/* slasd6.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 "clapack.h"
/* Table of constant values */
static integer c__0 = 0;
static real c_b7 = 1.f;
static integer c__1 = 1;
static integer c_n1 = -1;
/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr,
integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta,
integer *idxq, integer *perm, integer *givptr, integer *givcol,
integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
work, integer *iwork, integer *info)
{
/* System generated locals */
integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
poles_dim1, poles_offset, i__1;
real r__1, r__2;
/* Local variables */
integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), slasd7_(integer *, integer *, integer *, integer *,
integer *, real *, real *, real *, real *, real *, real *, real *,
real *, real *, real *, integer *, integer *, integer *, integer
*, integer *, integer *, integer *, real *, integer *, real *,
real *, integer *), slasd8_(integer *, integer *, real *, real *,
real *, real *, real *, real *, integer *, real *, real *,
integer *);
integer isigma;
extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
char *, integer *, integer *, real *, real *, integer *, integer *
, real *, integer *, integer *), slamrg_(integer *,
integer *, real *, integer *, integer *, integer *);
real orgnrm;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLASD6 computes the SVD of an updated upper bidiagonal matrix B */
/* obtained by merging two smaller ones by appending a row. This */
/* routine is used only for the problem which requires all singular */
/* values and optionally singular vector matrices in factored form. */
/* B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
/* A related subroutine, SLASD1, handles the case in which all singular */
/* values and singular vectors of the bidiagonal matrix are desired. */
/* SLASD6 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 singular values of B can be computed using D1, D2, the first */
/* components of all the right singular vectors of the lower block, and */
/* the last components of all the right singular vectors of the upper */
/* block. These components are stored and updated in VF and VL, */
/* respectively, in SLASD6. Hence U and VT are not explicitly */
/* referenced. */
/* The singular values are stored in D. The algorithm consists of two */
/* stages: */
/* The first stage consists of deflating the size of the problem */
/* when there are multiple singular values or if there is a zero */
/* 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 SLASD7. */
/* The second stage consists of calculating the updated */
/* singular values. This is done by finding the roots of the */
/* secular equation via the routine SLASD4 (as called by SLASD8). */
/* This routine also updates VF and VL and computes the distances */
/* between the updated singular values and the old singular */
/* values. */
/* SLASD6 is called from SLASDA. */
/* Arguments */
/* ========= */
/* ICOMPQ (input) INTEGER */
/* Specifies whether singular vectors are to be computed in */
/* factored form: */
/* = 0: Compute singular values only. */
/* = 1: Compute singular vectors in factored form as well. */
/* 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) REAL array, dimension (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. */
/* VF (input/output) REAL array, dimension (M) */
/* On entry, VF(1:NL+1) contains the first components of all */
/* right singular vectors of the upper block; and VF(NL+2:M) */
/* contains the first components of all right singular vectors */
/* of the lower block. On exit, VF contains the first components */
/* of all right singular vectors of the bidiagonal matrix. */
/* VL (input/output) REAL array, dimension (M) */
/* On entry, VL(1:NL+1) contains the last components of all */
/* right singular vectors of the upper block; and VL(NL+2:M) */
/* contains the last components of all right singular vectors of */
/* the lower block. On exit, VL contains the last components of */
/* all right singular vectors of the bidiagonal matrix. */
/* ALPHA (input/output) REAL */
/* Contains the diagonal element associated with the added row. */
/* BETA (input/output) REAL */
/* Contains the off-diagonal element associated with the added */
/* row. */
/* 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. */
/* PERM (output) INTEGER array, dimension ( N ) */
/* The permutations (from deflation and sorting) to be applied */
/* to each block. Not referenced if ICOMPQ = 0. */
/* GIVPTR (output) INTEGER */
/* The number of Givens rotations which took place in this */
/* subproblem. Not referenced if ICOMPQ = 0. */
/* GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 ) */
/* Each pair of numbers indicates a pair of columns to take place */
/* in a Givens rotation. Not referenced if ICOMPQ = 0. */
/* LDGCOL (input) INTEGER */
/* leading dimension of GIVCOL, must be at least N. */
/* GIVNUM (output) REAL array, dimension ( LDGNUM, 2 ) */
/* Each number indicates the C or S value to be used in the */
/* corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
/* LDGNUM (input) INTEGER */
/* The leading dimension of GIVNUM and POLES, must be at least N. */
/* POLES (output) REAL array, dimension ( LDGNUM, 2 ) */
/* On exit, POLES(1,*) is an array containing the new singular */
/* values obtained from solving the secular equation, and */
/* POLES(2,*) is an array containing the poles in the secular */
/* equation. Not referenced if ICOMPQ = 0. */
/* DIFL (output) REAL array, dimension ( N ) */
/* On exit, DIFL(I) is the distance between I-th updated */
/* (undeflated) singular value and the I-th (undeflated) old */
/* singular value. */
/* DIFR (output) REAL array, */
/* dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and */
/* dimension ( N ) if ICOMPQ = 0. */
/* On exit, DIFR(I, 1) is the distance between I-th updated */
/* (undeflated) singular value and the I+1-th (undeflated) old */
/* singular value. */
/* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
/* normalizing factors for the right singular vector matrix. */
/* See SLASD8 for details on DIFL and DIFR. */
/* Z (output) REAL array, dimension ( M ) */
/* The first elements of this array contain the components */
/* of the deflation-adjusted updating row vector. */
/* K (output) INTEGER */
/* Contains the dimension of the non-deflated matrix, */
/* This is the order of the related secular equation. 1 <= K <=N. */
/* C (output) REAL */
/* C contains garbage if SQRE =0 and the C-value of a Givens */
/* rotation related to the right null space if SQRE = 1. */
/* S (output) REAL */
/* S contains garbage if SQRE =0 and the S-value of a Givens */
/* rotation related to the right null space if SQRE = 1. */
/* WORK (workspace) REAL array, dimension ( 4 * M ) */
/* IWORK (workspace) INTEGER array, dimension ( 3 * N ) */
/* 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__;
--vf;
--vl;
--idxq;
--perm;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1;
givcol -= givcol_offset;
poles_dim1 = *ldgnum;
poles_offset = 1 + poles_dim1;
poles -= poles_offset;
givnum_dim1 = *ldgnum;
givnum_offset = 1 + givnum_dim1;
givnum -= givnum_offset;
--difl;
--difr;
--z__;
--work;
--iwork;
/* Function Body */
*info = 0;
n = *nl + *nr + 1;
m = n + *sqre;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*nl < 1) {
*info = -2;
} else if (*nr < 1) {
*info = -3;
} else if (*sqre < 0 || *sqre > 1) {
*info = -4;
} else if (*ldgcol < n) {
*info = -14;
} else if (*ldgnum < n) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLASD6", &i__1);
return 0;
}
/* 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 SLASD7 and SLASD8. */
isigma = 1;
iw = isigma + n;
ivfw = iw + m;
ivlw = ivfw + m;
idx = 1;
idxc = idx + n;
idxp = idxc + n;
/* Scale. */
/* Computing MAX */
r__1 = dabs(*alpha), r__2 = dabs(*beta);
orgnrm = dmax(r__1,r__2);
d__[*nl + 1] = 0.f;
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if ((r__1 = d__[i__], dabs(r__1)) > orgnrm) {
orgnrm = (r__1 = d__[i__], dabs(r__1));
}
/* L10: */
}
slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
*alpha /= orgnrm;
*beta /= orgnrm;
/* Sort and Deflate singular values. */
slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
info);
/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
ldgnum, &work[isigma], &work[iw], info);
/* Save the poles if ICOMPQ = 1. */
if (*icompq == 1) {
scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
}
/* Unscale. */
slascl_("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;
slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
return 0;
/* End of SLASD6 */
} /* slasd6_ */