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opencv/3rdparty/lapack/dgesdd.c

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#include "clapack.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
static doublereal c_b227 = 0.;
static doublereal c_b248 = 1.;
/* Subroutine */ int dgesdd_(char *jobz, integer *m, integer *n, doublereal *
a, integer *lda, doublereal *s, doublereal *u, integer *ldu,
doublereal *vt, integer *ldvt, doublereal *work, integer *lwork,
integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
i__2, i__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, ie, il, ir, iu, blk;
doublereal dum[1], eps;
integer ivt, iscl;
doublereal anrm;
integer idum[1], ierr, itau;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
integer chunk, minmn, wrkbl, itaup, itauq, mnthr;
logical wntqa;
integer nwork;
logical wntqn, wntqo, wntqs;
extern /* Subroutine */ int dbdsdc_(char *, char *, integer *, doublereal
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *), dgebrd_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
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 *),
dgeqrf_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *), dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
xerbla_(char *, integer *), dorgbr_(char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
doublereal bignum;
extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dorgqr_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
integer ldwrkl, ldwrkr, minwrk, ldwrku, maxwrk, ldwkvt;
doublereal smlnum;
logical wntqas, lquery;
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGESDD computes the singular value decomposition (SVD) of a real */
/* M-by-N matrix A, optionally computing the left and right singular */
/* vectors. If singular vectors are desired, it uses a */
/* divide-and-conquer algorithm. */
/* The SVD is written */
/* A = U * SIGMA * transpose(V) */
/* where SIGMA is an M-by-N matrix which is zero except for its */
/* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
/* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
/* are the singular values of A; they are real and non-negative, and */
/* are returned in descending order. The first min(m,n) columns of */
/* U and V are the left and right singular vectors of A. */
/* Note that the routine returns VT = V**T, not V. */
/* The divide and conquer algorithm makes very mild assumptions about */
/* floating point arithmetic. It will work on machines with a guard */
/* digit in add/subtract, or on those binary machines without guard */
/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. */
/* Arguments */
/* ========= */
/* JOBZ (input) CHARACTER*1 */
/* Specifies options for computing all or part of the matrix U: */
/* = 'A': all M columns of U and all N rows of V**T are */
/* returned in the arrays U and VT; */
/* = 'S': the first min(M,N) columns of U and the first */
/* min(M,N) rows of V**T are returned in the arrays U */
/* and VT; */
/* = 'O': If M >= N, the first N columns of U are overwritten */
/* on the array A and all rows of V**T are returned in */
/* the array VT; */
/* otherwise, all columns of U are returned in the */
/* array U and the first M rows of V**T are overwritten */
/* in the array A; */
/* = 'N': no columns of U or rows of V**T are computed. */
/* M (input) INTEGER */
/* The number of rows of the input matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the input matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, */
/* if JOBZ = 'O', A is overwritten with the first N columns */
/* of U (the left singular vectors, stored */
/* columnwise) if M >= N; */
/* A is overwritten with the first M rows */
/* of V**T (the right singular vectors, stored */
/* rowwise) otherwise. */
/* if JOBZ .ne. 'O', the contents of A are destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* S (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The singular values of A, sorted so that S(i) >= S(i+1). */
/* U (output) DOUBLE PRECISION array, dimension (LDU,UCOL) */
/* UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
/* UCOL = min(M,N) if JOBZ = 'S'. */
/* If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
/* orthogonal matrix U; */
/* if JOBZ = 'S', U contains the first min(M,N) columns of U */
/* (the left singular vectors, stored columnwise); */
/* if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= 1; if */
/* JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
/* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) */
/* If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
/* N-by-N orthogonal matrix V**T; */
/* if JOBZ = 'S', VT contains the first min(M,N) rows of */
/* V**T (the right singular vectors, stored rowwise); */
/* if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
/* LDVT (input) INTEGER */
/* The leading dimension of the array VT. LDVT >= 1; if */
/* JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
/* if JOBZ = 'S', LDVT >= min(M,N). */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 1. */
/* If JOBZ = 'N', */
/* LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)). */
/* If JOBZ = 'O', */
/* LWORK >= 3*min(M,N)*min(M,N) + */
/* max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)). */
/* If JOBZ = 'S' or 'A' */
/* LWORK >= 3*min(M,N)*min(M,N) + */
/* max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)). */
/* For good performance, LWORK should generally be larger. */
/* If LWORK = -1 but other input arguments are legal, WORK(1) */
/* returns the optimal LWORK. */
/* IWORK (workspace) INTEGER array, dimension (8*min(M,N)) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: DBDSDC did not converge, updating process failed. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ming Gu and Huan Ren, Computer Science Division, University of */
/* California at Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. 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;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
wntqa = lsame_(jobz, "A");
wntqs = lsame_(jobz, "S");
wntqas = wntqa || wntqs;
wntqo = lsame_(jobz, "O");
wntqn = lsame_(jobz, "N");
lquery = *lwork == -1;
if (! (wntqa || wntqs || wntqo || wntqn)) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
m) {
*info = -8;
} else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
wntqo && *m >= *n && *ldvt < *n) {
*info = -10;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "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 DBDSDC */
mnthr = (integer) (minmn * 11. / 6.);
if (wntqn) {
bdspac = *n * 7;
} else {
bdspac = *n * 3 * *n + (*n << 2);
}
if (*m >= mnthr) {
if (wntqn) {
/* Path 1 (M much larger than N, JOBZ='N') */
wrkbl = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1,
"DGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n;
maxwrk = max(i__1,i__2);
minwrk = bdspac + *n;
} else if (wntqo) {
/* Path 2 (M much larger than N, JOBZ='O') */
wrkbl = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "DORGQR",
" ", m, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1,
"DGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "QLN", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + (*n << 1) * *n;
minwrk = bdspac + (*n << 1) * *n + *n * 3;
} else if (wntqs) {
/* Path 3 (M much larger than N, JOBZ='S') */
wrkbl = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "DORGQR",
" ", m, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1,
"DGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "QLN", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + *n * *n;
minwrk = bdspac + *n * *n + *n * 3;
} else if (wntqa) {
/* Path 4 (M much larger than N, JOBZ='A') */
wrkbl = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *m * ilaenv_(&c__1, "DORGQR",
" ", m, m, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + (*n << 1) * ilaenv_(&c__1,
"DGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "QLN", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + *n * *n;
minwrk = bdspac + *n * *n + *n * 3;
}
} else {
/* Path 5 (M at least N, but not much larger) */
wrkbl = *n * 3 + (*m + *n) * ilaenv_(&c__1, "DGEBRD", " ", m,
n, &c_n1, &c_n1);
if (wntqn) {
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n * 3;
maxwrk = max(i__1,i__2);
minwrk = *n * 3 + max(*m,bdspac);
} else if (wntqo) {
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "QLN", m, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + *m * *n;
/* Computing MAX */
i__1 = *m, i__2 = *n * *n + bdspac;
minwrk = *n * 3 + max(i__1,i__2);
} else if (wntqs) {
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "QLN", m, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n * 3;
maxwrk = max(i__1,i__2);
minwrk = *n * 3 + max(*m,bdspac);
} else if (wntqa) {
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + *n * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = bdspac + *n * 3;
maxwrk = max(i__1,i__2);
minwrk = *n * 3 + max(*m,bdspac);
}
}
} else if (minmn > 0) {
/* Compute space needed for DBDSDC */
mnthr = (integer) (minmn * 11. / 6.);
if (wntqn) {
bdspac = *m * 7;
} else {
bdspac = *m * 3 * *m + (*m << 2);
}
if (*n >= mnthr) {
if (wntqn) {
/* Path 1t (N much larger than M, JOBZ='N') */
wrkbl = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1,
"DGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m;
maxwrk = max(i__1,i__2);
minwrk = bdspac + *m;
} else if (wntqo) {
/* Path 2t (N much larger than M, JOBZ='O') */
wrkbl = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "DORGLQ",
" ", m, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1,
"DGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "PRT", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + (*m << 1) * *m;
minwrk = bdspac + (*m << 1) * *m + *m * 3;
} else if (wntqs) {
/* Path 3t (N much larger than M, JOBZ='S') */
wrkbl = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "DORGLQ",
" ", m, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1,
"DGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "PRT", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + *m * *m;
minwrk = bdspac + *m * *m + *m * 3;
} else if (wntqa) {
/* Path 4t (N much larger than M, JOBZ='A') */
wrkbl = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *n * ilaenv_(&c__1, "DORGLQ",
" ", n, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + (*m << 1) * ilaenv_(&c__1,
"DGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "PRT", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + *m * *m;
minwrk = bdspac + *m * *m + *m * 3;
}
} else {
/* Path 5t (N greater than M, but not much larger) */
wrkbl = *m * 3 + (*m + *n) * ilaenv_(&c__1, "DGEBRD", " ", m,
n, &c_n1, &c_n1);
if (wntqn) {
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
maxwrk = max(i__1,i__2);
minwrk = *m * 3 + max(*n,bdspac);
} else if (wntqo) {
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "PRT", m, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
wrkbl = max(i__1,i__2);
maxwrk = wrkbl + *m * *n;
/* Computing MAX */
i__1 = *n, i__2 = *m * *m + bdspac;
minwrk = *m * 3 + max(i__1,i__2);
} else if (wntqs) {
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "PRT", m, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
maxwrk = max(i__1,i__2);
minwrk = *m * 3 + max(*n,bdspac);
} else if (wntqa) {
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "QLN", m, m, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR"
, "PRT", n, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m * 3;
maxwrk = max(i__1,i__2);
minwrk = *m * 3 + max(*n,bdspac);
}
}
}
maxwrk = max(maxwrk,minwrk);
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGESDD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = sqrt(dlamch_("S")) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = dlange_("M", m, n, &a[a_offset], lda, dum);
iscl = 0;
if (anrm > 0. && anrm < smlnum) {
iscl = 1;
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
ierr);
} else if (anrm > bignum) {
iscl = 1;
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
ierr);
}
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 (wntqn) {
/* Path 1 (M much larger than N, JOBZ='N') */
/* No singular vectors to be computed */
itau = 1;
nwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Zero out below R */
i__1 = *n - 1;
i__2 = *n - 1;
dlaset_("L", &i__1, &i__2, &c_b227, &c_b227, &a[a_dim1 + 2],
lda);
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__1 = *lwork - nwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
nwork = ie + *n;
/* Perform bidiagonal SVD, computing singular values only */
/* (Workspace: need N+BDSPAC) */
dbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
/* Path 2 (M much larger than N, JOBZ = 'O') */
/* N left singular vectors to be overwritten on A and */
/* N right singular vectors to be computed in VT */
ir = 1;
/* WORK(IR) is LDWRKR by N */
if (*lwork >= *lda * *n + *n * *n + *n * 3 + bdspac) {
ldwrkr = *lda;
} else {
ldwrkr = (*lwork - *n * *n - *n * 3 - bdspac) / *n;
}
itau = ir + ldwrkr * *n;
nwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__1 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__1 = *n - 1;
i__2 = *n - 1;
dlaset_("L", &i__1, &i__2, &c_b227, &c_b227, &work[ir + 1], &
ldwrkr);
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__1 = *lwork - nwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
&i__1, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
nwork = 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__1 = *lwork - nwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/* WORK(IU) is N by N */
iu = nwork;
nwork = iu + *n * *n;
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in WORK(IU) and computing right */
/* singular vectors of bidiagonal matrix in VT */
/* (Workspace: need N+N*N+BDSPAC) */
dbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite WORK(IU) by left singular vectors of R */
/* and VT by right singular vectors of R */
/* (Workspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
itauq], &work[iu], n, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IU), storing result in WORK(IR) and copying to A */
/* (Workspace: need 2*N*N, prefer N*N+M*N) */
i__1 = *m;
i__2 = ldwrkr;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = min(i__3,ldwrkr);
dgemm_("N", "N", &chunk, n, n, &c_b248, &a[i__ + a_dim1],
lda, &work[iu], n, &c_b227, &work[ir], &ldwrkr);
dlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
a_dim1], lda);
/* L10: */
}
} else if (wntqs) {
/* Path 3 (M much larger than N, JOBZ='S') */
/* N left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
ir = 1;
/* WORK(IR) is N by N */
ldwrkr = *n;
itau = ir + ldwrkr * *n;
nwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__2 = *n - 1;
i__1 = *n - 1;
dlaset_("L", &i__2, &i__1, &c_b227, &c_b227, &work[ir + 1], &
ldwrkr);
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
&i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - nwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagoal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* (Workspace: need N+BDSPAC) */
dbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of R and VT */
/* by right singular vectors of R */
/* (Workspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IR), storing result in U */
/* (Workspace: need N*N) */
dlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
dgemm_("N", "N", m, n, n, &c_b248, &a[a_offset], lda, &work[
ir], &ldwrkr, &c_b227, &u[u_offset], ldu);
} else if (wntqa) {
/* Path 4 (M much larger than N, JOBZ='A') */
/* M left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
iu = 1;
/* WORK(IU) is N by N */
ldwrku = *n;
itau = iu + ldwrku * *n;
nwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
/* Generate Q in U */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
&i__2, &ierr);
/* Produce R in A, zeroing out other entries */
i__2 = *n - 1;
i__1 = *n - 1;
dlaset_("L", &i__2, &i__1, &c_b227, &c_b227, &a[a_dim1 + 2],
lda);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - nwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in WORK(IU) and computing right */
/* singular vectors of bidiagonal matrix in VT */
/* (Workspace: need N+N*N+BDSPAC) */
dbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite WORK(IU) by left singular vectors of R and VT */
/* by right singular vectors of R */
/* (Workspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IU), storing result in A */
/* (Workspace: need N*N) */
dgemm_("N", "N", m, n, n, &c_b248, &u[u_offset], ldu, &work[
iu], &ldwrku, &c_b227, &a[a_offset], lda);
/* Copy left singular vectors of A from A to U */
dlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
}
} else {
/* M .LT. MNTHR */
/* Path 5 (M at least N, but not much larger) */
/* Reduce to bidiagonal form without QR decomposition */
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize A */
/* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB) */
i__2 = *lwork - nwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__2, &ierr);
if (wntqn) {
/* Perform bidiagonal SVD, only computing singular values */
/* (Workspace: need N+BDSPAC) */
dbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
iu = nwork;
if (*lwork >= *m * *n + *n * 3 + bdspac) {
/* WORK( IU ) is M by N */
ldwrku = *m;
nwork = iu + ldwrku * *n;
dlaset_("F", m, n, &c_b227, &c_b227, &work[iu], &ldwrku);
} else {
/* WORK( IU ) is N by N */
ldwrku = *n;
nwork = iu + ldwrku * *n;
/* WORK(IR) is LDWRKR by N */
ir = nwork;
ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
}
nwork = iu + ldwrku * *n;
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in WORK(IU) and computing right */
/* singular vectors of bidiagonal matrix in VT */
/* (Workspace: need N+N*N+BDSPAC) */
dbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], &ldwrku, &
vt[vt_offset], ldvt, dum, idum, &work[nwork], &iwork[
1], info);
/* Overwrite VT by right singular vectors of A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
if (*lwork >= *m * *n + *n * 3 + bdspac) {
/* Overwrite WORK(IU) by left singular vectors of A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
ierr);
/* Copy left singular vectors of A from WORK(IU) to A */
dlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
} else {
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - nwork + 1;
dorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
work[nwork], &i__2, &ierr);
/* Multiply Q in A by left singular vectors of */
/* bidiagonal matrix in WORK(IU), storing result in */
/* WORK(IR) and copying to A */
/* (Workspace: need 2*N*N, prefer N*N+M*N) */
i__2 = *m;
i__1 = ldwrkr;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = min(i__3,ldwrkr);
dgemm_("N", "N", &chunk, n, n, &c_b248, &a[i__ +
a_dim1], lda, &work[iu], &ldwrku, &c_b227, &
work[ir], &ldwrkr);
dlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
a_dim1], lda);
/* L20: */
}
}
} else if (wntqs) {
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* (Workspace: need N+BDSPAC) */
dlaset_("F", m, n, &c_b227, &c_b227, &u[u_offset], ldu);
dbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* (Workspace: need 3*N, prefer 2*N+N*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
} else if (wntqa) {
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* (Workspace: need N+BDSPAC) */
dlaset_("F", m, m, &c_b227, &c_b227, &u[u_offset], ldu);
dbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Set the right corner of U to identity matrix */
if (*m > *n) {
i__1 = *m - *n;
i__2 = *m - *n;
dlaset_("F", &i__1, &i__2, &c_b227, &c_b248, &u[*n + 1 + (
*n + 1) * u_dim1], ldu);
}
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* (Workspace: need N*N+2*N+M, prefer N*N+2*N+M*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
}
}
} 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 (wntqn) {
/* Path 1t (N much larger than M, JOBZ='N') */
/* No singular vectors to be computed */
itau = 1;
nwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__1 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Zero out above L */
i__1 = *m - 1;
i__2 = *m - 1;
dlaset_("U", &i__1, &i__2, &c_b227, &c_b227, &a[(a_dim1 << 1)
+ 1], lda);
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__1 = *lwork - nwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
nwork = ie + *m;
/* Perform bidiagonal SVD, computing singular values only */
/* (Workspace: need M+BDSPAC) */
dbdsdc_("U", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
/* Path 2t (N much larger than M, JOBZ='O') */
/* M right singular vectors to be overwritten on A and */
/* M left singular vectors to be computed in U */
ivt = 1;
/* IVT is M by M */
il = ivt + *m * *m;
if (*lwork >= *m * *n + *m * *m + *m * 3 + bdspac) {
/* WORK(IL) is M by N */
ldwrkl = *m;
chunk = *n;
} else {
ldwrkl = *m;
chunk = (*lwork - *m * *m) / *m;
}
itau = il + ldwrkl * *m;
nwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__1 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy L to WORK(IL), zeroing about above it */
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
i__1 = *m - 1;
i__2 = *m - 1;
dlaset_("U", &i__1, &i__2, &c_b227, &c_b227, &work[il +
ldwrkl], &ldwrkl);
/* Generate Q in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__1 = *lwork - nwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
&i__1, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in WORK(IL) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__1 = *lwork - nwork + 1;
dgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U, and computing right singular */
/* vectors of bidiagonal matrix in WORK(IVT) */
/* (Workspace: need M+M*M+BDSPAC) */
dbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
work[ivt], m, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of L and WORK(IVT) */
/* by right singular vectors of L */
/* (Workspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
itaup], &work[ivt], m, &work[nwork], &i__1, &ierr);
/* Multiply right singular vectors of L in WORK(IVT) by Q */
/* in A, storing result in WORK(IL) and copying to A */
/* (Workspace: need 2*M*M, prefer M*M+M*N) */
i__1 = *n;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = min(i__3,chunk);
dgemm_("N", "N", m, &blk, m, &c_b248, &work[ivt], m, &a[
i__ * a_dim1 + 1], lda, &c_b227, &work[il], &
ldwrkl);
dlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
+ 1], lda);
/* L30: */
}
} else if (wntqs) {
/* Path 3t (N much larger than M, JOBZ='S') */
/* M right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
il = 1;
/* WORK(IL) is M by M */
ldwrkl = *m;
itau = il + ldwrkl * *m;
nwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy L to WORK(IL), zeroing out above it */
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
i__2 = *m - 1;
i__1 = *m - 1;
dlaset_("U", &i__2, &i__1, &c_b227, &c_b227, &work[il +
ldwrkl], &ldwrkl);
/* Generate Q in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
&i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
nwork = 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 - nwork + 1;
dgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* (Workspace: need M+BDSPAC) */
dbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of L and VT */
/* by right singular vectors of L */
/* (Workspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/* Multiply right singular vectors of L in WORK(IL) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
dlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
dgemm_("N", "N", m, n, m, &c_b248, &work[il], &ldwrkl, &a[
a_offset], lda, &c_b227, &vt[vt_offset], ldvt);
} else if (wntqa) {
/* Path 4t (N much larger than M, JOBZ='A') */
/* N right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
ivt = 1;
/* WORK(IVT) is M by M */
ldwkvt = *m;
itau = ivt + ldwkvt * *m;
nwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
/* Generate Q in VT */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
nwork], &i__2, &ierr);
/* Produce L in A, zeroing out other entries */
i__2 = *m - 1;
i__1 = *m - 1;
dlaset_("U", &i__2, &i__1, &c_b227, &c_b227, &a[(a_dim1 << 1)
+ 1], lda);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in A */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__2 = *lwork - nwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in WORK(IVT) */
/* (Workspace: need M+M*M+BDSPAC) */
dbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
, info);
/* Overwrite U by left singular vectors of L and WORK(IVT) */
/* by right singular vectors of L */
/* (Workspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, m, m, &a[a_offset], lda, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
ierr);
/* Multiply right singular vectors of L in WORK(IVT) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
dgemm_("N", "N", m, n, m, &c_b248, &work[ivt], &ldwkvt, &vt[
vt_offset], ldvt, &c_b227, &a[a_offset], lda);
/* Copy right singular vectors of A from A to VT */
dlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
}
} else {
/* N .LT. MNTHR */
/* Path 5t (N greater than M, but not much larger) */
/* Reduce to bidiagonal form without LQ decomposition */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize A */
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__2 = *lwork - nwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__2, &ierr);
if (wntqn) {
/* Perform bidiagonal SVD, only computing singular values */
/* (Workspace: need M+BDSPAC) */
dbdsdc_("L", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
ldwkvt = *m;
ivt = nwork;
if (*lwork >= *m * *n + *m * 3 + bdspac) {
/* WORK( IVT ) is M by N */
dlaset_("F", m, n, &c_b227, &c_b227, &work[ivt], &ldwkvt);
nwork = ivt + ldwkvt * *n;
} else {
/* WORK( IVT ) is M by M */
nwork = ivt + ldwkvt * *m;
il = nwork;
/* WORK(IL) is M by CHUNK */
chunk = (*lwork - *m * *m - *m * 3) / *m;
}
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in WORK(IVT) */
/* (Workspace: need M*M+BDSPAC) */
dbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
, info);
/* Overwrite U by left singular vectors of A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
if (*lwork >= *m * *n + *m * 3 + bdspac) {
/* Overwrite WORK(IVT) by left singular vectors of A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
&ierr);
/* Copy right singular vectors of A from WORK(IVT) to A */
dlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
} else {
/* Generate P**T in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - nwork + 1;
dorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
work[nwork], &i__2, &ierr);
/* Multiply Q in A by right singular vectors of */
/* bidiagonal matrix in WORK(IVT), storing result in */
/* WORK(IL) and copying to A */
/* (Workspace: need 2*M*M, prefer M*M+M*N) */
i__2 = *n;
i__1 = chunk;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = min(i__3,chunk);
dgemm_("N", "N", m, &blk, m, &c_b248, &work[ivt], &
ldwkvt, &a[i__ * a_dim1 + 1], lda, &c_b227, &
work[il], m);
dlacpy_("F", m, &blk, &work[il], m, &a[i__ * a_dim1 +
1], lda);
/* L40: */
}
}
} else if (wntqs) {
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* (Workspace: need M+BDSPAC) */
dlaset_("F", m, n, &c_b227, &c_b227, &vt[vt_offset], ldvt);
dbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* (Workspace: need 3*M, prefer 2*M+M*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
} else if (wntqa) {
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* (Workspace: need M+BDSPAC) */
dlaset_("F", n, n, &c_b227, &c_b227, &vt[vt_offset], ldvt);
dbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Set the right corner of VT to identity matrix */
if (*n > *m) {
i__1 = *n - *m;
i__2 = *n - *m;
dlaset_("F", &i__1, &i__2, &c_b227, &c_b248, &vt[*m + 1 +
(*m + 1) * vt_dim1], ldvt);
}
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* (Workspace: need 2*M+N, prefer 2*M+N*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
}
}
}
/* Undo scaling if necessary */
if (iscl == 1) {
if (anrm > bignum) {
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
if (anrm < smlnum) {
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
}
/* Return optimal workspace in WORK(1) */
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGESDD */
} /* dgesdd_ */