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- /* dgesvd.f -- translated by f2c (version 20061008).
- You must link the resulting object file with libf2c:
- on Microsoft Windows system, link with libf2c.lib;
- on Linux or Unix systems, link with .../path/to/libf2c.a -lm
- or, if you install libf2c.a in a standard place, with -lf2c -lm
- -- in that order, at the end of the command line, as in
- cc *.o -lf2c -lm
- Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
- http://www.netlib.org/f2c/libf2c.zip
- */
- #include "f2c.h"
- #include "blaswrap.h"
- /* Table of constant values */
- static integer c__6 = 6;
- static integer c__0 = 0;
- static integer c__2 = 2;
- static integer c__1 = 1;
- static integer c_n1 = -1;
- static doublereal c_b421 = 0.;
- static doublereal c_b443 = 1.;
- /* Subroutine */ int _starpu_dgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
- doublereal *a, integer *lda, doublereal *s, doublereal *u, integer *
- ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork,
- integer *info)
- {
- /* System generated locals */
- address a__1[2];
- integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2],
- i__2, i__3, i__4;
- char ch__1[2];
- /* Builtin functions */
- /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
- double sqrt(doublereal);
- /* Local variables */
- integer i__, ie, ir, iu, blk, ncu;
- doublereal dum[1], eps;
- integer nru, iscl;
- doublereal anrm;
- integer ierr, itau, ncvt, nrvt;
- extern /* Subroutine */ int _starpu_dgemm_(char *, char *, integer *, integer *,
- integer *, doublereal *, doublereal *, integer *, doublereal *,
- integer *, doublereal *, doublereal *, integer *);
- extern logical _starpu_lsame_(char *, char *);
- integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork;
- logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
- extern /* Subroutine */ int _starpu_dgebrd_(integer *, integer *, doublereal *,
- integer *, doublereal *, doublereal *, doublereal *, doublereal *,
- doublereal *, integer *, integer *);
- extern doublereal _starpu_dlamch_(char *), _starpu_dlange_(char *, integer *,
- integer *, doublereal *, integer *, doublereal *);
- integer bdspac;
- extern /* Subroutine */ int _starpu_dgelqf_(integer *, integer *, doublereal *,
- integer *, doublereal *, doublereal *, integer *, integer *),
- _starpu_dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
- integer *, integer *, doublereal *, integer *, integer *),
- _starpu_dgeqrf_(integer *, integer *, doublereal *, integer *,
- doublereal *, doublereal *, integer *, integer *), _starpu_dlacpy_(char *,
- integer *, integer *, doublereal *, integer *, doublereal *,
- integer *), _starpu_dlaset_(char *, integer *, integer *,
- doublereal *, doublereal *, doublereal *, integer *),
- _starpu_dbdsqr_(char *, integer *, integer *, integer *, integer *,
- doublereal *, doublereal *, doublereal *, integer *, doublereal *,
- integer *, doublereal *, integer *, doublereal *, integer *), _starpu_dorgbr_(char *, integer *, integer *, integer *,
- doublereal *, integer *, doublereal *, doublereal *, integer *,
- integer *);
- doublereal bignum;
- extern /* Subroutine */ int _starpu_xerbla_(char *, integer *);
- extern integer _starpu_ilaenv_(integer *, char *, char *, integer *, integer *,
- integer *, integer *);
- extern /* Subroutine */ int _starpu_dormbr_(char *, char *, char *, integer *,
- integer *, integer *, doublereal *, integer *, doublereal *,
- doublereal *, integer *, doublereal *, integer *, integer *), _starpu_dorglq_(integer *, integer *, integer *,
- doublereal *, integer *, doublereal *, doublereal *, integer *,
- integer *), _starpu_dorgqr_(integer *, integer *, integer *, doublereal *,
- integer *, doublereal *, doublereal *, integer *, integer *);
- integer ldwrkr, minwrk, ldwrku, maxwrk;
- doublereal smlnum;
- logical lquery, wntuas, wntvas;
- /* -- LAPACK driver routine (version 3.2) -- */
- /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
- /* November 2006 */
- /* .. Scalar Arguments .. */
- /* .. */
- /* .. Array Arguments .. */
- /* .. */
- /* Purpose */
- /* ======= */
- /* DGESVD computes the singular value decomposition (SVD) of a real */
- /* M-by-N matrix A, optionally computing the left and/or right singular */
- /* vectors. The SVD is written */
- /* A = U * SIGMA * transpose(V) */
- /* where SIGMA is an M-by-N matrix which is zero except for its */
- /* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
- /* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
- /* are the singular values of A; they are real and non-negative, and */
- /* are returned in descending order. The first min(m,n) columns of */
- /* U and V are the left and right singular vectors of A. */
- /* Note that the routine returns V**T, not V. */
- /* Arguments */
- /* ========= */
- /* JOBU (input) CHARACTER*1 */
- /* Specifies options for computing all or part of the matrix U: */
- /* = 'A': all M columns of U are returned in array U: */
- /* = 'S': the first min(m,n) columns of U (the left singular */
- /* vectors) are returned in the array U; */
- /* = 'O': the first min(m,n) columns of U (the left singular */
- /* vectors) are overwritten on the array A; */
- /* = 'N': no columns of U (no left singular vectors) are */
- /* computed. */
- /* JOBVT (input) CHARACTER*1 */
- /* Specifies options for computing all or part of the matrix */
- /* V**T: */
- /* = 'A': all N rows of V**T are returned in the array VT; */
- /* = 'S': the first min(m,n) rows of V**T (the right singular */
- /* vectors) are returned in the array VT; */
- /* = 'O': the first min(m,n) rows of V**T (the right singular */
- /* vectors) are overwritten on the array A; */
- /* = 'N': no rows of V**T (no right singular vectors) are */
- /* computed. */
- /* JOBVT and JOBU cannot both be 'O'. */
- /* 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 JOBU = 'O', A is overwritten with the first min(m,n) */
- /* columns of U (the left singular vectors, */
- /* stored columnwise); */
- /* if JOBVT = 'O', A is overwritten with the first min(m,n) */
- /* rows of V**T (the right singular vectors, */
- /* stored rowwise); */
- /* if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */
- /* are destroyed. */
- /* 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) */
- /* (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. */
- /* If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */
- /* if JOBU = 'S', U contains the first min(m,n) columns of U */
- /* (the left singular vectors, stored columnwise); */
- /* if JOBU = 'N' or 'O', U is not referenced. */
- /* LDU (input) INTEGER */
- /* The leading dimension of the array U. LDU >= 1; if */
- /* JOBU = 'S' or 'A', LDU >= M. */
- /* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) */
- /* If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */
- /* V**T; */
- /* if JOBVT = 'S', VT contains the first min(m,n) rows of */
- /* V**T (the right singular vectors, stored rowwise); */
- /* if JOBVT = 'N' or 'O', VT is not referenced. */
- /* LDVT (input) INTEGER */
- /* The leading dimension of the array VT. LDVT >= 1; if */
- /* JOBVT = 'A', LDVT >= N; if JOBVT = '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; */
- /* if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */
- /* superdiagonal elements of an upper bidiagonal matrix B */
- /* whose diagonal is in S (not necessarily sorted). B */
- /* satisfies A = U * B * VT, so it has the same singular values */
- /* as A, and singular vectors related by U and VT. */
- /* LWORK (input) INTEGER */
- /* The dimension of the array WORK. */
- /* LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)). */
- /* For good performance, LWORK should generally be larger. */
- /* If LWORK = -1, then a workspace query is assumed; the routine */
- /* only calculates the optimal size of the WORK array, returns */
- /* this value as the first entry of the WORK array, and no error */
- /* message related to LWORK is issued by XERBLA. */
- /* INFO (output) INTEGER */
- /* = 0: successful exit. */
- /* < 0: if INFO = -i, the i-th argument had an illegal value. */
- /* > 0: if DBDSQR did not converge, INFO specifies how many */
- /* superdiagonals of an intermediate bidiagonal form B */
- /* did not converge to zero. See the description of WORK */
- /* above for details. */
- /* ===================================================================== */
- /* .. Parameters .. */
- /* .. */
- /* .. Local Scalars .. */
- /* .. */
- /* .. Local Arrays .. */
- /* .. */
- /* .. External Subroutines .. */
- /* .. */
- /* .. External Functions .. */
- /* .. */
- /* .. Intrinsic Functions .. */
- /* .. */
- /* .. Executable Statements .. */
- /* Test the input arguments */
- /* Parameter adjustments */
- a_dim1 = *lda;
- a_offset = 1 + a_dim1;
- a -= a_offset;
- --s;
- u_dim1 = *ldu;
- u_offset = 1 + u_dim1;
- u -= u_offset;
- vt_dim1 = *ldvt;
- vt_offset = 1 + vt_dim1;
- vt -= vt_offset;
- --work;
- /* Function Body */
- *info = 0;
- minmn = min(*m,*n);
- wntua = _starpu_lsame_(jobu, "A");
- wntus = _starpu_lsame_(jobu, "S");
- wntuas = wntua || wntus;
- wntuo = _starpu_lsame_(jobu, "O");
- wntun = _starpu_lsame_(jobu, "N");
- wntva = _starpu_lsame_(jobvt, "A");
- wntvs = _starpu_lsame_(jobvt, "S");
- wntvas = wntva || wntvs;
- wntvo = _starpu_lsame_(jobvt, "O");
- wntvn = _starpu_lsame_(jobvt, "N");
- lquery = *lwork == -1;
- if (! (wntua || wntus || wntuo || wntun)) {
- *info = -1;
- } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
- *info = -2;
- } else if (*m < 0) {
- *info = -3;
- } else if (*n < 0) {
- *info = -4;
- } else if (*lda < max(1,*m)) {
- *info = -6;
- } else if (*ldu < 1 || wntuas && *ldu < *m) {
- *info = -9;
- } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
- *info = -11;
- }
- /* Compute workspace */
- /* (Note: Comments in the code beginning "Workspace:" describe the */
- /* minimal amount of workspace needed at that point in the code, */
- /* as well as the preferred amount for good performance. */
- /* NB refers to the optimal block size for the immediately */
- /* following subroutine, as returned by ILAENV.) */
- if (*info == 0) {
- minwrk = 1;
- maxwrk = 1;
- if (*m >= *n && minmn > 0) {
- /* Compute space needed for DBDSQR */
- /* Writing concatenation */
- i__1[0] = 1, a__1[0] = jobu;
- i__1[1] = 1, a__1[1] = jobvt;
- s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
- mnthr = _starpu_ilaenv_(&c__6, "DGESVD", ch__1, m, n, &c__0, &c__0);
- bdspac = *n * 5;
- if (*m >= mnthr) {
- if (wntun) {
- /* Path 1 (M much larger than N, JOBU='N') */
- maxwrk = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- maxwrk = max(i__2,i__3);
- if (wntvo || wntvas) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&
- c__1, "DORGBR", "P", n, n, n, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- maxwrk = max(maxwrk,bdspac);
- /* Computing MAX */
- i__2 = *n << 2;
- minwrk = max(i__2,bdspac);
- } else if (wntuo && wntvn) {
- /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *n * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- /* Computing MAX */
- i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;
- maxwrk = max(i__2,i__3);
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntuo && wntvas) {
- /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
- /* 'A') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *n * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- /* Computing MAX */
- i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;
- maxwrk = max(i__2,i__3);
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntus && wntvn) {
- /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *n * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *n * *n + wrkbl;
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntus && wntvo) {
- /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *n * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = (*n << 1) * *n + wrkbl;
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntus && wntvas) {
- /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
- /* 'A') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *n * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *n * *n + wrkbl;
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntua && wntvn) {
- /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *m * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, m, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *n * *n + wrkbl;
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntua && wntvo) {
- /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *m * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, m, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = (*n << 1) * *n + wrkbl;
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- } else if (wntua && wntvas) {
- /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
- /* 'A') */
- wrkbl = *n + *n * _starpu_ilaenv_(&c__1, "DGEQRF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n + *m * _starpu_ilaenv_(&c__1, "DORGQR",
- " ", m, m, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", n, n, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", n, n, n, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *n * *n + wrkbl;
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- }
- } else {
- /* Path 10 (M at least N, but not much larger) */
- maxwrk = *n * 3 + (*m + *n) * _starpu_ilaenv_(&c__1, "DGEBRD", " ", m,
- n, &c_n1, &c_n1);
- if (wntus || wntuo) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *n * 3 + *n * _starpu_ilaenv_(&c__1, "DORG"
- "BR", "Q", m, n, n, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- if (wntua) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *n * 3 + *m * _starpu_ilaenv_(&c__1, "DORG"
- "BR", "Q", m, m, n, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- if (! wntvn) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *n * 3 + (*n - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", n, n, n, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- maxwrk = max(maxwrk,bdspac);
- /* Computing MAX */
- i__2 = *n * 3 + *m;
- minwrk = max(i__2,bdspac);
- }
- } else if (minmn > 0) {
- /* Compute space needed for DBDSQR */
- /* Writing concatenation */
- i__1[0] = 1, a__1[0] = jobu;
- i__1[1] = 1, a__1[1] = jobvt;
- s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
- mnthr = _starpu_ilaenv_(&c__6, "DGESVD", ch__1, m, n, &c__0, &c__0);
- bdspac = *m * 5;
- if (*n >= mnthr) {
- if (wntvn) {
- /* Path 1t(N much larger than M, JOBVT='N') */
- maxwrk = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- maxwrk = max(i__2,i__3);
- if (wntuo || wntuas) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1,
- "DORGBR", "Q", m, m, m, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- maxwrk = max(maxwrk,bdspac);
- /* Computing MAX */
- i__2 = *m << 2;
- minwrk = max(i__2,bdspac);
- } else if (wntvo && wntun) {
- /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *m * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", m, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- /* Computing MAX */
- i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m;
- maxwrk = max(i__2,i__3);
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntvo && wntuas) {
- /* Path 3t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='O') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *m * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", m, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- /* Computing MAX */
- i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m;
- maxwrk = max(i__2,i__3);
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntvs && wntun) {
- /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *m * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", m, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *m * *m + wrkbl;
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntvs && wntuo) {
- /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *m * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", m, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = (*m << 1) * *m + wrkbl;
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntvs && wntuas) {
- /* Path 6t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='S') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *m * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", m, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *m * *m + wrkbl;
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntva && wntun) {
- /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *n * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", n, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *m * *m + wrkbl;
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntva && wntuo) {
- /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *n * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", n, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = (*m << 1) * *m + wrkbl;
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- } else if (wntva && wntuas) {
- /* Path 9t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='A') */
- wrkbl = *m + *m * _starpu_ilaenv_(&c__1, "DGELQF", " ", m, n, &
- c_n1, &c_n1);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m + *n * _starpu_ilaenv_(&c__1, "DORGLQ",
- " ", n, n, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m << 1) * _starpu_ilaenv_(&c__1,
- "DGEBRD", " ", m, m, &c_n1, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "P", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1, "DORGBR"
- , "Q", m, m, m, &c_n1);
- wrkbl = max(i__2,i__3);
- wrkbl = max(wrkbl,bdspac);
- maxwrk = *m * *m + wrkbl;
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- }
- } else {
- /* Path 10t(N greater than M, but not much larger) */
- maxwrk = *m * 3 + (*m + *n) * _starpu_ilaenv_(&c__1, "DGEBRD", " ", m,
- n, &c_n1, &c_n1);
- if (wntvs || wntvo) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *m * 3 + *m * _starpu_ilaenv_(&c__1, "DORG"
- "BR", "P", m, n, m, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- if (wntva) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *m * 3 + *n * _starpu_ilaenv_(&c__1, "DORG"
- "BR", "P", n, n, m, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- if (! wntun) {
- /* Computing MAX */
- i__2 = maxwrk, i__3 = *m * 3 + (*m - 1) * _starpu_ilaenv_(&c__1,
- "DORGBR", "Q", m, m, m, &c_n1);
- maxwrk = max(i__2,i__3);
- }
- maxwrk = max(maxwrk,bdspac);
- /* Computing MAX */
- i__2 = *m * 3 + *n;
- minwrk = max(i__2,bdspac);
- }
- }
- maxwrk = max(maxwrk,minwrk);
- work[1] = (doublereal) maxwrk;
- if (*lwork < minwrk && ! lquery) {
- *info = -13;
- }
- }
- if (*info != 0) {
- i__2 = -(*info);
- _starpu_xerbla_("DGESVD", &i__2);
- return 0;
- } else if (lquery) {
- return 0;
- }
- /* Quick return if possible */
- if (*m == 0 || *n == 0) {
- return 0;
- }
- /* Get machine constants */
- eps = _starpu_dlamch_("P");
- smlnum = sqrt(_starpu_dlamch_("S")) / eps;
- bignum = 1. / smlnum;
- /* Scale A if max element outside range [SMLNUM,BIGNUM] */
- anrm = _starpu_dlange_("M", m, n, &a[a_offset], lda, dum);
- iscl = 0;
- if (anrm > 0. && anrm < smlnum) {
- iscl = 1;
- _starpu_dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
- ierr);
- } else if (anrm > bignum) {
- iscl = 1;
- _starpu_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 (wntun) {
- /* Path 1 (M much larger than N, JOBU='N') */
- /* No left singular vectors to be computed */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
- i__2, &ierr);
- /* Zero out below R */
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &a[a_dim1 + 2],
- lda);
- ie = 1;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in A */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- ncvt = 0;
- if (wntvo || wntvas) {
- /* If right singular vectors desired, generate P'. */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &
- work[iwork], &i__2, &ierr);
- ncvt = *n;
- }
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in A if desired */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork],
- info);
- /* If right singular vectors desired in VT, copy them there */
- if (wntvas) {
- _starpu_dlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- }
- } else if (wntuo && wntvn) {
- /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
- /* N left singular vectors to be overwritten on A and */
- /* no right singular vectors to be computed */
- /* Computing MAX */
- i__2 = *n << 2;
- if (*lwork >= *n * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n + *n;
- if (*lwork >= max(i__2,i__3) + *lda * *n) {
- /* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
- ldwrku = *lda;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n + *n;
- if (*lwork >= max(i__2,i__3) + *n * *n) {
- /* WORK(IU) is LDA by N, WORK(IR) is N by N */
- ldwrku = *lda;
- ldwrkr = *n;
- } else {
- /* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
- ldwrku = (*lwork - *n * *n - *n) / *n;
- ldwrkr = *n;
- }
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
- /* Copy R to WORK(IR) and zero out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[ir + 1]
- , &ldwrkr);
- /* Generate Q in A */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- /* Generate left vectors bidiagonalizing R */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
- work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) */
- /* (Workspace: need N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, &
- c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork]
- , info);
- iu = ie + *n;
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in WORK(IU) and copying to A */
- /* (Workspace: need N*N+2*N, prefer N*N+M*N+N) */
- i__2 = *m;
- i__3 = ldwrku;
- for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__3) {
- /* Computing MIN */
- i__4 = *m - i__ + 1;
- chunk = min(i__4,ldwrku);
- _starpu_dgemm_("N", "N", &chunk, n, n, &c_b443, &a[i__ +
- a_dim1], lda, &work[ir], &ldwrkr, &c_b421, &
- work[iu], &ldwrku);
- _starpu_dlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
- a_dim1], lda);
- /* L10: */
- }
- } else {
- /* Insufficient workspace for a fast algorithm */
- ie = 1;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize A */
- /* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__3, &ierr);
- /* Generate left vectors bidiagonalizing A */
- /* (Workspace: need 4*N, prefer 3*N+N*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
- work[iwork], &i__3, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, &
- c__1, &a[a_offset], lda, dum, &c__1, &work[iwork],
- info);
- }
- } else if (wntuo && wntvas) {
- /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
- /* N left singular vectors to be overwritten on A and */
- /* N right singular vectors to be computed in VT */
- /* Computing MAX */
- i__3 = *n << 2;
- if (*lwork >= *n * *n + max(i__3,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n + *n;
- if (*lwork >= max(i__3,i__2) + *lda * *n) {
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
- ldwrku = *lda;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n + *n;
- if (*lwork >= max(i__3,i__2) + *n * *n) {
- /* WORK(IU) is LDA by N and WORK(IR) is N by N */
- ldwrku = *lda;
- ldwrkr = *n;
- } else {
- /* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
- ldwrku = (*lwork - *n * *n - *n) / *n;
- ldwrkr = *n;
- }
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__3, &ierr);
- /* Copy R to VT, zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__3 = *n - 1;
- i__2 = *n - 1;
- _starpu_dlaset_("L", &i__3, &i__2, &c_b421, &c_b421, &vt[
- vt_dim1 + 2], ldvt);
- }
- /* Generate Q in A */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__3, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in VT, copying result to WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &i__3, &
- ierr);
- _starpu_dlacpy_("L", n, n, &vt[vt_offset], ldvt, &work[ir], &
- ldwrkr);
- /* Generate left vectors bidiagonalizing R in WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
- work[iwork], &i__3, &ierr);
- /* Generate right vectors bidiagonalizing R in VT */
- /* (Workspace: need N*N+4*N-1, prefer N*N+3*N+(N-1)*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
- &work[iwork], &i__3, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) and computing right */
- /* singular vectors of R in VT */
- /* (Workspace: need N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1,
- &work[iwork], info);
- iu = ie + *n;
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in WORK(IU) and copying to A */
- /* (Workspace: need N*N+2*N, prefer N*N+M*N+N) */
- i__3 = *m;
- i__2 = ldwrku;
- for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
- i__2) {
- /* Computing MIN */
- i__4 = *m - i__ + 1;
- chunk = min(i__4,ldwrku);
- _starpu_dgemm_("N", "N", &chunk, n, n, &c_b443, &a[i__ +
- a_dim1], lda, &work[ir], &ldwrkr, &c_b421, &
- work[iu], &ldwrku);
- _starpu_dlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
- a_dim1], lda);
- /* L20: */
- }
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
- /* Copy R to VT, zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &vt[
- vt_dim1 + 2], ldvt);
- }
- /* Generate Q in A */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in VT */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &i__2, &
- ierr);
- /* Multiply Q in A by left vectors bidiagonalizing R */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt, &
- work[itauq], &a[a_offset], lda, &work[iwork], &
- i__2, &ierr);
- /* Generate right vectors bidiagonalizing R in VT */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A and computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
- work[iwork], info);
- }
- } else if (wntus) {
- if (wntvn) {
- /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
- /* N left singular vectors to be computed in U and */
- /* no right singular vectors to be computed */
- /* Computing MAX */
- i__2 = *n << 2;
- if (*lwork >= *n * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- if (*lwork >= wrkbl + *lda * *n) {
- /* WORK(IR) is LDA by N */
- ldwrkr = *lda;
- } else {
- /* WORK(IR) is N by N */
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy R to WORK(IR), zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[ir
- + 1], &ldwrkr);
- /* Generate Q in A */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Generate left vectors bidiagonalizing R in WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) */
- /* (Workspace: need N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, &c__0, n, &c__0, &s[1], &work[ie],
- dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, &
- work[iwork], info);
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IR), storing result in U */
- /* (Workspace: need N*N) */
- _starpu_dgemm_("N", "N", m, n, n, &c_b443, &a[a_offset], lda,
- &work[ir], &ldwrkr, &c_b421, &u[u_offset],
- ldu);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Zero out below R in A */
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &a[
- a_dim1 + 2], lda);
- /* Bidiagonalize R in A */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply Q in U by left vectors bidiagonalizing R */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &c__0, m, &c__0, &s[1], &work[ie],
- dum, &c__1, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- }
- } else if (wntvo) {
- /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
- /* N left singular vectors to be computed in U and */
- /* N right singular vectors to be overwritten on A */
- /* Computing MAX */
- i__2 = *n << 2;
- if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *n) {
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
- /* WORK(IU) is LDA by N and WORK(IR) is N by N */
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- } else {
- /* WORK(IU) is N by N and WORK(IR) is N by N */
- ldwrku = *n;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy R to WORK(IU), zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + 1], &ldwrku);
- /* Generate Q in A */
- /* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (Workspace: need 2*N*N+4*N, */
- /* prefer 2*N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- /* Generate right bidiagonalizing vectors in WORK(IR) */
- /* (Workspace: need 2*N*N+4*N-1, */
- /* prefer 2*N*N+3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in WORK(IR) */
- /* (Workspace: need 2*N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &work[
- ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1,
- &work[iwork], info);
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IU), storing result in U */
- /* (Workspace: need N*N) */
- _starpu_dgemm_("N", "N", m, n, n, &c_b443, &a[a_offset], lda,
- &work[iu], &ldwrku, &c_b421, &u[u_offset],
- ldu);
- /* Copy right singular vectors of R to A */
- /* (Workspace: need N*N) */
- _starpu_dlacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
- lda);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Zero out below R in A */
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &a[
- a_dim1 + 2], lda);
- /* Bidiagonalize R in A */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply Q in U by left vectors bidiagonalizing R */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
- /* Generate right vectors bidiagonalizing R in A */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, &u[u_offset], ldu, dum, &c__1,
- &work[iwork], info);
- }
- } else if (wntvas) {
- /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
- /* or 'A') */
- /* N left singular vectors to be computed in U and */
- /* N right singular vectors to be computed in VT */
- /* Computing MAX */
- i__2 = *n << 2;
- if (*lwork >= *n * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + *lda * *n) {
- /* WORK(IU) is LDA by N */
- ldwrku = *lda;
- } else {
- /* WORK(IU) is N by N */
- ldwrku = *n;
- }
- itau = iu + ldwrku * *n;
- iwork = itau + *n;
- /* Compute A=Q*R */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy R to WORK(IU), zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + 1], &ldwrku);
- /* Generate Q in A */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IU), copying result to VT */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
- ldvt);
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- /* Generate right bidiagonalizing vectors in VT */
- /* (Workspace: need N*N+4*N-1, */
- /* prefer N*N+3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in VT */
- /* (Workspace: need N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &work[iu], &ldwrku, dum, &
- c__1, &work[iwork], info);
- /* Multiply Q in A by left singular vectors of R in */
- /* WORK(IU), storing result in U */
- /* (Workspace: need N*N) */
- _starpu_dgemm_("N", "N", m, n, n, &c_b443, &a[a_offset], lda,
- &work[iu], &ldwrku, &c_b421, &u[u_offset],
- ldu);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy R to VT, zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &vt[
- vt_dim1 + 2], ldvt);
- }
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in VT */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie],
- &work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in VT */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
- &work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr);
- /* Generate right bidiagonalizing vectors in VT */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, dum, &
- c__1, &work[iwork], info);
- }
- }
- } else if (wntua) {
- if (wntvn) {
- /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
- /* M left singular vectors to be computed in U and */
- /* no right singular vectors to be computed */
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3);
- if (*lwork >= *n * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- if (*lwork >= wrkbl + *lda * *n) {
- /* WORK(IR) is LDA by N */
- ldwrkr = *lda;
- } else {
- /* WORK(IR) is N by N */
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Copy R to WORK(IR), zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[ir
- + 1], &ldwrkr);
- /* Generate Q in U */
- /* (Workspace: need N*N+N+M, prefer N*N+N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Generate left bidiagonalizing vectors in WORK(IR) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IR) */
- /* (Workspace: need N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, &c__0, n, &c__0, &s[1], &work[ie],
- dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, &
- work[iwork], info);
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IR), storing result in A */
- /* (Workspace: need N*N) */
- _starpu_dgemm_("N", "N", m, n, n, &c_b443, &u[u_offset], ldu,
- &work[ir], &ldwrkr, &c_b421, &a[a_offset],
- lda);
- /* Copy left singular vectors of A from A to U */
- _starpu_dlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need N+M, prefer N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Zero out below R in A */
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &a[
- a_dim1 + 2], lda);
- /* Bidiagonalize R in A */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in A */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &c__0, m, &c__0, &s[1], &work[ie],
- dum, &c__1, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- }
- } else if (wntvo) {
- /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
- /* M left singular vectors to be computed in U and */
- /* N right singular vectors to be overwritten on A */
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3);
- if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *n) {
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *n) * *n) {
- /* WORK(IU) is LDA by N and WORK(IR) is N by N */
- ldwrku = *lda;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- } else {
- /* WORK(IU) is N by N and WORK(IR) is N by N */
- ldwrku = *n;
- ir = iu + ldwrku * *n;
- ldwrkr = *n;
- }
- itau = ir + ldwrkr * *n;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy R to WORK(IU), zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + 1], &ldwrku);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (Workspace: need 2*N*N+4*N, */
- /* prefer 2*N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- /* Generate right bidiagonalizing vectors in WORK(IR) */
- /* (Workspace: need 2*N*N+4*N-1, */
- /* prefer 2*N*N+3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in WORK(IR) */
- /* (Workspace: need 2*N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &work[
- ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1,
- &work[iwork], info);
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IU), storing result in A */
- /* (Workspace: need N*N) */
- _starpu_dgemm_("N", "N", m, n, n, &c_b443, &u[u_offset], ldu,
- &work[iu], &ldwrku, &c_b421, &a[a_offset],
- lda);
- /* Copy left singular vectors of A from A to U */
- _starpu_dlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Copy right singular vectors of R from WORK(IR) to A */
- _starpu_dlacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
- lda);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need N+M, prefer N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Zero out below R in A */
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &a[
- a_dim1 + 2], lda);
- /* Bidiagonalize R in A */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in A */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
- work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr)
- ;
- /* Generate right bidiagonalizing vectors in A */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, &u[u_offset], ldu, dum, &c__1,
- &work[iwork], info);
- }
- } else if (wntvas) {
- /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
- /* or 'A') */
- /* M left singular vectors to be computed in U and */
- /* N right singular vectors to be computed in VT */
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3);
- if (*lwork >= *n * *n + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + *lda * *n) {
- /* WORK(IU) is LDA by N */
- ldwrku = *lda;
- } else {
- /* WORK(IU) is N by N */
- ldwrku = *n;
- }
- itau = iu + ldwrku * *n;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need N*N+N+M, prefer N*N+N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy R to WORK(IU), zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + 1], &ldwrku);
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in WORK(IU), copying result to VT */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
- ldvt);
- /* Generate left bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- /* Generate right bidiagonalizing vectors in VT */
- /* (Workspace: need N*N+4*N-1, */
- /* prefer N*N+3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of R in WORK(IU) and computing */
- /* right singular vectors of R in VT */
- /* (Workspace: need N*N+BDSPAC) */
- _starpu_dbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &work[iu], &ldwrku, dum, &
- c__1, &work[iwork], info);
- /* Multiply Q in U by left singular vectors of R in */
- /* WORK(IU), storing result in A */
- /* (Workspace: need N*N) */
- _starpu_dgemm_("N", "N", m, n, n, &c_b443, &u[u_offset], ldu,
- &work[iu], &ldwrku, &c_b421, &a[a_offset],
- lda);
- /* Copy left singular vectors of A from A to U */
- _starpu_dlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *n;
- /* Compute A=Q*R, copying result to U */
- /* (Workspace: need 2*N, prefer N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
- ldu);
- /* Generate Q in U */
- /* (Workspace: need N+M, prefer N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy R from A to VT, zeroing out below it */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- if (*n > 1) {
- i__2 = *n - 1;
- i__3 = *n - 1;
- _starpu_dlaset_("L", &i__2, &i__3, &c_b421, &c_b421, &vt[
- vt_dim1 + 2], ldvt);
- }
- ie = itau;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize R in VT */
- /* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie],
- &work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply Q in U by left bidiagonalizing vectors */
- /* in VT */
- /* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
- &work[itauq], &u[u_offset], ldu, &work[iwork],
- &i__2, &ierr);
- /* Generate right bidiagonalizing vectors in VT */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
- itaup], &work[iwork], &i__2, &ierr)
- ;
- iwork = ie + *n;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, dum, &
- c__1, &work[iwork], info);
- }
- }
- }
- } else {
- /* M .LT. MNTHR */
- /* Path 10 (M at least N, but not much larger) */
- /* Reduce to bidiagonal form without QR decomposition */
- ie = 1;
- itauq = ie + *n;
- itaup = itauq + *n;
- iwork = itaup + *n;
- /* Bidiagonalize A */
- /* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
- work[itaup], &work[iwork], &i__2, &ierr);
- if (wntuas) {
- /* If left singular vectors desired in U, copy result to U */
- /* and generate left bidiagonalizing vectors in U */
- /* (Workspace: need 3*N+NCU, prefer 3*N+NCU*NB) */
- _starpu_dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
- if (wntus) {
- ncu = *n;
- }
- if (wntua) {
- ncu = *m;
- }
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
- work[iwork], &i__2, &ierr);
- }
- if (wntvas) {
- /* If right singular vectors desired in VT, copy result to */
- /* VT and generate right bidiagonalizing vectors in VT */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- _starpu_dlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
- work[iwork], &i__2, &ierr);
- }
- if (wntuo) {
- /* If left singular vectors desired in A, generate left */
- /* bidiagonalizing vectors in A */
- /* (Workspace: need 4*N, prefer 3*N+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
- iwork], &i__2, &ierr);
- }
- if (wntvo) {
- /* If right singular vectors desired in A, generate right */
- /* bidiagonalizing vectors in A */
- /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
- iwork], &i__2, &ierr);
- }
- iwork = ie + *n;
- if (wntuas || wntuo) {
- nru = *m;
- }
- if (wntun) {
- nru = 0;
- }
- if (wntvas || wntvo) {
- ncvt = *n;
- }
- if (wntvn) {
- ncvt = 0;
- }
- if (! wntuo && ! wntvo) {
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- } else if (! wntuo && wntvo) {
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[
- iwork], info);
- } else {
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in A and computing right singular */
- /* vectors in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
- work[iwork], info);
- }
- }
- } else {
- /* A has more columns than rows. If A has sufficiently more */
- /* columns than rows, first reduce using the LQ decomposition (if */
- /* sufficient workspace available) */
- if (*n >= mnthr) {
- if (wntvn) {
- /* Path 1t(N much larger than M, JOBVT='N') */
- /* No right singular vectors to be computed */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
- i__2, &ierr);
- /* Zero out above L */
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &a[(a_dim1 << 1)
- + 1], lda);
- ie = 1;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in A */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- if (wntuo || wntuas) {
- /* If left singular vectors desired, generate Q */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq], &
- work[iwork], &i__2, &ierr);
- }
- iwork = ie + *m;
- nru = 0;
- if (wntuo || wntuas) {
- nru = *m;
- }
- /* Perform bidiagonal QR iteration, computing left singular */
- /* vectors of A in A if desired */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, &
- c__1, &a[a_offset], lda, dum, &c__1, &work[iwork],
- info);
- /* If left singular vectors desired in U, copy them there */
- if (wntuas) {
- _starpu_dlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- }
- } else if (wntvo && wntun) {
- /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
- /* M right singular vectors to be overwritten on A and */
- /* no left singular vectors to be computed */
- /* Computing MAX */
- i__2 = *m << 2;
- if (*lwork >= *m * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n + *m;
- if (*lwork >= max(i__2,i__3) + *lda * *m) {
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__2 = wrkbl, i__3 = *lda * *n + *m;
- if (*lwork >= max(i__2,i__3) + *m * *m) {
- /* WORK(IU) is LDA by N and WORK(IR) is M by M */
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *m;
- } else {
- /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
- ldwrku = *m;
- chunk = (*lwork - *m * *m - *m) / *m;
- ldwrkr = *m;
- }
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
- /* Copy L to WORK(IR) and zero out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[ir +
- ldwrkr], &ldwrkr);
- /* Generate Q in A */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IR) */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- /* Generate right vectors bidiagonalizing L */
- /* (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
- work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of L in WORK(IR) */
- /* (Workspace: need M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[
- ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork]
- , info);
- iu = ie + *m;
- /* Multiply right singular vectors of L in WORK(IR) by Q */
- /* in A, storing result in WORK(IU) and copying to A */
- /* (Workspace: need M*M+2*M, prefer M*M+M*N+M) */
- i__2 = *n;
- i__3 = chunk;
- for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
- i__3) {
- /* Computing MIN */
- i__4 = *n - i__ + 1;
- blk = min(i__4,chunk);
- _starpu_dgemm_("N", "N", m, &blk, m, &c_b443, &work[ir], &
- ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b421, &
- work[iu], &ldwrku);
- _starpu_dlacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
- a_dim1 + 1], lda);
- /* L30: */
- }
- } else {
- /* Insufficient workspace for a fast algorithm */
- ie = 1;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize A */
- /* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__3, &ierr);
- /* Generate right vectors bidiagonalizing A */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
- work[iwork], &i__3, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, dum, &c__1, dum, &c__1, &work[
- iwork], info);
- }
- } else if (wntvo && wntuas) {
- /* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
- /* M right singular vectors to be overwritten on A and */
- /* M left singular vectors to be computed in U */
- /* Computing MAX */
- i__3 = *m << 2;
- if (*lwork >= *m * *m + max(i__3,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n + *m;
- if (*lwork >= max(i__3,i__2) + *lda * *m) {
- /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *lda;
- } else /* if(complicated condition) */ {
- /* Computing MAX */
- i__3 = wrkbl, i__2 = *lda * *n + *m;
- if (*lwork >= max(i__3,i__2) + *m * *m) {
- /* WORK(IU) is LDA by N and WORK(IR) is M by M */
- ldwrku = *lda;
- chunk = *n;
- ldwrkr = *m;
- } else {
- /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
- ldwrku = *m;
- chunk = (*lwork - *m * *m - *m) / *m;
- ldwrkr = *m;
- }
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__3, &ierr);
- /* Copy L to U, zeroing about above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__3 = *m - 1;
- i__2 = *m - 1;
- _starpu_dlaset_("U", &i__3, &i__2, &c_b421, &c_b421, &u[(u_dim1 <<
- 1) + 1], ldu);
- /* Generate Q in A */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__3, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in U, copying result to WORK(IR) */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__3, &ierr);
- _starpu_dlacpy_("U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr);
- /* Generate right vectors bidiagonalizing L in WORK(IR) */
- /* (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
- work[iwork], &i__3, &ierr);
- /* Generate left vectors bidiagonalizing L in U */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB) */
- i__3 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
- work[iwork], &i__3, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in U, and computing right */
- /* singular vectors of L in WORK(IR) */
- /* (Workspace: need M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[ir],
- &ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[
- iwork], info);
- iu = ie + *m;
- /* Multiply right singular vectors of L in WORK(IR) by Q */
- /* in A, storing result in WORK(IU) and copying to A */
- /* (Workspace: need M*M+2*M, prefer M*M+M*N+M)) */
- i__3 = *n;
- i__2 = chunk;
- for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
- i__2) {
- /* Computing MIN */
- i__4 = *n - i__ + 1;
- blk = min(i__4,chunk);
- _starpu_dgemm_("N", "N", m, &blk, m, &c_b443, &work[ir], &
- ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b421, &
- work[iu], &ldwrku);
- _starpu_dlacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
- a_dim1 + 1], lda);
- /* L40: */
- }
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
- , &i__2, &ierr);
- /* Copy L to U, zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &u[(u_dim1 <<
- 1) + 1], ldu);
- /* Generate Q in A */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in U */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[
- itauq], &work[itaup], &work[iwork], &i__2, &ierr);
- /* Multiply right vectors bidiagonalizing L by Q in A */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &u[u_offset], ldu, &work[
- itaup], &a[a_offset], lda, &work[iwork], &i__2, &
- ierr);
- /* Generate left vectors bidiagonalizing L in U */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
- work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- }
- } else if (wntvs) {
- if (wntun) {
- /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
- /* M right singular vectors to be computed in VT and */
- /* no left singular vectors to be computed */
- /* Computing MAX */
- i__2 = *m << 2;
- if (*lwork >= *m * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- if (*lwork >= wrkbl + *lda * *m) {
- /* WORK(IR) is LDA by M */
- ldwrkr = *lda;
- } else {
- /* WORK(IR) is M by M */
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy L to WORK(IR), zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[ir
- + ldwrkr], &ldwrkr);
- /* Generate Q in A */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IR) */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Generate right vectors bidiagonalizing L in */
- /* WORK(IR) */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of L in WORK(IR) */
- /* (Workspace: need M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, &c__0, &c__0, &s[1], &work[ie], &
- work[ir], &ldwrkr, dum, &c__1, dum, &c__1, &
- work[iwork], info);
- /* Multiply right singular vectors of L in WORK(IR) by */
- /* Q in A, storing result in VT */
- /* (Workspace: need M*M) */
- _starpu_dgemm_("N", "N", m, n, m, &c_b443, &work[ir], &ldwrkr,
- &a[a_offset], lda, &c_b421, &vt[vt_offset],
- ldvt);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy result to VT */
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Zero out above L in A */
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &a[(
- a_dim1 << 1) + 1], lda);
- /* Bidiagonalize L in A */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply right vectors bidiagonalizing L by Q in VT */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, &c__0, &c__0, &s[1], &work[ie], &
- vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, &
- work[iwork], info);
- }
- } else if (wntuo) {
- /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
- /* M right singular vectors to be computed in VT and */
- /* M left singular vectors to be overwritten on A */
- /* Computing MAX */
- i__2 = *m << 2;
- if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *m) {
- /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
- /* WORK(IU) is LDA by M and WORK(IR) is M by M */
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- } else {
- /* WORK(IU) is M by M and WORK(IR) is M by M */
- ldwrku = *m;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy L to WORK(IU), zeroing out below it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + ldwrku], &ldwrku);
- /* Generate Q in A */
- /* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (Workspace: need 2*M*M+4*M, */
- /* prefer 2*M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need 2*M*M+4*M-1, */
- /* prefer 2*M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in WORK(IR) */
- /* (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in WORK(IR) and computing */
- /* right singular vectors of L in WORK(IU) */
- /* (Workspace: need 2*M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
- iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1,
- &work[iwork], info);
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in A, storing result in VT */
- /* (Workspace: need M*M) */
- _starpu_dgemm_("N", "N", m, n, m, &c_b443, &work[iu], &ldwrku,
- &a[a_offset], lda, &c_b421, &vt[vt_offset],
- ldvt);
- /* Copy left singular vectors of L to A */
- /* (Workspace: need M*M) */
- _starpu_dlacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
- lda);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Zero out above L in A */
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &a[(
- a_dim1 << 1) + 1], lda);
- /* Bidiagonalize L in A */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply right vectors bidiagonalizing L by Q in VT */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors of L in A */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, compute left */
- /* singular vectors of A in A and compute right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, dum, &
- c__1, &work[iwork], info);
- }
- } else if (wntuas) {
- /* Path 6t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='S') */
- /* M right singular vectors to be computed in VT and */
- /* M left singular vectors to be computed in U */
- /* Computing MAX */
- i__2 = *m << 2;
- if (*lwork >= *m * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + *lda * *m) {
- /* WORK(IU) is LDA by N */
- ldwrku = *lda;
- } else {
- /* WORK(IU) is LDA by M */
- ldwrku = *m;
- }
- itau = iu + ldwrku * *m;
- iwork = itau + *m;
- /* Compute A=L*Q */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- /* Copy L to WORK(IU), zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + ldwrku], &ldwrku);
- /* Generate Q in A */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IU), copying result to U */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
- ldu);
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need M*M+4*M-1, */
- /* prefer M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in U */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in U and computing right */
- /* singular vectors of L in WORK(IU) */
- /* (Workspace: need M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
- iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in A, storing result in VT */
- /* (Workspace: need M*M) */
- _starpu_dgemm_("N", "N", m, n, m, &c_b443, &work[iu], &ldwrku,
- &a[a_offset], lda, &c_b421, &vt[vt_offset],
- ldvt);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy L to U, zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
- ldu);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &u[(
- u_dim1 << 1) + 1], ldu);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in U */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply right bidiagonalizing vectors in U by Q */
- /* in VT */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &u[u_offset], ldu, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in U */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, dum, &
- c__1, &work[iwork], info);
- }
- }
- } else if (wntva) {
- if (wntun) {
- /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
- /* N right singular vectors to be computed in VT and */
- /* no left singular vectors to be computed */
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3);
- if (*lwork >= *m * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- ir = 1;
- if (*lwork >= wrkbl + *lda * *m) {
- /* WORK(IR) is LDA by M */
- ldwrkr = *lda;
- } else {
- /* WORK(IR) is M by M */
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Copy L to WORK(IR), zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
- ldwrkr);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[ir
- + ldwrkr], &ldwrkr);
- /* Generate Q in VT */
- /* (Workspace: need M*M+M+N, prefer M*M+M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IR) */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Generate right bidiagonalizing vectors in WORK(IR) */
- /* (Workspace: need M*M+4*M-1, */
- /* prefer M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of L in WORK(IR) */
- /* (Workspace: need M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, &c__0, &c__0, &s[1], &work[ie], &
- work[ir], &ldwrkr, dum, &c__1, dum, &c__1, &
- work[iwork], info);
- /* Multiply right singular vectors of L in WORK(IR) by */
- /* Q in VT, storing result in A */
- /* (Workspace: need M*M) */
- _starpu_dgemm_("N", "N", m, n, m, &c_b443, &work[ir], &ldwrkr,
- &vt[vt_offset], ldvt, &c_b421, &a[a_offset],
- lda);
- /* Copy right singular vectors of A from A to VT */
- _starpu_dlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need M+N, prefer M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Zero out above L in A */
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &a[(
- a_dim1 << 1) + 1], lda);
- /* Bidiagonalize L in A */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply right bidiagonalizing vectors in A by Q */
- /* in VT */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, &c__0, &c__0, &s[1], &work[ie], &
- vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, &
- work[iwork], info);
- }
- } else if (wntuo) {
- /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
- /* N right singular vectors to be computed in VT and */
- /* M left singular vectors to be overwritten on A */
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3);
- if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + (*lda << 1) * *m) {
- /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *lda;
- } else if (*lwork >= wrkbl + (*lda + *m) * *m) {
- /* WORK(IU) is LDA by M and WORK(IR) is M by M */
- ldwrku = *lda;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- } else {
- /* WORK(IU) is M by M and WORK(IR) is M by M */
- ldwrku = *m;
- ir = iu + ldwrku * *m;
- ldwrkr = *m;
- }
- itau = ir + ldwrkr * *m;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy L to WORK(IU), zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + ldwrku], &ldwrku);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IU), copying result to */
- /* WORK(IR) */
- /* (Workspace: need 2*M*M+4*M, */
- /* prefer 2*M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
- ldwrkr);
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need 2*M*M+4*M-1, */
- /* prefer 2*M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in WORK(IR) */
- /* (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
- , &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in WORK(IR) and computing */
- /* right singular vectors of L in WORK(IU) */
- /* (Workspace: need 2*M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
- iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1,
- &work[iwork], info);
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in VT, storing result in A */
- /* (Workspace: need M*M) */
- _starpu_dgemm_("N", "N", m, n, m, &c_b443, &work[iu], &ldwrku,
- &vt[vt_offset], ldvt, &c_b421, &a[a_offset],
- lda);
- /* Copy right singular vectors of A from A to VT */
- _starpu_dlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Copy left singular vectors of A from WORK(IR) to A */
- _starpu_dlacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
- lda);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need M+N, prefer M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Zero out above L in A */
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &a[(
- a_dim1 << 1) + 1], lda);
- /* Bidiagonalize L in A */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply right bidiagonalizing vectors in A by Q */
- /* in VT */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in A */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in A and computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, dum, &
- c__1, &work[iwork], info);
- }
- } else if (wntuas) {
- /* Path 9t(N much larger than M, JOBU='S' or 'A', */
- /* JOBVT='A') */
- /* N right singular vectors to be computed in VT and */
- /* M left singular vectors to be computed in U */
- /* Computing MAX */
- i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3);
- if (*lwork >= *m * *m + max(i__2,bdspac)) {
- /* Sufficient workspace for a fast algorithm */
- iu = 1;
- if (*lwork >= wrkbl + *lda * *m) {
- /* WORK(IU) is LDA by M */
- ldwrku = *lda;
- } else {
- /* WORK(IU) is M by M */
- ldwrku = *m;
- }
- itau = iu + ldwrku * *m;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need M*M+M+N, prefer M*M+M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy L to WORK(IU), zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
- ldwrku);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &work[iu
- + ldwrku], &ldwrku);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in WORK(IU), copying result to U */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- _starpu_dlacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
- ldu);
- /* Generate right bidiagonalizing vectors in WORK(IU) */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
- , &work[iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in U */
- /* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of L in U and computing right */
- /* singular vectors of L in WORK(IU) */
- /* (Workspace: need M*M+BDSPAC) */
- _starpu_dbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
- iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- /* Multiply right singular vectors of L in WORK(IU) by */
- /* Q in VT, storing result in A */
- /* (Workspace: need M*M) */
- _starpu_dgemm_("N", "N", m, n, m, &c_b443, &work[iu], &ldwrku,
- &vt[vt_offset], ldvt, &c_b421, &a[a_offset],
- lda);
- /* Copy right singular vectors of A from A to VT */
- _starpu_dlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- } else {
- /* Insufficient workspace for a fast algorithm */
- itau = 1;
- iwork = itau + *m;
- /* Compute A=L*Q, copying result to VT */
- /* (Workspace: need 2*M, prefer M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
- iwork], &i__2, &ierr);
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
- ldvt);
- /* Generate Q in VT */
- /* (Workspace: need M+N, prefer M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
- work[iwork], &i__2, &ierr);
- /* Copy L to U, zeroing out above it */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
- ldu);
- i__2 = *m - 1;
- i__3 = *m - 1;
- _starpu_dlaset_("U", &i__2, &i__3, &c_b421, &c_b421, &u[(
- u_dim1 << 1) + 1], ldu);
- ie = itau;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize L in U */
- /* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &
- work[itauq], &work[itaup], &work[iwork], &
- i__2, &ierr);
- /* Multiply right bidiagonalizing vectors in U by Q */
- /* in VT */
- /* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dormbr_("P", "L", "T", m, n, m, &u[u_offset], ldu, &
- work[itaup], &vt[vt_offset], ldvt, &work[
- iwork], &i__2, &ierr);
- /* Generate left bidiagonalizing vectors in U */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
- &work[iwork], &i__2, &ierr);
- iwork = ie + *m;
- /* Perform bidiagonal QR iteration, computing left */
- /* singular vectors of A in U and computing right */
- /* singular vectors of A in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, dum, &
- c__1, &work[iwork], info);
- }
- }
- }
- } else {
- /* N .LT. MNTHR */
- /* Path 10t(N greater than M, but not much larger) */
- /* Reduce to bidiagonal form without LQ decomposition */
- ie = 1;
- itauq = ie + *m;
- itaup = itauq + *m;
- iwork = itaup + *m;
- /* Bidiagonalize A */
- /* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
- work[itaup], &work[iwork], &i__2, &ierr);
- if (wntuas) {
- /* If left singular vectors desired in U, copy result to U */
- /* and generate left bidiagonalizing vectors in U */
- /* (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB) */
- _starpu_dlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
- iwork], &i__2, &ierr);
- }
- if (wntvas) {
- /* If right singular vectors desired in VT, copy result to */
- /* VT and generate right bidiagonalizing vectors in VT */
- /* (Workspace: need 3*M+NRVT, prefer 3*M+NRVT*NB) */
- _starpu_dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
- if (wntva) {
- nrvt = *n;
- }
- if (wntvs) {
- nrvt = *m;
- }
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
- &work[iwork], &i__2, &ierr);
- }
- if (wntuo) {
- /* If left singular vectors desired in A, generate left */
- /* bidiagonalizing vectors in A */
- /* (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
- iwork], &i__2, &ierr);
- }
- if (wntvo) {
- /* If right singular vectors desired in A, generate right */
- /* bidiagonalizing vectors in A */
- /* (Workspace: need 4*M, prefer 3*M+M*NB) */
- i__2 = *lwork - iwork + 1;
- _starpu_dorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
- iwork], &i__2, &ierr);
- }
- iwork = ie + *m;
- if (wntuas || wntuo) {
- nru = *m;
- }
- if (wntun) {
- nru = 0;
- }
- if (wntvas || wntvo) {
- ncvt = *n;
- }
- if (wntvn) {
- ncvt = 0;
- }
- if (! wntuo && ! wntvo) {
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, &
- work[iwork], info);
- } else if (! wntuo && wntvo) {
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in U and computing right singular */
- /* vectors in A */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[
- a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[
- iwork], info);
- } else {
- /* Perform bidiagonal QR iteration, if desired, computing */
- /* left singular vectors in A and computing right singular */
- /* vectors in VT */
- /* (Workspace: need BDSPAC) */
- _starpu_dbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
- vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
- work[iwork], info);
- }
- }
- }
- /* If DBDSQR failed to converge, copy unconverged superdiagonals */
- /* to WORK( 2:MINMN ) */
- if (*info != 0) {
- if (ie > 2) {
- i__2 = minmn - 1;
- for (i__ = 1; i__ <= i__2; ++i__) {
- work[i__ + 1] = work[i__ + ie - 1];
- /* L50: */
- }
- }
- if (ie < 2) {
- for (i__ = minmn - 1; i__ >= 1; --i__) {
- work[i__ + 1] = work[i__ + ie - 1];
- /* L60: */
- }
- }
- }
- /* Undo scaling if necessary */
- if (iscl == 1) {
- if (anrm > bignum) {
- _starpu_dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
- minmn, &ierr);
- }
- if (*info != 0 && anrm > bignum) {
- i__2 = minmn - 1;
- _starpu_dlascl_("G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2],
- &minmn, &ierr);
- }
- if (anrm < smlnum) {
- _starpu_dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
- minmn, &ierr);
- }
- if (*info != 0 && anrm < smlnum) {
- i__2 = minmn - 1;
- _starpu_dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2],
- &minmn, &ierr);
- }
- }
- /* Return optimal workspace in WORK(1) */
- work[1] = (doublereal) maxwrk;
- return 0;
- /* End of DGESVD */
- } /* _starpu_dgesvd_ */
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