC = cpotrs.o cgetrs.o cpotrf.o cgetrf.o
DLASRC = \
+ dpotrf2.o \
dbdsvdx.o \
dgbbrd.o dgbcon.o dgbequ.o dgbrfs.o dgbsv.o \
dgbsvx.o dgbtf2.o dgbtrf.o dgbtrs.o dgebak.o dgebal.o dgebd2.o \
endif
ZLASRC = \
+ zpotrf2.o \
zbdsqr.o zgbbrd.o zgbcon.o zgbequ.o zgbrfs.o zgbsv.o zgbsvx.o \
zgbtf2.o zgbtrf.o zgbtrs.o zgebak.o zgebal.o zgebd2.o zgebrd.o \
zgecon.o zgeequ.o zgees.o zgeesx.o zgeev.o zgeevx.o \
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
- EXTERNAL CGEMM, CHERK, CPOTF2, CTRSM, XERBLA
+ EXTERNAL CGEMM, CHERK, CPOTRF2, CTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
*
* Use unblocked code.
*
- CALL CPOTF2( UPLO, N, A, LDA, INFO )
+ CALL CPOTRF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
JB = MIN( NB, N-J+1 )
CALL CHERK( 'Upper', 'Conjugate transpose', JB, J-1,
$ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
- CALL CPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
+ CALL CPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
JB = MIN( NB, N-J+1 )
CALL CHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
$ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
- CALL CPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
+ CALL CPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
--- /dev/null
+*> \brief \b CPOTRF2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* RECURSIVE SUBROUTINE CPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* COMPLEX A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CPOTRF2 computes the Cholesky factorization of a real symmetric
+*> positive definite matrix A using the recursive algorithm.
+*>
+*> The factorization has the form
+*> A = U**H * U, if UPLO = 'U', or
+*> A = L * L**H, if UPLO = 'L',
+*> where U is an upper triangular matrix and L is lower triangular.
+*>
+*> This is the recursive version of the algorithm. It divides
+*> the matrix into four submatrices:
+*>
+*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
+*> A = [ -----|----- ] with n1 = n/2
+*> [ A21 | A22 ] n2 = n-n1
+*>
+*> The subroutine calls itself to factor A11. Update and scale A21
+*> or A12, update A22 then calls itself to factor A22.
+*>
+*> \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, if INFO = 0, the factor U or L from the Cholesky
+*> factorization A = U**H*U or A = L*L**H.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \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, the leading minor of order i is not
+*> positive definite, and the factorization could not be
+*> completed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2015
+*
+*> \ingroup complexPOcomputational
+*
+* =====================================================================
+ RECURSIVE SUBROUTINE CPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* -- LAPACK computational routine (version 3.6.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2015
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ COMPLEX A( LDA, * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
+ COMPLEX CONE
+ PARAMETER ( CONE = (1.0E+0, 0.0E+0) )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER N1, N2, IINFO
+ REAL AJJ
+* ..
+* .. External Functions ..
+ LOGICAL LSAME, SISNAN
+ EXTERNAL LSAME, SISNAN
+* ..
+* .. External Subroutines ..
+ EXTERNAL CHERK, CTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, REAL, SQRT
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters
+*
+ 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( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'CPOTRF2', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+* N=1 case
+*
+ IF( N.EQ.1 ) THEN
+*
+* Test for non-positive-definiteness
+*
+ AJJ = REAL( A( 1, 1 ) )
+ IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN
+ INFO = 1
+ RETURN
+ END IF
+*
+* Factor
+*
+ A( 1, 1 ) = SQRT( AJJ )
+*
+* Use recursive code
+*
+ ELSE
+ N1 = N/2
+ N2 = N-N1
+*
+* Factor A11
+*
+ CALL CPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = U**H*U
+*
+ IF( UPPER ) THEN
+*
+* Update and scale A12
+*
+ CALL CTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE,
+ $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL CHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+*
+ CALL CPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+*
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = L*L**H
+*
+ ELSE
+*
+* Update and scale A21
+*
+ CALL CTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE,
+ $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL CHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+*
+ CALL CPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+*
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+*
+ END IF
+ END IF
+ RETURN
+*
+* End of CPOTRF2
+*
+ END
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
- EXTERNAL DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA
+ EXTERNAL DGEMM, DPOTRF2, DSYRK, DTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
*
* Use unblocked code.
*
- CALL DPOTF2( UPLO, N, A, LDA, INFO )
+ CALL DPOTRF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
JB = MIN( NB, N-J+1 )
CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
$ A( 1, J ), LDA, ONE, A( J, J ), LDA )
- CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
+ CALL DPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
JB = MIN( NB, N-J+1 )
CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
$ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
- CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
+ CALL DPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
--- /dev/null
+*> \brief \b DPOTRF2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* REAL A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DPOTRF2 computes the Cholesky factorization of a real symmetric
+*> positive definite matrix A using the recursive algorithm.
+*>
+*> The factorization has the form
+*> A = U**T * U, if UPLO = 'U', or
+*> A = L * L**T, if UPLO = 'L',
+*> where U is an upper triangular matrix and L is lower triangular.
+*>
+*> This is the recursive version of the algorithm. It divides
+*> the matrix into four submatrices:
+*>
+*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
+*> A = [ -----|----- ] with n1 = n/2
+*> [ A21 | A22 ] n2 = n-n1
+*>
+*> The subroutine calls itself to factor A11. Update and scale A21
+*> or A12, update A22 then calls itself to factor A22.
+*>
+*> \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, if INFO = 0, the factor U or L from the Cholesky
+*> factorization A = U**T*U or A = L*L**T.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \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, the leading minor of order i is not
+*> positive definite, and the factorization could not be
+*> completed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2015
+*
+*> \ingroup doublePOcomputational
+*
+* =====================================================================
+ RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* -- LAPACK computational routine (version 3.6.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2015
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE, ZERO
+ PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER N1, N2, IINFO
+* ..
+* .. External Functions ..
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
+* ..
+* .. External Subroutines ..
+ EXTERNAL DSYRK, DTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, SQRT
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters
+*
+ 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( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DPOTRF2', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+* N=1 case
+*
+ IF( N.EQ.1 ) THEN
+*
+* Test for non-positive-definiteness
+*
+ IF( A( 1, 1 ).LE.ZERO.OR.DISNAN( A( 1, 1 ) ) ) THEN
+ INFO = 1
+ RETURN
+ END IF
+*
+* Factor
+*
+ A( 1, 1 ) = SQRT( A( 1, 1 ) )
+*
+* Use recursive code
+*
+ ELSE
+ N1 = N/2
+ N2 = N-N1
+*
+* Factor A11
+*
+ CALL DPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = U**T*U
+*
+ IF( UPPER ) THEN
+*
+* Update and scale A12
+*
+ CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE,
+ $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL DSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+ CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = L*L**T
+*
+ ELSE
+*
+* Update and scale A21
+*
+ CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE,
+ $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL DSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+ CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+ END IF
+ END IF
+ RETURN
+*
+* End of DPOTRF2
+*
+ END
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
- EXTERNAL SGEMM, SPOTF2, SSYRK, STRSM, XERBLA
+ EXTERNAL SGEMM, SPOTRF2, SSYRK, STRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
*
* Use unblocked code.
*
- CALL SPOTF2( UPLO, N, A, LDA, INFO )
+ CALL SPOTRF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
JB = MIN( NB, N-J+1 )
CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
$ A( 1, J ), LDA, ONE, A( J, J ), LDA )
- CALL SPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
+ CALL SPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
JB = MIN( NB, N-J+1 )
CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
$ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
- CALL SPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
+ CALL SPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
--- /dev/null
+*> \brief \b SPOTRF2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* RECURSIVE SUBROUTINE SPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* REAL A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SPOTRF2 computes the Cholesky factorization of a real symmetric
+*> positive definite matrix A using the recursive algorithm.
+*>
+*> The factorization has the form
+*> A = U**T * U, if UPLO = 'U', or
+*> A = L * L**T, if UPLO = 'L',
+*> where U is an upper triangular matrix and L is lower triangular.
+*>
+*> This is the recursive version of the algorithm. It divides
+*> the matrix into four submatrices:
+*>
+*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
+*> A = [ -----|----- ] with n1 = n/2
+*> [ A21 | A22 ] n2 = n-n1
+*>
+*> The subroutine calls itself to factor A11. Update and scale A21
+*> or A12, update A22 then call itself to factor A22.
+*>
+*> \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, if INFO = 0, the factor U or L from the Cholesky
+*> factorization A = U**T*U or A = L*L**T.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \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, the leading minor of order i is not
+*> positive definite, and the factorization could not be
+*> completed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2015
+*
+*> \ingroup realPOcomputational
+*
+* =====================================================================
+ RECURSIVE SUBROUTINE SPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* -- LAPACK computational routine (version 3.6.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2015
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ REAL A( LDA, * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER ( ONE = 1.0E+0, ZERO=0.0E+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER N1, N2, IINFO
+* ..
+* .. External Functions ..
+ LOGICAL LSAME, SISNAN
+ EXTERNAL LSAME, SISNAN
+* ..
+* .. External Subroutines ..
+ EXTERNAL SGEMM, SSYRK, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, SQRT
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters
+*
+ 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( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'SPOTRF2', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+* N=1 case
+*
+ IF( N.EQ.1 ) THEN
+*
+* Test for non-positive-definiteness
+*
+ IF( A( 1, 1 ).LE.ZERO.OR.SISNAN( A( 1, 1 ) ) ) THEN
+ INFO = 1
+ RETURN
+ END IF
+*
+* Factor
+*
+ A( 1, 1 ) = SQRT( A( 1, 1 ) )
+*
+* Use recursive code
+*
+ ELSE
+ N1 = N/2
+ N2 = N-N1
+*
+* Factor A11
+*
+ CALL SPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = U**T*U
+*
+ IF( UPPER ) THEN
+*
+* Update and scale A12
+*
+ CALL STRSM( 'L', 'U', 'T', 'N', N1, N2, ONE,
+ $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL SSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+ CALL SPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = L*L**T
+*
+ ELSE
+*
+* Update and scale A21
+*
+ CALL STRSM( 'R', 'L', 'T', 'N', N2, N1, ONE,
+ $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL SSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+ CALL SPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+ END IF
+ END IF
+ RETURN
+*
+* End of SPOTRF2
+*
+ END
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
- EXTERNAL XERBLA, ZGEMM, ZHERK, ZPOTF2, ZTRSM
+ EXTERNAL XERBLA, ZGEMM, ZHERK, ZPOTRF2, ZTRSM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
*
* Use unblocked code.
*
- CALL ZPOTF2( UPLO, N, A, LDA, INFO )
+ CALL ZPOTRF2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code.
JB = MIN( NB, N-J+1 )
CALL ZHERK( 'Upper', 'Conjugate transpose', JB, J-1,
$ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
- CALL ZPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
+ CALL ZPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
JB = MIN( NB, N-J+1 )
CALL ZHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
$ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
- CALL ZPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
+ CALL ZPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO )
IF( INFO.NE.0 )
$ GO TO 30
IF( J+JB.LE.N ) THEN
--- /dev/null
+*> \brief \b ZPOTRF2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZPOTRF2 computes the Cholesky factorization of a real symmetric
+*> positive definite matrix A using the recursive algorithm.
+*>
+*> The factorization has the form
+*> A = U**H * U, if UPLO = 'U', or
+*> A = L * L**H, if UPLO = 'L',
+*> where U is an upper triangular matrix and L is lower triangular.
+*>
+*> This is the recursive version of the algorithm. It divides
+*> the matrix into four submatrices:
+*>
+*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
+*> A = [ -----|----- ] with n1 = n/2
+*> [ A21 | A22 ] n2 = n-n1
+*>
+*> The subroutine calls itself to factor A11. Update and scale A21
+*> or A12, update A22 then call itself to factor A22.
+*>
+*> \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 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 factor U or L from the Cholesky
+*> factorization A = U**H*U or A = L*L**H.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \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, the leading minor of order i is not
+*> positive definite, and the factorization could not be
+*> completed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2015
+*
+*> \ingroup complex16POcomputational
+*
+* =====================================================================
+ RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
+*
+* -- LAPACK computational routine (version 3.6.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2015
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ COMPLEX*16 A( LDA, * )
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE, ZERO
+ PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+ COMPLEX*16 CONE
+ PARAMETER ( CONE = (1.0D+0, 0.0D+0) )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER N1, N2, IINFO
+ DOUBLE PRECISION AJJ
+* ..
+* .. External Functions ..
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
+* ..
+* .. External Subroutines ..
+ EXTERNAL ZHERK, ZTRSM, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, DBLE, SQRT
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters
+*
+ 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( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -4
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZPOTRF2', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+* N=1 case
+*
+ IF( N.EQ.1 ) THEN
+*
+* Test for non-positive-definiteness
+*
+ AJJ = DBLE( A( 1, 1 ) )
+ IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
+ INFO = 1
+ RETURN
+ END IF
+*
+* Factor
+*
+ A( 1, 1 ) = SQRT( AJJ )
+*
+* Use recursive code
+*
+ ELSE
+ N1 = N/2
+ N2 = N-N1
+*
+* Factor A11
+*
+ CALL ZPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = U**H*U
+*
+ IF( UPPER ) THEN
+*
+* Update and scale A12
+*
+ CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE,
+ $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL ZHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+ CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+*
+* Compute the Cholesky factorization A = L*L**H
+*
+ ELSE
+*
+* Update and scale A21
+*
+ CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE,
+ $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
+*
+* Update and factor A22
+*
+ CALL ZHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
+ $ ONE, A( N1+1, N1+1 ), LDA )
+ CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
+ IF ( IINFO.NE.0 ) THEN
+ INFO = IINFO + N1
+ RETURN
+ END IF
+ END IF
+ END IF
+ RETURN
+*
+* End of ZPOTRF2
+*
+ END
projects / platform / upstream / lapack.git / commitdiff