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/* slaed9.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 slaed9_(integer *k, integer *kstart, integer *kstop,
integer *n, real *d__, real *q, integer *ldq, real *rho, real *dlamda,
real *w, real *s, integer *lds, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal), r_sign(real *, real *);
/* Local variables */
integer i__, j;
real temp;
extern doublereal snrm2_(integer *, real *, integer *);
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), slaed4_(integer *, integer *, real *, real *, real *,
real *, real *, integer *);
extern doublereal slamc3_(real *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAED9 finds the roots of the secular equation, as defined by the */
/* values in D, Z, and RHO, between KSTART and KSTOP. It makes the */
/* appropriate calls to SLAED4 and then stores the new matrix of */
/* eigenvectors for use in calculating the next level of Z vectors. */
/* Arguments */
/* ========= */
/* K (input) INTEGER */
/* The number of terms in the rational function to be solved by */
/* SLAED4. K >= 0. */
/* KSTART (input) INTEGER */
/* KSTOP (input) INTEGER */
/* The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */
/* are to be computed. 1 <= KSTART <= KSTOP <= K. */
/* N (input) INTEGER */
/* The number of rows and columns in the Q matrix. */
/* N >= K (delation may result in N > K). */
/* D (output) REAL array, dimension (N) */
/* D(I) contains the updated eigenvalues */
/* for KSTART <= I <= KSTOP. */
/* Q (workspace) REAL array, dimension (LDQ,N) */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max( 1, N ). */
/* RHO (input) REAL */
/* The value of the parameter in the rank one update equation. */
/* RHO >= 0 required. */
/* DLAMDA (input) REAL array, dimension (K) */
/* The first K elements of this array contain the old roots */
/* of the deflated updating problem. These are the poles */
/* of the secular equation. */
/* W (input) REAL array, dimension (K) */
/* The first K elements of this array contain the components */
/* of the deflation-adjusted updating vector. */
/* S (output) REAL array, dimension (LDS, K) */
/* Will contain the eigenvectors of the repaired matrix which */
/* will be stored for subsequent Z vector calculation and */
/* multiplied by the previously accumulated eigenvectors */
/* to update the system. */
/* LDS (input) INTEGER */
/* The leading dimension of S. LDS >= max( 1, K ). */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = 1, an eigenvalue did not converge */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Jeff Rutter, Computer Science Division, University of California */
/* at Berkeley, USA */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--dlamda;
--w;
s_dim1 = *lds;
s_offset = 1 + s_dim1;
s -= s_offset;
/* Function Body */
*info = 0;
if (*k < 0) {
*info = -1;
} else if (*kstart < 1 || *kstart > max(1,*k)) {
*info = -2;
} else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) {
*info = -3;
} else if (*n < *k) {
*info = -4;
} else if (*ldq < max(1,*k)) {
*info = -7;
} else if (*lds < max(1,*k)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLAED9", &i__1);
return 0;
}
/* Quick return if possible */
if (*k == 0) {
return 0;
}
/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
/* be computed with high relative accuracy (barring over/underflow). */
/* This is a problem on machines without a guard digit in */
/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
/* which on any of these machines zeros out the bottommost */
/* bit of DLAMDA(I) if it is 1; this makes the subsequent */
/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
/* occurs. On binary machines with a guard digit (almost all */
/* machines) it does not change DLAMDA(I) at all. On hexadecimal */
/* and decimal machines with a guard digit, it slightly */
/* changes the bottommost bits of DLAMDA(I). It does not account */
/* for hexadecimal or decimal machines without guard digits */
/* (we know of none). We use a subroutine call to compute */
/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
/* this code. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
/* L10: */
}
i__1 = *kstop;
for (j = *kstart; j <= i__1; ++j) {
slaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
info);
/* If the zero finder fails, the computation is terminated. */
if (*info != 0) {
goto L120;
}
/* L20: */
}
if (*k == 1 || *k == 2) {
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *k;
for (j = 1; j <= i__2; ++j) {
s[j + i__ * s_dim1] = q[j + i__ * q_dim1];
/* L30: */
}
/* L40: */
}
goto L120;
}
/* Compute updated W. */
scopy_(k, &w[1], &c__1, &s[s_offset], &c__1);
/* Initialize W(I) = Q(I,I) */
i__1 = *ldq + 1;
scopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
/* L50: */
}
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
/* L60: */
}
/* L70: */
}
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
r__1 = sqrt(-w[i__]);
w[i__] = r_sign(&r__1, &s[i__ + s_dim1]);
/* L80: */
}
/* Compute eigenvectors of the modified rank-1 modification. */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = 1; i__ <= i__2; ++i__) {
q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1];
/* L90: */
}
temp = snrm2_(k, &q[j * q_dim1 + 1], &c__1);
i__2 = *k;
for (i__ = 1; i__ <= i__2; ++i__) {
s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp;
/* L100: */
}
/* L110: */
}
L120:
return 0;
/* End of SLAED9 */
} /* slaed9_ */
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