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cgesdd.c
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/* cgesdd.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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
/* Subroutine */ int cgesdd_(char *jobz, integer *m, integer *n, complex *a,
integer *lda, real *s, complex *u, integer *ldu, complex *vt, integer
*ldvt, complex *work, integer *lwork, real *rwork, integer *iwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
i__2, i__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, ie, il, ir, iu, blk;
real dum[1], eps;
integer iru, ivt, iscl;
real anrm;
integer idum[1], ierr, itau, irvt;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
extern logical lsame_(char *, char *);
integer chunk, minmn, wrkbl, itaup, itauq;
logical wntqa;
integer nwork;
extern /* Subroutine */ int clacp2_(char *, integer *, integer *, real *,
integer *, complex *, integer *);
logical wntqn, wntqo, wntqs;
integer mnthr1, mnthr2;
extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *,
integer *, real *, real *, complex *, complex *, complex *,
integer *, integer *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *), clacrm_(
integer *, integer *, complex *, integer *, real *, integer *,
complex *, integer *, real *), clarcm_(integer *, integer *, real
*, integer *, complex *, integer *, complex *, integer *, real *),
clascl_(char *, integer *, integer *, real *, real *, integer *,
integer *, complex *, integer *, integer *), sbdsdc_(char
*, char *, integer *, real *, real *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer
*, complex *, complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), claset_(char *,
integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int cungbr_(char *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, integer
*);
real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *), cunmbr_(char *, char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *), cunglq_(
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, integer *);
integer ldwrkl;
extern /* Subroutine */ int cungqr_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
integer ldwrkr, minwrk, ldwrku, maxwrk, ldwkvt;
real smlnum;
logical wntqas;
integer nrwork;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* 8-15-00: Improve consistency of WS calculations (eca) */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGESDD 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 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) REAL array, dimension (min(M,N)) */
/* The singular values of A, sorted so that S(i) >= S(i+1). */
/* U (output) COMPLEX 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 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 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) REAL 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 SBDSDC did not converge. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ming Gu and Huan Ren, Computer Science Division, University of */
/* California at Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--s;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
mnthr1 = (integer) (minmn * 17.f / 9.f);
mnthr2 = (integer) (minmn * 5.f / 3.f);
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, "CGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n << 1) * ilaenv_(&
c__1, "CGEBRD", " ", n, n, &c_n1, &c_n1);
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, "CGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "CUNGQR",
" ", m, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + (*n << 1) * ilaenv_(&
c__1, "CGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "QLN", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "PRC", n, n, n, &c_n1);
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, "CGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *n * ilaenv_(&c__1, "CUNGQR",
" ", m, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + (*n << 1) * ilaenv_(&
c__1, "CGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "QLN", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "PRC", n, n, n, &c_n1);
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, "CGEQRF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + *m * ilaenv_(&c__1, "CUNGQR",
" ", m, m, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + (*n << 1) * ilaenv_(&
c__1, "CGEBRD", " ", n, n, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "QLN", n, n, n, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "PRC", n, n, n, &c_n1);
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, "CGEBRD",
" ", m, n, &c_n1, &c_n1);
minwrk = (*n << 1) + *m;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "P", n, n, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "Q", m, n, n, &c_n1);
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,
"CUNGBR", "P", n, n, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "Q", m, n, n, &c_n1);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "P", n, n, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "Q", m, m, n, &c_n1);
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, "CGEBRD",
" ", m, n, &c_n1, &c_n1);
minwrk = (*n << 1) + *m;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "PRC", n, n, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "QLN", m, n, n, &c_n1);
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,
"CUNMBR", "PRC", n, n, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNMBR", "QLN", m, n, n, &c_n1);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "PRC", n, n, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "QLN", m, m, n, &c_n1);
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, "CGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + (*m << 1) * ilaenv_(&
c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1);
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, "CGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "CUNGLQ",
" ", m, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + (*m << 1) * ilaenv_(&
c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "PRC", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "QLN", m, m, m, &c_n1);
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, "CGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *m * ilaenv_(&c__1, "CUNGLQ",
" ", m, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + (*m << 1) * ilaenv_(&
c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "PRC", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "QLN", m, m, m, &c_n1);
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, "CGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + *n * ilaenv_(&c__1, "CUNGLQ",
" ", n, n, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + (*m << 1) * ilaenv_(&
c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "PRC", m, m, m, &c_n1);
wrkbl = max(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "QLN", m, m, m, &c_n1);
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, "CGEBRD",
" ", m, n, &c_n1, &c_n1);
minwrk = (*m << 1) + *n;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "P", m, n, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "Q", m, m, n, &c_n1);
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,
"CUNGBR", "P", m, n, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "Q", m, m, n, &c_n1);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "P", n, n, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "Q", m, m, n, &c_n1);
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, "CGEBRD",
" ", m, n, &c_n1, &c_n1);
minwrk = (*m << 1) + *n;
if (wntqo) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "PRC", m, n, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNMBR", "QLN", m, m, n, &c_n1);
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,
"CUNGBR", "PRC", m, n, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "QLN", m, m, n, &c_n1);
maxwrk = max(i__1,i__2);
} else if (wntqa) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *n * ilaenv_(&c__1,
"CUNGBR", "PRC", n, n, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"CUNGBR", "QLN", m, m, n, &c_n1);
maxwrk = max(i__1,i__2);
}
}
}
maxwrk = max(maxwrk,minwrk);
}
if (*info == 0) {
work[1].r = (real) maxwrk, work[1].i = 0.f;
if (*lwork < minwrk && *lwork != -1) {
*info = -13;
}
}
/* Quick returns */
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGESDD", &i__1);
return 0;
}
if (*lwork == -1) {
return 0;
}
if (*m == 0 || *n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = sqrt(slamch_("S")) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", m, n, &a[a_offset], lda, dum);
iscl = 0;
if (anrm > 0.f && anrm < smlnum) {
iscl = 1;
clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
ierr);
} else if (anrm > bignum) {
iscl = 1;
clascl_("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;
cgeqrf_(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;
claset_("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;
cgebrd_(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) */
sbdsdc_("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;
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy R to WORK( IR ), zeroing out below it */
clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__1 = *n - 1;
i__2 = *n - 1;
claset_("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;
cungqr_(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;
cgebrd_(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;
sbdsdc_("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) */
clacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
i__1 = *lwork - nwork + 1;
cunmbr_("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) */
clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__1 = *lwork - nwork + 1;
cunmbr_("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);
cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1],
lda, &work[iu], &ldwrku, &c_b1, &work[ir], &
ldwrkr);
clacpy_("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;
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__2 = *n - 1;
i__1 = *n - 1;
claset_("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;
cungqr_(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;
cgebrd_(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;
sbdsdc_("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) */
clacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
i__2 = *lwork - nwork + 1;
cunmbr_("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) */
clacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
i__2 = *lwork - nwork + 1;
cunmbr_("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) */
clacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
cgemm_("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;
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
clacpy_("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;
cungqr_(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;
claset_("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;
cgebrd_(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) */
sbdsdc_("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) */