#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zgesdd_(char *jobz, integer *m, integer *n, doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u, integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work, integer *lwork, doublereal *rwork, integer *iwork, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 8-15-00: Improve consistency of WS calculations (eca) Purpose ======= ZGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. The SVD is written A = U * SIGMA * conjugate-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 unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A. Note that the routine returns VT = V**H, not V. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments ========= JOBZ (input) CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**H are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**H are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten in the array A and all rows of V**H are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**H are overwritten in the array A; = 'N': no columns of U or rows of V**H are computed. M (input) INTEGER The number of rows of the input matrix A. M >= 0. N (input) INTEGER The number of columns of the input matrix A. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**H (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). S (output) DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1). U (output) COMPLEX*16 array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. LDU (input) INTEGER The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. VT (output) COMPLEX*16 array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. LDVT (input) INTEGER The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N). WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= 1. if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N). if JOBZ = 'O', LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N). if JOBZ = 'S' or 'A', LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N). For good performance, LWORK should generally be larger. If LWORK = -1, a workspace query is assumed. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed. RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) If JOBZ = 'N', LRWORK >= 5*min(M,N). Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 7*min(M,N) IWORK (workspace) INTEGER array, dimension (8*min(M,N)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The updating process of DBDSDC did not converge. Further Details =============== Based on contributions by Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA ===================================================================== Test the input arguments Parameter adjustments */ /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__1 = 1; static integer c_n1 = -1; static integer c__0 = 0; /* System generated locals */ integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2, i__3; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer i__, ie, il, ir, iu, blk; static doublereal dum[1], eps; static integer iru, ivt, iscl; static doublereal anrm; static integer idum[1], ierr, itau, irvt; extern logical lsame_(char *, char *); static integer chunk, minmn; extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); static integer wrkbl, itaup, itauq; static logical wntqa; static integer nwork; static logical wntqn, wntqo, wntqs; extern /* Subroutine */ int zlacp2_(char *, integer *, integer *, doublereal *, integer *, doublecomplex *, integer *); static integer mnthr1, mnthr2; extern /* Subroutine */ int dbdsdc_(char *, char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *); extern /* Subroutine */ int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), xerbla_(char *, integer *), zgebrd_(integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); static doublereal bignum; extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zgelqf_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zlacrm_(integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, doublecomplex *, integer *, doublereal *) , zlarcm_(integer *, integer *, doublereal *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *), zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, integer *), zgeqrf_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer * ); static integer ldwrkl; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); static integer ldwrkr, minwrk, ldwrku, maxwrk; extern /* Subroutine */ int zungbr_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); static integer ldwkvt; static doublereal smlnum; static logical wntqas; extern /* Subroutine */ int zunmbr_(char *, char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ), zunglq_(integer *, integer *, integer * , doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); static integer nrwork; extern /* Subroutine */ int zungqr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); 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; --rwork; --iwork; /* Function Body */ *info = 0; minmn = min(*m,*n); mnthr1 = (integer) (minmn * 17. / 9.); mnthr2 = (integer) (minmn * 5. / 3.); wntqa = lsame_(jobz, "A"); wntqs = lsame_(jobz, "S"); wntqas = wntqa || wntqs; wntqo = lsame_(jobz, "O"); wntqn = lsame_(jobz, "N"); minwrk = 1; maxwrk = 1; if (! (wntqa || wntqs || wntqo || wntqn)) { *info = -1; } else if (*m < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*lda < max(1,*m)) { *info = -5; } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < * m) { *info = -8; } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn || wntqo && *m >= *n && *ldvt < *n) { *info = -10; } /* Compute workspace (Note: Comments in the code beginning "Workspace:" describe the minimal amount of workspace needed at that point in the code, as well as the preferred amount for good performance. CWorkspace refers to complex workspace, and RWorkspace to real workspace. NB refers to the optimal block size for the immediately following subroutine, as returned by ILAENV.) */ if (*info == 0 && *m > 0 && *n > 0) { if (*m >= *n) { /* There is no complex work space needed for bidiagonal SVD The real work space needed for bidiagonal SVD is BDSPAC for computing singular values and singular vectors; BDSPAN for computing singular values only. BDSPAC = 5*N*N + 7*N BDSPAN = MAX(7*N+4, 3*N+2+SMLSIZ*(SMLSIZ+8)) */ if (*m >= mnthr1) { if (wntqn) { /* Path 1 (M much larger than N, JOBZ='N') */ maxwrk = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + (*n << 1) * ilaenv_(& c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); minwrk = *n * 3; } else if (wntqo) { /* Path 2 (M much larger than N, JOBZ='O') */ wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + (*n << 1) * ilaenv_(& c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "QLN", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); maxwrk = *m * *n + *n * *n + wrkbl; minwrk = (*n << 1) * *n + *n * 3; } else if (wntqs) { /* Path 3 (M much larger than N, JOBZ='S') */ wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + (*n << 1) * ilaenv_(& c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "QLN", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); maxwrk = *n * *n + wrkbl; minwrk = *n * *n + *n * 3; } else if (wntqa) { /* Path 4 (M much larger than N, JOBZ='A') */ wrkbl = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *n + *m * ilaenv_(&c__1, "ZUNGQR", " ", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + (*n << 1) * ilaenv_(& c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "QLN", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); maxwrk = *n * *n + wrkbl; minwrk = *n * *n + (*n << 1) + *m; } } else if (*m >= mnthr2) { /* Path 5 (M much larger than N, but not as much as MNTHR1) */ maxwrk = (*n << 1) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); minwrk = (*n << 1) + *m; if (wntqo) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "Q", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); maxwrk += *m * *n; minwrk += *n * *n; } else if (wntqs) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "Q", m, n, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); } else if (wntqa) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); } } else { /* Path 6 (M at least N, but not much larger) */ maxwrk = (*n << 1) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); minwrk = (*n << 1) + *m; if (wntqo) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "QLN", m, n, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); maxwrk += *m * *n; minwrk += *n * *n; } else if (wntqs) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNMBR", "QLN", m, n, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); } else if (wntqa) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "PRC", n, n, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); } } } else { /* There is no complex work space needed for bidiagonal SVD The real work space needed for bidiagonal SVD is BDSPAC for computing singular values and singular vectors; BDSPAN for computing singular values only. BDSPAC = 5*M*M + 7*M BDSPAN = MAX(7*M+4, 3*M+2+SMLSIZ*(SMLSIZ+8)) */ if (*n >= mnthr1) { if (wntqn) { /* Path 1t (N much larger than M, JOBZ='N') */ maxwrk = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + (*m << 1) * ilaenv_(& c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); minwrk = *m * 3; } else if (wntqo) { /* Path 2t (N much larger than M, JOBZ='O') */ wrkbl = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "ZUNGLQ", " ", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + (*m << 1) * ilaenv_(& c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "PRC", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "QLN", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); maxwrk = *m * *n + *m * *m + wrkbl; minwrk = (*m << 1) * *m + *m * 3; } else if (wntqs) { /* Path 3t (N much larger than M, JOBZ='S') */ wrkbl = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "ZUNGLQ", " ", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + (*m << 1) * ilaenv_(& c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "PRC", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "QLN", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); maxwrk = *m * *m + wrkbl; minwrk = *m * *m + *m * 3; } else if (wntqa) { /* Path 4t (N much larger than M, JOBZ='A') */ wrkbl = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, & c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = wrkbl, i__2 = *m + *n * ilaenv_(&c__1, "ZUNGLQ", " ", n, n, m, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + (*m << 1) * ilaenv_(& c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "PRC", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); /* Computing MAX */ i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "QLN", m, m, m, &c_n1, (ftnlen)6, (ftnlen)3); wrkbl = max(i__1,i__2); maxwrk = *m * *m + wrkbl; minwrk = *m * *m + (*m << 1) + *n; } } else if (*n >= mnthr2) { /* Path 5t (N much larger than M, but not as much as MNTHR1) */ maxwrk = (*m << 1) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); minwrk = (*m << 1) + *n; if (wntqo) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); maxwrk += *m * *n; minwrk += *m * *m; } else if (wntqs) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); } else if (wntqa) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "P", n, n, m, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "Q", m, m, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1,i__2); } } else { /* Path 6t (N greater than M, but not much larger) */ maxwrk = (*m << 1) + (*m + *n) * ilaenv_(&c__1, "ZGEBRD", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); minwrk = (*m << 1) + *n; if (wntqo) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "PRC", m, n, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNMBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); maxwrk += *m * *n; minwrk += *m * *m; } else if (wntqs) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "PRC", m, n, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); } else if (wntqa) { /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *n * ilaenv_(&c__1, "ZUNGBR", "PRC", n, n, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "ZUNGBR", "QLN", m, m, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1,i__2); } } } maxwrk = max(maxwrk,minwrk); } if (*info == 0) { work[1].r = (doublereal) maxwrk, work[1].i = 0.; if (*lwork < minwrk && *lwork != -1) { *info = -13; } } /* Quick returns */ if (*info != 0) { i__1 = -(*info); xerbla_("ZGESDD", &i__1); return 0; } if (*lwork == -1) { return 0; } if (*m == 0 || *n == 0) { return 0; } /* Get machine constants */ eps = dlamch_("P"); smlnum = sqrt(dlamch_("S")) / eps; bignum = 1. / smlnum; /* Scale A if max element outside range [SMLNUM,BIGNUM] */ anrm = zlange_("M", m, n, &a[a_offset], lda, dum); iscl = 0; if (anrm > 0. && anrm < smlnum) { iscl = 1; zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & ierr); } else if (anrm > bignum) { iscl = 1; zlascl_("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 >= mnthr1) { if (wntqn) { /* Path 1 (M much larger than N, JOBZ='N') No singular vectors to be computed */ itau = 1; nwork = itau + *n; /* Compute A=Q*R (CWorkspace: need 2*N, prefer N+N*NB) (RWorkspace: need 0) */ i__1 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Zero out below R */ i__1 = *n - 1; i__2 = *n - 1; zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda); ie = 1; itauq = 1; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A (CWorkspace: need 3*N, prefer 2*N+2*N*NB) (RWorkspace: need N) */ i__1 = *lwork - nwork + 1; zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); nrwork = ie + *n; /* Perform bidiagonal SVD, compute singular values only (CWorkspace: 0) (RWorkspace: need BDSPAN) */ dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { /* Path 2 (M much larger than N, JOBZ='O') N left singular vectors to be overwritten on A and N right singular vectors to be computed in VT */ iu = 1; /* WORK(IU) is N by N */ ldwrku = *n; ir = iu + ldwrku * *n; if (*lwork >= *m * *n + *n * *n + *n * 3) { /* WORK(IR) is M by N */ ldwrkr = *m; } else { ldwrkr = (*lwork - *n * *n - *n * 3) / *n; } itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R (CWorkspace: need N*N+2*N, prefer M*N+N+N*NB) (RWorkspace: 0) */ i__1 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy R to WORK( IR ), zeroing out below it */ zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__1 = *n - 1; i__2 = *n - 1; zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], & ldwrkr); /* Generate Q in A (CWorkspace: need 2*N, prefer N+N*NB) (RWorkspace: 0) */ i__1 = *lwork - nwork + 1; zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = 1; itauq = itau; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) (CWorkspace: need N*N+3*N, prefer M*N+2*N+2*N*NB) (RWorkspace: need N) */ i__1 = *lwork - nwork + 1; zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of R in WORK(IRU) and computing right singular vectors of R in WORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = ie + *n; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) Overwrite WORK(IU) by the left singular vectors of R (CWorkspace: need 2*N*N+3*N, prefer M*N+N*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__1, & ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by the right singular vectors of R (CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); /* Multiply Q in A by left singular vectors of R in WORK(IU), storing result in WORK(IR) and copying to A (CWorkspace: need 2*N*N, prefer N*N+M*N) (RWorkspace: 0) */ i__1 = *m; i__2 = ldwrkr; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = min(i__3,ldwrkr); zgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1], lda, &work[iu], &ldwrku, &c_b1, &work[ir], & ldwrkr); zlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + a_dim1], lda); /* L10: */ } } else if (wntqs) { /* Path 3 (M much larger than N, JOBZ='S') N left singular vectors to be computed in U and N right singular vectors to be computed in VT */ ir = 1; /* WORK(IR) is N by N */ ldwrkr = *n; itau = ir + ldwrkr * *n; nwork = itau + *n; /* Compute A=Q*R (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy R to WORK(IR), zeroing out below it */ zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr); i__2 = *n - 1; i__1 = *n - 1; zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], & ldwrkr); /* Generate Q in A (CWorkspace: need 2*N, prefer N+N*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = 1; itauq = itau; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in WORK(IR) (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) (RWorkspace: need N) */ i__2 = *lwork - nwork + 1; zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = ie + *n; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of R (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of R (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply Q in A by left singular vectors of R in WORK(IR), storing result in U (CWorkspace: need N*N) (RWorkspace: 0) */ zlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr); zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir], &ldwrkr, &c_b1, &u[u_offset], ldu); } else if (wntqa) { /* Path 4 (M much larger than N, JOBZ='A') M left singular vectors to be computed in U and N right singular vectors to be computed in VT */ iu = 1; /* WORK(IU) is N by N */ ldwrku = *n; itau = iu + ldwrku * *n; nwork = itau + *n; /* Compute A=Q*R, copying result to U (CWorkspace: need 2*N, prefer N+N*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); /* Generate Q in U (CWorkspace: need N+M, prefer N+M*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork], &i__2, &ierr); /* Produce R in A, zeroing out below it */ i__2 = *n - 1; i__1 = *n - 1; zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda); ie = 1; itauq = itau; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize R in A (CWorkspace: need 3*N, prefer 2*N+2*N*NB) (RWorkspace: need N) */ i__2 = *lwork - nwork + 1; zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); iru = ie + *n; irvt = iru + *n * *n; nrwork = irvt + *n * *n; /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) Overwrite WORK(IU) by left singular vectors of R (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__2, & ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of R (CWorkspace: need 3*N, prefer 2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); /* Multiply Q in U by left singular vectors of R in WORK(IU), storing result in A (CWorkspace: need N*N) (RWorkspace: 0) */ zgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &work[iu], &ldwrku, &c_b1, &a[a_offset], lda); /* Copy left singular vectors of A from A to U */ zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } } else if (*m >= mnthr2) { /* MNTHR2 <= M < MNTHR1 Path 5 (M much larger than N, but not as much as MNTHR1) Reduce to bidiagonal form without QR decomposition, use ZUNGBR and matrix multiplication to compute singular vectors */ ie = 1; nrwork = ie + *n; itauq = 1; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize A (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) (RWorkspace: need N) */ i__2 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Compute singular values only (Cworkspace: 0) (Rworkspace: need BDSPAN) */ dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { iu = nwork; iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; /* Copy A to VT, generate P**H (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: 0) */ zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__2, &ierr); /* Generate Q in A (CWorkspace: need 2*N, prefer N+N*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[ nwork], &i__2, &ierr); if (*lwork >= *m * *n + *n * 3) { /* WORK( IU ) is M by N */ ldwrku = *m; } else { /* WORK(IU) is LDWRKU by N */ ldwrku = (*lwork - *n * 3) / *n; } nwork = iu + ldwrku * *n; /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply real matrix RWORK(IRVT) by P**H in VT, storing the result in WORK(IU), copying to VT (Cworkspace: need 0) (Rworkspace: need 3*N*N) */ zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu] , &ldwrku, &rwork[nrwork]); zlacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt); /* Multiply Q in A by real matrix RWORK(IRU), storing the result in WORK(IU), copying to A (CWorkspace: need N*N, prefer M*N) (Rworkspace: need 3*N*N, prefer N*N+2*M*N) */ nrwork = irvt; i__2 = *m; i__1 = ldwrku; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = min(i__3,ldwrku); zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n, &work[iu], &ldwrku, &rwork[nrwork]); zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ + a_dim1], lda); /* L20: */ } } else if (wntqs) { /* Copy A to VT, generate P**H (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: 0) */ zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__1, &ierr); /* Copy A to U, generate Q (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: 0) */ zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply real matrix RWORK(IRVT) by P**H in VT, storing the result in A, copying to VT (Cworkspace: need 0) (Rworkspace: need 3*N*N) */ zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Multiply Q in U by real matrix RWORK(IRU), storing the result in A, copying to U (CWorkspace: need 0) (Rworkspace: need N*N+2*M*N) */ nrwork = irvt; zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } else { /* Copy A to VT, generate P**H (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: 0) */ zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__1, &ierr); /* Copy A to U, generate Q (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: 0) */ zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply real matrix RWORK(IRVT) by P**H in VT, storing the result in A, copying to VT (Cworkspace: need 0) (Rworkspace: need 3*N*N) */ zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Multiply Q in U by real matrix RWORK(IRU), storing the result in A, copying to U (CWorkspace: 0) (Rworkspace: need 3*N*N) */ nrwork = irvt; zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu); } } else { /* M .LT. MNTHR2 Path 6 (M at least N, but not much larger) Reduce to bidiagonal form without QR decomposition Use ZUNMBR to compute singular vectors */ ie = 1; nrwork = ie + *n; itauq = 1; itaup = itauq + *n; nwork = itaup + *n; /* Bidiagonalize A (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) (RWorkspace: need N) */ i__1 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, &ierr); if (wntqn) { /* Compute singular values only (Cworkspace: 0) (Rworkspace: need BDSPAN) */ dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { iu = nwork; iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; if (*lwork >= *m * *n + *n * 3) { /* WORK( IU ) is M by N */ ldwrku = *m; } else { /* WORK( IU ) is LDWRKU by N */ ldwrku = (*lwork - *n * 3) / *n; } nwork = iu + ldwrku * *n; /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of A (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: need 0) */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); if (*lwork >= *m * *n + *n * 3) { /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) Overwrite WORK(IU) by left singular vectors of A, copying to A (Cworkspace: need M*N+2*N, prefer M*N+N+N*NB) (Rworkspace: need 0) */ zlaset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku); zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &work[iu], &ldwrku, &work[nwork], &i__1, & ierr); zlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda); } else { /* Generate Q in A (Cworkspace: need 2*N, prefer N+N*NB) (Rworkspace: need 0) */ i__1 = *lwork - nwork + 1; zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], & work[nwork], &i__1, &ierr); /* Multiply Q in A by real matrix RWORK(IRU), storing the result in WORK(IU), copying to A (CWorkspace: need N*N, prefer M*N) (Rworkspace: need 3*N*N, prefer N*N+2*M*N) */ nrwork = irvt; i__1 = *m; i__2 = ldwrku; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *m - i__ + 1; chunk = min(i__3,ldwrku); zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n, &work[iu], &ldwrku, &rwork[nrwork]); zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ + a_dim1], lda); /* L30: */ } } } else if (wntqs) { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of A (CWorkspace: need 3*N, prefer 2*N+N*NB) (RWorkspace: 0) */ zlaset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu) ; zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of A (CWorkspace: need 3*N, prefer 2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); } else { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = nrwork; irvt = iru + *n * *n; nrwork = irvt + *n * *n; dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, & rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1], info); /* Set the right corner of U to identity matrix */ zlaset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu) ; if (*m > *n) { i__2 = *m - *n; i__1 = *m - *n; zlaset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n + 1) * u_dim1], ldu); } /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of A (CWorkspace: need 2*N+M, prefer 2*N+M*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of A (CWorkspace: need 3*N, prefer 2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, & ierr); } } } else { /* A has more columns than rows. If A has sufficiently more columns than rows, first reduce using the LQ decomposition (if sufficient workspace available) */ if (*n >= mnthr1) { if (wntqn) { /* Path 1t (N much larger than M, JOBZ='N') No singular vectors to be computed */ itau = 1; nwork = itau + *m; /* Compute A=L*Q (CWorkspace: need 2*M, prefer M+M*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Zero out above L */ i__2 = *m - 1; i__1 = *m - 1; zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1] , lda); ie = 1; itauq = 1; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A (CWorkspace: need 3*M, prefer 2*M+2*M*NB) (RWorkspace: need M) */ i__2 = *lwork - nwork + 1; zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); nrwork = ie + *m; /* Perform bidiagonal SVD, compute singular values only (CWorkspace: 0) (RWorkspace: need BDSPAN) */ dbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { /* Path 2t (N much larger than M, JOBZ='O') M right singular vectors to be overwritten on A and M left singular vectors to be computed in U */ ivt = 1; ldwkvt = *m; /* WORK(IVT) is M by M */ il = ivt + ldwkvt * *m; if (*lwork >= *m * *n + *m * *m + *m * 3) { /* WORK(IL) M by N */ ldwrkl = *m; chunk = *n; } else { /* WORK(IL) is M by CHUNK */ ldwrkl = *m; chunk = (*lwork - *m * *m - *m * 3) / *m; } itau = il + ldwrkl * chunk; nwork = itau + *m; /* Compute A=L*Q (CWorkspace: need 2*M, prefer M+M*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__2, &ierr); /* Copy L to WORK(IL), zeroing about above it */ zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__2 = *m - 1; i__1 = *m - 1; zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], & ldwrkl); /* Generate Q in A (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) (RWorkspace: 0) */ i__2 = *lwork - nwork + 1; zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__2, &ierr); ie = 1; itauq = itau; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL) (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) (RWorkspace: need M) */ i__2 = *lwork - nwork + 1; zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = ie + *m; irvt = iru + *m * *m; nrwork = irvt + *m * *m; dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) Overwrite WORK(IU) by the left singular vectors of L (CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) Overwrite WORK(IVT) by the right singular vectors of L (CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB) (RWorkspace: 0) */ zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, & ierr); /* Multiply right singular vectors of L in WORK(IL) by Q in A, storing result in WORK(IL) and copying to A (CWorkspace: need 2*M*M, prefer M*M+M*N)) (RWorkspace: 0) */ i__2 = *n; i__1 = chunk; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = min(i__3,chunk); zgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__ * a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl); zlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1 + 1], lda); /* L40: */ } } else if (wntqs) { /* Path 3t (N much larger than M, JOBZ='S') M right singular vectors to be computed in VT and M left singular vectors to be computed in U */ il = 1; /* WORK(IL) is M by M */ ldwrkl = *m; itau = il + ldwrkl * *m; nwork = itau + *m; /* Compute A=L*Q (CWorkspace: need 2*M, prefer M+M*NB) (RWorkspace: 0) */ i__1 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); /* Copy L to WORK(IL), zeroing out above it */ zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl); i__1 = *m - 1; i__2 = *m - 1; zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], & ldwrkl); /* Generate Q in A (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) (RWorkspace: 0) */ i__1 = *lwork - nwork + 1; zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, &ierr); ie = 1; itauq = itau; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in WORK(IL) (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) (RWorkspace: need M) */ i__1 = *lwork - nwork + 1; zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = ie + *m; irvt = iru + *m * *m; nrwork = irvt + *m * *m; dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of L (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) (RWorkspace: 0) */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by left singular vectors of L (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) (RWorkspace: 0) */ zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); /* Copy VT to WORK(IL), multiply right singular vectors of L in WORK(IL) by Q in A, storing result in VT (CWorkspace: need M*M) (RWorkspace: 0) */ zlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl); zgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[ a_offset], lda, &c_b1, &vt[vt_offset], ldvt); } else if (wntqa) { /* Path 9t (N much larger than M, JOBZ='A') N right singular vectors to be computed in VT and M left singular vectors to be computed in U */ ivt = 1; /* WORK(IVT) is M by M */ ldwkvt = *m; itau = ivt + ldwkvt * *m; nwork = itau + *m; /* Compute A=L*Q, copying result to VT (CWorkspace: need 2*M, prefer M+M*NB) (RWorkspace: 0) */ i__1 = *lwork - nwork + 1; zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], & i__1, &ierr); zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); /* Generate Q in VT (CWorkspace: need M+N, prefer M+N*NB) (RWorkspace: 0) */ i__1 = *lwork - nwork + 1; zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[ nwork], &i__1, &ierr); /* Produce L in A, zeroing out above it */ i__1 = *m - 1; i__2 = *m - 1; zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1] , lda); ie = 1; itauq = itau; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize L in A (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) (RWorkspace: need M) */ i__1 = *lwork - nwork + 1; zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[ itauq], &work[itaup], &work[nwork], &i__1, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ iru = ie + *m; irvt = iru + *m * *m; nrwork = irvt + *m * *m; dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of L (CWorkspace: need 3*M, prefer 2*M+M*NB) (RWorkspace: 0) */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) Overwrite WORK(IVT) by right singular vectors of L (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) (RWorkspace: 0) */ zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, & ierr); /* Multiply right singular vectors of L in WORK(IVT) by Q in VT, storing result in A (CWorkspace: need M*M) (RWorkspace: 0) */ zgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[ vt_offset], ldvt, &c_b1, &a[a_offset], lda); /* Copy right singular vectors of A from A to VT */ zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } } else if (*n >= mnthr2) { /* MNTHR2 <= N < MNTHR1 Path 5t (N much larger than M, but not as much as MNTHR1) Reduce to bidiagonal form without QR decomposition, use ZUNGBR and matrix multiplication to compute singular vectors */ ie = 1; nrwork = ie + *m; itauq = 1; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) (RWorkspace: M) */ i__1 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, &ierr); if (wntqn) { /* Compute singular values only (Cworkspace: 0) (Rworkspace: need BDSPAN) */ dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; ivt = nwork; /* Copy A to U, generate Q (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: 0) */ zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__1, &ierr); /* Generate P**H in A (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: 0) */ i__1 = *lwork - nwork + 1; zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ nwork], &i__1, &ierr); ldwkvt = *m; if (*lwork >= *m * *n + *m * 3) { /* WORK( IVT ) is M by N */ nwork = ivt + ldwkvt * *n; chunk = *n; } else { /* WORK( IVT ) is M by CHUNK */ chunk = (*lwork - *m * 3) / *m; nwork = ivt + ldwkvt * chunk; } /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply Q in U by real matrix RWORK(IRVT) storing the result in WORK(IVT), copying to U (Cworkspace: need 0) (Rworkspace: need 2*M*M) */ zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], & ldwkvt, &rwork[nrwork]); zlacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu); /* Multiply RWORK(IRVT) by P**H in A, storing the result in WORK(IVT), copying to A (CWorkspace: need M*M, prefer M*N) (Rworkspace: need 2*M*M, prefer 2*M*N) */ nrwork = iru; i__1 = *n; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = min(i__3,chunk); zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1], lda, &work[ivt], &ldwkvt, &rwork[nrwork]); zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ * a_dim1 + 1], lda); /* L50: */ } } else if (wntqs) { /* Copy A to U, generate Q (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: 0) */ zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__2, &ierr); /* Copy A to VT, generate P**H (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: 0) */ zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply Q in U by real matrix RWORK(IRU), storing the result in A, copying to U (CWorkspace: need 0) (Rworkspace: need 3*M*M) */ zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu); /* Multiply real matrix RWORK(IRVT) by P**H in VT, storing the result in A, copying to VT (Cworkspace: need 0) (Rworkspace: need M*M+2*M*N) */ nrwork = iru; zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } else { /* Copy A to U, generate Q (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: 0) */ zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ nwork], &i__2, &ierr); /* Copy A to VT, generate P**H (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: 0) */ zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); i__2 = *lwork - nwork + 1; zungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], & work[nwork], &i__2, &ierr); /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Multiply Q in U by real matrix RWORK(IRU), storing the result in A, copying to U (CWorkspace: need 0) (Rworkspace: need 3*M*M) */ zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu); /* Multiply real matrix RWORK(IRVT) by P**H in VT, storing the result in A, copying to VT (Cworkspace: need 0) (Rworkspace: need M*M+2*M*N) */ zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[ a_offset], lda, &rwork[nrwork]); zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt); } } else { /* N .LT. MNTHR2 Path 6t (N greater than M, but not much larger) Reduce to bidiagonal form without LQ decomposition Use ZUNMBR to compute singular vectors */ ie = 1; nrwork = ie + *m; itauq = 1; itaup = itauq + *m; nwork = itaup + *m; /* Bidiagonalize A (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) (RWorkspace: M) */ i__2 = *lwork - nwork + 1; zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__2, &ierr); if (wntqn) { /* Compute singular values only (Cworkspace: 0) (Rworkspace: need BDSPAN) */ dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, & c__1, dum, idum, &rwork[nrwork], &iwork[1], info); } else if (wntqo) { ldwkvt = *m; ivt = nwork; if (*lwork >= *m * *n + *m * 3) { /* WORK( IVT ) is M by N */ zlaset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt); nwork = ivt + ldwkvt * *n; } else { /* WORK( IVT ) is M by CHUNK */ chunk = (*lwork - *m * 3) / *m; nwork = ivt + ldwkvt * chunk; } /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of A (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: need 0) */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__2 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr); if (*lwork >= *m * *n + *m * 3) { /* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) Overwrite WORK(IVT) by right singular vectors of A, copying to A (Cworkspace: need M*N+2*M, prefer M*N+M+M*NB) (Rworkspace: need 0) */ zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt); i__2 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[ itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &ierr); zlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda); } else { /* Generate P**H in A (Cworkspace: need 2*M, prefer M+M*NB) (Rworkspace: need 0) */ i__2 = *lwork - nwork + 1; zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], & work[nwork], &i__2, &ierr); /* Multiply Q in A by real matrix RWORK(IRU), storing the result in WORK(IU), copying to A (CWorkspace: need M*M, prefer M*N) (Rworkspace: need 3*M*M, prefer M*M+2*M*N) */ nrwork = iru; i__2 = *n; i__1 = chunk; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Computing MIN */ i__3 = *n - i__ + 1; blk = min(i__3,chunk); zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1] , lda, &work[ivt], &ldwkvt, &rwork[nrwork]); zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ * a_dim1 + 1], lda); /* L60: */ } } } else if (wntqs) { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of A (CWorkspace: need 3*M, prefer 2*M+M*NB) (RWorkspace: M*M) */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of A (CWorkspace: need 3*M, prefer 2*M+M*NB) (RWorkspace: M*M) */ zlaset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt); zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } else { /* Perform bidiagonal SVD, computing left singular vectors of bidiagonal matrix in RWORK(IRU) and computing right singular vectors of bidiagonal matrix in RWORK(IRVT) (CWorkspace: need 0) (RWorkspace: need BDSPAC) */ irvt = nrwork; iru = irvt + *m * *m; nrwork = iru + *m * *m; dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, & rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1], info); /* Copy real matrix RWORK(IRU) to complex matrix U Overwrite U by left singular vectors of A (CWorkspace: need 3*M, prefer 2*M+M*NB) (RWorkspace: M*M) */ zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu); i__1 = *lwork - nwork + 1; zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[ itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr); /* Set all of VT to identity matrix */ zlaset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt); /* Copy real matrix RWORK(IRVT) to complex matrix VT Overwrite VT by right singular vectors of A (CWorkspace: need 2*M+N, prefer 2*M+N*NB) (RWorkspace: M*M) */ zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt); i__1 = *lwork - nwork + 1; zunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[ itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, & ierr); } } } /* Undo scaling if necessary */ if (iscl == 1) { if (anrm > bignum) { dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } if (*info != 0 && anrm > bignum) { i__1 = minmn - 1; dlascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &c__1, &rwork[ ie], &minmn, &ierr); } if (anrm < smlnum) { dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, &ierr); } if (*info != 0 && anrm < smlnum) { i__1 = minmn - 1; dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[ ie], &minmn, &ierr); } } /* Return optimal workspace in WORK(1) */ work[1].r = (doublereal) maxwrk, work[1].i = 0.; return 0; /* End of ZGESDD */ } /* zgesdd_ */