/* dlasd7.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 dlasd7_(integer *icompq, integer *nl, integer *nr,
integer *sqre, integer *k, doublereal *d__, doublereal *z__,
doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl,
doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal *
dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm,
integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
integer *ldgnum, doublereal *c__, doublereal *s, integer *info)
{
/* System generated locals */
integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
integer i__, j, m, n, k2;
doublereal z1;
integer jp;
doublereal eps, tau, tol;
integer nlp1, nlp2, idxi, idxj;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
integer idxjp;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer jprev;
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), xerbla_(char *, integer *);
doublereal hlftol;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLASD7 merges the two sets of singular values together into a single */
/* sorted set. Then it tries to deflate the size of the problem. There */
/* are two ways in which deflation can occur: when two or more singular */
/* values are close together or if there is a tiny entry in the Z */
/* vector. For each such occurrence the order of the related */
/* secular equation problem is reduced by one. */
/* DLASD7 is called from DLASD6. */
/* Arguments */
/* ========= */
/* ICOMPQ (input) INTEGER */
/* Specifies whether singular vectors are to be computed */
/* in compact form, as follows: */
/* = 0: Compute singular values only. */
/* = 1: Compute singular vectors of upper */
/* bidiagonal matrix in compact form. */
/* 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 */
/* N = NL + NR + 1 rows and */
/* M = N + SQRE >= N columns. */
/* K (output) INTEGER */
/* Contains the dimension of the non-deflated matrix, this is */
/* the order of the related secular equation. 1 <= K <=N. */
/* D (input/output) DOUBLE PRECISION array, dimension ( N ) */
/* On entry D contains the singular values of the two submatrices */
/* to be combined. On exit D contains the trailing (N-K) updated */
/* singular values (those which were deflated) sorted into */
/* increasing order. */
/* Z (output) DOUBLE PRECISION array, dimension ( M ) */
/* On exit Z contains the updating row vector in the secular */
/* equation. */
/* ZW (workspace) DOUBLE PRECISION array, dimension ( M ) */
/* Workspace for Z. */
/* VF (input/output) DOUBLE PRECISION 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. */
/* VFW (workspace) DOUBLE PRECISION array, dimension ( M ) */
/* Workspace for VF. */
/* VL (input/output) DOUBLE PRECISION 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. */
/* VLW (workspace) DOUBLE PRECISION array, dimension ( M ) */
/* Workspace for VL. */
/* ALPHA (input) DOUBLE PRECISION */
/* Contains the diagonal element associated with the added row. */
/* BETA (input) DOUBLE PRECISION */
/* Contains the off-diagonal element associated with the added */
/* row. */
/* DSIGMA (output) DOUBLE PRECISION array, dimension ( N ) */
/* Contains a copy of the diagonal elements (K-1 singular values */
/* and one zero) in the secular equation. */
/* IDX (workspace) INTEGER array, dimension ( N ) */
/* This will contain the permutation used to sort the contents of */
/* D into ascending order. */
/* IDXP (workspace) INTEGER array, dimension ( N ) */
/* This will contain the permutation used to place deflated */
/* values of D at the end of the array. On output IDXP(2:K) */
/* points to the nondeflated D-values and IDXP(K+1:N) */
/* points to the deflated singular values. */
/* IDXQ (input) INTEGER array, dimension ( N ) */
/* This contains the permutation which separately sorts the two */
/* sub-problems in D into ascending order. Note that entries in */
/* the first half of this permutation must first be moved one */
/* position backward; and entries in the second half */
/* must first have NL+1 added to their values. */
/* PERM (output) INTEGER array, dimension ( N ) */
/* The permutations (from deflation and sorting) to be applied */
/* to each singular 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 */
/* The leading dimension of GIVCOL, must be at least N. */
/* GIVNUM (output) DOUBLE PRECISION 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, must be at least N. */
/* C (output) DOUBLE PRECISION */
/* 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) DOUBLE PRECISION */
/* S contains garbage if SQRE =0 and the S-value of a Givens */
/* rotation related to the right null space if SQRE = 1. */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* 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__;
--z__;
--zw;
--vf;
--vfw;
--vl;
--vlw;
--dsigma;
--idx;
--idxp;
--idxq;
--perm;
givcol_dim1 = *ldgcol;
givcol_offset = 1 + givcol_dim1;
givcol -= givcol_offset;
givnum_dim1 = *ldgnum;
givnum_offset = 1 + givnum_dim1;
givnum -= givnum_offset;
/* 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 = -22;
} else if (*ldgnum < n) {
*info = -24;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLASD7", &i__1);
return 0;
}
nlp1 = *nl + 1;
nlp2 = *nl + 2;
if (*icompq == 1) {
*givptr = 0;
}
/* Generate the first part of the vector Z and move the singular */
/* values in the first part of D one position backward. */
z1 = *alpha * vl[nlp1];
vl[nlp1] = 0.;
tau = vf[nlp1];
for (i__ = *nl; i__ >= 1; --i__) {
z__[i__ + 1] = *alpha * vl[i__];
vl[i__] = 0.;
vf[i__ + 1] = vf[i__];
d__[i__ + 1] = d__[i__];
idxq[i__ + 1] = idxq[i__] + 1;
/* L10: */
}
vf[1] = tau;
/* Generate the second part of the vector Z. */
i__1 = m;
for (i__ = nlp2; i__ <= i__1; ++i__) {
z__[i__] = *beta * vf[i__];
vf[i__] = 0.;
/* L20: */
}
/* Sort the singular values into increasing order */
i__1 = n;
for (i__ = nlp2; i__ <= i__1; ++i__) {
idxq[i__] += nlp1;
/* L30: */
}
/* DSIGMA, IDXC, IDXC, and ZW are used as storage space. */
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
dsigma[i__] = d__[idxq[i__]];
zw[i__] = z__[idxq[i__]];
vfw[i__] = vf[idxq[i__]];
vlw[i__] = vl[idxq[i__]];
/* L40: */
}
dlamrg_(nl, nr, &dsigma[2], &c__1, &c__1, &idx[2]);
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
idxi = idx[i__] + 1;
d__[i__] = dsigma[idxi];
z__[i__] = zw[idxi];
vf[i__] = vfw[idxi];
vl[i__] = vlw[idxi];
/* L50: */
}
/* Calculate the allowable deflation tolerence */
eps = dlamch_("Epsilon");
/* Computing MAX */
d__1 = abs(*alpha), d__2 = abs(*beta);
tol = max(d__1,d__2);
/* Computing MAX */
d__2 = (d__1 = d__[n], abs(d__1));
tol = eps * 64. * max(d__2,tol);
/* There are 2 kinds of deflation -- first a value in the z-vector */
/* is small, second two (or more) singular values are very close */
/* together (their difference is small). */
/* If the value in the z-vector is small, we simply permute the */
/* array so that the corresponding singular value is moved to the */
/* end. */
/* If two values in the D-vector are close, we perform a two-sided */
/* rotation designed to make one of the corresponding z-vector */
/* entries zero, and then permute the array so that the deflated */
/* singular value is moved to the end. */
/* If there are multiple singular values then the problem deflates. */
/* Here the number of equal singular values are found. As each equal */
/* singular value is found, an elementary reflector is computed to */
/* rotate the corresponding singular subspace so that the */
/* corresponding components of Z are zero in this new basis. */
*k = 1;
k2 = n + 1;
i__1 = n;
for (j = 2; j <= i__1; ++j) {
if ((d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
idxp[k2] = j;
if (j == n) {
goto L100;
}
} else {
jprev = j;
goto L70;
}
/* L60: */
}
L70:
j = jprev;
L80:
++j;
if (j > n) {
goto L90;
}
if ((d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
idxp[k2] = j;
} else {
/* Check if singular values are close enough to allow deflation. */
if ((d__1 = d__[j] - d__[jprev], abs(d__1)) <= tol) {
/* Deflation is possible. */
*s = z__[jprev];
*c__ = z__[j];
/* Find sqrt(a**2+b**2) without overflow or */
/* destructive underflow. */
tau = dlapy2_(c__, s);
z__[j] = tau;
z__[jprev] = 0.;
*c__ /= tau;
*s = -(*s) / tau;
/* Record the appropriate Givens rotation */
if (*icompq == 1) {
++(*givptr);
idxjp = idxq[idx[jprev] + 1];
idxj = idxq[idx[j] + 1];
if (idxjp <= nlp1) {
--idxjp;
}
if (idxj <= nlp1) {
--idxj;
}
givcol[*givptr + (givcol_dim1 << 1)] = idxjp;
givcol[*givptr + givcol_dim1] = idxj;
givnum[*givptr + (givnum_dim1 << 1)] = *c__;
givnum[*givptr + givnum_dim1] = *s;
}
drot_(&c__1, &vf[jprev], &c__1, &vf[j], &c__1, c__, s);
drot_(&c__1, &vl[jprev], &c__1, &vl[j], &c__1, c__, s);
--k2;
idxp[k2] = jprev;
jprev = j;
} else {
++(*k);
zw[*k] = z__[jprev];
dsigma[*k] = d__[jprev];
idxp[*k] = jprev;
jprev = j;
}
}
goto L80;
L90:
/* Record the last singular value. */
++(*k);
zw[*k] = z__[jprev];
dsigma[*k] = d__[jprev];
idxp[*k] = jprev;
L100:
/* Sort the singular values into DSIGMA. The singular values which */
/* were not deflated go into the first K slots of DSIGMA, except */
/* that DSIGMA(1) is treated separately. */
i__1 = n;
for (j = 2; j <= i__1; ++j) {
jp = idxp[j];
dsigma[j] = d__[jp];
vfw[j] = vf[jp];
vlw[j] = vl[jp];
/* L110: */
}
if (*icompq == 1) {
i__1 = n;
for (j = 2; j <= i__1; ++j) {
jp = idxp[j];
perm[j] = idxq[idx[jp] + 1];
if (perm[j] <= nlp1) {
--perm[j];
}
/* L120: */
}
}
/* The deflated singular values go back into the last N - K slots of */
/* D. */
i__1 = n - *k;
dcopy_(&i__1, &dsigma[*k + 1], &c__1, &d__[*k + 1], &c__1);
/* Determine DSIGMA(1), DSIGMA(2), Z(1), VF(1), VL(1), VF(M), and */
/* VL(M). */
dsigma[1] = 0.;
hlftol = tol / 2.;
if (abs(dsigma[2]) <= hlftol) {
dsigma[2] = hlftol;
}
if (m > n) {
z__[1] = dlapy2_(&z1, &z__[m]);
if (z__[1] <= tol) {
*c__ = 1.;
*s = 0.;
z__[1] = tol;
} else {
*c__ = z1 / z__[1];
*s = -z__[m] / z__[1];
}
drot_(&c__1, &vf[m], &c__1, &vf[1], &c__1, c__, s);
drot_(&c__1, &vl[m], &c__1, &vl[1], &c__1, c__, s);
} else {
if (abs(z1) <= tol) {
z__[1] = tol;
} else {
z__[1] = z1;
}
}
/* Restore Z, VF, and VL. */
i__1 = *k - 1;
dcopy_(&i__1, &zw[2], &c__1, &z__[2], &c__1);
i__1 = n - 1;
dcopy_(&i__1, &vfw[2], &c__1, &vf[2], &c__1);
i__1 = n - 1;
dcopy_(&i__1, &vlw[2], &c__1, &vl[2], &c__1);
return 0;
/* End of DLASD7 */
} /* dlasd7_ */