version 1.4, 2010/08/06 15:32:24
|
version 1.13, 2012/12/14 14:22:29
|
Line 1
|
Line 1
|
SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, |
*> \brief <b> DGESVD computes the singular value decomposition (SVD) for GE matrices</b> |
$ WORK, LWORK, INFO ) |
|
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download DGESVD + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesvd.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesvd.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesvd.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, |
|
* WORK, LWORK, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER JOBU, JOBVT |
|
* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N |
|
* .. |
|
* .. Array Arguments .. |
|
* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), |
|
* $ VT( LDVT, * ), WORK( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> DGESVD computes the singular value decomposition (SVD) of a real |
|
*> M-by-N matrix A, optionally computing the left and/or right singular |
|
*> vectors. The SVD is written |
|
*> |
|
*> A = U * SIGMA * transpose(V) |
|
*> |
|
*> where SIGMA is an M-by-N matrix which is zero except for its |
|
*> min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and |
|
*> V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA |
|
*> are the singular values of A; they are real and non-negative, and |
|
*> are returned in descending order. The first min(m,n) columns of |
|
*> U and V are the left and right singular vectors of A. |
|
*> |
|
*> Note that the routine returns V**T, not V. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] JOBU |
|
*> \verbatim |
|
*> JOBU is CHARACTER*1 |
|
*> Specifies options for computing all or part of the matrix U: |
|
*> = 'A': all M columns of U are returned in array U: |
|
*> = 'S': the first min(m,n) columns of U (the left singular |
|
*> vectors) are returned in the array U; |
|
*> = 'O': the first min(m,n) columns of U (the left singular |
|
*> vectors) are overwritten on the array A; |
|
*> = 'N': no columns of U (no left singular vectors) are |
|
*> computed. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] JOBVT |
|
*> \verbatim |
|
*> JOBVT is CHARACTER*1 |
|
*> Specifies options for computing all or part of the matrix |
|
*> V**T: |
|
*> = 'A': all N rows of V**T are returned in the array VT; |
|
*> = 'S': the first min(m,n) rows of V**T (the right singular |
|
*> vectors) are returned in the array VT; |
|
*> = 'O': the first min(m,n) rows of V**T (the right singular |
|
*> vectors) are overwritten on the array A; |
|
*> = 'N': no rows of V**T (no right singular vectors) are |
|
*> computed. |
|
*> |
|
*> JOBVT and JOBU cannot both be 'O'. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] M |
|
*> \verbatim |
|
*> M is INTEGER |
|
*> The number of rows of the input matrix A. M >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The number of columns of the input matrix A. N >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] A |
|
*> \verbatim |
|
*> A is DOUBLE PRECISION array, dimension (LDA,N) |
|
*> On entry, the M-by-N matrix A. |
|
*> On exit, |
|
*> if JOBU = 'O', A is overwritten with the first min(m,n) |
|
*> columns of U (the left singular vectors, |
|
*> stored columnwise); |
|
*> if JOBVT = 'O', A is overwritten with the first min(m,n) |
|
*> rows of V**T (the right singular vectors, |
|
*> stored rowwise); |
|
*> if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A |
|
*> are destroyed. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of the array A. LDA >= max(1,M). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] S |
|
*> \verbatim |
|
*> S is DOUBLE PRECISION array, dimension (min(M,N)) |
|
*> The singular values of A, sorted so that S(i) >= S(i+1). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] U |
|
*> \verbatim |
|
*> U is DOUBLE PRECISION array, dimension (LDU,UCOL) |
|
*> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. |
|
*> If JOBU = 'A', U contains the M-by-M orthogonal matrix U; |
|
*> if JOBU = 'S', U contains the first min(m,n) columns of U |
|
*> (the left singular vectors, stored columnwise); |
|
*> if JOBU = 'N' or 'O', U is not referenced. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDU |
|
*> \verbatim |
|
*> LDU is INTEGER |
|
*> The leading dimension of the array U. LDU >= 1; if |
|
*> JOBU = 'S' or 'A', LDU >= M. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] VT |
|
*> \verbatim |
|
*> VT is DOUBLE PRECISION array, dimension (LDVT,N) |
|
*> If JOBVT = 'A', VT contains the N-by-N orthogonal matrix |
|
*> V**T; |
|
*> if JOBVT = 'S', VT contains the first min(m,n) rows of |
|
*> V**T (the right singular vectors, stored rowwise); |
|
*> if JOBVT = 'N' or 'O', VT is not referenced. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDVT |
|
*> \verbatim |
|
*> LDVT is INTEGER |
|
*> The leading dimension of the array VT. LDVT >= 1; if |
|
*> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,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; |
|
*> if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged |
|
*> superdiagonal elements of an upper bidiagonal matrix B |
|
*> whose diagonal is in S (not necessarily sorted). B |
|
*> satisfies A = U * B * VT, so it has the same singular values |
|
*> as A, and singular vectors related by U and VT. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LWORK |
|
*> \verbatim |
|
*> LWORK is INTEGER |
|
*> The dimension of the array WORK. |
|
*> LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): |
|
*> - PATH 1 (M much larger than N, JOBU='N') |
|
*> - PATH 1t (N much larger than M, JOBVT='N') |
|
*> LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths |
|
*> For good performance, LWORK should generally be larger. |
|
*> |
|
*> 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 DBDSQR did not converge, INFO specifies how many |
|
*> superdiagonals of an intermediate bidiagonal form B |
|
*> did not converge to zero. See the description of WORK |
|
*> above for details. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date April 2012 |
|
* |
|
*> \ingroup doubleGEsing |
|
* |
|
* ===================================================================== |
|
SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, |
|
$ VT, LDVT, WORK, LWORK, INFO ) |
|
* |
|
* -- LAPACK driver routine (version 3.4.1) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* April 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBU, JOBVT |
CHARACTER JOBU, JOBVT |
Line 15
|
Line 225
|
$ VT( LDVT, * ), WORK( * ) |
$ VT( LDVT, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DGESVD computes the singular value decomposition (SVD) of a real |
|
* M-by-N matrix A, optionally computing the left and/or right singular |
|
* vectors. The SVD is written |
|
* |
|
* A = U * SIGMA * transpose(V) |
|
* |
|
* where SIGMA is an M-by-N matrix which is zero except for its |
|
* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and |
|
* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA |
|
* are the singular values of A; they are real and non-negative, and |
|
* are returned in descending order. The first min(m,n) columns of |
|
* U and V are the left and right singular vectors of A. |
|
* |
|
* Note that the routine returns V**T, not V. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* JOBU (input) CHARACTER*1 |
|
* Specifies options for computing all or part of the matrix U: |
|
* = 'A': all M columns of U are returned in array U: |
|
* = 'S': the first min(m,n) columns of U (the left singular |
|
* vectors) are returned in the array U; |
|
* = 'O': the first min(m,n) columns of U (the left singular |
|
* vectors) are overwritten on the array A; |
|
* = 'N': no columns of U (no left singular vectors) are |
|
* computed. |
|
* |
|
* JOBVT (input) CHARACTER*1 |
|
* Specifies options for computing all or part of the matrix |
|
* V**T: |
|
* = 'A': all N rows of V**T are returned in the array VT; |
|
* = 'S': the first min(m,n) rows of V**T (the right singular |
|
* vectors) are returned in the array VT; |
|
* = 'O': the first min(m,n) rows of V**T (the right singular |
|
* vectors) are overwritten on the array A; |
|
* = 'N': no rows of V**T (no right singular vectors) are |
|
* computed. |
|
* |
|
* JOBVT and JOBU cannot both be 'O'. |
|
* |
|
* M (input) INTEGER |
|
* The number of rows of the input matrix A. M >= 0. |
|
* |
|
* N (input) INTEGER |
|
* The number of columns of the input matrix A. N >= 0. |
|
* |
|
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
|
* On entry, the M-by-N matrix A. |
|
* On exit, |
|
* if JOBU = 'O', A is overwritten with the first min(m,n) |
|
* columns of U (the left singular vectors, |
|
* stored columnwise); |
|
* if JOBVT = 'O', A is overwritten with the first min(m,n) |
|
* rows of V**T (the right singular vectors, |
|
* stored rowwise); |
|
* if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A |
|
* are destroyed. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1,M). |
|
* |
|
* S (output) DOUBLE PRECISION array, dimension (min(M,N)) |
|
* The singular values of A, sorted so that S(i) >= S(i+1). |
|
* |
|
* U (output) DOUBLE PRECISION array, dimension (LDU,UCOL) |
|
* (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. |
|
* If JOBU = 'A', U contains the M-by-M orthogonal matrix U; |
|
* if JOBU = 'S', U contains the first min(m,n) columns of U |
|
* (the left singular vectors, stored columnwise); |
|
* if JOBU = 'N' or 'O', U is not referenced. |
|
* |
|
* LDU (input) INTEGER |
|
* The leading dimension of the array U. LDU >= 1; if |
|
* JOBU = 'S' or 'A', LDU >= M. |
|
* |
|
* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) |
|
* If JOBVT = 'A', VT contains the N-by-N orthogonal matrix |
|
* V**T; |
|
* if JOBVT = 'S', VT contains the first min(m,n) rows of |
|
* V**T (the right singular vectors, stored rowwise); |
|
* if JOBVT = 'N' or 'O', VT is not referenced. |
|
* |
|
* LDVT (input) INTEGER |
|
* The leading dimension of the array VT. LDVT >= 1; if |
|
* JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). |
|
* |
|
* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
|
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK; |
|
* if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged |
|
* superdiagonal elements of an upper bidiagonal matrix B |
|
* whose diagonal is in S (not necessarily sorted). B |
|
* satisfies A = U * B * VT, so it has the same singular values |
|
* as A, and singular vectors related by U and VT. |
|
* |
|
* LWORK (input) INTEGER |
|
* The dimension of the array WORK. |
|
* LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)). |
|
* For good performance, LWORK should generally be larger. |
|
* |
|
* 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. |
|
* |
|
* INFO (output) INTEGER |
|
* = 0: successful exit. |
|
* < 0: if INFO = -i, the i-th argument had an illegal value. |
|
* > 0: if DBDSQR did not converge, INFO specifies how many |
|
* superdiagonals of an intermediate bidiagonal form B |
|
* did not converge to zero. See the description of WORK |
|
* above for details. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 144
|
Line 238
|
$ ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU, |
$ ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU, |
$ MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU, |
$ MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU, |
$ NRVT, WRKBL |
$ NRVT, WRKBL |
|
INTEGER LWORK_DGEQRF, LWORK_DORGQR_N, LWORK_DORGQR_M, |
|
$ LWORK_DGEBRD, LWORK_DORGBR_P, LWORK_DORGBR_Q, |
|
$ LWORK_DGELQF, LWORK_DORGLQ_N, LWORK_DORGLQ_M |
DOUBLE PRECISION ANRM, BIGNUM, EPS, SMLNUM |
DOUBLE PRECISION ANRM, BIGNUM, EPS, SMLNUM |
* .. |
* .. |
* .. Local Arrays .. |
* .. Local Arrays .. |
Line 215
|
Line 312
|
* |
* |
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 ) |
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 ) |
BDSPAC = 5*N |
BDSPAC = 5*N |
|
* Compute space needed for DGEQRF |
|
CALL DGEQRF( M, N, A, LDA, DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DGEQRF=DUM(1) |
|
* Compute space needed for DORGQR |
|
CALL DORGQR( M, N, N, A, LDA, DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DORGQR_N=DUM(1) |
|
CALL DORGQR( M, M, N, A, LDA, DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DORGQR_M=DUM(1) |
|
* Compute space needed for DGEBRD |
|
CALL DGEBRD( N, N, A, LDA, S, DUM(1), DUM(1), |
|
$ DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DGEBRD=DUM(1) |
|
* Compute space needed for DORGBR P |
|
CALL DORGBR( 'P', N, N, N, A, LDA, DUM(1), |
|
$ DUM(1), -1, IERR ) |
|
LWORK_DORGBR_P=DUM(1) |
|
* Compute space needed for DORGBR Q |
|
CALL DORGBR( 'Q', N, N, N, A, LDA, DUM(1), |
|
$ DUM(1), -1, IERR ) |
|
LWORK_DORGBR_Q=DUM(1) |
|
* |
IF( M.GE.MNTHR ) THEN |
IF( M.GE.MNTHR ) THEN |
IF( WNTUN ) THEN |
IF( WNTUN ) THEN |
* |
* |
* Path 1 (M much larger than N, JOBU='N') |
* Path 1 (M much larger than N, JOBU='N') |
* |
* |
MAXWRK = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, |
MAXWRK = N + LWORK_DGEQRF |
$ -1 ) |
MAXWRK = MAX( MAXWRK, 3*N+LWORK_DGEBRD ) |
MAXWRK = MAX( MAXWRK, 3*N+2*N* |
|
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
|
IF( WNTVO .OR. WNTVAS ) |
IF( WNTVO .OR. WNTVAS ) |
$ MAXWRK = MAX( MAXWRK, 3*N+( N-1 )* |
$ MAXWRK = MAX( MAXWRK, 3*N+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
|
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MINWRK = MAX( 4*N, BDSPAC ) |
MINWRK = MAX( 4*N, BDSPAC ) |
ELSE IF( WNTUO .AND. WNTVN ) THEN |
ELSE IF( WNTUO .AND. WNTVN ) THEN |
* |
* |
* Path 2 (M much larger than N, JOBU='O', JOBVT='N') |
* Path 2 (M much larger than N, JOBU='O', JOBVT='N') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_N ) |
$ N, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N ) |
MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 248
|
Line 360
|
* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or |
* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or |
* 'A') |
* 'A') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_N ) |
$ N, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_P ) |
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+( N-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N ) |
MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 264
|
Line 372
|
* |
* |
* Path 4 (M much larger than N, JOBU='S', JOBVT='N') |
* Path 4 (M much larger than N, JOBU='S', JOBVT='N') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_N ) |
$ N, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = N*N + WRKBL |
MAXWRK = N*N + WRKBL |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 278
|
Line 383
|
* |
* |
* Path 5 (M much larger than N, JOBU='S', JOBVT='O') |
* Path 5 (M much larger than N, JOBU='S', JOBVT='O') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_N ) |
$ N, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_P ) |
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+( N-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = 2*N*N + WRKBL |
MAXWRK = 2*N*N + WRKBL |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 295
|
Line 396
|
* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or |
* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or |
* 'A') |
* 'A') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_N ) |
$ N, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_P ) |
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+( N-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = N*N + WRKBL |
MAXWRK = N*N + WRKBL |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 311
|
Line 408
|
* |
* |
* Path 7 (M much larger than N, JOBU='A', JOBVT='N') |
* Path 7 (M much larger than N, JOBU='A', JOBVT='N') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_M ) |
$ M, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = N*N + WRKBL |
MAXWRK = N*N + WRKBL |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 325
|
Line 419
|
* |
* |
* Path 8 (M much larger than N, JOBU='A', JOBVT='O') |
* Path 8 (M much larger than N, JOBU='A', JOBVT='O') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_M ) |
$ M, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_P ) |
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+( N-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = 2*N*N + WRKBL |
MAXWRK = 2*N*N + WRKBL |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 342
|
Line 432
|
* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or |
* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or |
* 'A') |
* 'A') |
* |
* |
WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) |
WRKBL = N + LWORK_DGEQRF |
WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M, |
WRKBL = MAX( WRKBL, N+LWORK_DORGQR_M ) |
$ M, N, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*N+2*N* |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*N+LWORK_DORGBR_P ) |
WRKBL = MAX( WRKBL, 3*N+N* |
|
$ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*N+( N-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = N*N + WRKBL |
MAXWRK = N*N + WRKBL |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
Line 359
|
Line 445
|
* |
* |
* Path 10 (M at least N, but not much larger) |
* Path 10 (M at least N, but not much larger) |
* |
* |
MAXWRK = 3*N + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N, |
CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1), |
$ -1, -1 ) |
$ DUM(1), DUM(1), -1, IERR ) |
IF( WNTUS .OR. WNTUO ) |
LWORK_DGEBRD=DUM(1) |
$ MAXWRK = MAX( MAXWRK, 3*N+N* |
MAXWRK = 3*N + LWORK_DGEBRD |
$ ILAENV( 1, 'DORGBR', 'Q', M, N, N, -1 ) ) |
IF( WNTUS .OR. WNTUO ) THEN |
IF( WNTUA ) |
CALL DORGBR( 'Q', M, N, N, A, LDA, DUM(1), |
$ MAXWRK = MAX( MAXWRK, 3*N+M* |
$ DUM(1), -1, IERR ) |
$ ILAENV( 1, 'DORGBR', 'Q', M, M, N, -1 ) ) |
LWORK_DORGBR_Q=DUM(1) |
IF( .NOT.WNTVN ) |
MAXWRK = MAX( MAXWRK, 3*N+LWORK_DORGBR_Q ) |
$ MAXWRK = MAX( MAXWRK, 3*N+( N-1 )* |
END IF |
$ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) ) |
IF( WNTUA ) THEN |
|
CALL DORGBR( 'Q', M, M, N, A, LDA, DUM(1), |
|
$ DUM(1), -1, IERR ) |
|
LWORK_DORGBR_Q=DUM(1) |
|
MAXWRK = MAX( MAXWRK, 3*N+LWORK_DORGBR_Q ) |
|
END IF |
|
IF( .NOT.WNTVN ) THEN |
|
MAXWRK = MAX( MAXWRK, 3*N+LWORK_DORGBR_P ) |
|
END IF |
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
MINWRK = MAX( 3*N+M, BDSPAC ) |
END IF |
END IF |
Line 379
|
Line 473
|
* |
* |
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 ) |
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 ) |
BDSPAC = 5*M |
BDSPAC = 5*M |
|
* Compute space needed for DGELQF |
|
CALL DGELQF( M, N, A, LDA, DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DGELQF=DUM(1) |
|
* Compute space needed for DORGLQ |
|
CALL DORGLQ( N, N, M, DUM(1), N, DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DORGLQ_N=DUM(1) |
|
CALL DORGLQ( M, N, M, A, LDA, DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DORGLQ_M=DUM(1) |
|
* Compute space needed for DGEBRD |
|
CALL DGEBRD( M, M, A, LDA, S, DUM(1), DUM(1), |
|
$ DUM(1), DUM(1), -1, IERR ) |
|
LWORK_DGEBRD=DUM(1) |
|
* Compute space needed for DORGBR P |
|
CALL DORGBR( 'P', M, M, M, A, N, DUM(1), |
|
$ DUM(1), -1, IERR ) |
|
LWORK_DORGBR_P=DUM(1) |
|
* Compute space needed for DORGBR Q |
|
CALL DORGBR( 'Q', M, M, M, A, N, DUM(1), |
|
$ DUM(1), -1, IERR ) |
|
LWORK_DORGBR_Q=DUM(1) |
IF( N.GE.MNTHR ) THEN |
IF( N.GE.MNTHR ) THEN |
IF( WNTVN ) THEN |
IF( WNTVN ) THEN |
* |
* |
* Path 1t(N much larger than M, JOBVT='N') |
* Path 1t(N much larger than M, JOBVT='N') |
* |
* |
MAXWRK = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, |
MAXWRK = M + LWORK_DGELQF |
$ -1 ) |
MAXWRK = MAX( MAXWRK, 3*M+LWORK_DGEBRD ) |
MAXWRK = MAX( MAXWRK, 3*M+2*M* |
|
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
|
IF( WNTUO .OR. WNTUAS ) |
IF( WNTUO .OR. WNTUAS ) |
$ MAXWRK = MAX( MAXWRK, 3*M+M* |
$ MAXWRK = MAX( MAXWRK, 3*M+LWORK_DORGBR_Q ) |
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
|
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MINWRK = MAX( 4*M, BDSPAC ) |
MINWRK = MAX( 4*M, BDSPAC ) |
ELSE IF( WNTVO .AND. WNTUN ) THEN |
ELSE IF( WNTVO .AND. WNTUN ) THEN |
* |
* |
* Path 2t(N much larger than M, JOBU='N', JOBVT='O') |
* Path 2t(N much larger than M, JOBU='N', JOBVT='O') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_M ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M ) |
MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 412
|
Line 520
|
* Path 3t(N much larger than M, JOBU='S' or 'A', |
* Path 3t(N much larger than M, JOBU='S' or 'A', |
* JOBVT='O') |
* JOBVT='O') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_M ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_Q ) |
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+M* |
|
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M ) |
MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 428
|
Line 532
|
* |
* |
* Path 4t(N much larger than M, JOBU='N', JOBVT='S') |
* Path 4t(N much larger than M, JOBU='N', JOBVT='S') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_M ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = M*M + WRKBL |
MAXWRK = M*M + WRKBL |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 442
|
Line 543
|
* |
* |
* Path 5t(N much larger than M, JOBU='O', JOBVT='S') |
* Path 5t(N much larger than M, JOBU='O', JOBVT='S') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_M ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_Q ) |
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+M* |
|
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = 2*M*M + WRKBL |
MAXWRK = 2*M*M + WRKBL |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 459
|
Line 556
|
* Path 6t(N much larger than M, JOBU='S' or 'A', |
* Path 6t(N much larger than M, JOBU='S' or 'A', |
* JOBVT='S') |
* JOBVT='S') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_M ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_Q ) |
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+M* |
|
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = M*M + WRKBL |
MAXWRK = M*M + WRKBL |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 475
|
Line 568
|
* |
* |
* Path 7t(N much larger than M, JOBU='N', JOBVT='A') |
* Path 7t(N much larger than M, JOBU='N', JOBVT='A') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_N ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = M*M + WRKBL |
MAXWRK = M*M + WRKBL |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 489
|
Line 579
|
* |
* |
* Path 8t(N much larger than M, JOBU='O', JOBVT='A') |
* Path 8t(N much larger than M, JOBU='O', JOBVT='A') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_N ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_Q ) |
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+M* |
|
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = 2*M*M + WRKBL |
MAXWRK = 2*M*M + WRKBL |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 506
|
Line 592
|
* Path 9t(N much larger than M, JOBU='S' or 'A', |
* Path 9t(N much larger than M, JOBU='S' or 'A', |
* JOBVT='A') |
* JOBVT='A') |
* |
* |
WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) |
WRKBL = M + LWORK_DGELQF |
WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N, |
WRKBL = MAX( WRKBL, M+LWORK_DORGLQ_N ) |
$ N, M, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DGEBRD ) |
WRKBL = MAX( WRKBL, 3*M+2*M* |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) |
WRKBL = MAX( WRKBL, 3*M+LWORK_DORGBR_Q ) |
WRKBL = MAX( WRKBL, 3*M+( M-1 )* |
|
$ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, 3*M+M* |
|
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
|
WRKBL = MAX( WRKBL, BDSPAC ) |
WRKBL = MAX( WRKBL, BDSPAC ) |
MAXWRK = M*M + WRKBL |
MAXWRK = M*M + WRKBL |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
Line 523
|
Line 605
|
* |
* |
* Path 10t(N greater than M, but not much larger) |
* Path 10t(N greater than M, but not much larger) |
* |
* |
MAXWRK = 3*M + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N, |
CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1), |
$ -1, -1 ) |
$ DUM(1), DUM(1), -1, IERR ) |
IF( WNTVS .OR. WNTVO ) |
LWORK_DGEBRD=DUM(1) |
$ MAXWRK = MAX( MAXWRK, 3*M+M* |
MAXWRK = 3*M + LWORK_DGEBRD |
$ ILAENV( 1, 'DORGBR', 'P', M, N, M, -1 ) ) |
IF( WNTVS .OR. WNTVO ) THEN |
IF( WNTVA ) |
* Compute space needed for DORGBR P |
$ MAXWRK = MAX( MAXWRK, 3*M+N* |
CALL DORGBR( 'P', M, N, M, A, N, DUM(1), |
$ ILAENV( 1, 'DORGBR', 'P', N, N, M, -1 ) ) |
$ DUM(1), -1, IERR ) |
IF( .NOT.WNTUN ) |
LWORK_DORGBR_P=DUM(1) |
$ MAXWRK = MAX( MAXWRK, 3*M+( M-1 )* |
MAXWRK = MAX( MAXWRK, 3*M+LWORK_DORGBR_P ) |
$ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) ) |
END IF |
|
IF( WNTVA ) THEN |
|
CALL DORGBR( 'P', N, N, M, A, N, DUM(1), |
|
$ DUM(1), -1, IERR ) |
|
LWORK_DORGBR_P=DUM(1) |
|
MAXWRK = MAX( MAXWRK, 3*M+LWORK_DORGBR_P ) |
|
END IF |
|
IF( .NOT.WNTUN ) THEN |
|
MAXWRK = MAX( MAXWRK, 3*M+LWORK_DORGBR_Q ) |
|
END IF |
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MAXWRK = MAX( MAXWRK, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
MINWRK = MAX( 3*M+N, BDSPAC ) |
END IF |
END IF |