1553 lines
59 KiB
Fortran
1553 lines
59 KiB
Fortran
*> \brief \b SGESDD
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SGESDD + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgesdd.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgesdd.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgesdd.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
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* WORK, LWORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBZ
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* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* REAL A( LDA, * ), S( * ), U( LDU, * ),
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* $ VT( LDVT, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SGESDD computes the singular value decomposition (SVD) of a real
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*> M-by-N matrix A, optionally computing the left and right singular
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*> vectors. If singular vectors are desired, it uses a
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*> divide-and-conquer algorithm.
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*>
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*> The SVD is written
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*>
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*> A = U * SIGMA * transpose(V)
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*>
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*> where SIGMA is an M-by-N matrix which is zero except for its
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*> min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
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*> V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
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*> are the singular values of A; they are real and non-negative, and
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*> are returned in descending order. The first min(m,n) columns of
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*> U and V are the left and right singular vectors of A.
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*>
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*> Note that the routine returns VT = V**T, not V.
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*>
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*> The divide and conquer algorithm makes very mild assumptions about
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*> floating point arithmetic. It will work on machines with a guard
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*> digit in add/subtract, or on those binary machines without guard
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*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
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*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
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*> without guard digits, but we know of none.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] JOBZ
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*> \verbatim
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*> JOBZ is CHARACTER*1
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*> Specifies options for computing all or part of the matrix U:
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*> = 'A': all M columns of U and all N rows of V**T are
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*> returned in the arrays U and VT;
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*> = 'S': the first min(M,N) columns of U and the first
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*> min(M,N) rows of V**T are returned in the arrays U
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*> and VT;
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*> = 'O': If M >= N, the first N columns of U are overwritten
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*> on the array A and all rows of V**T are returned in
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*> the array VT;
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*> otherwise, all columns of U are returned in the
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*> array U and the first M rows of V**T are overwritten
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*> in the array A;
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*> = 'N': no columns of U or rows of V**T are computed.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the input matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the input matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> On entry, the M-by-N matrix A.
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*> On exit,
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*> if JOBZ = 'O', A is overwritten with the first N columns
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*> of U (the left singular vectors, stored
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*> columnwise) if M >= N;
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*> A is overwritten with the first M rows
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*> of V**T (the right singular vectors, stored
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*> rowwise) otherwise.
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*> if JOBZ .ne. 'O', the contents of A are destroyed.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is REAL array, dimension (min(M,N))
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*> The singular values of A, sorted so that S(i) >= S(i+1).
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*> \endverbatim
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*>
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*> \param[out] U
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*> \verbatim
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*> U is REAL array, dimension (LDU,UCOL)
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*> UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
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*> UCOL = min(M,N) if JOBZ = 'S'.
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*> If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
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*> orthogonal matrix U;
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*> if JOBZ = 'S', U contains the first min(M,N) columns of U
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*> (the left singular vectors, stored columnwise);
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*> if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
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*> \endverbatim
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*>
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*> \param[in] LDU
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*> \verbatim
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*> LDU is INTEGER
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*> The leading dimension of the array U. LDU >= 1; if
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*> JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
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*> \endverbatim
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*>
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*> \param[out] VT
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*> \verbatim
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*> VT is REAL array, dimension (LDVT,N)
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*> If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
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*> N-by-N orthogonal matrix V**T;
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*> if JOBZ = 'S', VT contains the first min(M,N) rows of
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*> V**T (the right singular vectors, stored rowwise);
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*> if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
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*> \endverbatim
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*>
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*> \param[in] LDVT
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*> \verbatim
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*> LDVT is INTEGER
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*> The leading dimension of the array VT. LDVT >= 1;
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*> if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
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*> if JOBZ = 'S', LDVT >= min(M,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= 1.
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*> If LWORK = -1, a workspace query is assumed. The optimal
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*> size for the WORK array is calculated and stored in WORK(1),
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*> and no other work except argument checking is performed.
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*>
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*> Let mx = max(M,N) and mn = min(M,N).
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*> If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn ).
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*> If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn ).
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*> If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn.
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*> If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx.
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*> These are not tight minimums in all cases; see comments inside code.
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*> For good performance, LWORK should generally be larger;
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*> a query is recommended.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (8*min(M,N))
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit.
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*> < 0: if INFO = -i, the i-th argument had an illegal value.
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*> > 0: SBDSDC did not converge, updating process failed.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date June 2016
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*
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*> \ingroup realGEsing
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*
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*> \par Contributors:
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* ==================
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*>
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*> Ming Gu and Huan Ren, Computer Science Division, University of
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*> California at Berkeley, USA
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*>
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* =====================================================================
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SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
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$ WORK, LWORK, IWORK, INFO )
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implicit none
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*
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* -- LAPACK driver routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* June 2016
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*
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* .. Scalar Arguments ..
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CHARACTER JOBZ
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INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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REAL A( LDA, * ), S( * ), U( LDU, * ),
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$ VT( LDVT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
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INTEGER BDSPAC, BLK, CHUNK, I, IE, IERR, IL,
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$ IR, ISCL, ITAU, ITAUP, ITAUQ, IU, IVT, LDWKVT,
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$ LDWRKL, LDWRKR, LDWRKU, MAXWRK, MINMN, MINWRK,
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$ MNTHR, NWORK, WRKBL
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INTEGER LWORK_SGEBRD_MN, LWORK_SGEBRD_MM,
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$ LWORK_SGEBRD_NN, LWORK_SGELQF_MN,
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$ LWORK_SGEQRF_MN,
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$ LWORK_SORGBR_P_MM, LWORK_SORGBR_Q_NN,
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$ LWORK_SORGLQ_MN, LWORK_SORGLQ_NN,
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$ LWORK_SORGQR_MM, LWORK_SORGQR_MN,
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$ LWORK_SORMBR_PRT_MM, LWORK_SORMBR_QLN_MM,
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$ LWORK_SORMBR_PRT_MN, LWORK_SORMBR_QLN_MN,
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$ LWORK_SORMBR_PRT_NN, LWORK_SORMBR_QLN_NN
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REAL ANRM, BIGNUM, EPS, SMLNUM
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* ..
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* .. Local Arrays ..
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INTEGER IDUM( 1 )
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REAL DUM( 1 )
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* ..
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* .. External Subroutines ..
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EXTERNAL SBDSDC, SGEBRD, SGELQF, SGEMM, SGEQRF, SLACPY,
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$ SLASCL, SLASET, SORGBR, SORGLQ, SORGQR, SORMBR,
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$ XERBLA
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* ..
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* .. External Functions ..
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LOGICAL LSAME, SISNAN
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REAL SLAMCH, SLANGE
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EXTERNAL SLAMCH, SLANGE, LSAME, SISNAN
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC INT, MAX, MIN, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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MINMN = MIN( M, N )
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WNTQA = LSAME( JOBZ, 'A' )
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WNTQS = LSAME( JOBZ, 'S' )
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WNTQAS = WNTQA .OR. WNTQS
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WNTQO = LSAME( JOBZ, 'O' )
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WNTQN = LSAME( JOBZ, 'N' )
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LQUERY = ( LWORK.EQ.-1 )
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*
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IF( .NOT.( WNTQA .OR. WNTQS .OR. WNTQO .OR. WNTQN ) ) THEN
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INFO = -1
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ELSE IF( M.LT.0 ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -5
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ELSE IF( LDU.LT.1 .OR. ( WNTQAS .AND. LDU.LT.M ) .OR.
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$ ( WNTQO .AND. M.LT.N .AND. LDU.LT.M ) ) THEN
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INFO = -8
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ELSE IF( LDVT.LT.1 .OR. ( WNTQA .AND. LDVT.LT.N ) .OR.
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$ ( WNTQS .AND. LDVT.LT.MINMN ) .OR.
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$ ( WNTQO .AND. M.GE.N .AND. LDVT.LT.N ) ) THEN
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INFO = -10
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END IF
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*
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* Compute workspace
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* Note: Comments in the code beginning "Workspace:" describe the
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* minimal amount of workspace allocated at that point in the code,
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* as well as the preferred amount for good performance.
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* NB refers to the optimal block size for the immediately
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* following subroutine, as returned by ILAENV.
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*
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IF( INFO.EQ.0 ) THEN
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MINWRK = 1
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MAXWRK = 1
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BDSPAC = 0
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MNTHR = INT( MINMN*11.0E0 / 6.0E0 )
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IF( M.GE.N .AND. MINMN.GT.0 ) THEN
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*
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* Compute space needed for SBDSDC
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*
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IF( WNTQN ) THEN
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* sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6)
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* keep 7*N for backwards compatibility.
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BDSPAC = 7*N
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ELSE
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BDSPAC = 3*N*N + 4*N
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END IF
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*
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* Compute space preferred for each routine
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CALL SGEBRD( M, N, DUM(1), M, DUM(1), DUM(1), DUM(1),
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$ DUM(1), DUM(1), -1, IERR )
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LWORK_SGEBRD_MN = INT( DUM(1) )
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*
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CALL SGEBRD( N, N, DUM(1), N, DUM(1), DUM(1), DUM(1),
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$ DUM(1), DUM(1), -1, IERR )
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LWORK_SGEBRD_NN = INT( DUM(1) )
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*
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CALL SGEQRF( M, N, DUM(1), M, DUM(1), DUM(1), -1, IERR )
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LWORK_SGEQRF_MN = INT( DUM(1) )
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*
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CALL SORGBR( 'Q', N, N, N, DUM(1), N, DUM(1), DUM(1), -1,
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$ IERR )
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LWORK_SORGBR_Q_NN = INT( DUM(1) )
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*
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CALL SORGQR( M, M, N, DUM(1), M, DUM(1), DUM(1), -1, IERR )
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LWORK_SORGQR_MM = INT( DUM(1) )
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*
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CALL SORGQR( M, N, N, DUM(1), M, DUM(1), DUM(1), -1, IERR )
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LWORK_SORGQR_MN = INT( DUM(1) )
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*
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CALL SORMBR( 'P', 'R', 'T', N, N, N, DUM(1), N,
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$ DUM(1), DUM(1), N, DUM(1), -1, IERR )
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LWORK_SORMBR_PRT_NN = INT( DUM(1) )
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*
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CALL SORMBR( 'Q', 'L', 'N', N, N, N, DUM(1), N,
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$ DUM(1), DUM(1), N, DUM(1), -1, IERR )
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LWORK_SORMBR_QLN_NN = INT( DUM(1) )
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*
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CALL SORMBR( 'Q', 'L', 'N', M, N, N, DUM(1), M,
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$ DUM(1), DUM(1), M, DUM(1), -1, IERR )
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LWORK_SORMBR_QLN_MN = INT( DUM(1) )
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*
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CALL SORMBR( 'Q', 'L', 'N', M, M, N, DUM(1), M,
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$ DUM(1), DUM(1), M, DUM(1), -1, IERR )
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LWORK_SORMBR_QLN_MM = INT( DUM(1) )
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*
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IF( M.GE.MNTHR ) THEN
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IF( WNTQN ) THEN
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*
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* Path 1 (M >> N, JOBZ='N')
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*
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WRKBL = N + LWORK_SGEQRF_MN
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WRKBL = MAX( WRKBL, 3*N + LWORK_SGEBRD_NN )
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MAXWRK = MAX( WRKBL, BDSPAC + N )
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MINWRK = BDSPAC + N
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ELSE IF( WNTQO ) THEN
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*
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* Path 2 (M >> N, JOBZ='O')
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*
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WRKBL = N + LWORK_SGEQRF_MN
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WRKBL = MAX( WRKBL, N + LWORK_SORGQR_MN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SGEBRD_NN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_QLN_NN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_PRT_NN )
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WRKBL = MAX( WRKBL, 3*N + BDSPAC )
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MAXWRK = WRKBL + 2*N*N
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MINWRK = BDSPAC + 2*N*N + 3*N
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ELSE IF( WNTQS ) THEN
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*
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* Path 3 (M >> N, JOBZ='S')
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*
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WRKBL = N + LWORK_SGEQRF_MN
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WRKBL = MAX( WRKBL, N + LWORK_SORGQR_MN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SGEBRD_NN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_QLN_NN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_PRT_NN )
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WRKBL = MAX( WRKBL, 3*N + BDSPAC )
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MAXWRK = WRKBL + N*N
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MINWRK = BDSPAC + N*N + 3*N
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ELSE IF( WNTQA ) THEN
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*
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* Path 4 (M >> N, JOBZ='A')
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*
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WRKBL = N + LWORK_SGEQRF_MN
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WRKBL = MAX( WRKBL, N + LWORK_SORGQR_MM )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SGEBRD_NN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_QLN_NN )
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WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_PRT_NN )
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WRKBL = MAX( WRKBL, 3*N + BDSPAC )
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MAXWRK = WRKBL + N*N
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MINWRK = N*N + MAX( 3*N + BDSPAC, N + M )
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END IF
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ELSE
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*
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* Path 5 (M >= N, but not much larger)
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*
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WRKBL = 3*N + LWORK_SGEBRD_MN
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IF( WNTQN ) THEN
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* Path 5n (M >= N, jobz='N')
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MAXWRK = MAX( WRKBL, 3*N + BDSPAC )
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MINWRK = 3*N + MAX( M, BDSPAC )
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ELSE IF( WNTQO ) THEN
|
|
* Path 5o (M >= N, jobz='O')
|
|
WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_PRT_NN )
|
|
WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_QLN_MN )
|
|
WRKBL = MAX( WRKBL, 3*N + BDSPAC )
|
|
MAXWRK = WRKBL + M*N
|
|
MINWRK = 3*N + MAX( M, N*N + BDSPAC )
|
|
ELSE IF( WNTQS ) THEN
|
|
* Path 5s (M >= N, jobz='S')
|
|
WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_QLN_MN )
|
|
WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_PRT_NN )
|
|
MAXWRK = MAX( WRKBL, 3*N + BDSPAC )
|
|
MINWRK = 3*N + MAX( M, BDSPAC )
|
|
ELSE IF( WNTQA ) THEN
|
|
* Path 5a (M >= N, jobz='A')
|
|
WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*N + LWORK_SORMBR_PRT_NN )
|
|
MAXWRK = MAX( WRKBL, 3*N + BDSPAC )
|
|
MINWRK = 3*N + MAX( M, BDSPAC )
|
|
END IF
|
|
END IF
|
|
ELSE IF( MINMN.GT.0 ) THEN
|
|
*
|
|
* Compute space needed for SBDSDC
|
|
*
|
|
IF( WNTQN ) THEN
|
|
* sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6)
|
|
* keep 7*N for backwards compatibility.
|
|
BDSPAC = 7*M
|
|
ELSE
|
|
BDSPAC = 3*M*M + 4*M
|
|
END IF
|
|
*
|
|
* Compute space preferred for each routine
|
|
CALL SGEBRD( M, N, DUM(1), M, DUM(1), DUM(1), DUM(1),
|
|
$ DUM(1), DUM(1), -1, IERR )
|
|
LWORK_SGEBRD_MN = INT( DUM(1) )
|
|
*
|
|
CALL SGEBRD( M, M, A, M, S, DUM(1), DUM(1),
|
|
$ DUM(1), DUM(1), -1, IERR )
|
|
LWORK_SGEBRD_MM = INT( DUM(1) )
|
|
*
|
|
CALL SGELQF( M, N, A, M, DUM(1), DUM(1), -1, IERR )
|
|
LWORK_SGELQF_MN = INT( DUM(1) )
|
|
*
|
|
CALL SORGLQ( N, N, M, DUM(1), N, DUM(1), DUM(1), -1, IERR )
|
|
LWORK_SORGLQ_NN = INT( DUM(1) )
|
|
*
|
|
CALL SORGLQ( M, N, M, A, M, DUM(1), DUM(1), -1, IERR )
|
|
LWORK_SORGLQ_MN = INT( DUM(1) )
|
|
*
|
|
CALL SORGBR( 'P', M, M, M, A, N, DUM(1), DUM(1), -1, IERR )
|
|
LWORK_SORGBR_P_MM = INT( DUM(1) )
|
|
*
|
|
CALL SORMBR( 'P', 'R', 'T', M, M, M, DUM(1), M,
|
|
$ DUM(1), DUM(1), M, DUM(1), -1, IERR )
|
|
LWORK_SORMBR_PRT_MM = INT( DUM(1) )
|
|
*
|
|
CALL SORMBR( 'P', 'R', 'T', M, N, M, DUM(1), M,
|
|
$ DUM(1), DUM(1), M, DUM(1), -1, IERR )
|
|
LWORK_SORMBR_PRT_MN = INT( DUM(1) )
|
|
*
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, M, DUM(1), N,
|
|
$ DUM(1), DUM(1), N, DUM(1), -1, IERR )
|
|
LWORK_SORMBR_PRT_NN = INT( DUM(1) )
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, M, DUM(1), M,
|
|
$ DUM(1), DUM(1), M, DUM(1), -1, IERR )
|
|
LWORK_SORMBR_QLN_MM = INT( DUM(1) )
|
|
*
|
|
IF( N.GE.MNTHR ) THEN
|
|
IF( WNTQN ) THEN
|
|
*
|
|
* Path 1t (N >> M, JOBZ='N')
|
|
*
|
|
WRKBL = M + LWORK_SGELQF_MN
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SGEBRD_MM )
|
|
MAXWRK = MAX( WRKBL, BDSPAC + M )
|
|
MINWRK = BDSPAC + M
|
|
ELSE IF( WNTQO ) THEN
|
|
*
|
|
* Path 2t (N >> M, JOBZ='O')
|
|
*
|
|
WRKBL = M + LWORK_SGELQF_MN
|
|
WRKBL = MAX( WRKBL, M + LWORK_SORGLQ_MN )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SGEBRD_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_PRT_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + BDSPAC )
|
|
MAXWRK = WRKBL + 2*M*M
|
|
MINWRK = BDSPAC + 2*M*M + 3*M
|
|
ELSE IF( WNTQS ) THEN
|
|
*
|
|
* Path 3t (N >> M, JOBZ='S')
|
|
*
|
|
WRKBL = M + LWORK_SGELQF_MN
|
|
WRKBL = MAX( WRKBL, M + LWORK_SORGLQ_MN )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SGEBRD_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_PRT_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + BDSPAC )
|
|
MAXWRK = WRKBL + M*M
|
|
MINWRK = BDSPAC + M*M + 3*M
|
|
ELSE IF( WNTQA ) THEN
|
|
*
|
|
* Path 4t (N >> M, JOBZ='A')
|
|
*
|
|
WRKBL = M + LWORK_SGELQF_MN
|
|
WRKBL = MAX( WRKBL, M + LWORK_SORGLQ_NN )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SGEBRD_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_PRT_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + BDSPAC )
|
|
MAXWRK = WRKBL + M*M
|
|
MINWRK = M*M + MAX( 3*M + BDSPAC, M + N )
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Path 5t (N > M, but not much larger)
|
|
*
|
|
WRKBL = 3*M + LWORK_SGEBRD_MN
|
|
IF( WNTQN ) THEN
|
|
* Path 5tn (N > M, jobz='N')
|
|
MAXWRK = MAX( WRKBL, 3*M + BDSPAC )
|
|
MINWRK = 3*M + MAX( N, BDSPAC )
|
|
ELSE IF( WNTQO ) THEN
|
|
* Path 5to (N > M, jobz='O')
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_PRT_MN )
|
|
WRKBL = MAX( WRKBL, 3*M + BDSPAC )
|
|
MAXWRK = WRKBL + M*N
|
|
MINWRK = 3*M + MAX( N, M*M + BDSPAC )
|
|
ELSE IF( WNTQS ) THEN
|
|
* Path 5ts (N > M, jobz='S')
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_PRT_MN )
|
|
MAXWRK = MAX( WRKBL, 3*M + BDSPAC )
|
|
MINWRK = 3*M + MAX( N, BDSPAC )
|
|
ELSE IF( WNTQA ) THEN
|
|
* Path 5ta (N > M, jobz='A')
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_QLN_MM )
|
|
WRKBL = MAX( WRKBL, 3*M + LWORK_SORMBR_PRT_NN )
|
|
MAXWRK = MAX( WRKBL, 3*M + BDSPAC )
|
|
MINWRK = 3*M + MAX( N, BDSPAC )
|
|
END IF
|
|
END IF
|
|
END IF
|
|
|
|
MAXWRK = MAX( MAXWRK, MINWRK )
|
|
WORK( 1 ) = MAXWRK
|
|
*
|
|
IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
|
|
INFO = -12
|
|
END IF
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'SGESDD', -INFO )
|
|
RETURN
|
|
ELSE IF( LQUERY ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Get machine constants
|
|
*
|
|
EPS = SLAMCH( 'P' )
|
|
SMLNUM = SQRT( SLAMCH( 'S' ) ) / EPS
|
|
BIGNUM = ONE / SMLNUM
|
|
*
|
|
* Scale A if max element outside range [SMLNUM,BIGNUM]
|
|
*
|
|
ANRM = SLANGE( 'M', M, N, A, LDA, DUM )
|
|
IF( SISNAN( ANRM ) ) THEN
|
|
INFO = -4
|
|
RETURN
|
|
END IF
|
|
ISCL = 0
|
|
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
|
|
ISCL = 1
|
|
CALL SLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR )
|
|
ELSE IF( ANRM.GT.BIGNUM ) THEN
|
|
ISCL = 1
|
|
CALL SLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, IERR )
|
|
END IF
|
|
*
|
|
IF( M.GE.N ) THEN
|
|
*
|
|
* A has at least as many rows as columns. If A has sufficiently
|
|
* more rows than columns, first reduce using the QR
|
|
* decomposition (if sufficient workspace available)
|
|
*
|
|
IF( M.GE.MNTHR ) THEN
|
|
*
|
|
IF( WNTQN ) THEN
|
|
*
|
|
* Path 1 (M >> N, JOBZ='N')
|
|
* No singular vectors to be computed
|
|
*
|
|
ITAU = 1
|
|
NWORK = ITAU + N
|
|
*
|
|
* Compute A=Q*R
|
|
* Workspace: need N [tau] + N [work]
|
|
* Workspace: prefer N [tau] + N*NB [work]
|
|
*
|
|
CALL SGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Zero out below R
|
|
*
|
|
CALL SLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA )
|
|
IE = 1
|
|
ITAUQ = IE + N
|
|
ITAUP = ITAUQ + N
|
|
NWORK = ITAUP + N
|
|
*
|
|
* Bidiagonalize R in A
|
|
* Workspace: need 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + 2*N*NB [work]
|
|
*
|
|
CALL SGEBRD( N, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
|
|
$ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
|
|
$ IERR )
|
|
NWORK = IE + N
|
|
*
|
|
* Perform bidiagonal SVD, computing singular values only
|
|
* Workspace: need N [e] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'N', N, S, WORK( IE ), DUM, 1, DUM, 1,
|
|
$ DUM, IDUM, WORK( NWORK ), IWORK, INFO )
|
|
*
|
|
ELSE IF( WNTQO ) THEN
|
|
*
|
|
* Path 2 (M >> N, JOBZ = 'O')
|
|
* N left singular vectors to be overwritten on A and
|
|
* N right singular vectors to be computed in VT
|
|
*
|
|
IR = 1
|
|
*
|
|
* WORK(IR) is LDWRKR by N
|
|
*
|
|
IF( LWORK .GE. LDA*N + N*N + 3*N + BDSPAC ) THEN
|
|
LDWRKR = LDA
|
|
ELSE
|
|
LDWRKR = ( LWORK - N*N - 3*N - BDSPAC ) / N
|
|
END IF
|
|
ITAU = IR + LDWRKR*N
|
|
NWORK = ITAU + N
|
|
*
|
|
* Compute A=Q*R
|
|
* Workspace: need N*N [R] + N [tau] + N [work]
|
|
* Workspace: prefer N*N [R] + N [tau] + N*NB [work]
|
|
*
|
|
CALL SGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Copy R to WORK(IR), zeroing out below it
|
|
*
|
|
CALL SLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR )
|
|
CALL SLASET( 'L', N - 1, N - 1, ZERO, ZERO, WORK(IR+1),
|
|
$ LDWRKR )
|
|
*
|
|
* Generate Q in A
|
|
* Workspace: need N*N [R] + N [tau] + N [work]
|
|
* Workspace: prefer N*N [R] + N [tau] + N*NB [work]
|
|
*
|
|
CALL SORGQR( M, N, N, A, LDA, WORK( ITAU ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
IE = ITAU
|
|
ITAUQ = IE + N
|
|
ITAUP = ITAUQ + N
|
|
NWORK = ITAUP + N
|
|
*
|
|
* Bidiagonalize R in WORK(IR)
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work]
|
|
*
|
|
CALL SGEBRD( N, N, WORK( IR ), LDWRKR, S, WORK( IE ),
|
|
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* WORK(IU) is N by N
|
|
*
|
|
IU = NWORK
|
|
NWORK = IU + N*N
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in WORK(IU) and computing right
|
|
* singular vectors of bidiagonal matrix in VT
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ), N,
|
|
$ VT, LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Overwrite WORK(IU) by left singular vectors of R
|
|
* and VT by right singular vectors of R
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N [work]
|
|
* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', N, N, N, WORK( IR ), LDWRKR,
|
|
$ WORK( ITAUQ ), WORK( IU ), N, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, N, WORK( IR ), LDWRKR,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply Q in A by left singular vectors of R in
|
|
* WORK(IU), storing result in WORK(IR) and copying to A
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U]
|
|
* Workspace: prefer M*N [R] + 3*N [e, tauq, taup] + N*N [U]
|
|
*
|
|
DO 10 I = 1, M, LDWRKR
|
|
CHUNK = MIN( M - I + 1, LDWRKR )
|
|
CALL SGEMM( 'N', 'N', CHUNK, N, N, ONE, A( I, 1 ),
|
|
$ LDA, WORK( IU ), N, ZERO, WORK( IR ),
|
|
$ LDWRKR )
|
|
CALL SLACPY( 'F', CHUNK, N, WORK( IR ), LDWRKR,
|
|
$ A( I, 1 ), LDA )
|
|
10 CONTINUE
|
|
*
|
|
ELSE IF( WNTQS ) THEN
|
|
*
|
|
* Path 3 (M >> N, JOBZ='S')
|
|
* N left singular vectors to be computed in U and
|
|
* N right singular vectors to be computed in VT
|
|
*
|
|
IR = 1
|
|
*
|
|
* WORK(IR) is N by N
|
|
*
|
|
LDWRKR = N
|
|
ITAU = IR + LDWRKR*N
|
|
NWORK = ITAU + N
|
|
*
|
|
* Compute A=Q*R
|
|
* Workspace: need N*N [R] + N [tau] + N [work]
|
|
* Workspace: prefer N*N [R] + N [tau] + N*NB [work]
|
|
*
|
|
CALL SGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Copy R to WORK(IR), zeroing out below it
|
|
*
|
|
CALL SLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR )
|
|
CALL SLASET( 'L', N - 1, N - 1, ZERO, ZERO, WORK(IR+1),
|
|
$ LDWRKR )
|
|
*
|
|
* Generate Q in A
|
|
* Workspace: need N*N [R] + N [tau] + N [work]
|
|
* Workspace: prefer N*N [R] + N [tau] + N*NB [work]
|
|
*
|
|
CALL SORGQR( M, N, N, A, LDA, WORK( ITAU ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
IE = ITAU
|
|
ITAUQ = IE + N
|
|
ITAUP = ITAUQ + N
|
|
NWORK = ITAUP + N
|
|
*
|
|
* Bidiagonalize R in WORK(IR)
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work]
|
|
*
|
|
CALL SGEBRD( N, N, WORK( IR ), LDWRKR, S, WORK( IE ),
|
|
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagoal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in VT
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
|
|
$ LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of R and VT
|
|
* by right singular vectors of R
|
|
* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', N, N, N, WORK( IR ), LDWRKR,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, N, WORK( IR ), LDWRKR,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply Q in A by left singular vectors of R in
|
|
* WORK(IR), storing result in U
|
|
* Workspace: need N*N [R]
|
|
*
|
|
CALL SLACPY( 'F', N, N, U, LDU, WORK( IR ), LDWRKR )
|
|
CALL SGEMM( 'N', 'N', M, N, N, ONE, A, LDA, WORK( IR ),
|
|
$ LDWRKR, ZERO, U, LDU )
|
|
*
|
|
ELSE IF( WNTQA ) THEN
|
|
*
|
|
* Path 4 (M >> N, JOBZ='A')
|
|
* M left singular vectors to be computed in U and
|
|
* N right singular vectors to be computed in VT
|
|
*
|
|
IU = 1
|
|
*
|
|
* WORK(IU) is N by N
|
|
*
|
|
LDWRKU = N
|
|
ITAU = IU + LDWRKU*N
|
|
NWORK = ITAU + N
|
|
*
|
|
* Compute A=Q*R, copying result to U
|
|
* Workspace: need N*N [U] + N [tau] + N [work]
|
|
* Workspace: prefer N*N [U] + N [tau] + N*NB [work]
|
|
*
|
|
CALL SGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SLACPY( 'L', M, N, A, LDA, U, LDU )
|
|
*
|
|
* Generate Q in U
|
|
* Workspace: need N*N [U] + N [tau] + M [work]
|
|
* Workspace: prefer N*N [U] + N [tau] + M*NB [work]
|
|
CALL SORGQR( M, M, N, U, LDU, WORK( ITAU ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Produce R in A, zeroing out other entries
|
|
*
|
|
CALL SLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA )
|
|
IE = ITAU
|
|
ITAUQ = IE + N
|
|
ITAUP = ITAUQ + N
|
|
NWORK = ITAUP + N
|
|
*
|
|
* Bidiagonalize R in A
|
|
* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + 2*N*NB [work]
|
|
*
|
|
CALL SGEBRD( N, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
|
|
$ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
|
|
$ IERR )
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in WORK(IU) and computing right
|
|
* singular vectors of bidiagonal matrix in VT
|
|
* Workspace: need N*N [U] + 3*N [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ), N,
|
|
$ VT, LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Overwrite WORK(IU) by left singular vectors of R and VT
|
|
* by right singular vectors of R
|
|
* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', N, N, N, A, LDA,
|
|
$ WORK( ITAUQ ), WORK( IU ), LDWRKU,
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, N, A, LDA,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply Q in U by left singular vectors of R in
|
|
* WORK(IU), storing result in A
|
|
* Workspace: need N*N [U]
|
|
*
|
|
CALL SGEMM( 'N', 'N', M, N, N, ONE, U, LDU, WORK( IU ),
|
|
$ LDWRKU, ZERO, A, LDA )
|
|
*
|
|
* Copy left singular vectors of A from A to U
|
|
*
|
|
CALL SLACPY( 'F', M, N, A, LDA, U, LDU )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* M .LT. MNTHR
|
|
*
|
|
* Path 5 (M >= N, but not much larger)
|
|
* Reduce to bidiagonal form without QR decomposition
|
|
*
|
|
IE = 1
|
|
ITAUQ = IE + N
|
|
ITAUP = ITAUQ + N
|
|
NWORK = ITAUP + N
|
|
*
|
|
* Bidiagonalize A
|
|
* Workspace: need 3*N [e, tauq, taup] + M [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + (M+N)*NB [work]
|
|
*
|
|
CALL SGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
|
|
$ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
|
|
$ IERR )
|
|
IF( WNTQN ) THEN
|
|
*
|
|
* Path 5n (M >= N, JOBZ='N')
|
|
* Perform bidiagonal SVD, only computing singular values
|
|
* Workspace: need 3*N [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'N', N, S, WORK( IE ), DUM, 1, DUM, 1,
|
|
$ DUM, IDUM, WORK( NWORK ), IWORK, INFO )
|
|
ELSE IF( WNTQO ) THEN
|
|
* Path 5o (M >= N, JOBZ='O')
|
|
IU = NWORK
|
|
IF( LWORK .GE. M*N + 3*N + BDSPAC ) THEN
|
|
*
|
|
* WORK( IU ) is M by N
|
|
*
|
|
LDWRKU = M
|
|
NWORK = IU + LDWRKU*N
|
|
CALL SLASET( 'F', M, N, ZERO, ZERO, WORK( IU ),
|
|
$ LDWRKU )
|
|
* IR is unused; silence compile warnings
|
|
IR = -1
|
|
ELSE
|
|
*
|
|
* WORK( IU ) is N by N
|
|
*
|
|
LDWRKU = N
|
|
NWORK = IU + LDWRKU*N
|
|
*
|
|
* WORK(IR) is LDWRKR by N
|
|
*
|
|
IR = NWORK
|
|
LDWRKR = ( LWORK - N*N - 3*N ) / N
|
|
END IF
|
|
NWORK = IU + LDWRKU*N
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in WORK(IU) and computing right
|
|
* singular vectors of bidiagonal matrix in VT
|
|
* Workspace: need 3*N [e, tauq, taup] + N*N [U] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ),
|
|
$ LDWRKU, VT, LDVT, DUM, IDUM, WORK( NWORK ),
|
|
$ IWORK, INFO )
|
|
*
|
|
* Overwrite VT by right singular vectors of A
|
|
* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, N, A, LDA,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
IF( LWORK .GE. M*N + 3*N + BDSPAC ) THEN
|
|
*
|
|
* Path 5o-fast
|
|
* Overwrite WORK(IU) by left singular vectors of A
|
|
* Workspace: need 3*N [e, tauq, taup] + M*N [U] + N [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + M*N [U] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, N, N, A, LDA,
|
|
$ WORK( ITAUQ ), WORK( IU ), LDWRKU,
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Copy left singular vectors of A from WORK(IU) to A
|
|
*
|
|
CALL SLACPY( 'F', M, N, WORK( IU ), LDWRKU, A, LDA )
|
|
ELSE
|
|
*
|
|
* Path 5o-slow
|
|
* Generate Q in A
|
|
* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work]
|
|
*
|
|
CALL SORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply Q in A by left singular vectors of
|
|
* bidiagonal matrix in WORK(IU), storing result in
|
|
* WORK(IR) and copying to A
|
|
* Workspace: need 3*N [e, tauq, taup] + N*N [U] + NB*N [R]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + M*N [R]
|
|
*
|
|
DO 20 I = 1, M, LDWRKR
|
|
CHUNK = MIN( M - I + 1, LDWRKR )
|
|
CALL SGEMM( 'N', 'N', CHUNK, N, N, ONE, A( I, 1 ),
|
|
$ LDA, WORK( IU ), LDWRKU, ZERO,
|
|
$ WORK( IR ), LDWRKR )
|
|
CALL SLACPY( 'F', CHUNK, N, WORK( IR ), LDWRKR,
|
|
$ A( I, 1 ), LDA )
|
|
20 CONTINUE
|
|
END IF
|
|
*
|
|
ELSE IF( WNTQS ) THEN
|
|
*
|
|
* Path 5s (M >= N, JOBZ='S')
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in VT
|
|
* Workspace: need 3*N [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SLASET( 'F', M, N, ZERO, ZERO, U, LDU )
|
|
CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
|
|
$ LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of A and VT
|
|
* by right singular vectors of A
|
|
* Workspace: need 3*N [e, tauq, taup] + N [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, N, N, A, LDA,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, N, A, LDA,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
ELSE IF( WNTQA ) THEN
|
|
*
|
|
* Path 5a (M >= N, JOBZ='A')
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in VT
|
|
* Workspace: need 3*N [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SLASET( 'F', M, M, ZERO, ZERO, U, LDU )
|
|
CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
|
|
$ LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Set the right corner of U to identity matrix
|
|
*
|
|
IF( M.GT.N ) THEN
|
|
CALL SLASET( 'F', M - N, M - N, ZERO, ONE, U(N+1,N+1),
|
|
$ LDU )
|
|
END IF
|
|
*
|
|
* Overwrite U by left singular vectors of A and VT
|
|
* by right singular vectors of A
|
|
* Workspace: need 3*N [e, tauq, taup] + M [work]
|
|
* Workspace: prefer 3*N [e, tauq, taup] + M*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, M, A, LDA,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* A has more columns than rows. If A has sufficiently more
|
|
* columns than rows, first reduce using the LQ decomposition (if
|
|
* sufficient workspace available)
|
|
*
|
|
IF( N.GE.MNTHR ) THEN
|
|
*
|
|
IF( WNTQN ) THEN
|
|
*
|
|
* Path 1t (N >> M, JOBZ='N')
|
|
* No singular vectors to be computed
|
|
*
|
|
ITAU = 1
|
|
NWORK = ITAU + M
|
|
*
|
|
* Compute A=L*Q
|
|
* Workspace: need M [tau] + M [work]
|
|
* Workspace: prefer M [tau] + M*NB [work]
|
|
*
|
|
CALL SGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Zero out above L
|
|
*
|
|
CALL SLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), LDA )
|
|
IE = 1
|
|
ITAUQ = IE + M
|
|
ITAUP = ITAUQ + M
|
|
NWORK = ITAUP + M
|
|
*
|
|
* Bidiagonalize L in A
|
|
* Workspace: need 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + 2*M*NB [work]
|
|
*
|
|
CALL SGEBRD( M, M, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
|
|
$ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
|
|
$ IERR )
|
|
NWORK = IE + M
|
|
*
|
|
* Perform bidiagonal SVD, computing singular values only
|
|
* Workspace: need M [e] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'N', M, S, WORK( IE ), DUM, 1, DUM, 1,
|
|
$ DUM, IDUM, WORK( NWORK ), IWORK, INFO )
|
|
*
|
|
ELSE IF( WNTQO ) THEN
|
|
*
|
|
* Path 2t (N >> M, JOBZ='O')
|
|
* M right singular vectors to be overwritten on A and
|
|
* M left singular vectors to be computed in U
|
|
*
|
|
IVT = 1
|
|
*
|
|
* WORK(IVT) is M by M
|
|
* WORK(IL) is M by M; it is later resized to M by chunk for gemm
|
|
*
|
|
IL = IVT + M*M
|
|
IF( LWORK .GE. M*N + M*M + 3*M + BDSPAC ) THEN
|
|
LDWRKL = M
|
|
CHUNK = N
|
|
ELSE
|
|
LDWRKL = M
|
|
CHUNK = ( LWORK - M*M ) / M
|
|
END IF
|
|
ITAU = IL + LDWRKL*M
|
|
NWORK = ITAU + M
|
|
*
|
|
* Compute A=L*Q
|
|
* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work]
|
|
* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work]
|
|
*
|
|
CALL SGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Copy L to WORK(IL), zeroing about above it
|
|
*
|
|
CALL SLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWRKL )
|
|
CALL SLASET( 'U', M - 1, M - 1, ZERO, ZERO,
|
|
$ WORK( IL + LDWRKL ), LDWRKL )
|
|
*
|
|
* Generate Q in A
|
|
* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work]
|
|
* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work]
|
|
*
|
|
CALL SORGLQ( M, N, M, A, LDA, WORK( ITAU ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
IE = ITAU
|
|
ITAUQ = IE + M
|
|
ITAUP = ITAUQ + M
|
|
NWORK = ITAUP + M
|
|
*
|
|
* Bidiagonalize L in WORK(IL)
|
|
* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work]
|
|
*
|
|
CALL SGEBRD( M, M, WORK( IL ), LDWRKL, S, WORK( IE ),
|
|
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U, and computing right singular
|
|
* vectors of bidiagonal matrix in WORK(IVT)
|
|
* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU,
|
|
$ WORK( IVT ), M, DUM, IDUM, WORK( NWORK ),
|
|
$ IWORK, INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of L and WORK(IVT)
|
|
* by right singular vectors of L
|
|
* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, M, WORK( IL ), LDWRKL,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', M, M, M, WORK( IL ), LDWRKL,
|
|
$ WORK( ITAUP ), WORK( IVT ), M,
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply right singular vectors of L in WORK(IVT) by Q
|
|
* in A, storing result in WORK(IL) and copying to A
|
|
* Workspace: need M*M [VT] + M*M [L]
|
|
* Workspace: prefer M*M [VT] + M*N [L]
|
|
* At this point, L is resized as M by chunk.
|
|
*
|
|
DO 30 I = 1, N, CHUNK
|
|
BLK = MIN( N - I + 1, CHUNK )
|
|
CALL SGEMM( 'N', 'N', M, BLK, M, ONE, WORK( IVT ), M,
|
|
$ A( 1, I ), LDA, ZERO, WORK( IL ), LDWRKL )
|
|
CALL SLACPY( 'F', M, BLK, WORK( IL ), LDWRKL,
|
|
$ A( 1, I ), LDA )
|
|
30 CONTINUE
|
|
*
|
|
ELSE IF( WNTQS ) THEN
|
|
*
|
|
* Path 3t (N >> M, JOBZ='S')
|
|
* M right singular vectors to be computed in VT and
|
|
* M left singular vectors to be computed in U
|
|
*
|
|
IL = 1
|
|
*
|
|
* WORK(IL) is M by M
|
|
*
|
|
LDWRKL = M
|
|
ITAU = IL + LDWRKL*M
|
|
NWORK = ITAU + M
|
|
*
|
|
* Compute A=L*Q
|
|
* Workspace: need M*M [L] + M [tau] + M [work]
|
|
* Workspace: prefer M*M [L] + M [tau] + M*NB [work]
|
|
*
|
|
CALL SGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Copy L to WORK(IL), zeroing out above it
|
|
*
|
|
CALL SLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWRKL )
|
|
CALL SLASET( 'U', M - 1, M - 1, ZERO, ZERO,
|
|
$ WORK( IL + LDWRKL ), LDWRKL )
|
|
*
|
|
* Generate Q in A
|
|
* Workspace: need M*M [L] + M [tau] + M [work]
|
|
* Workspace: prefer M*M [L] + M [tau] + M*NB [work]
|
|
*
|
|
CALL SORGLQ( M, N, M, A, LDA, WORK( ITAU ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
IE = ITAU
|
|
ITAUQ = IE + M
|
|
ITAUP = ITAUQ + M
|
|
NWORK = ITAUP + M
|
|
*
|
|
* Bidiagonalize L in WORK(IU).
|
|
* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work]
|
|
*
|
|
CALL SGEBRD( M, M, WORK( IL ), LDWRKL, S, WORK( IE ),
|
|
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in VT
|
|
* Workspace: need M*M [L] + 3*M [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU, VT,
|
|
$ LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of L and VT
|
|
* by right singular vectors of L
|
|
* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + M*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, M, WORK( IL ), LDWRKL,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', M, M, M, WORK( IL ), LDWRKL,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply right singular vectors of L in WORK(IL) by
|
|
* Q in A, storing result in VT
|
|
* Workspace: need M*M [L]
|
|
*
|
|
CALL SLACPY( 'F', M, M, VT, LDVT, WORK( IL ), LDWRKL )
|
|
CALL SGEMM( 'N', 'N', M, N, M, ONE, WORK( IL ), LDWRKL,
|
|
$ A, LDA, ZERO, VT, LDVT )
|
|
*
|
|
ELSE IF( WNTQA ) THEN
|
|
*
|
|
* Path 4t (N >> M, JOBZ='A')
|
|
* N right singular vectors to be computed in VT and
|
|
* M left singular vectors to be computed in U
|
|
*
|
|
IVT = 1
|
|
*
|
|
* WORK(IVT) is M by M
|
|
*
|
|
LDWKVT = M
|
|
ITAU = IVT + LDWKVT*M
|
|
NWORK = ITAU + M
|
|
*
|
|
* Compute A=L*Q, copying result to VT
|
|
* Workspace: need M*M [VT] + M [tau] + M [work]
|
|
* Workspace: prefer M*M [VT] + M [tau] + M*NB [work]
|
|
*
|
|
CALL SGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SLACPY( 'U', M, N, A, LDA, VT, LDVT )
|
|
*
|
|
* Generate Q in VT
|
|
* Workspace: need M*M [VT] + M [tau] + N [work]
|
|
* Workspace: prefer M*M [VT] + M [tau] + N*NB [work]
|
|
*
|
|
CALL SORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Produce L in A, zeroing out other entries
|
|
*
|
|
CALL SLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), LDA )
|
|
IE = ITAU
|
|
ITAUQ = IE + M
|
|
ITAUP = ITAUQ + M
|
|
NWORK = ITAUP + M
|
|
*
|
|
* Bidiagonalize L in A
|
|
* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup] + 2*M*NB [work]
|
|
*
|
|
CALL SGEBRD( M, M, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
|
|
$ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
|
|
$ IERR )
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in WORK(IVT)
|
|
* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU,
|
|
$ WORK( IVT ), LDWKVT, DUM, IDUM,
|
|
$ WORK( NWORK ), IWORK, INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of L and WORK(IVT)
|
|
* by right singular vectors of L
|
|
* Workspace: need M*M [VT] + 3*M [e, tauq, taup]+ M [work]
|
|
* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup]+ M*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, M, A, LDA,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', M, M, M, A, LDA,
|
|
$ WORK( ITAUP ), WORK( IVT ), LDWKVT,
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply right singular vectors of L in WORK(IVT) by
|
|
* Q in VT, storing result in A
|
|
* Workspace: need M*M [VT]
|
|
*
|
|
CALL SGEMM( 'N', 'N', M, N, M, ONE, WORK( IVT ), LDWKVT,
|
|
$ VT, LDVT, ZERO, A, LDA )
|
|
*
|
|
* Copy right singular vectors of A from A to VT
|
|
*
|
|
CALL SLACPY( 'F', M, N, A, LDA, VT, LDVT )
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* N .LT. MNTHR
|
|
*
|
|
* Path 5t (N > M, but not much larger)
|
|
* Reduce to bidiagonal form without LQ decomposition
|
|
*
|
|
IE = 1
|
|
ITAUQ = IE + M
|
|
ITAUP = ITAUQ + M
|
|
NWORK = ITAUP + M
|
|
*
|
|
* Bidiagonalize A
|
|
* Workspace: need 3*M [e, tauq, taup] + N [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + (M+N)*NB [work]
|
|
*
|
|
CALL SGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
|
|
$ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
|
|
$ IERR )
|
|
IF( WNTQN ) THEN
|
|
*
|
|
* Path 5tn (N > M, JOBZ='N')
|
|
* Perform bidiagonal SVD, only computing singular values
|
|
* Workspace: need 3*M [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'L', 'N', M, S, WORK( IE ), DUM, 1, DUM, 1,
|
|
$ DUM, IDUM, WORK( NWORK ), IWORK, INFO )
|
|
ELSE IF( WNTQO ) THEN
|
|
* Path 5to (N > M, JOBZ='O')
|
|
LDWKVT = M
|
|
IVT = NWORK
|
|
IF( LWORK .GE. M*N + 3*M + BDSPAC ) THEN
|
|
*
|
|
* WORK( IVT ) is M by N
|
|
*
|
|
CALL SLASET( 'F', M, N, ZERO, ZERO, WORK( IVT ),
|
|
$ LDWKVT )
|
|
NWORK = IVT + LDWKVT*N
|
|
* IL is unused; silence compile warnings
|
|
IL = -1
|
|
ELSE
|
|
*
|
|
* WORK( IVT ) is M by M
|
|
*
|
|
NWORK = IVT + LDWKVT*M
|
|
IL = NWORK
|
|
*
|
|
* WORK(IL) is M by CHUNK
|
|
*
|
|
CHUNK = ( LWORK - M*M - 3*M ) / M
|
|
END IF
|
|
*
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in WORK(IVT)
|
|
* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + BDSPAC
|
|
*
|
|
CALL SBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU,
|
|
$ WORK( IVT ), LDWKVT, DUM, IDUM,
|
|
$ WORK( NWORK ), IWORK, INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of A
|
|
* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
*
|
|
IF( LWORK .GE. M*N + 3*M + BDSPAC ) THEN
|
|
*
|
|
* Path 5to-fast
|
|
* Overwrite WORK(IVT) by left singular vectors of A
|
|
* Workspace: need 3*M [e, tauq, taup] + M*N [VT] + M [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + M*N [VT] + M*NB [work]
|
|
*
|
|
CALL SORMBR( 'P', 'R', 'T', M, N, M, A, LDA,
|
|
$ WORK( ITAUP ), WORK( IVT ), LDWKVT,
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Copy right singular vectors of A from WORK(IVT) to A
|
|
*
|
|
CALL SLACPY( 'F', M, N, WORK( IVT ), LDWKVT, A, LDA )
|
|
ELSE
|
|
*
|
|
* Path 5to-slow
|
|
* Generate P**T in A
|
|
* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work]
|
|
*
|
|
CALL SORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
|
|
$ WORK( NWORK ), LWORK - NWORK + 1, IERR )
|
|
*
|
|
* Multiply Q in A by right singular vectors of
|
|
* bidiagonal matrix in WORK(IVT), storing result in
|
|
* WORK(IL) and copying to A
|
|
* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M*NB [L]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*N [L]
|
|
*
|
|
DO 40 I = 1, N, CHUNK
|
|
BLK = MIN( N - I + 1, CHUNK )
|
|
CALL SGEMM( 'N', 'N', M, BLK, M, ONE, WORK( IVT ),
|
|
$ LDWKVT, A( 1, I ), LDA, ZERO,
|
|
$ WORK( IL ), M )
|
|
CALL SLACPY( 'F', M, BLK, WORK( IL ), M, A( 1, I ),
|
|
$ LDA )
|
|
40 CONTINUE
|
|
END IF
|
|
ELSE IF( WNTQS ) THEN
|
|
*
|
|
* Path 5ts (N > M, JOBZ='S')
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in VT
|
|
* Workspace: need 3*M [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SLASET( 'F', M, N, ZERO, ZERO, VT, LDVT )
|
|
CALL SBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU, VT,
|
|
$ LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Overwrite U by left singular vectors of A and VT
|
|
* by right singular vectors of A
|
|
* Workspace: need 3*M [e, tauq, taup] + M [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + M*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', M, N, M, A, LDA,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
ELSE IF( WNTQA ) THEN
|
|
*
|
|
* Path 5ta (N > M, JOBZ='A')
|
|
* Perform bidiagonal SVD, computing left singular vectors
|
|
* of bidiagonal matrix in U and computing right singular
|
|
* vectors of bidiagonal matrix in VT
|
|
* Workspace: need 3*M [e, tauq, taup] + BDSPAC
|
|
*
|
|
CALL SLASET( 'F', N, N, ZERO, ZERO, VT, LDVT )
|
|
CALL SBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU, VT,
|
|
$ LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
|
|
$ INFO )
|
|
*
|
|
* Set the right corner of VT to identity matrix
|
|
*
|
|
IF( N.GT.M ) THEN
|
|
CALL SLASET( 'F', N-M, N-M, ZERO, ONE, VT(M+1,M+1),
|
|
$ LDVT )
|
|
END IF
|
|
*
|
|
* Overwrite U by left singular vectors of A and VT
|
|
* by right singular vectors of A
|
|
* Workspace: need 3*M [e, tauq, taup] + N [work]
|
|
* Workspace: prefer 3*M [e, tauq, taup] + N*NB [work]
|
|
*
|
|
CALL SORMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
|
|
$ WORK( ITAUQ ), U, LDU, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
CALL SORMBR( 'P', 'R', 'T', N, N, M, A, LDA,
|
|
$ WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
|
|
$ LWORK - NWORK + 1, IERR )
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
* Undo scaling if necessary
|
|
*
|
|
IF( ISCL.EQ.1 ) THEN
|
|
IF( ANRM.GT.BIGNUM )
|
|
$ CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
|
|
$ IERR )
|
|
IF( ANRM.LT.SMLNUM )
|
|
$ CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
|
|
$ IERR )
|
|
END IF
|
|
*
|
|
* Return optimal workspace in WORK(1)
|
|
*
|
|
WORK( 1 ) = MAXWRK
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SGESDD
|
|
*
|
|
END
|