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/* dlasd0.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__0 = 0;
static integer c__2 = 2;
/* Subroutine */ int dlasd0_(integer *n, integer *sqre, doublereal *d__,
doublereal *e, doublereal *u, integer *ldu, doublereal *vt, integer *
ldvt, integer *smlsiz, integer *iwork, doublereal *work, integer *
info)
{
/* System generated locals */
integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
/* Builtin functions */
integer pow_ii(integer *, integer *);
/* Local variables */
integer i__, j, m, i1, ic, lf, nd, ll, nl, nr, im1, ncc, nlf, nrf, iwk,
lvl, ndb1, nlp1, nrp1;
doublereal beta;
integer idxq, nlvl;
doublereal alpha;
integer inode, ndiml, idxqc, ndimr, itemp, sqrei;
extern /* Subroutine */ int dlasd1_(integer *, integer *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, integer *, integer *, doublereal *,
integer *), dlasdq_(char *, integer *, integer *, integer *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *), dlasdt_(integer *, integer *,
integer *, integer *, integer *, integer *, integer *), xerbla_(
char *, integer *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* Using a divide and conquer approach, DLASD0 computes the singular */
/* value decomposition (SVD) of a real upper bidiagonal N-by-M */
/* matrix B with diagonal D and offdiagonal E, where M = N + SQRE. */
/* The algorithm computes orthogonal matrices U and VT such that */
/* B = U * S * VT. The singular values S are overwritten on D. */
/* A related subroutine, DLASDA, computes only the singular values, */
/* and optionally, the singular vectors in compact form. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* On entry, the row dimension of the upper bidiagonal matrix. */
/* This is also the dimension of the main diagonal array D. */
/* SQRE (input) INTEGER */
/* Specifies the column dimension of the bidiagonal matrix. */
/* = 0: The bidiagonal matrix has column dimension M = N; */
/* = 1: The bidiagonal matrix has column dimension M = N+1; */
/* D (input/output) DOUBLE PRECISION array, dimension (N) */
/* On entry D contains the main diagonal of the bidiagonal */
/* matrix. */
/* On exit D, if INFO = 0, contains its singular values. */
/* E (input) DOUBLE PRECISION array, dimension (M-1) */
/* Contains the subdiagonal entries of the bidiagonal matrix. */
/* On exit, E has been destroyed. */
/* U (output) DOUBLE PRECISION array, dimension at least (LDQ, N) */
/* On exit, U contains the left singular vectors. */
/* LDU (input) INTEGER */
/* On entry, leading dimension of U. */
/* VT (output) DOUBLE PRECISION array, dimension at least (LDVT, M) */
/* On exit, VT' contains the right singular vectors. */
/* LDVT (input) INTEGER */
/* On entry, leading dimension of VT. */
/* SMLSIZ (input) INTEGER */
/* On entry, maximum size of the subproblems at the */
/* bottom of the computation tree. */
/* IWORK (workspace) INTEGER work array. */
/* Dimension must be at least (8 * N) */
/* WORK (workspace) DOUBLE PRECISION work array. */
/* Dimension must be at least (3 * M**2 + 2 * M) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = 1, an singular value did not converge */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ming Gu and Huan Ren, Computer Science Division, University of */
/* California at Berkeley, USA */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
--e;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
--iwork;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*sqre < 0 || *sqre > 1) {
*info = -2;
}
m = *n + *sqre;
if (*ldu < *n) {
*info = -6;
} else if (*ldvt < m) {
*info = -8;
} else if (*smlsiz < 3) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLASD0", &i__1);
return 0;
}
/* If the input matrix is too small, call DLASDQ to find the SVD. */
if (*n <= *smlsiz) {
dlasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset],
ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], info);
return 0;
}
/* Set up the computation tree. */
inode = 1;
ndiml = inode + *n;
ndimr = ndiml + *n;
idxq = ndimr + *n;
iwk = idxq + *n;
dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
smlsiz);
/* For the nodes on bottom level of the tree, solve */
/* their subproblems by DLASDQ. */
ndb1 = (nd + 1) / 2;
ncc = 0;
i__1 = nd;
for (i__ = ndb1; i__ <= i__1; ++i__) {
/* IC : center row of each node */
/* NL : number of rows of left subproblem */
/* NR : number of rows of right subproblem */
/* NLF: starting row of the left subproblem */
/* NRF: starting row of the right subproblem */
i1 = i__ - 1;
ic = iwork[inode + i1];
nl = iwork[ndiml + i1];
nlp1 = nl + 1;
nr = iwork[ndimr + i1];
nrp1 = nr + 1;
nlf = ic - nl;
nrf = ic + 1;
sqrei = 1;
dlasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &vt[
nlf + nlf * vt_dim1], ldvt, &u[nlf + nlf * u_dim1], ldu, &u[
nlf + nlf * u_dim1], ldu, &work[1], info);
if (*info != 0) {
return 0;
}
itemp = idxq + nlf - 2;
i__2 = nl;
for (j = 1; j <= i__2; ++j) {
iwork[itemp + j] = j;
/* L10: */
}
if (i__ == nd) {
sqrei = *sqre;
} else {
sqrei = 1;
}
nrp1 = nr + sqrei;
dlasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &vt[
nrf + nrf * vt_dim1], ldvt, &u[nrf + nrf * u_dim1], ldu, &u[
nrf + nrf * u_dim1], ldu, &work[1], info);
if (*info != 0) {
return 0;
}
itemp = idxq + ic;
i__2 = nr;
for (j = 1; j <= i__2; ++j) {
iwork[itemp + j - 1] = j;
/* L20: */
}
/* L30: */
}
/* Now conquer each subproblem bottom-up. */
for (lvl = nlvl; lvl >= 1; --lvl) {
/* Find the first node LF and last node LL on the */
/* current level LVL. */
if (lvl == 1) {
lf = 1;
ll = 1;
} else {
i__1 = lvl - 1;
lf = pow_ii(&c__2, &i__1);
ll = (lf << 1) - 1;
}
i__1 = ll;
for (i__ = lf; i__ <= i__1; ++i__) {
im1 = i__ - 1;
ic = iwork[inode + im1];
nl = iwork[ndiml + im1];
nr = iwork[ndimr + im1];
nlf = ic - nl;
if (*sqre == 0 && i__ == ll) {
sqrei = *sqre;
} else {
sqrei = 1;
}
idxqc = idxq + nlf - 1;
alpha = d__[ic];
beta = e[ic];
dlasd1_(&nl, &nr, &sqrei, &d__[nlf], &alpha, &beta, &u[nlf + nlf *
u_dim1], ldu, &vt[nlf + nlf * vt_dim1], ldvt, &iwork[
idxqc], &iwork[iwk], &work[1], info);
if (*info != 0) {
return 0;
}
/* L40: */
}
/* L50: */
}
return 0;
/* End of DLASD0 */
} /* dlasd0_ */
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