--- rpl/lapack/lapack/dgesdd.f 2010/04/21 13:45:14 1.2
+++ rpl/lapack/lapack/dgesdd.f 2014/01/27 09:28:17 1.14
@@ -1,10 +1,225 @@
+*> \brief \b DGESDD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGESDD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
+* LWORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ
+* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ),
+* $ VT( LDVT, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGESDD computes the singular value decomposition (SVD) of a real
+*> M-by-N matrix A, optionally computing the left and right singular
+*> vectors. If singular vectors are desired, it uses a
+*> divide-and-conquer algorithm.
+*>
+*> 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 VT = V**T, not V.
+*>
+*> The divide and conquer algorithm makes very mild assumptions about
+*> floating point arithmetic. It will work on machines with a guard
+*> digit in add/subtract, or on those binary machines without guard
+*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
+*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
+*> without guard digits, but we know of none.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBZ
+*> \verbatim
+*> JOBZ is CHARACTER*1
+*> Specifies options for computing all or part of the matrix U:
+*> = 'A': all M columns of U and all N rows of V**T are
+*> returned in the arrays U and VT;
+*> = 'S': the first min(M,N) columns of U and the first
+*> min(M,N) rows of V**T are returned in the arrays U
+*> and VT;
+*> = 'O': If M >= N, the first N columns of U are overwritten
+*> on the array A and all rows of V**T are returned in
+*> the array VT;
+*> otherwise, all columns of U are returned in the
+*> array U and the first M rows of V**T are overwritten
+*> in the array A;
+*> = 'N': no columns of U or rows of V**T are computed.
+*> \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 JOBZ = 'O', A is overwritten with the first N columns
+*> of U (the left singular vectors, stored
+*> columnwise) if M >= N;
+*> A is overwritten with the first M rows
+*> of V**T (the right singular vectors, stored
+*> rowwise) otherwise.
+*> if JOBZ .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)
+*> UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
+*> UCOL = min(M,N) if JOBZ = 'S'.
+*> If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
+*> orthogonal matrix U;
+*> if JOBZ = 'S', U contains the first min(M,N) columns of U
+*> (the left singular vectors, stored columnwise);
+*> if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDU
+*> \verbatim
+*> LDU is INTEGER
+*> The leading dimension of the array U. LDU >= 1; if
+*> JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
+*> \endverbatim
+*>
+*> \param[out] VT
+*> \verbatim
+*> VT is DOUBLE PRECISION array, dimension (LDVT,N)
+*> If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
+*> N-by-N orthogonal matrix V**T;
+*> if JOBZ = 'S', VT contains the first min(M,N) rows of
+*> V**T (the right singular vectors, stored rowwise);
+*> if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDVT
+*> \verbatim
+*> LDVT is INTEGER
+*> The leading dimension of the array VT. LDVT >= 1; if
+*> JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
+*> if JOBZ = '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;
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= 1.
+*> If JOBZ = 'N',
+*> LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)).
+*> If JOBZ = 'O',
+*> LWORK >= 3*min(M,N) +
+*> max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
+*> If JOBZ = 'S' or 'A'
+*> LWORK >= min(M,N)*(6+4*min(M,N))+max(M,N)
+*> For good performance, LWORK should generally be larger.
+*> If LWORK = -1 but other input arguments are legal, WORK(1)
+*> returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (8*min(M,N))
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> > 0: DBDSDC did not converge, updating process failed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2013
+*
+*> \ingroup doubleGEsing
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ming Gu and Huan Ren, Computer Science Division, University of
+*> California at Berkeley, USA
+*>
+* =====================================================================
SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
$ LWORK, IWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2.1) --
+* -- LAPACK driver routine (version 3.5.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* March 2009
+* November 2013
*
* .. Scalar Arguments ..
CHARACTER JOBZ
@@ -16,131 +231,6 @@
$ VT( LDVT, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DGESDD computes the singular value decomposition (SVD) of a real
-* M-by-N matrix A, optionally computing the left and right singular
-* vectors. If singular vectors are desired, it uses a
-* divide-and-conquer algorithm.
-*
-* 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 VT = V**T, not V.
-*
-* The divide and conquer algorithm makes very mild assumptions about
-* floating point arithmetic. It will work on machines with a guard
-* digit in add/subtract, or on those binary machines without guard
-* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-* Cray-2. It could conceivably fail on hexadecimal or decimal machines
-* without guard digits, but we know of none.
-*
-* Arguments
-* =========
-*
-* JOBZ (input) CHARACTER*1
-* Specifies options for computing all or part of the matrix U:
-* = 'A': all M columns of U and all N rows of V**T are
-* returned in the arrays U and VT;
-* = 'S': the first min(M,N) columns of U and the first
-* min(M,N) rows of V**T are returned in the arrays U
-* and VT;
-* = 'O': If M >= N, the first N columns of U are overwritten
-* on the array A and all rows of V**T are returned in
-* the array VT;
-* otherwise, all columns of U are returned in the
-* array U and the first M rows of V**T are overwritten
-* in the array A;
-* = 'N': no columns of U or rows of V**T are computed.
-*
-* 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 JOBZ = 'O', A is overwritten with the first N columns
-* of U (the left singular vectors, stored
-* columnwise) if M >= N;
-* A is overwritten with the first M rows
-* of V**T (the right singular vectors, stored
-* rowwise) otherwise.
-* if JOBZ .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)
-* UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
-* UCOL = min(M,N) if JOBZ = 'S'.
-* If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
-* orthogonal matrix U;
-* if JOBZ = 'S', U contains the first min(M,N) columns of U
-* (the left singular vectors, stored columnwise);
-* if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
-*
-* LDU (input) INTEGER
-* The leading dimension of the array U. LDU >= 1; if
-* JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
-*
-* VT (output) DOUBLE PRECISION array, dimension (LDVT,N)
-* If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
-* N-by-N orthogonal matrix V**T;
-* if JOBZ = 'S', VT contains the first min(M,N) rows of
-* V**T (the right singular vectors, stored rowwise);
-* if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
-*
-* LDVT (input) INTEGER
-* The leading dimension of the array VT. LDVT >= 1; if
-* JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
-* if JOBZ = '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;
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= 1.
-* If JOBZ = 'N',
-* LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)).
-* If JOBZ = 'O',
-* LWORK >= 3*min(M,N) +
-* max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
-* If JOBZ = 'S' or 'A'
-* LWORK >= 3*min(M,N) +
-* max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)).
-* For good performance, LWORK should generally be larger.
-* If LWORK = -1 but other input arguments are legal, WORK(1)
-* returns the optimal LWORK.
-*
-* IWORK (workspace) INTEGER array, dimension (8*min(M,N))
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: DBDSDC did not converge, updating process failed.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Ming Gu and Huan Ren, Computer Science Division, University of
-* California at Berkeley, USA
-*
* =====================================================================
*
* .. Parameters ..
@@ -281,7 +371,7 @@
$ ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
WRKBL = MAX( WRKBL, BDSPAC+3*N )
MAXWRK = WRKBL + N*N
- MINWRK = BDSPAC + N*N + 3*N
+ MINWRK = BDSPAC + N*N + 2*N + M
END IF
ELSE
*
@@ -675,14 +765,14 @@
NWORK = 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+N+M, prefer N*N+N+M*NB)
*
CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
$ LWORK-NWORK+1, IERR )
CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
* Generate Q in U
-* (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+* (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
$ WORK( NWORK ), LWORK-NWORK+1, IERR )
*