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/* dlasd1.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 doublereal c_b7 = 1.;
static integer c__1 = 1;
static integer c_n1 = -1;
/* Subroutine */ int dlasd1_(integer *nl, integer *nr, integer *sqre,
doublereal *d__, doublereal *alpha, doublereal *beta, doublereal *u,
integer *ldu, doublereal *vt, integer *ldvt, integer *idxq, integer *
iwork, doublereal *work, integer *info)
{
/* System generated locals */
integer u_dim1, u_offset, vt_dim1, vt_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
integer i__, k, m, n, n1, n2, iq, iz, iu2, ldq, idx, ldu2, ivt2, idxc,
idxp, ldvt2;
extern /* Subroutine */ int dlasd2_(integer *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *), dlasd3_(
integer *, integer *, integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *),
dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, integer *, doublereal *, integer *, integer *),
dlamrg_(integer *, integer *, doublereal *, integer *, integer *,
integer *);
integer isigma;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal orgnrm;
integer coltyp;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B, */
/* where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0. */
/* A related subroutine DLASD7 handles the case in which the singular */
/* values (and the singular vectors in factored form) are desired. */
/* DLASD1 computes the SVD as follows: */
/* ( D1(in) 0 0 0 ) */
/* B = U(in) * ( Z1' a Z2' b ) * VT(in) */
/* ( 0 0 D2(in) 0 ) */
/* = U(out) * ( D(out) 0) * VT(out) */
/* where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M */
/* with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
/* elsewhere; and the entry b is empty if SQRE = 0. */
/* The left singular vectors of the original matrix are stored in U, and */
/* the transpose of the right singular vectors are stored in VT, and the */
/* singular values are in D. The algorithm consists of three stages: */
/* The first stage consists of deflating the size of the problem */
/* when there are multiple singular values or when there are zeros in */
/* the Z vector. For each such occurence the dimension of the */
/* secular equation problem is reduced by one. This stage is */
/* performed by the routine DLASD2. */
/* The second stage consists of calculating the updated */
/* singular values. This is done by finding the square roots of the */
/* roots of the secular equation via the routine DLASD4 (as called */
/* by DLASD3). This routine also calculates the singular vectors of */
/* the current problem. */
/* The final stage consists of computing the updated singular vectors */
/* directly using the updated singular values. The singular vectors */
/* for the current problem are multiplied with the singular vectors */
/* from the overall problem. */
/* Arguments */
/* ========= */
/* NL (input) INTEGER */
/* The row dimension of the upper block. NL >= 1. */
/* NR (input) INTEGER */
/* The row dimension of the lower block. NR >= 1. */
/* SQRE (input) INTEGER */
/* = 0: the lower block is an NR-by-NR square matrix. */
/* = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
/* The bidiagonal matrix has row dimension N = NL + NR + 1, */
/* and column dimension M = N + SQRE. */
/* D (input/output) DOUBLE PRECISION array, */
/* dimension (N = NL+NR+1). */
/* On entry D(1:NL,1:NL) contains the singular values of the */
/* upper block; and D(NL+2:N) contains the singular values of */
/* the lower block. On exit D(1:N) contains the singular values */
/* of the modified matrix. */
/* ALPHA (input/output) DOUBLE PRECISION */
/* Contains the diagonal element associated with the added row. */
/* BETA (input/output) DOUBLE PRECISION */
/* Contains the off-diagonal element associated with the added */
/* row. */
/* U (input/output) DOUBLE PRECISION array, dimension(LDU,N) */
/* On entry U(1:NL, 1:NL) contains the left singular vectors of */
/* the upper block; U(NL+2:N, NL+2:N) contains the left singular */
/* vectors of the lower block. On exit U contains the left */
/* singular vectors of the bidiagonal matrix. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= max( 1, N ). */
/* VT (input/output) DOUBLE PRECISION array, dimension(LDVT,M) */
/* where M = N + SQRE. */
/* On entry VT(1:NL+1, 1:NL+1)' contains the right singular */
/* vectors of the upper block; VT(NL+2:M, NL+2:M)' contains */
/* the right singular vectors of the lower block. On exit */
/* VT' contains the right singular vectors of the */
/* bidiagonal matrix. */
/* LDVT (input) INTEGER */
/* The leading dimension of the array VT. LDVT >= max( 1, M ). */
/* IDXQ (output) INTEGER array, dimension(N) */
/* This contains the permutation which will reintegrate the */
/* subproblem just solved back into sorted order, i.e. */
/* D( IDXQ( I = 1, N ) ) will be in ascending order. */
/* IWORK (workspace) INTEGER array, dimension( 4 * N ) */
/* WORK (workspace) DOUBLE PRECISION array, dimension( 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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
--idxq;
--iwork;
--work;
/* Function Body */
*info = 0;
if (*nl < 1) {
*info = -1;
} else if (*nr < 1) {
*info = -2;
} else if (*sqre < 0 || *sqre > 1) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLASD1", &i__1);
return 0;
}
n = *nl + *nr + 1;
m = n + *sqre;
/* The following values are for bookkeeping purposes only. They are */
/* integer pointers which indicate the portion of the workspace */
/* used by a particular array in DLASD2 and DLASD3. */
ldu2 = n;
ldvt2 = m;
iz = 1;
isigma = iz + m;
iu2 = isigma + n;
ivt2 = iu2 + ldu2 * n;
iq = ivt2 + ldvt2 * m;
idx = 1;
idxc = idx + n;
coltyp = idxc + n;
idxp = coltyp + n;
/* Scale. */
/* Computing MAX */
d__1 = abs(*alpha), d__2 = abs(*beta);
orgnrm = max(d__1,d__2);
d__[*nl + 1] = 0.;
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if ((d__1 = d__[i__], abs(d__1)) > orgnrm) {
orgnrm = (d__1 = d__[i__], abs(d__1));
}
/* L10: */
}
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
*alpha /= orgnrm;
*beta /= orgnrm;
/* Deflate singular values. */
dlasd2_(nl, nr, sqre, &k, &d__[1], &work[iz], alpha, beta, &u[u_offset],
ldu, &vt[vt_offset], ldvt, &work[isigma], &work[iu2], &ldu2, &
work[ivt2], &ldvt2, &iwork[idxp], &iwork[idx], &iwork[idxc], &
idxq[1], &iwork[coltyp], info);
/* Solve Secular Equation and update singular vectors. */
ldq = k;
dlasd3_(nl, nr, sqre, &k, &d__[1], &work[iq], &ldq, &work[isigma], &u[
u_offset], ldu, &work[iu2], &ldu2, &vt[vt_offset], ldvt, &work[
ivt2], &ldvt2, &iwork[idxc], &iwork[coltyp], &work[iz], info);
if (*info != 0) {
return 0;
}
/* Unscale. */
dlascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);
/* Prepare the IDXQ sorting permutation. */
n1 = k;
n2 = n - k;
dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
return 0;
/* End of DLASD1 */
} /* dlasd1_ */
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