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/* slasdq.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int slasdq_(char *uplo, integer *sqre, integer *n, integer *
ncvt, integer *nru, integer *ncc, real *d__, real *e, real *vt,
integer *ldvt, real *u, integer *ldu, real *c__, integer *ldc, real *
work, integer *info)
{
/* System generated locals */
integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
i__2;
/* Local variables */
integer i__, j;
real r__, cs, sn;
integer np1, isub;
real smin;
integer sqre1;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int slasr_(char *, char *, char *, integer *,
integer *, real *, real *, real *, integer *);
integer iuplo;
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
integer *), xerbla_(char *, integer *), slartg_(real *,
real *, real *, real *, real *);
logical rotate;
extern /* Subroutine */ int sbdsqr_(char *, integer *, integer *, integer
*, integer *, real *, real *, real *, integer *, real *, integer *
, real *, integer *, real *, integer *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLASDQ computes the singular value decomposition (SVD) of a real */
/* (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */
/* E, accumulating the transformations if desired. Letting B denote */
/* the input bidiagonal matrix, the algorithm computes orthogonal */
/* matrices Q and P such that B = Q * S * P' (P' denotes the transpose */
/* of P). The singular values S are overwritten on D. */
/* The input matrix U is changed to U * Q if desired. */
/* The input matrix VT is changed to P' * VT if desired. */
/* The input matrix C is changed to Q' * C if desired. */
/* See "Computing Small Singular Values of Bidiagonal Matrices With */
/* Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */
/* LAPACK Working Note #3, for a detailed description of the algorithm. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* On entry, UPLO specifies whether the input bidiagonal matrix */
/* is upper or lower bidiagonal, and wether it is square are */
/* not. */
/* UPLO = 'U' or 'u' B is upper bidiagonal. */
/* UPLO = 'L' or 'l' B is lower bidiagonal. */
/* SQRE (input) INTEGER */
/* = 0: then the input matrix is N-by-N. */
/* = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */
/* (N+1)-by-N if UPLU = 'L'. */
/* The bidiagonal matrix has */
/* N = NL + NR + 1 rows and */
/* M = N + SQRE >= N columns. */
/* N (input) INTEGER */
/* On entry, N specifies the number of rows and columns */
/* in the matrix. N must be at least 0. */
/* NCVT (input) INTEGER */
/* On entry, NCVT specifies the number of columns of */
/* the matrix VT. NCVT must be at least 0. */
/* NRU (input) INTEGER */
/* On entry, NRU specifies the number of rows of */
/* the matrix U. NRU must be at least 0. */
/* NCC (input) INTEGER */
/* On entry, NCC specifies the number of columns of */
/* the matrix C. NCC must be at least 0. */
/* D (input/output) REAL array, dimension (N) */
/* On entry, D contains the diagonal entries of the */
/* bidiagonal matrix whose SVD is desired. On normal exit, */
/* D contains the singular values in ascending order. */
/* E (input/output) REAL array. */
/* dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */
/* On entry, the entries of E contain the offdiagonal entries */
/* of the bidiagonal matrix whose SVD is desired. On normal */
/* exit, E will contain 0. If the algorithm does not converge, */
/* D and E will contain the diagonal and superdiagonal entries */
/* of a bidiagonal matrix orthogonally equivalent to the one */
/* given as input. */
/* VT (input/output) REAL array, dimension (LDVT, NCVT) */
/* On entry, contains a matrix which on exit has been */
/* premultiplied by P', dimension N-by-NCVT if SQRE = 0 */
/* and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */
/* LDVT (input) INTEGER */
/* On entry, LDVT specifies the leading dimension of VT as */
/* declared in the calling (sub) program. LDVT must be at */
/* least 1. If NCVT is nonzero LDVT must also be at least N. */
/* U (input/output) REAL array, dimension (LDU, N) */
/* On entry, contains a matrix which on exit has been */
/* postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */
/* and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */
/* LDU (input) INTEGER */
/* On entry, LDU specifies the leading dimension of U as */
/* declared in the calling (sub) program. LDU must be at */
/* least max( 1, NRU ) . */
/* C (input/output) REAL array, dimension (LDC, NCC) */
/* On entry, contains an N-by-NCC matrix which on exit */
/* has been premultiplied by Q' dimension N-by-NCC if SQRE = 0 */
/* and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */
/* LDC (input) INTEGER */
/* On entry, LDC specifies the leading dimension of C as */
/* declared in the calling (sub) program. LDC must be at */
/* least 1. If NCC is nonzero, LDC must also be at least N. */
/* WORK (workspace) REAL array, dimension (4*N) */
/* Workspace. Only referenced if one of NCVT, NRU, or NCC is */
/* nonzero, and if N is at least 2. */
/* INFO (output) INTEGER */
/* On exit, a value of 0 indicates a successful exit. */
/* If INFO < 0, argument number -INFO is illegal. */
/* If INFO > 0, the algorithm did not converge, and INFO */
/* specifies how many superdiagonals 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 .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
iuplo = 0;
if (lsame_(uplo, "U")) {
iuplo = 1;
}
if (lsame_(uplo, "L")) {
iuplo = 2;
}
if (iuplo == 0) {
*info = -1;
} else if (*sqre < 0 || *sqre > 1) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ncvt < 0) {
*info = -4;
} else if (*nru < 0) {
*info = -5;
} else if (*ncc < 0) {
*info = -6;
} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) {
*info = -10;
} else if (*ldu < max(1,*nru)) {
*info = -12;
} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLASDQ", &i__1);
return 0;
}
if (*n == 0) {
return 0;
}
/* ROTATE is true if any singular vectors desired, false otherwise */
rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
np1 = *n + 1;
sqre1 = *sqre;
/* If matrix non-square upper bidiagonal, rotate to be lower */
/* bidiagonal. The rotations are on the right. */
if (iuplo == 1 && sqre1 == 1) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
slartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
d__[i__] = r__;
e[i__] = sn * d__[i__ + 1];
d__[i__ + 1] = cs * d__[i__ + 1];
if (rotate) {
work[i__] = cs;
work[*n + i__] = sn;
}
/* L10: */
}
slartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
d__[*n] = r__;
e[*n] = 0.f;
if (rotate) {
work[*n] = cs;
work[*n + *n] = sn;
}
iuplo = 2;
sqre1 = 0;
/* Update singular vectors if desired. */
if (*ncvt > 0) {
slasr_("L", "V", "F", &np1, ncvt, &work[1], &work[np1], &vt[
vt_offset], ldvt);
}
}
/* If matrix lower bidiagonal, rotate to be upper bidiagonal */
/* by applying Givens rotations on the left. */
if (iuplo == 2) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
slartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
d__[i__] = r__;
e[i__] = sn * d__[i__ + 1];
d__[i__ + 1] = cs * d__[i__ + 1];
if (rotate) {
work[i__] = cs;
work[*n + i__] = sn;
}
/* L20: */
}
/* If matrix (N+1)-by-N lower bidiagonal, one additional */
/* rotation is needed. */
if (sqre1 == 1) {
slartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
d__[*n] = r__;
if (rotate) {
work[*n] = cs;
work[*n + *n] = sn;
}
}
/* Update singular vectors if desired. */
if (*nru > 0) {
if (sqre1 == 0) {
slasr_("R", "V", "F", nru, n, &work[1], &work[np1], &u[
u_offset], ldu);
} else {
slasr_("R", "V", "F", nru, &np1, &work[1], &work[np1], &u[
u_offset], ldu);
}
}
if (*ncc > 0) {
if (sqre1 == 0) {
slasr_("L", "V", "F", n, ncc, &work[1], &work[np1], &c__[
c_offset], ldc);
} else {
slasr_("L", "V", "F", &np1, ncc, &work[1], &work[np1], &c__[
c_offset], ldc);
}
}
}
/* Call SBDSQR to compute the SVD of the reduced real */
/* N-by-N upper bidiagonal matrix. */
sbdsqr_("U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[
u_offset], ldu, &c__[c_offset], ldc, &work[1], info);
/* Sort the singular values into ascending order (insertion sort on */
/* singular values, but only one transposition per singular vector) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Scan for smallest D(I). */
isub = i__;
smin = d__[i__];
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (d__[j] < smin) {
isub = j;
smin = d__[j];
}
/* L30: */
}
if (isub != i__) {
/* Swap singular values and vectors. */
d__[isub] = d__[i__];
d__[i__] = smin;
if (*ncvt > 0) {
sswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1],
ldvt);
}
if (*nru > 0) {
sswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1]
, &c__1);
}
if (*ncc > 0) {
sswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc)
;
}
}
/* L40: */
}
return 0;
/* End of SLASDQ */
} /* slasdq_ */
|
