--- rpl/lapack/lapack/dgesvd.f 2010/01/26 15:22:45 1.1
+++ rpl/lapack/lapack/dgesvd.f 2017/06/17 10:53:49 1.17
@@ -1,10 +1,220 @@
- SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
- $ WORK, LWORK, INFO )
+*> \brief DGESVD computes the singular value decomposition (SVD) for GE matrices
*
-* -- LAPACK driver routine (version 3.2) --
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGESVD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \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 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* April 2012
*
* .. Scalar Arguments ..
CHARACTER JOBU, JOBVT
@@ -15,122 +225,6 @@
$ 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 ..
@@ -144,6 +238,9 @@
$ ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
$ MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
$ 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
* ..
* .. Local Arrays ..
@@ -215,163 +312,160 @@
*
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 )
BDSPAC = 5*N
+* Compute space needed for DGEQRF
+ CALL DGEQRF( M, N, A, LDA, DUM(1), DUM(1), -1, IERR )
+ LWORK_DGEQRF = INT( DUM(1) )
+* Compute space needed for DORGQR
+ CALL DORGQR( M, N, N, A, LDA, DUM(1), DUM(1), -1, IERR )
+ LWORK_DORGQR_N = INT( DUM(1) )
+ CALL DORGQR( M, M, N, A, LDA, DUM(1), DUM(1), -1, IERR )
+ LWORK_DORGQR_M = INT( 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 = INT( 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 = INT( 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 = INT( DUM(1) )
+*
IF( M.GE.MNTHR ) THEN
IF( WNTUN ) THEN
*
* Path 1 (M much larger than N, JOBU='N')
*
- MAXWRK = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1,
- $ -1 )
- MAXWRK = MAX( MAXWRK, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
+ MAXWRK = N + LWORK_DGEQRF
+ MAXWRK = MAX( MAXWRK, 3*N + LWORK_DGEBRD )
IF( WNTVO .OR. WNTVAS )
- $ MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
- $ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
+ $ MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR_P )
MAXWRK = MAX( MAXWRK, BDSPAC )
MINWRK = MAX( 4*N, BDSPAC )
ELSE IF( WNTUO .AND. WNTVN ) THEN
*
* Path 2 (M much larger than N, JOBU='O', JOBVT='N')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
- $ N, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+N*
- $ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
+ WRKBL = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
- MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MAXWRK = MAX( N*N + WRKBL, N*N + M*N + N )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUO .AND. WNTVAS ) THEN
*
* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or
* 'A')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
- $ N, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- 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 = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
- MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MAXWRK = MAX( N*N + WRKBL, N*N + M*N + N )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUS .AND. WNTVN ) THEN
*
* Path 4 (M much larger than N, JOBU='S', JOBVT='N')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
- $ N, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+N*
- $ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
+ WRKBL = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = N*N + WRKBL
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUS .AND. WNTVO ) THEN
*
* Path 5 (M much larger than N, JOBU='S', JOBVT='O')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
- $ N, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- 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 = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = 2*N*N + WRKBL
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUS .AND. WNTVAS ) THEN
*
* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or
* 'A')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
- $ N, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- 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 = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = N*N + WRKBL
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUA .AND. WNTVN ) THEN
*
* Path 7 (M much larger than N, JOBU='A', JOBVT='N')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M,
- $ M, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+N*
- $ ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
+ WRKBL = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_M )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = N*N + WRKBL
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUA .AND. WNTVO ) THEN
*
* Path 8 (M much larger than N, JOBU='A', JOBVT='O')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M,
- $ M, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- 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 = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_M )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = 2*N*N + WRKBL
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
ELSE IF( WNTUA .AND. WNTVAS ) THEN
*
* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or
* 'A')
*
- WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M,
- $ M, N, -1 ) )
- WRKBL = MAX( WRKBL, 3*N+2*N*
- $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- 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 = N + LWORK_DGEQRF
+ WRKBL = MAX( WRKBL, N + LWORK_DORGQR_M )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q )
+ WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = N*N + WRKBL
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
END IF
ELSE
*
* Path 10 (M at least N, but not much larger)
*
- MAXWRK = 3*N + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N,
- $ -1, -1 )
- IF( WNTUS .OR. WNTUO )
- $ MAXWRK = MAX( MAXWRK, 3*N+N*
- $ ILAENV( 1, 'DORGBR', 'Q', M, N, N, -1 ) )
- IF( WNTUA )
- $ MAXWRK = MAX( MAXWRK, 3*N+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, N, -1 ) )
- IF( .NOT.WNTVN )
- $ MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
- $ ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
+ CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1),
+ $ DUM(1), DUM(1), -1, IERR )
+ LWORK_DGEBRD = INT( DUM(1) )
+ MAXWRK = 3*N + LWORK_DGEBRD
+ IF( WNTUS .OR. WNTUO ) THEN
+ CALL DORGBR( 'Q', M, N, N, A, LDA, DUM(1),
+ $ DUM(1), -1, IERR )
+ LWORK_DORGBR_Q = INT( DUM(1) )
+ MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR_Q )
+ END IF
+ IF( WNTUA ) THEN
+ CALL DORGBR( 'Q', M, M, N, A, LDA, DUM(1),
+ $ DUM(1), -1, IERR )
+ LWORK_DORGBR_Q = INT( 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 )
- MINWRK = MAX( 3*N+M, BDSPAC )
+ MINWRK = MAX( 3*N + M, BDSPAC )
END IF
ELSE IF( MINMN.GT.0 ) THEN
*
@@ -379,163 +473,160 @@
*
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 )
BDSPAC = 5*M
+* Compute space needed for DGELQF
+ CALL DGELQF( M, N, A, LDA, DUM(1), DUM(1), -1, IERR )
+ LWORK_DGELQF = INT( DUM(1) )
+* Compute space needed for DORGLQ
+ CALL DORGLQ( N, N, M, DUM(1), N, DUM(1), DUM(1), -1, IERR )
+ LWORK_DORGLQ_N = INT( DUM(1) )
+ CALL DORGLQ( M, N, M, A, LDA, DUM(1), DUM(1), -1, IERR )
+ LWORK_DORGLQ_M = INT( 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 = INT( 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 = INT( 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 = INT( DUM(1) )
IF( N.GE.MNTHR ) THEN
IF( WNTVN ) THEN
*
* Path 1t(N much larger than M, JOBVT='N')
*
- MAXWRK = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1,
- $ -1 )
- MAXWRK = MAX( MAXWRK, 3*M+2*M*
- $ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
+ MAXWRK = M + LWORK_DGELQF
+ MAXWRK = MAX( MAXWRK, 3*M + LWORK_DGEBRD )
IF( WNTUO .OR. WNTUAS )
- $ MAXWRK = MAX( MAXWRK, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ $ MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR_Q )
MAXWRK = MAX( MAXWRK, BDSPAC )
MINWRK = MAX( 4*M, BDSPAC )
ELSE IF( WNTVO .AND. WNTUN ) THEN
*
* Path 2t(N much larger than M, JOBU='N', JOBVT='O')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+( M-1 )*
- $ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
- MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M )
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MAXWRK = MAX( M*M + WRKBL, M*M + M*N + M )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVO .AND. WNTUAS ) THEN
*
* Path 3t(N much larger than M, JOBU='S' or 'A',
* JOBVT='O')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ 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, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
- MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M )
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MAXWRK = MAX( M*M + WRKBL, M*M + M*N + M )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVS .AND. WNTUN ) THEN
*
* Path 4t(N much larger than M, JOBU='N', JOBVT='S')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+( M-1 )*
- $ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = M*M + WRKBL
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVS .AND. WNTUO ) THEN
*
* Path 5t(N much larger than M, JOBU='O', JOBVT='S')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ 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, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = 2*M*M + WRKBL
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVS .AND. WNTUAS ) THEN
*
* Path 6t(N much larger than M, JOBU='S' or 'A',
* JOBVT='S')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ 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, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = M*M + WRKBL
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVA .AND. WNTUN ) THEN
*
* Path 7t(N much larger than M, JOBU='N', JOBVT='A')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+( M-1 )*
- $ ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_N )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = M*M + WRKBL
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVA .AND. WNTUO ) THEN
*
* Path 8t(N much larger than M, JOBU='O', JOBVT='A')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ 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, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_N )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = 2*M*M + WRKBL
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
ELSE IF( WNTVA .AND. WNTUAS ) THEN
*
* Path 9t(N much larger than M, JOBU='S' or 'A',
* JOBVT='A')
*
- WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N,
- $ N, M, -1 ) )
- WRKBL = MAX( WRKBL, 3*M+2*M*
- $ 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, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ WRKBL = M + LWORK_DGELQF
+ WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_N )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P )
+ WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q )
WRKBL = MAX( WRKBL, BDSPAC )
MAXWRK = M*M + WRKBL
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
END IF
ELSE
*
* Path 10t(N greater than M, but not much larger)
*
- MAXWRK = 3*M + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N,
- $ -1, -1 )
- IF( WNTVS .OR. WNTVO )
- $ MAXWRK = MAX( MAXWRK, 3*M+M*
- $ ILAENV( 1, 'DORGBR', 'P', M, N, M, -1 ) )
- IF( WNTVA )
- $ MAXWRK = MAX( MAXWRK, 3*M+N*
- $ ILAENV( 1, 'DORGBR', 'P', N, N, M, -1 ) )
- IF( .NOT.WNTUN )
- $ MAXWRK = MAX( MAXWRK, 3*M+( M-1 )*
- $ ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
+ CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1),
+ $ DUM(1), DUM(1), -1, IERR )
+ LWORK_DGEBRD = INT( DUM(1) )
+ MAXWRK = 3*M + LWORK_DGEBRD
+ IF( WNTVS .OR. WNTVO ) THEN
+* Compute space needed for DORGBR P
+ CALL DORGBR( 'P', M, N, M, A, N, DUM(1),
+ $ DUM(1), -1, IERR )
+ LWORK_DORGBR_P = INT( DUM(1) )
+ MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR_P )
+ END IF
+ IF( WNTVA ) THEN
+ CALL DORGBR( 'P', N, N, M, A, N, DUM(1),
+ $ DUM(1), -1, IERR )
+ LWORK_DORGBR_P = INT( 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 )
- MINWRK = MAX( 3*M+N, BDSPAC )
+ MINWRK = MAX( 3*M + N, BDSPAC )
END IF
END IF
MAXWRK = MAX( MAXWRK, MINWRK )
@@ -594,21 +685,24 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Zero out below R
*
- CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA )
+ IF( N .GT. 1 ) THEN
+ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
+ $ LDA )
+ END IF
IE = 1
ITAUQ = IE + N
ITAUP = ITAUQ + N
IWORK = ITAUP + N
*
* Bidiagonalize R in A
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
$ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
@@ -617,7 +711,7 @@
IF( WNTVO .OR. WNTVAS ) THEN
*
* If right singular vectors desired, generate P'.
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -648,13 +742,13 @@
* Sufficient workspace for a fast algorithm
*
IR = 1
- IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+LDA*N ) THEN
+ IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + LDA*N ) THEN
*
* WORK(IU) is LDA by N, WORK(IR) is LDA by N
*
LDWRKU = LDA
LDWRKR = LDA
- ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+N*N ) THEN
+ ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + N*N ) THEN
*
* WORK(IU) is LDA by N, WORK(IR) is N by N
*
@@ -671,7 +765,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -683,7 +777,7 @@
$ LDWRKR )
*
* Generate Q in A
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -693,14 +787,14 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate left vectors bidiagonalizing R
-* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
$ WORK( ITAUQ ), WORK( IWORK ),
@@ -709,7 +803,7 @@
*
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IR)
-* (Workspace: need N*N+BDSPAC)
+* (Workspace: need N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM, 1,
$ WORK( IR ), LDWRKR, DUM, 1,
@@ -718,7 +812,7 @@
*
* Multiply Q in A by left singular vectors of R in
* WORK(IR), storing result in WORK(IU) and copying to A
-* (Workspace: need N*N+2*N, prefer N*N+M*N+N)
+* (Workspace: need N*N + 2*N, prefer N*N + M*N + N)
*
DO 10 I = 1, M, LDWRKU
CHUNK = MIN( M-I+1, LDWRKU )
@@ -739,14 +833,14 @@
IWORK = ITAUP + N
*
* Bidiagonalize A
-* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB)
+* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB)
*
CALL DGEBRD( M, N, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate left vectors bidiagonalizing A
-* (Workspace: need 4*N, prefer 3*N+N*NB)
+* (Workspace: need 4*N, prefer 3*N + N*NB)
*
CALL DORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -772,13 +866,13 @@
* Sufficient workspace for a fast algorithm
*
IR = 1
- IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+LDA*N ) THEN
+ IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + LDA*N ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is LDA by N
*
LDWRKU = LDA
LDWRKR = LDA
- ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+N*N ) THEN
+ ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + N*N ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is N by N
*
@@ -795,7 +889,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -808,7 +902,7 @@
$ VT( 2, 1 ), LDVT )
*
* Generate Q in A
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -818,7 +912,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in VT, copying result to WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -826,14 +920,14 @@
CALL DLACPY( 'L', N, N, VT, LDVT, WORK( IR ), LDWRKR )
*
* Generate left vectors bidiagonalizing R in WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
$ WORK( ITAUQ ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right vectors bidiagonalizing R in VT
-* (Workspace: need N*N+4*N-1, prefer N*N+3*N+(N-1)*NB)
+* (Workspace: need N*N + 4*N-1, prefer N*N + 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -842,7 +936,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IR) and computing right
* singular vectors of R in VT
-* (Workspace: need N*N+BDSPAC)
+* (Workspace: need N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT, LDVT,
$ WORK( IR ), LDWRKR, DUM, 1,
@@ -851,7 +945,7 @@
*
* Multiply Q in A by left singular vectors of R in
* WORK(IR), storing result in WORK(IU) and copying to A
-* (Workspace: need N*N+2*N, prefer N*N+M*N+N)
+* (Workspace: need N*N + 2*N, prefer N*N + M*N + N)
*
DO 20 I = 1, M, LDWRKU
CHUNK = MIN( M-I+1, LDWRKU )
@@ -870,7 +964,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -883,7 +977,7 @@
$ VT( 2, 1 ), LDVT )
*
* Generate Q in A
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -893,21 +987,21 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in VT
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Multiply Q in A by left vectors bidiagonalizing R
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT,
$ WORK( ITAUQ ), A, LDA, WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right vectors bidiagonalizing R in VT
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -951,7 +1045,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -964,7 +1058,7 @@
$ WORK( IR+1 ), LDWRKR )
*
* Generate Q in A
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -974,7 +1068,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -982,7 +1076,7 @@
$ LWORK-IWORK+1, IERR )
*
* Generate left vectors bidiagonalizing R in WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
$ WORK( ITAUQ ), WORK( IWORK ),
@@ -991,7 +1085,7 @@
*
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IR)
-* (Workspace: need N*N+BDSPAC)
+* (Workspace: need N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM,
$ 1, WORK( IR ), LDWRKR, DUM, 1,
@@ -1012,14 +1106,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1030,18 +1124,20 @@
*
* Zero out below R in A
*
- CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
- $ LDA )
+ IF( N .GT. 1 ) THEN
+ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
+ $ A( 2, 1 ), LDA )
+ END IF
*
* Bidiagonalize R in A
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Multiply Q in U by left vectors bidiagonalizing R
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
$ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
@@ -1076,7 +1172,7 @@
LDWRKU = LDA
IR = IU + LDWRKU*N
LDWRKR = LDA
- ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN
+ ELSE IF( LWORK.GE.WRKBL+( LDA + N )*N ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is N by N
*
@@ -1095,7 +1191,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
+* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1108,7 +1204,7 @@
$ WORK( IU+1 ), LDWRKU )
*
* Generate Q in A
-* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
+* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB)
*
CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1119,7 +1215,7 @@
*
* Bidiagonalize R in WORK(IU), copying result to
* WORK(IR)
-* (Workspace: need 2*N*N+4*N,
+* (Workspace: need 2*N*N + 4*N,
* prefer 2*N*N+3*N+2*N*NB)
*
CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
@@ -1130,14 +1226,14 @@
$ WORK( IR ), LDWRKR )
*
* Generate left bidiagonalizing vectors in WORK(IU)
-* (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB)
+* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
$ WORK( ITAUQ ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in WORK(IR)
-* (Workspace: need 2*N*N+4*N-1,
+* (Workspace: need 2*N*N + 4*N-1,
* prefer 2*N*N+3*N+(N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, WORK( IR ), LDWRKR,
@@ -1148,7 +1244,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IU) and computing
* right singular vectors of R in WORK(IR)
-* (Workspace: need 2*N*N+BDSPAC)
+* (Workspace: need 2*N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ),
$ WORK( IR ), LDWRKR, WORK( IU ),
@@ -1175,14 +1271,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1193,25 +1289,27 @@
*
* Zero out below R in A
*
- CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
- $ LDA )
+ IF( N .GT. 1 ) THEN
+ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
+ $ A( 2, 1 ), LDA )
+ END IF
*
* Bidiagonalize R in A
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Multiply Q in U by left vectors bidiagonalizing R
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
$ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right vectors bidiagonalizing R in A
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1255,7 +1353,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1268,7 +1366,7 @@
$ WORK( IU+1 ), LDWRKU )
*
* Generate Q in A
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1278,7 +1376,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in WORK(IU), copying result to VT
-* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -1288,14 +1386,14 @@
$ LDVT )
*
* Generate left bidiagonalizing vectors in WORK(IU)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
$ WORK( ITAUQ ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in VT
-* (Workspace: need N*N+4*N-1,
+* (Workspace: need N*N + 4*N-1,
* prefer N*N+3*N+(N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
@@ -1305,7 +1403,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IU) and computing
* right singular vectors of R in VT
-* (Workspace: need N*N+BDSPAC)
+* (Workspace: need N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT,
$ LDVT, WORK( IU ), LDWRKU, DUM, 1,
@@ -1326,14 +1424,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1350,7 +1448,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in VT
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -1358,14 +1456,14 @@
*
* Multiply Q in U by left bidiagonalizing vectors
* in VT
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT,
$ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in VT
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1412,7 +1510,7 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1426,7 +1524,7 @@
$ WORK( IR+1 ), LDWRKR )
*
* Generate Q in U
-* (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
+* (Workspace: need N*N + N + M, prefer N*N + N + M*NB)
*
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1436,7 +1534,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -1444,7 +1542,7 @@
$ LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in WORK(IR)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
$ WORK( ITAUQ ), WORK( IWORK ),
@@ -1453,7 +1551,7 @@
*
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IR)
-* (Workspace: need N*N+BDSPAC)
+* (Workspace: need N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM,
$ 1, WORK( IR ), LDWRKR, DUM, 1,
@@ -1478,14 +1576,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need N+M, prefer N+M*NB)
+* (Workspace: need N + M, prefer N + M*NB)
*
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1496,11 +1594,13 @@
*
* Zero out below R in A
*
- CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
- $ LDA )
+ IF( N .GT. 1 ) THEN
+ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
+ $ A( 2, 1 ), LDA )
+ END IF
*
* Bidiagonalize R in A
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -1508,7 +1608,7 @@
*
* Multiply Q in U by left bidiagonalizing vectors
* in A
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
$ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
@@ -1543,7 +1643,7 @@
LDWRKU = LDA
IR = IU + LDWRKU*N
LDWRKR = LDA
- ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN
+ ELSE IF( LWORK.GE.WRKBL+( LDA + N )*N ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is N by N
*
@@ -1562,14 +1662,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
+* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB)
+* (Workspace: need 2*N*N + N + M, prefer 2*N*N + N + M*NB)
*
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1587,7 +1687,7 @@
*
* Bidiagonalize R in WORK(IU), copying result to
* WORK(IR)
-* (Workspace: need 2*N*N+4*N,
+* (Workspace: need 2*N*N + 4*N,
* prefer 2*N*N+3*N+2*N*NB)
*
CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
@@ -1598,14 +1698,14 @@
$ WORK( IR ), LDWRKR )
*
* Generate left bidiagonalizing vectors in WORK(IU)
-* (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB)
+* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
$ WORK( ITAUQ ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in WORK(IR)
-* (Workspace: need 2*N*N+4*N-1,
+* (Workspace: need 2*N*N + 4*N-1,
* prefer 2*N*N+3*N+(N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, WORK( IR ), LDWRKR,
@@ -1616,7 +1716,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IU) and computing
* right singular vectors of R in WORK(IR)
-* (Workspace: need 2*N*N+BDSPAC)
+* (Workspace: need 2*N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ),
$ WORK( IR ), LDWRKR, WORK( IU ),
@@ -1646,14 +1746,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need N+M, prefer N+M*NB)
+* (Workspace: need N + M, prefer N + M*NB)
*
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1664,11 +1764,13 @@
*
* Zero out below R in A
*
- CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
- $ LDA )
+ IF( N .GT. 1 ) THEN
+ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
+ $ A( 2, 1 ), LDA )
+ END IF
*
* Bidiagonalize R in A
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -1676,14 +1778,14 @@
*
* Multiply Q in U by left bidiagonalizing vectors
* in A
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
$ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in A
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1727,14 +1829,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
+* (Workspace: need N*N + N + M, prefer N*N + N + M*NB)
*
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1751,7 +1853,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in WORK(IU), copying result to VT
-* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -1761,14 +1863,14 @@
$ LDVT )
*
* Generate left bidiagonalizing vectors in WORK(IU)
-* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
+* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB)
*
CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
$ WORK( ITAUQ ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in VT
-* (Workspace: need N*N+4*N-1,
+* (Workspace: need N*N + 4*N-1,
* prefer N*N+3*N+(N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
@@ -1778,7 +1880,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of R in WORK(IU) and computing
* right singular vectors of R in VT
-* (Workspace: need N*N+BDSPAC)
+* (Workspace: need N*N + BDSPAC)
*
CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT,
$ LDVT, WORK( IU ), LDWRKU, DUM, 1,
@@ -1803,14 +1905,14 @@
IWORK = ITAU + N
*
* Compute A=Q*R, copying result to U
-* (Workspace: need 2*N, prefer N+N*NB)
+* (Workspace: need 2*N, prefer N + N*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need N+M, prefer N+M*NB)
+* (Workspace: need N + M, prefer N + M*NB)
*
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1827,7 +1929,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize R in VT
-* (Workspace: need 4*N, prefer 3*N+2*N*NB)
+* (Workspace: need 4*N, prefer 3*N + 2*N*NB)
*
CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -1835,14 +1937,14 @@
*
* Multiply Q in U by left bidiagonalizing vectors
* in VT
-* (Workspace: need 3*N+M, prefer 3*N+M*NB)
+* (Workspace: need 3*N + M, prefer 3*N + M*NB)
*
CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT,
$ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in VT
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1876,7 +1978,7 @@
IWORK = ITAUP + N
*
* Bidiagonalize A
-* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB)
+* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB)
*
CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
$ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
@@ -1885,7 +1987,7 @@
*
* If left singular vectors desired in U, copy result to U
* and generate left bidiagonalizing vectors in U
-* (Workspace: need 3*N+NCU, prefer 3*N+NCU*NB)
+* (Workspace: need 3*N + NCU, prefer 3*N + NCU*NB)
*
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
IF( WNTUS )
@@ -1899,7 +2001,7 @@
*
* If right singular vectors desired in VT, copy result to
* VT and generate right bidiagonalizing vectors in VT
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT )
CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
@@ -1909,7 +2011,7 @@
*
* If left singular vectors desired in A, generate left
* bidiagonalizing vectors in A
-* (Workspace: need 4*N, prefer 3*N+N*NB)
+* (Workspace: need 4*N, prefer 3*N + N*NB)
*
CALL DORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1918,7 +2020,7 @@
*
* If right singular vectors desired in A, generate right
* bidiagonalizing vectors in A
-* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
+* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB)
*
CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -1980,7 +2082,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
@@ -1994,7 +2096,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in A
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
$ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
@@ -2002,7 +2104,7 @@
IF( WNTUO .OR. WNTUAS ) THEN
*
* If left singular vectors desired, generate Q
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2035,14 +2137,14 @@
* Sufficient workspace for a fast algorithm
*
IR = 1
- IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+LDA*M ) THEN
+ IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + LDA*M ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is LDA by M
*
LDWRKU = LDA
CHUNK = N
LDWRKR = LDA
- ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+M*M ) THEN
+ ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + M*M ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is M by M
*
@@ -2061,7 +2163,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2073,7 +2175,7 @@
$ WORK( IR+LDWRKR ), LDWRKR )
*
* Generate Q in A
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2083,14 +2185,14 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in WORK(IR)
-* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate right vectors bidiagonalizing L
-* (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
+* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
$ WORK( ITAUP ), WORK( IWORK ),
@@ -2099,7 +2201,7 @@
*
* Perform bidiagonal QR iteration, computing right
* singular vectors of L in WORK(IR)
-* (Workspace: need M*M+BDSPAC)
+* (Workspace: need M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ),
$ WORK( IR ), LDWRKR, DUM, 1, DUM, 1,
@@ -2108,7 +2210,7 @@
*
* Multiply right singular vectors of L in WORK(IR) by Q
* in A, storing result in WORK(IU) and copying to A
-* (Workspace: need M*M+2*M, prefer M*M+M*N+M)
+* (Workspace: need M*M + 2*M, prefer M*M + M*N + M)
*
DO 30 I = 1, N, CHUNK
BLK = MIN( N-I+1, CHUNK )
@@ -2129,14 +2231,14 @@
IWORK = ITAUP + M
*
* Bidiagonalize A
-* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB)
+* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB)
*
CALL DGEBRD( M, N, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate right vectors bidiagonalizing A
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2162,14 +2264,14 @@
* Sufficient workspace for a fast algorithm
*
IR = 1
- IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+LDA*M ) THEN
+ IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + LDA*M ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is LDA by M
*
LDWRKU = LDA
CHUNK = N
LDWRKR = LDA
- ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+M*M ) THEN
+ ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + M*M ) THEN
*
* WORK(IU) is LDA by N and WORK(IR) is M by M
*
@@ -2188,7 +2290,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2200,7 +2302,7 @@
$ LDU )
*
* Generate Q in A
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2210,7 +2312,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in U, copying result to WORK(IR)
-* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -2218,14 +2320,14 @@
CALL DLACPY( 'U', M, M, U, LDU, WORK( IR ), LDWRKR )
*
* Generate right vectors bidiagonalizing L in WORK(IR)
-* (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
+* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
$ WORK( ITAUP ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate left vectors bidiagonalizing L in U
-* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2234,7 +2336,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of L in U, and computing right
* singular vectors of L in WORK(IR)
-* (Workspace: need M*M+BDSPAC)
+* (Workspace: need M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
$ WORK( IR ), LDWRKR, U, LDU, DUM, 1,
@@ -2243,7 +2345,7 @@
*
* Multiply right singular vectors of L in WORK(IR) by Q
* in A, storing result in WORK(IU) and copying to A
-* (Workspace: need M*M+2*M, prefer M*M+M*N+M))
+* (Workspace: need M*M + 2*M, prefer M*M + M*N + M))
*
DO 40 I = 1, N, CHUNK
BLK = MIN( N-I+1, CHUNK )
@@ -2262,7 +2364,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2274,7 +2376,7 @@
$ LDU )
*
* Generate Q in A
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2284,21 +2386,21 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in U
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Multiply right vectors bidiagonalizing L by Q in A
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU,
$ WORK( ITAUP ), A, LDA, WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate left vectors bidiagonalizing L in U
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2342,7 +2444,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2355,7 +2457,7 @@
$ WORK( IR+LDWRKR ), LDWRKR )
*
* Generate Q in A
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2365,7 +2467,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in WORK(IR)
-* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -2374,7 +2476,7 @@
*
* Generate right vectors bidiagonalizing L in
* WORK(IR)
-* (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
$ WORK( ITAUP ), WORK( IWORK ),
@@ -2383,7 +2485,7 @@
*
* Perform bidiagonal QR iteration, computing right
* singular vectors of L in WORK(IR)
-* (Workspace: need M*M+BDSPAC)
+* (Workspace: need M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ),
$ WORK( IR ), LDWRKR, DUM, 1, DUM, 1,
@@ -2404,7 +2506,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2414,7 +2516,7 @@
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2429,14 +2531,14 @@
$ LDA )
*
* Bidiagonalize L in A
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Multiply right vectors bidiagonalizing L by Q in VT
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
$ WORK( ITAUP ), VT, LDVT,
@@ -2471,7 +2573,7 @@
LDWRKU = LDA
IR = IU + LDWRKU*M
LDWRKR = LDA
- ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN
+ ELSE IF( LWORK.GE.WRKBL+( LDA + M )*M ) THEN
*
* WORK(IU) is LDA by M and WORK(IR) is M by M
*
@@ -2490,7 +2592,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
+* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2503,7 +2605,7 @@
$ WORK( IU+LDWRKU ), LDWRKU )
*
* Generate Q in A
-* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
+* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB)
*
CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2514,7 +2616,7 @@
*
* Bidiagonalize L in WORK(IU), copying result to
* WORK(IR)
-* (Workspace: need 2*M*M+4*M,
+* (Workspace: need 2*M*M + 4*M,
* prefer 2*M*M+3*M+2*M*NB)
*
CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
@@ -2525,7 +2627,7 @@
$ WORK( IR ), LDWRKR )
*
* Generate right bidiagonalizing vectors in WORK(IU)
-* (Workspace: need 2*M*M+4*M-1,
+* (Workspace: need 2*M*M + 4*M-1,
* prefer 2*M*M+3*M+(M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
@@ -2533,7 +2635,7 @@
$ LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in WORK(IR)
-* (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB)
+* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, WORK( IR ), LDWRKR,
$ WORK( ITAUQ ), WORK( IWORK ),
@@ -2543,7 +2645,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of L in WORK(IR) and computing
* right singular vectors of L in WORK(IU)
-* (Workspace: need 2*M*M+BDSPAC)
+* (Workspace: need 2*M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
$ WORK( IU ), LDWRKU, WORK( IR ),
@@ -2570,14 +2672,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2592,21 +2694,21 @@
$ LDA )
*
* Bidiagonalize L in A
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Multiply right vectors bidiagonalizing L by Q in VT
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
$ WORK( ITAUP ), VT, LDVT,
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors of L in A
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2650,7 +2752,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2663,7 +2765,7 @@
$ WORK( IU+LDWRKU ), LDWRKU )
*
* Generate Q in A
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2673,7 +2775,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in WORK(IU), copying result to U
-* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -2683,7 +2785,7 @@
$ LDU )
*
* Generate right bidiagonalizing vectors in WORK(IU)
-* (Workspace: need M*M+4*M-1,
+* (Workspace: need M*M + 4*M-1,
* prefer M*M+3*M+(M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
@@ -2691,7 +2793,7 @@
$ LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in U
-* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2700,7 +2802,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of L in U and computing right
* singular vectors of L in WORK(IU)
-* (Workspace: need M*M+BDSPAC)
+* (Workspace: need M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
$ WORK( IU ), LDWRKU, U, LDU, DUM, 1,
@@ -2721,14 +2823,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2744,7 +2846,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in U
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -2752,14 +2854,14 @@
*
* Multiply right bidiagonalizing vectors in U by Q
* in VT
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU,
$ WORK( ITAUP ), VT, LDVT,
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in U
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2786,7 +2888,7 @@
* N right singular vectors to be computed in VT and
* no left singular vectors to be computed
*
- IF( LWORK.GE.M*M+MAX( N+M, 4*M, BDSPAC ) ) THEN
+ IF( LWORK.GE.M*M+MAX( N + M, 4*M, BDSPAC ) ) THEN
*
* Sufficient workspace for a fast algorithm
*
@@ -2806,7 +2908,7 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2820,7 +2922,7 @@
$ WORK( IR+LDWRKR ), LDWRKR )
*
* Generate Q in VT
-* (Workspace: need M*M+M+N, prefer M*M+M+N*NB)
+* (Workspace: need M*M + M + N, prefer M*M + M + N*NB)
*
CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2830,7 +2932,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in WORK(IR)
-* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -2838,7 +2940,7 @@
$ LWORK-IWORK+1, IERR )
*
* Generate right bidiagonalizing vectors in WORK(IR)
-* (Workspace: need M*M+4*M-1,
+* (Workspace: need M*M + 4*M-1,
* prefer M*M+3*M+(M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
@@ -2848,7 +2950,7 @@
*
* Perform bidiagonal QR iteration, computing right
* singular vectors of L in WORK(IR)
-* (Workspace: need M*M+BDSPAC)
+* (Workspace: need M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ),
$ WORK( IR ), LDWRKR, DUM, 1, DUM, 1,
@@ -2873,14 +2975,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need M+N, prefer M+N*NB)
+* (Workspace: need M + N, prefer M + N*NB)
*
CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2895,7 +2997,7 @@
$ LDA )
*
* Bidiagonalize L in A
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -2903,7 +3005,7 @@
*
* Multiply right bidiagonalizing vectors in A by Q
* in VT
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
$ WORK( ITAUP ), VT, LDVT,
@@ -2926,7 +3028,7 @@
* N right singular vectors to be computed in VT and
* M left singular vectors to be overwritten on A
*
- IF( LWORK.GE.2*M*M+MAX( N+M, 4*M, BDSPAC ) ) THEN
+ IF( LWORK.GE.2*M*M+MAX( N + M, 4*M, BDSPAC ) ) THEN
*
* Sufficient workspace for a fast algorithm
*
@@ -2938,7 +3040,7 @@
LDWRKU = LDA
IR = IU + LDWRKU*M
LDWRKR = LDA
- ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN
+ ELSE IF( LWORK.GE.WRKBL+( LDA + M )*M ) THEN
*
* WORK(IU) is LDA by M and WORK(IR) is M by M
*
@@ -2957,14 +3059,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
+* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB)
+* (Workspace: need 2*M*M + M + N, prefer 2*M*M + M + N*NB)
*
CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -2982,7 +3084,7 @@
*
* Bidiagonalize L in WORK(IU), copying result to
* WORK(IR)
-* (Workspace: need 2*M*M+4*M,
+* (Workspace: need 2*M*M + 4*M,
* prefer 2*M*M+3*M+2*M*NB)
*
CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
@@ -2993,7 +3095,7 @@
$ WORK( IR ), LDWRKR )
*
* Generate right bidiagonalizing vectors in WORK(IU)
-* (Workspace: need 2*M*M+4*M-1,
+* (Workspace: need 2*M*M + 4*M-1,
* prefer 2*M*M+3*M+(M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
@@ -3001,7 +3103,7 @@
$ LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in WORK(IR)
-* (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB)
+* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, WORK( IR ), LDWRKR,
$ WORK( ITAUQ ), WORK( IWORK ),
@@ -3011,7 +3113,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of L in WORK(IR) and computing
* right singular vectors of L in WORK(IU)
-* (Workspace: need 2*M*M+BDSPAC)
+* (Workspace: need 2*M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
$ WORK( IU ), LDWRKU, WORK( IR ),
@@ -3041,14 +3143,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need M+N, prefer M+N*NB)
+* (Workspace: need M + N, prefer M + N*NB)
*
CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3063,7 +3165,7 @@
$ LDA )
*
* Bidiagonalize L in A
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -3071,14 +3173,14 @@
*
* Multiply right bidiagonalizing vectors in A by Q
* in VT
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
$ WORK( ITAUP ), VT, LDVT,
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in A
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3102,7 +3204,7 @@
* N right singular vectors to be computed in VT and
* M left singular vectors to be computed in U
*
- IF( LWORK.GE.M*M+MAX( N+M, 4*M, BDSPAC ) ) THEN
+ IF( LWORK.GE.M*M+MAX( N + M, 4*M, BDSPAC ) ) THEN
*
* Sufficient workspace for a fast algorithm
*
@@ -3122,14 +3224,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need M*M+M+N, prefer M*M+M+N*NB)
+* (Workspace: need M*M + M + N, prefer M*M + M + N*NB)
*
CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3146,7 +3248,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in WORK(IU), copying result to U
-* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
$ WORK( IE ), WORK( ITAUQ ),
@@ -3156,14 +3258,14 @@
$ LDU )
*
* Generate right bidiagonalizing vectors in WORK(IU)
-* (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB)
*
CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
$ WORK( ITAUP ), WORK( IWORK ),
$ LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in U
-* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB)
+* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3172,7 +3274,7 @@
* Perform bidiagonal QR iteration, computing left
* singular vectors of L in U and computing right
* singular vectors of L in WORK(IU)
-* (Workspace: need M*M+BDSPAC)
+* (Workspace: need M*M + BDSPAC)
*
CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
$ WORK( IU ), LDWRKU, U, LDU, DUM, 1,
@@ -3197,14 +3299,14 @@
IWORK = ITAU + M
*
* Compute A=L*Q, copying result to VT
-* (Workspace: need 2*M, prefer M+M*NB)
+* (Workspace: need 2*M, prefer M + M*NB)
*
CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
*
* Generate Q in VT
-* (Workspace: need M+N, prefer M+N*NB)
+* (Workspace: need M + N, prefer M + N*NB)
*
CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3220,7 +3322,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize L in U
-* (Workspace: need 4*M, prefer 3*M+2*M*NB)
+* (Workspace: need 4*M, prefer 3*M + 2*M*NB)
*
CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ),
@@ -3228,14 +3330,14 @@
*
* Multiply right bidiagonalizing vectors in U by Q
* in VT
-* (Workspace: need 3*M+N, prefer 3*M+N*NB)
+* (Workspace: need 3*M + N, prefer 3*M + N*NB)
*
CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU,
$ WORK( ITAUP ), VT, LDVT,
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
*
* Generate left bidiagonalizing vectors in U
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3269,7 +3371,7 @@
IWORK = ITAUP + M
*
* Bidiagonalize A
-* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB)
+* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB)
*
CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
$ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
@@ -3278,7 +3380,7 @@
*
* If left singular vectors desired in U, copy result to U
* and generate left bidiagonalizing vectors in U
-* (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB)
+* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB)
*
CALL DLACPY( 'L', M, M, A, LDA, U, LDU )
CALL DORGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
@@ -3288,7 +3390,7 @@
*
* If right singular vectors desired in VT, copy result to
* VT and generate right bidiagonalizing vectors in VT
-* (Workspace: need 3*M+NRVT, prefer 3*M+NRVT*NB)
+* (Workspace: need 3*M + NRVT, prefer 3*M + NRVT*NB)
*
CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
IF( WNTVA )
@@ -3302,7 +3404,7 @@
*
* If left singular vectors desired in A, generate left
* bidiagonalizing vectors in A
-* (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB)
+* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB)
*
CALL DORGBR( 'Q', M, M, N, A, LDA, WORK( ITAUQ ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )
@@ -3311,7 +3413,7 @@
*
* If right singular vectors desired in A, generate right
* bidiagonalizing vectors in A
-* (Workspace: need 4*M, prefer 3*M+M*NB)
+* (Workspace: need 4*M, prefer 3*M + M*NB)
*
CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
$ WORK( IWORK ), LWORK-IWORK+1, IERR )