--- /dev/null
+#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_ */
projects / opencv / blobdiff