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1e8b2ad5a07fd32e63b55d7d52e1264829b96bb4
lammps/lib/linalg/dgesvd.cpp
Axel Kohlmeyer 1e8b2ad5a0 whitespace fixes
2022-12-28 13:48:43 -05:00

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/* fortran/dgesvd.f -- translated by f2c (version 20200916).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"
/* Table of constant values */
static integer c__6 = 6;
static integer c__0 = 0;
static integer c__2 = 2;
static integer c_n1 = -1;
static doublereal c_b57 = 0.;
static integer c__1 = 1;
static doublereal c_b79 = 1.;
/* > \brief <b> DGESVD computes the singular value decomposition (SVD) for GE matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DGESVD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesvd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesvd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesvd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */
/* WORK, LWORK, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER JOBU, JOBVT */
/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
/* .. */
/* .. Array Arguments .. */
/* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), */
/* $ VT( LDVT, * ), WORK( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DGESVD computes the singular value decomposition (SVD) of a real */
/* > M-by-N matrix A, optionally computing the left and/or right singular */
/* > vectors. The SVD is written */
/* > */
/* > A = U * SIGMA * transpose(V) */
/* > */
/* > where SIGMA is an M-by-N matrix which is zero except for its */
/* > min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
/* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
/* > are the singular values of A; they are real and non-negative, and */
/* > are returned in descending order. The first min(m,n) columns of */
/* > U and V are the left and right singular vectors of A. */
/* > */
/* > Note that the routine returns V**T, not V. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > Specifies options for computing all or part of the matrix U: */
/* > = 'A': all M columns of U are returned in array U: */
/* > = 'S': the first min(m,n) columns of U (the left singular */
/* > vectors) are returned in the array U; */
/* > = 'O': the first min(m,n) columns of U (the left singular */
/* > vectors) are overwritten on the array A; */
/* > = 'N': no columns of U (no left singular vectors) are */
/* > computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVT */
/* > \verbatim */
/* > JOBVT is CHARACTER*1 */
/* > Specifies options for computing all or part of the matrix */
/* > V**T: */
/* > = 'A': all N rows of V**T are returned in the array VT; */
/* > = 'S': the first min(m,n) rows of V**T (the right singular */
/* > vectors) are returned in the array VT; */
/* > = 'O': the first min(m,n) rows of V**T (the right singular */
/* > vectors) are overwritten on the array A; */
/* > = 'N': no rows of V**T (no right singular vectors) are */
/* > computed. */
/* > */
/* > JOBVT and JOBU cannot both be 'O'. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the input matrix A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the input matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > On exit, */
/* > if JOBU = 'O', A is overwritten with the first min(m,n) */
/* > columns of U (the left singular vectors, */
/* > stored columnwise); */
/* > if JOBVT = 'O', A is overwritten with the first min(m,n) */
/* > rows of V**T (the right singular vectors, */
/* > stored rowwise); */
/* > if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */
/* > are destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= max(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */
/* > The singular values of A, sorted so that S(i) >= S(i+1). */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* > U is DOUBLE PRECISION array, dimension (LDU,UCOL) */
/* > (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. */
/* > If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */
/* > if JOBU = 'S', U contains the first min(m,n) columns of U */
/* > (the left singular vectors, stored columnwise); */
/* > if JOBU = 'N' or 'O', U is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > The leading dimension of the array U. LDU >= 1; if */
/* > JOBU = 'S' or 'A', LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */
/* > If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */
/* > V**T; */
/* > if JOBVT = 'S', VT contains the first min(m,n) rows of */
/* > V**T (the right singular vectors, stored rowwise); */
/* > if JOBVT = 'N' or 'O', VT is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* > LDVT is INTEGER */
/* > The leading dimension of the array VT. LDVT >= 1; if */
/* > JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */
/* > if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */
/* > superdiagonal elements of an upper bidiagonal matrix B */
/* > whose diagonal is in S (not necessarily sorted). B */
/* > satisfies A = U * B * VT, so it has the same singular values */
/* > as A, and singular vectors related by U and VT. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. */
/* > LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): */
/* > - PATH 1 (M much larger than N, JOBU='N') */
/* > - PATH 1t (N much larger than M, JOBVT='N') */
/* > LWORK >= MAX(1,3*MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths */
/* > For good performance, LWORK should generally be larger. */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: if DBDSQR did not converge, INFO specifies how many */
/* > superdiagonals of an intermediate bidiagonal form B */
/* > did not converge to zero. See the description of WORK */
/* > above for details. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup doubleGEsing */
/* ===================================================================== */
/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
doublereal *a, integer *lda, doublereal *s, doublereal *u, integer *
ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork,
integer *info, ftnlen jobu_len, ftnlen jobvt_len)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2],
i__2, i__3, i__4;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
double sqrt(doublereal);
/* Local variables */
integer i__, ie, ir, iu, blk, ncu;
doublereal dum[1], eps;
integer nru, iscl;
doublereal anrm;
integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__,
lwork_dgeqrf__;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork;
logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *, ftnlen);
integer bdspac;
extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, integer *, doublereal *, integer *, integer *, ftnlen),
dgeqrf_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, ftnlen), dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, ftnlen),
dbdsqr_(char *, integer *, integer *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
ftnlen), dorgbr_(char *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *, ftnlen);
doublereal bignum;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *,
ftnlen, ftnlen, ftnlen), dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dorgqr_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
integer ldwrkr, minwrk, ldwrku, maxwrk;
doublereal smlnum;
logical lquery, wntuas, wntvas;
integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__,
lwork_dorglq_n__, lwork_dorgqr_m__, lwork_dorgqr_n__;
/* -- LAPACK driver routine -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--s;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
--work;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
wntua = lsame_(jobu, (char *)"A", (ftnlen)1, (ftnlen)1);
wntus = lsame_(jobu, (char *)"S", (ftnlen)1, (ftnlen)1);
wntuas = wntua || wntus;
wntuo = lsame_(jobu, (char *)"O", (ftnlen)1, (ftnlen)1);
wntun = lsame_(jobu, (char *)"N", (ftnlen)1, (ftnlen)1);
wntva = lsame_(jobvt, (char *)"A", (ftnlen)1, (ftnlen)1);
wntvs = lsame_(jobvt, (char *)"S", (ftnlen)1, (ftnlen)1);
wntvas = wntva || wntvs;
wntvo = lsame_(jobvt, (char *)"O", (ftnlen)1, (ftnlen)1);
wntvn = lsame_(jobvt, (char *)"N", (ftnlen)1, (ftnlen)1);
lquery = *lwork == -1;
if (! (wntua || wntus || wntuo || wntun)) {
*info = -1;
} else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else if (*ldu < 1 || wntuas && *ldu < *m) {
*info = -9;
} else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
*info = -11;
}
/* Compute workspace */
/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0) {
minwrk = 1;
maxwrk = 1;
if (*m >= *n && minmn > 0) {
/* Compute space needed for DBDSQR */
/* Writing concatenation */
i__1[0] = 1, a__1[0] = jobu;
i__1[1] = 1, a__1[1] = jobvt;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, (
ftnlen)6, (ftnlen)2);
bdspac = *n * 5;
/* Compute space needed for DGEQRF */
dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_dgeqrf__ = (integer) dum[0];
/* Compute space needed for DORGQR */
dorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_dorgqr_n__ = (integer) dum[0];
dorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_dorgqr_m__ = (integer) dum[0];
/* Compute space needed for DGEBRD */
dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1,
&ierr);
lwork_dgebrd__ = (integer) dum[0];
/* Compute space needed for DORGBR P */
dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, (
ftnlen)1);
lwork_dorgbr_p__ = (integer) dum[0];
/* Compute space needed for DORGBR Q */
dorgbr_((char *)"Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, (
ftnlen)1);
lwork_dorgbr_q__ = (integer) dum[0];
if (*m >= mnthr) {
if (wntun) {
/* Path 1 (M much larger than N, JOBU='N') */
maxwrk = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_dgebrd__;
maxwrk = max(i__2,i__3);
if (wntvo || wntvas) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__;
maxwrk = max(i__2,i__3);
}
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__2 = *n << 2;
minwrk = max(i__2,bdspac);
} else if (wntuo && wntvn) {
/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
/* Computing MAX */
i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;
maxwrk = max(i__2,i__3);
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntuo && wntvas) {
/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
/* 'A') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
/* Computing MAX */
i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;
maxwrk = max(i__2,i__3);
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntus && wntvn) {
/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntus && wntvo) {
/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = (*n << 1) * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntus && wntvas) {
/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
/* 'A') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntua && wntvn) {
/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntua && wntvo) {
/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = (*n << 1) * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
} else if (wntua && wntvas) {
/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
/* 'A') */
wrkbl = *n + lwork_dgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
}
} else {
/* Path 10 (M at least N, but not much larger) */
dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &
c_n1, &ierr);
lwork_dgebrd__ = (integer) dum[0];
maxwrk = *n * 3 + lwork_dgebrd__;
if (wntus || wntuo) {
dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1,
&ierr, (ftnlen)1);
lwork_dorgbr_q__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__;
maxwrk = max(i__2,i__3);
}
if (wntua) {
dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1,
&ierr, (ftnlen)1);
lwork_dorgbr_q__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__;
maxwrk = max(i__2,i__3);
}
if (! wntvn) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__;
maxwrk = max(i__2,i__3);
}
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = max(i__2,bdspac);
}
} else if (minmn > 0) {
/* Compute space needed for DBDSQR */
/* Writing concatenation */
i__1[0] = 1, a__1[0] = jobu;
i__1[1] = 1, a__1[1] = jobvt;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, (
ftnlen)6, (ftnlen)2);
bdspac = *m * 5;
/* Compute space needed for DGELQF */
dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_dgelqf__ = (integer) dum[0];
/* Compute space needed for DORGLQ */
dorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr);
lwork_dorglq_n__ = (integer) dum[0];
dorglq_(m, n, m, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_dorglq_m__ = (integer) dum[0];
/* Compute space needed for DGEBRD */
dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1,
&ierr);
lwork_dgebrd__ = (integer) dum[0];
/* Compute space needed for DORGBR P */
dorgbr_((char *)"P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, (
ftnlen)1);
lwork_dorgbr_p__ = (integer) dum[0];
/* Compute space needed for DORGBR Q */
dorgbr_((char *)"Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, (
ftnlen)1);
lwork_dorgbr_q__ = (integer) dum[0];
if (*n >= mnthr) {
if (wntvn) {
/* Path 1t(N much larger than M, JOBVT='N') */
maxwrk = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_dgebrd__;
maxwrk = max(i__2,i__3);
if (wntuo || wntuas) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__;
maxwrk = max(i__2,i__3);
}
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__2 = *m << 2;
minwrk = max(i__2,bdspac);
} else if (wntvo && wntun) {
/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
/* Computing MAX */
i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m;
maxwrk = max(i__2,i__3);
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntvo && wntuas) {
/* Path 3t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='O') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
/* Computing MAX */
i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m;
maxwrk = max(i__2,i__3);
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntvs && wntun) {
/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntvs && wntuo) {
/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = (*m << 1) * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntvs && wntuas) {
/* Path 6t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='S') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntva && wntun) {
/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntva && wntuo) {
/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = (*m << 1) * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
} else if (wntva && wntuas) {
/* Path 9t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='A') */
wrkbl = *m + lwork_dgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__;
wrkbl = max(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__;
wrkbl = max(i__2,i__3);
wrkbl = max(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
}
} else {
/* Path 10t(N greater than M, but not much larger) */
dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &
c_n1, &ierr);
lwork_dgebrd__ = (integer) dum[0];
maxwrk = *m * 3 + lwork_dgebrd__;
if (wntvs || wntvo) {
/* Compute space needed for DORGBR P */
dorgbr_((char *)"P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, &
ierr, (ftnlen)1);
lwork_dorgbr_p__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__;
maxwrk = max(i__2,i__3);
}
if (wntva) {
dorgbr_((char *)"P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, &
ierr, (ftnlen)1);
lwork_dorgbr_p__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__;
maxwrk = max(i__2,i__3);
}
if (! wntun) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__;
maxwrk = max(i__2,i__3);
}
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = max(i__2,bdspac);
}
}
maxwrk = max(maxwrk,minwrk);
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__2 = -(*info);
xerbla_((char *)"DGESVD", &i__2, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
/* Get machine constants */
eps = dlamch_((char *)"P", (ftnlen)1);
smlnum = sqrt(dlamch_((char *)"S", (ftnlen)1)) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, dum, (ftnlen)1);
iscl = 0;
if (anrm > 0. && anrm < smlnum) {
iscl = 1;
dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
ierr, (ftnlen)1);
} else if (anrm > bignum) {
iscl = 1;
dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
ierr, (ftnlen)1);
}
if (*m >= *n) {
/* 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 >= mnthr) {
if (wntun) {
/* Path 1 (M much larger than N, JOBU='N') */
/* No left singular vectors to be computed */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
i__2, &ierr);
/* Zero out below R */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2],
lda, (ftnlen)1);
}
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) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
ncvt = 0;
if (wntvo || wntvas) {
/* If right singular vectors desired, generate P'. */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &
work[iwork], &i__2, &ierr, (ftnlen)1);
ncvt = *n;
}
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in A if desired */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[
a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork],
info, (ftnlen)1);
/* If right singular vectors desired in VT, copy them there */
if (wntvas) {
dlacpy_((char *)"F", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
}
} else if (wntuo && wntvn) {
/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
/* N left singular vectors to be overwritten on A and */
/* no right singular vectors to be computed */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= *n * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *n;
if (*lwork >= max(i__2,i__3) + *lda * *n) {
/* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
ldwrku = *lda;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *n;
if (*lwork >= max(i__2,i__3) + *n * *n) {
/* WORK(IU) is LDA by N, WORK(IR) is N by N */
ldwrku = *lda;
ldwrkr = *n;
} else {
/* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
ldwrku = (*lwork - *n * *n - *n) / *n;
ldwrkr = *n;
}
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy R to WORK(IR) and zero out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr,
(ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1],
&ldwrkr, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
/* Generate left vectors bidiagonalizing R */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) */
/* (Workspace: need N*N + BDSPAC) */
dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, &
c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork]
, info, (ftnlen)1);
iu = ie + *n;
/* 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) */
i__2 = *m;
i__3 = ldwrku;
for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__3) {
/* Computing MIN */
i__4 = *m - i__ + 1;
chunk = min(i__4,ldwrku);
dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ +
a_dim1], lda, &work[ir], &ldwrkr, &c_b57, &
work[iu], &ldwrku, (ftnlen)1, (ftnlen)1);
dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
a_dim1], lda, (ftnlen)1);
/* L10: */
}
} else {
/* Insufficient workspace for a fast algorithm */
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize A */
/* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */
i__3 = *lwork - iwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
/* Generate left vectors bidiagonalizing A */
/* (Workspace: need 4*N, prefer 3*N + N*NB) */
i__3 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &
work[iwork], &i__3, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, &
c__1, &a[a_offset], lda, dum, &c__1, &work[iwork],
info, (ftnlen)1);
}
} else if (wntuo && wntvas) {
/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
/* N left singular vectors to be overwritten on A and */
/* N right singular vectors to be computed in VT */
/* Computing MAX */
i__3 = *n << 2;
if (*lwork >= *n * *n + max(i__3,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *n;
if (*lwork >= max(i__3,i__2) + *lda * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
ldwrku = *lda;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *n;
if (*lwork >= max(i__3,i__2) + *n * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
ldwrku = *lda;
ldwrkr = *n;
} else {
/* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
ldwrku = (*lwork - *n * *n - *n) / *n;
ldwrkr = *n;
}
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__3 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__3, &ierr);
/* Copy R to VT, zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
if (*n > 1) {
i__3 = *n - 1;
i__2 = *n - 1;
dlaset_((char *)"L", &i__3, &i__2, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt, (ftnlen)1);
}
/* Generate Q in A */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__3 = *lwork - iwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__3, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
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) */
i__3 = *lwork - iwork + 1;
dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &i__3, &
ierr);
dlacpy_((char *)"L", n, n, &vt[vt_offset], ldvt, &work[ir], &
ldwrkr, (ftnlen)1);
/* Generate left vectors bidiagonalizing R in WORK(IR) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */
i__3 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
work[iwork], &i__3, &ierr, (ftnlen)1);
/* Generate right vectors bidiagonalizing R in VT */
/* (Workspace: need N*N + 4*N-1, prefer N*N + 3*N + (N-1)*NB) */
i__3 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
&work[iwork], &i__3, &ierr, (ftnlen)1);
iwork = ie + *n;
/* 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) */
dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1,
&work[iwork], info, (ftnlen)1);
iu = ie + *n;
/* 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) */
i__3 = *m;
i__2 = ldwrku;
for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
i__2) {
/* Computing MIN */
i__4 = *m - i__ + 1;
chunk = min(i__4,ldwrku);
dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ +
a_dim1], lda, &work[ir], &ldwrkr, &c_b57, &
work[iu], &ldwrku, (ftnlen)1, (ftnlen)1);
dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
a_dim1], lda, (ftnlen)1);
/* L20: */
}
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy R to VT, zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt, (ftnlen)1);
}
/* Generate Q in A */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &i__2, &
ierr);
/* Multiply Q in A by left vectors bidiagonalizing R */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, &
work[itauq], &a[a_offset], lda, &work[iwork], &
i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1);
/* Generate right vectors bidiagonalizing R in VT */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in A and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
} else if (wntus) {
if (wntvn) {
/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
/* N left singular vectors to be computed in U and */
/* no right singular vectors to be computed */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= *n * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IR) is LDA by N */
ldwrkr = *lda;
} else {
/* WORK(IR) is N by N */
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &
ldwrkr, (ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
1], &ldwrkr, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate left vectors bidiagonalizing R in WORK(IR) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) */
/* (Workspace: need N*N + BDSPAC) */
dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie],
dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, &
work[iwork], info, (ftnlen)1);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IR), storing result in U */
/* (Workspace: need N*N) */
dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, &
work[ir], &ldwrkr, &c_b57, &u[u_offset], ldu,
(ftnlen)1, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda, (ftnlen)1);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left vectors bidiagonalizing R */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie],
dum, &c__1, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
} else if (wntvo) {
/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
/* N left singular vectors to be computed in U and */
/* N right singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *n) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *n;
} else {
/* WORK(IU) is N by N and WORK(IR) is N by N */
ldwrku = *n;
ir = iu + ldwrku * *n;
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*N*N + 4*N, */
/* prefer 2*N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], &
ldwrkr, (ftnlen)1);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate right bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*N*N + 4*N-1, */
/* prefer 2*N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* 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) */
dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[
ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1,
&work[iwork], info, (ftnlen)1);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IU), storing result in U */
/* (Workspace: need N*N) */
dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, &
work[iu], &ldwrku, &c_b57, &u[u_offset], ldu,
(ftnlen)1, (ftnlen)1);
/* Copy right singular vectors of R to A */
/* (Workspace: need N*N) */
dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset],
lda, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda, (ftnlen)1);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left vectors bidiagonalizing R */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1)
;
/* Generate right vectors bidiagonalizing R in A */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1,
&work[iwork], info, (ftnlen)1);
}
} else if (wntvas) {
/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
/* or 'A') */
/* N left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= *n * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IU) is LDA by N */
ldwrku = *lda;
} else {
/* WORK(IU) is N by N */
ldwrku = *n;
}
itau = iu + ldwrku * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
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) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need N*N + 4*N-1, */
/* prefer N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr, (ftnlen)1)
;
iwork = ie + *n;
/* 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) */
dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &work[iu], &ldwrku, dum, &
c__1, &work[iwork], info, (ftnlen)1);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IU), storing result in U */
/* (Workspace: need N*N) */
dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, &
work[iu], &ldwrku, &c_b57, &u[u_offset], ldu,
(ftnlen)1, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R to VT, zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt, (ftnlen)1);
}
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie],
&work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in VT */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt,
&work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)
1);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr, (ftnlen)1)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info, (ftnlen)1);
}
}
} else if (wntua) {
if (wntvn) {
/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
/* M left singular vectors to be computed in U and */
/* no right singular vectors to be computed */
/* Computing MAX */
i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3);
if (*lwork >= *n * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IR) is LDA by N */
ldwrkr = *lda;
} else {
/* WORK(IR) is N by N */
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Copy R to WORK(IR), zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &
ldwrkr, (ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
1], &ldwrkr, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate left bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) */
/* (Workspace: need N*N + BDSPAC) */
dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie],
dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, &
work[iwork], info, (ftnlen)1);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IR), storing result in A */
/* (Workspace: need N*N) */
dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, &
work[ir], &ldwrkr, &c_b57, &a[a_offset], lda,
(ftnlen)1, (ftnlen)1);
/* Copy left singular vectors of A from A to U */
dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need N + M, prefer N + M*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda, (ftnlen)1);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in A */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie],
dum, &c__1, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
} else if (wntvo) {
/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
/* M left singular vectors to be computed in U and */
/* N right singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3);
if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *n) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *n;
} else {
/* WORK(IU) is N by N and WORK(IR) is N by N */
ldwrku = *n;
ir = iu + ldwrku * *n;
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
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) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need 2*N*N + N + M, prefer 2*N*N + N + M*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku, (ftnlen)1);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*N*N + 4*N, */
/* prefer 2*N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], &
ldwrkr, (ftnlen)1);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate right bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*N*N + 4*N-1, */
/* prefer 2*N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* 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) */
dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[
ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1,
&work[iwork], info, (ftnlen)1);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IU), storing result in A */
/* (Workspace: need N*N) */
dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, &
work[iu], &ldwrku, &c_b57, &a[a_offset], lda,
(ftnlen)1, (ftnlen)1);
/* Copy left singular vectors of A from A to U */
dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Copy right singular vectors of R from WORK(IR) to A */
dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset],
lda, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need N + M, prefer N + M*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda, (ftnlen)1);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in A */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1)
;
/* Generate right bidiagonalizing vectors in A */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1,
&work[iwork], info, (ftnlen)1);
}
} else if (wntvas) {
/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
/* or 'A') */
/* M left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
/* Computing MAX */
i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3);
if (*lwork >= *n * *n + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IU) is LDA by N */
ldwrku = *lda;
} else {
/* WORK(IU) is N by N */
ldwrku = *n;
}
itau = iu + ldwrku * *n;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku, (ftnlen)1);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
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) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need N*N + 4*N-1, */
/* prefer N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr, (ftnlen)1)
;
iwork = ie + *n;
/* 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) */
dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &work[iu], &ldwrku, dum, &
c__1, &work[iwork], info, (ftnlen)1);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IU), storing result in A */
/* (Workspace: need N*N) */
dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, &
work[iu], &ldwrku, &c_b57, &a[a_offset], lda,
(ftnlen)1, (ftnlen)1);
/* Copy left singular vectors of A from A to U */
dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N + N*NB) */
i__2 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
/* Generate Q in U */
/* (Workspace: need N + M, prefer N + M*NB) */
i__2 = *lwork - iwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R from A to VT, zeroing out below it */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt, (ftnlen)1);
}
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT */
/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie],
&work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in VT */
/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt,
&work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)
1);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr, (ftnlen)1)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info, (ftnlen)1);
}
}
}
} else {
/* M .LT. MNTHR */
/* Path 10 (M at least N, but not much larger) */
/* Reduce to bidiagonal form without QR decomposition */
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize A */
/* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__2, &ierr);
if (wntuas) {
/* 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) */
dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (
ftnlen)1);
if (wntus) {
ncu = *n;
}
if (wntua) {
ncu = *m;
}
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
work[iwork], &i__2, &ierr, (ftnlen)1);
}
if (wntvas) {
/* 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) */
dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (
ftnlen)1);
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
work[iwork], &i__2, &ierr, (ftnlen)1);
}
if (wntuo) {
/* If left singular vectors desired in A, generate left */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*N, prefer 3*N + N*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
iwork], &i__2, &ierr, (ftnlen)1);
}
if (wntvo) {
/* If right singular vectors desired in A, generate right */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
iwork], &i__2, &ierr, (ftnlen)1);
}
iwork = ie + *n;
if (wntuas || wntuo) {
nru = *m;
}
if (wntun) {
nru = 0;
}
if (wntvas || wntvo) {
ncvt = *n;
}
if (wntvn) {
ncvt = 0;
}
if (! wntuo && ! wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
} else if (! wntuo && wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[
iwork], info, (ftnlen)1);
} else {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in A and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
}
} 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 >= mnthr) {
if (wntvn) {
/* Path 1t(N much larger than M, JOBVT='N') */
/* No right singular vectors to be computed */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
i__2, &ierr);
/* Zero out above L */
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) +
1], lda, (ftnlen)1);
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
if (wntuo || wntuas) {
/* If left singular vectors desired, generate Q */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], &
work[iwork], &i__2, &ierr, (ftnlen)1);
}
iwork = ie + *m;
nru = 0;
if (wntuo || wntuas) {
nru = *m;
}
/* Perform bidiagonal QR iteration, computing left singular */
/* vectors of A in A if desired */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, &
c__1, &a[a_offset], lda, dum, &c__1, &work[iwork],
info, (ftnlen)1);
/* If left singular vectors desired in U, copy them there */
if (wntuas) {
dlacpy_((char *)"F", m, m, &a[a_offset], lda, &u[u_offset], ldu, (
ftnlen)1);
}
} else if (wntvo && wntun) {
/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
/* M right singular vectors to be overwritten on A and */
/* no left singular vectors to be computed */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= *m * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *m;
if (*lwork >= max(i__2,i__3) + *lda * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *m;
if (*lwork >= max(i__2,i__3) + *m * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is M by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *m;
} else {
/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
ldwrku = *m;
chunk = (*lwork - *m * *m - *m) / *m;
ldwrkr = *m;
}
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy L to WORK(IR) and zero out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr,
(ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
ldwrkr], &ldwrkr, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IR) */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
/* Generate right vectors bidiagonalizing L */
/* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M + BDSPAC) */
dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[
ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork]
, info, (ftnlen)1);
iu = ie + *m;
/* 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) */
i__2 = *n;
i__3 = chunk;
for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__3) {
/* Computing MIN */
i__4 = *n - i__ + 1;
blk = min(i__4,chunk);
dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], &
ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, &
work[iu], &ldwrku, (ftnlen)1, (ftnlen)1);
dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ *
a_dim1 + 1], lda, (ftnlen)1);
/* L30: */
}
} else {
/* Insufficient workspace for a fast algorithm */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A */
/* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */
i__3 = *lwork - iwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
/* Generate right vectors bidiagonalizing A */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__3 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &
work[iwork], &i__3, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[
a_offset], lda, dum, &c__1, dum, &c__1, &work[
iwork], info, (ftnlen)1);
}
} else if (wntvo && wntuas) {
/* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
/* M right singular vectors to be overwritten on A and */
/* M left singular vectors to be computed in U */
/* Computing MAX */
i__3 = *m << 2;
if (*lwork >= *m * *m + max(i__3,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *m;
if (*lwork >= max(i__3,i__2) + *lda * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *m;
if (*lwork >= max(i__3,i__2) + *m * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is M by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *m;
} else {
/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
ldwrku = *m;
chunk = (*lwork - *m * *m - *m) / *m;
ldwrkr = *m;
}
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__3 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__3, &ierr);
/* Copy L to U, zeroing about above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (
ftnlen)1);
i__3 = *m - 1;
i__2 = *m - 1;
dlaset_((char *)"U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 <<
1) + 1], ldu, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__3 = *lwork - iwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
iwork], &i__3, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
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) */
i__3 = *lwork - iwork + 1;
dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
dlacpy_((char *)"U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr,
(ftnlen)1);
/* Generate right vectors bidiagonalizing L in WORK(IR) */
/* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */
i__3 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
work[iwork], &i__3, &ierr, (ftnlen)1);
/* Generate left vectors bidiagonalizing L in U */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */
i__3 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
work[iwork], &i__3, &ierr, (ftnlen)1);
iwork = ie + *m;
/* 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) */
dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ir],
&ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[
iwork], info, (ftnlen)1);
iu = ie + *m;
/* 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)) */
i__3 = *n;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
i__2) {
/* Computing MIN */
i__4 = *n - i__ + 1;
blk = min(i__4,chunk);
dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], &
ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, &
work[iu], &ldwrku, (ftnlen)1, (ftnlen)1);
dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ *
a_dim1 + 1], lda, (ftnlen)1);
/* L40: */
}
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy L to U, zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (
ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 <<
1) + 1], ldu, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
/* Multiply right vectors bidiagonalizing L by Q in A */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[
itaup], &a[a_offset], lda, &work[iwork], &i__2, &
ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1);
/* Generate left vectors bidiagonalizing L in U */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
} else if (wntvs) {
if (wntun) {
/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
/* M right singular vectors to be computed in VT and */
/* no left singular vectors to be computed */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= *m * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IR) is LDA by M */
ldwrkr = *lda;
} else {
/* WORK(IR) is M by M */
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy L to WORK(IR), zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &
ldwrkr, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
ldwrkr], &ldwrkr, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IR) */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate right vectors bidiagonalizing L in */
/* WORK(IR) */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M + BDSPAC) */
dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &
work[ir], &ldwrkr, dum, &c__1, dum, &c__1, &
work[iwork], info, (ftnlen)1);
/* Multiply right singular vectors of L in WORK(IR) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr,
&a[a_offset], lda, &c_b57, &vt[vt_offset],
ldvt, (ftnlen)1, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy result to VT */
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda, (ftnlen)1);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right vectors bidiagonalizing L by Q in VT */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (
ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], &
vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
} else if (wntuo) {
/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
/* M right singular vectors to be computed in VT and */
/* M left singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *m) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is M by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *m;
} else {
/* WORK(IU) is M by M and WORK(IR) is M by M */
ldwrku = *m;
ir = iu + ldwrku * *m;
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out below it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*M*M + 4*M, */
/* prefer 2*M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], &
ldwrkr, (ftnlen)1);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*M*M + 4*M-1, */
/* prefer 2*M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate left bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* 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) */
dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1,
&work[iwork], info, (ftnlen)1);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku,
&a[a_offset], lda, &c_b57, &vt[vt_offset],
ldvt, (ftnlen)1, (ftnlen)1);
/* Copy left singular vectors of L to A */
/* (Workspace: need M*M) */
dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset],
lda, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda, (ftnlen)1);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right vectors bidiagonalizing L by Q in VT */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (
ftnlen)1);
/* Generate left bidiagonalizing vectors of L in A */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, compute left */
/* singular vectors of A in A and compute right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &
c__1, &work[iwork], info, (ftnlen)1);
}
} else if (wntuas) {
/* Path 6t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='S') */
/* M right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= *m * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IU) is LDA by N */
ldwrku = *lda;
} else {
/* WORK(IU) is LDA by M */
ldwrku = *m;
}
itau = iu + ldwrku * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku, (ftnlen)1);
/* Generate Q in A */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
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) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset],
ldu, (ftnlen)1);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need M*M + 4*M-1, */
/* prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* 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) */
dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku,
&a[a_offset], lda, &c_b57, &vt[vt_offset],
ldvt, (ftnlen)1, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to U, zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1
<< 1) + 1], ldu, (ftnlen)1);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in U by Q */
/* in VT */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (
ftnlen)1);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info, (ftnlen)1);
}
}
} else if (wntva) {
if (wntun) {
/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
/* N right singular vectors to be computed in VT and */
/* no left singular vectors to be computed */
/* Computing MAX */
i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3);
if (*lwork >= *m * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IR) is LDA by M */
ldwrkr = *lda;
} else {
/* WORK(IR) is M by M */
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Copy L to WORK(IR), zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &
ldwrkr, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
ldwrkr], &ldwrkr, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IR) */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate right bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need M*M + 4*M-1, */
/* prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M + BDSPAC) */
dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &
work[ir], &ldwrkr, dum, &c__1, dum, &c__1, &
work[iwork], info, (ftnlen)1);
/* Multiply right singular vectors of L in WORK(IR) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr,
&vt[vt_offset], ldvt, &c_b57, &a[a_offset],
lda, (ftnlen)1, (ftnlen)1);
/* Copy right singular vectors of A from A to VT */
dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need M + N, prefer M + N*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda, (ftnlen)1);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in A by Q */
/* in VT */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (
ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], &
vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
} else if (wntuo) {
/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
/* N right singular vectors to be computed in VT and */
/* M left singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3);
if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *m) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is M by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *m;
} else {
/* WORK(IU) is M by M and WORK(IR) is M by M */
ldwrku = *m;
ir = iu + ldwrku * *m;
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
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) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need 2*M*M + M + N, prefer 2*M*M + M + N*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku, (ftnlen)1);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*M*M + 4*M, */
/* prefer 2*M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], &
ldwrkr, (ftnlen)1);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*M*M + 4*M-1, */
/* prefer 2*M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate left bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* 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) */
dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1,
&work[iwork], info, (ftnlen)1);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku,
&vt[vt_offset], ldvt, &c_b57, &a[a_offset],
lda, (ftnlen)1, (ftnlen)1);
/* Copy right singular vectors of A from A to VT */
dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Copy left singular vectors of A from WORK(IR) to A */
dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset],
lda, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need M + N, prefer M + N*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda, (ftnlen)1);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in A by Q */
/* in VT */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (
ftnlen)1);
/* Generate left bidiagonalizing vectors in A */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in A and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &
c__1, &work[iwork], info, (ftnlen)1);
}
} else if (wntuas) {
/* Path 9t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='A') */
/* N right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
/* Computing MAX */
i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3);
if (*lwork >= *m * *m + max(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IU) is LDA by M */
ldwrku = *lda;
} else {
/* WORK(IU) is M by M */
ldwrku = *m;
}
itau = iu + ldwrku * *m;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku, (ftnlen)1);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
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) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset],
ldu, (ftnlen)1);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr, (ftnlen)1);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* 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) */
dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku,
&vt[vt_offset], ldvt, &c_b57, &a[a_offset],
lda, (ftnlen)1, (ftnlen)1);
/* Copy right singular vectors of A from A to VT */
dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M + M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt, (ftnlen)1);
/* Generate Q in VT */
/* (Workspace: need M + N, prefer M + N*NB) */
i__2 = *lwork - iwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to U, zeroing out above it */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset],
ldu, (ftnlen)1);
i__2 = *m - 1;
i__3 = *m - 1;
dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1
<< 1) + 1], ldu, (ftnlen)1);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U */
/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in U by Q */
/* in VT */
/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */
i__2 = *lwork - iwork + 1;
dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (
ftnlen)1);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr, (ftnlen)1);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info, (ftnlen)1);
}
}
}
} else {
/* N .LT. MNTHR */
/* Path 10t(N greater than M, but not much larger) */
/* Reduce to bidiagonal form without LQ decomposition */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A */
/* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__2, &ierr);
if (wntuas) {
/* 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) */
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (
ftnlen)1);
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
iwork], &i__2, &ierr, (ftnlen)1);
}
if (wntvas) {
/* 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) */
dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (
ftnlen)1);
if (wntva) {
nrvt = *n;
}
if (wntvs) {
nrvt = *m;
}
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
&work[iwork], &i__2, &ierr, (ftnlen)1);
}
if (wntuo) {
/* If left singular vectors desired in A, generate left */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
iwork], &i__2, &ierr, (ftnlen)1);
}
if (wntvo) {
/* If right singular vectors desired in A, generate right */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*M, prefer 3*M + M*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
iwork], &i__2, &ierr, (ftnlen)1);
}
iwork = ie + *m;
if (wntuas || wntuo) {
nru = *m;
}
if (wntun) {
nru = 0;
}
if (wntvas || wntvo) {
ncvt = *n;
}
if (wntvn) {
ncvt = 0;
}
if (! wntuo && ! wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info, (ftnlen)1);
} else if (! wntuo && wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in A */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[
iwork], info, (ftnlen)1);
} else {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in A and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
work[iwork], info, (ftnlen)1);
}
}
}
/* If DBDSQR failed to converge, copy unconverged superdiagonals */
/* to WORK( 2:MINMN ) */
if (*info != 0) {
if (ie > 2) {
i__2 = minmn - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__ + 1] = work[i__ + ie - 1];
/* L50: */
}
}
if (ie < 2) {
for (i__ = minmn - 1; i__ >= 1; --i__) {
work[i__ + 1] = work[i__ + ie - 1];
/* L60: */
}
}
}
/* Undo scaling if necessary */
if (iscl == 1) {
if (anrm > bignum) {
dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr, (ftnlen)1);
}
if (*info != 0 && anrm > bignum) {
i__2 = minmn - 1;
dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2],
&minmn, &ierr, (ftnlen)1);
}
if (anrm < smlnum) {
dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr, (ftnlen)1);
}
if (*info != 0 && anrm < smlnum) {
i__2 = minmn - 1;
dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2],
&minmn, &ierr, (ftnlen)1);
}
}
/* Return optimal workspace in WORK(1) */
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGESVD */
} /* dgesvd_ */
#ifdef __cplusplus
}
#endif
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