📄 zgesdd.c
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#include "blaswrap.h"
/* -- translated by f2c (version 19990503).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Common Block Declarations */
struct {
doublereal ops, itcnt;
} latime_;
#define latime_1 latime_
/* 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;
/* 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)
{
/* 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 iscl;
static doublereal anrm;
static integer idum[1], ierr, itau, irvt, i__;
extern doublereal dopla_(char *, integer *, integer *, integer *, integer
*, integer *);
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 itaup, itauq, wrkbl;
static logical wntqa;
static integer nwork;
static logical wntqn, wntqo, wntqs;
extern doublereal dopla2_(char *, char *, integer *, integer *, integer *,
integer *, integer *), dopbl3_(char *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlacp2_(char *, integer *, integer *,
doublereal *, integer *, doublecomplex *, integer *);
static integer mnthr1, mnthr2, ie, nb;
extern /* Subroutine */ int dbdsdc_(char *, char *, integer *, doublereal
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *);
static integer il;
extern doublereal dlamch_(char *);
static integer ir, iu;
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 logical lquery;
static integer nrwork;
extern /* Subroutine */ int zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
static integer blk;
static doublereal dum[1], eps;
static integer iru, ivt;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define u_subscr(a_1,a_2) (a_2)*u_dim1 + a_1
#define u_ref(a_1,a_2) u[u_subscr(a_1,a_2)]
#define vt_subscr(a_1,a_2) (a_2)*vt_dim1 + a_1
#define vt_ref(a_1,a_2) vt[vt_subscr(a_1,a_2)]
/* -- LAPACK driver routine (instrumented to count ops, version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
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
on 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 VT;
= '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 (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 < 0 but other input arguments are legal, WORK(1)
returns the optimal LWORK.
RWORK (workspace) DOUBLE PRECISION array, dimension (LRWORK)
If JOBZ = 'N', LRWORK >= 7*min(M,N).
Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 5*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 */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--s;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1 * 1;
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;
lquery = *lwork == -1;
if (! (wntqa || wntqs || wntqo || wntqn)) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
m) {
*info = -8;
} else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
wntqo && *m >= *n && *ldvt < *n) {
*info = -10;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
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,
BDSPAC = 3*N*N + 4*N */
if (*m >= mnthr1) {
if (wntqn) {
/* Path 1 (M much larger than N, JOBZ='N') */
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 << 1) + (*n << 1) * ilaenv_(&
c__1, "ZGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)
6, (ftnlen)1);
wrkbl = max(i__1,i__2);
maxwrk = wrkbl;
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') */
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