260 lines
7.3 KiB
C
260 lines
7.3 KiB
C
#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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/* Subroutine */ int slaed9_(integer *k, integer *kstart, integer *kstop,
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integer *n, real *d__, real *q, integer *ldq, real *rho, real *dlamda,
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real *w, real *s, integer *lds, integer *info)
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{
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/* System generated locals */
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integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2;
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real r__1;
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/* Builtin functions */
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double sqrt(doublereal), r_sign(real *, real *);
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/* Local variables */
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integer i__, j;
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real temp;
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extern doublereal snrm2_(integer *, real *, integer *);
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
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integer *), slaed4_(integer *, integer *, real *, real *, real *,
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real *, real *, integer *);
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extern doublereal slamc3_(real *, real *);
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extern /* Subroutine */ int xerbla_(char *, integer *);
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SLAED9 finds the roots of the secular equation, as defined by the */
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/* values in D, Z, and RHO, between KSTART and KSTOP. It makes the */
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/* appropriate calls to SLAED4 and then stores the new matrix of */
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/* eigenvectors for use in calculating the next level of Z vectors. */
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/* Arguments */
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/* ========= */
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/* K (input) INTEGER */
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/* The number of terms in the rational function to be solved by */
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/* SLAED4. K >= 0. */
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/* KSTART (input) INTEGER */
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/* KSTOP (input) INTEGER */
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/* The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */
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/* are to be computed. 1 <= KSTART <= KSTOP <= K. */
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/* N (input) INTEGER */
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/* The number of rows and columns in the Q matrix. */
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/* N >= K (delation may result in N > K). */
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/* D (output) REAL array, dimension (N) */
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/* D(I) contains the updated eigenvalues */
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/* for KSTART <= I <= KSTOP. */
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/* Q (workspace) REAL array, dimension (LDQ,N) */
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/* LDQ (input) INTEGER */
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/* The leading dimension of the array Q. LDQ >= max( 1, N ). */
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/* RHO (input) REAL */
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/* The value of the parameter in the rank one update equation. */
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/* RHO >= 0 required. */
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/* DLAMDA (input) REAL array, dimension (K) */
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/* The first K elements of this array contain the old roots */
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/* of the deflated updating problem. These are the poles */
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/* of the secular equation. */
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/* W (input) REAL array, dimension (K) */
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/* The first K elements of this array contain the components */
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/* of the deflation-adjusted updating vector. */
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/* S (output) REAL array, dimension (LDS, K) */
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/* Will contain the eigenvectors of the repaired matrix which */
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/* will be stored for subsequent Z vector calculation and */
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/* multiplied by the previously accumulated eigenvectors */
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/* to update the system. */
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/* LDS (input) INTEGER */
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/* The leading dimension of S. LDS >= max( 1, K ). */
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/* INFO (output) INTEGER */
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/* = 0: successful exit. */
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > 0: if INFO = 1, an eigenvalue did not converge */
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/* Further Details */
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/* =============== */
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/* Based on contributions by */
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/* Jeff Rutter, Computer Science Division, University of California */
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/* at Berkeley, USA */
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/* ===================================================================== */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1;
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q -= q_offset;
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--dlamda;
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--w;
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s_dim1 = *lds;
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s_offset = 1 + s_dim1;
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s -= s_offset;
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/* Function Body */
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*info = 0;
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if (*k < 0) {
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*info = -1;
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} else if (*kstart < 1 || *kstart > max(1,*k)) {
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*info = -2;
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} else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) {
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*info = -3;
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} else if (*n < *k) {
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*info = -4;
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} else if (*ldq < max(1,*k)) {
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*info = -7;
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} else if (*lds < max(1,*k)) {
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*info = -12;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SLAED9", &i__1);
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return 0;
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}
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/* Quick return if possible */
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if (*k == 0) {
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return 0;
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}
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/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
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/* be computed with high relative accuracy (barring over/underflow). */
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/* This is a problem on machines without a guard digit in */
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/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
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/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
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/* which on any of these machines zeros out the bottommost */
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/* bit of DLAMDA(I) if it is 1; this makes the subsequent */
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/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
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/* occurs. On binary machines with a guard digit (almost all */
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/* machines) it does not change DLAMDA(I) at all. On hexadecimal */
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/* and decimal machines with a guard digit, it slightly */
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/* changes the bottommost bits of DLAMDA(I). It does not account */
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/* for hexadecimal or decimal machines without guard digits */
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/* (we know of none). We use a subroutine call to compute */
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/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
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/* this code. */
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
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/* L10: */
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}
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i__1 = *kstop;
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for (j = *kstart; j <= i__1; ++j) {
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slaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
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info);
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/* If the zero finder fails, the computation is terminated. */
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if (*info != 0) {
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goto L120;
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}
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/* L20: */
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}
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if (*k == 1 || *k == 2) {
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i__1 = *k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = *k;
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for (j = 1; j <= i__2; ++j) {
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s[j + i__ * s_dim1] = q[j + i__ * q_dim1];
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/* L30: */
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}
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/* L40: */
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}
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goto L120;
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}
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/* Compute updated W. */
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scopy_(k, &w[1], &c__1, &s[s_offset], &c__1);
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/* Initialize W(I) = Q(I,I) */
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i__1 = *ldq + 1;
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scopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
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/* L50: */
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}
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i__2 = *k;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
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/* L60: */
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}
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/* L70: */
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}
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i__1 = *k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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r__1 = sqrt(-w[i__]);
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w[i__] = r_sign(&r__1, &s[i__ + s_dim1]);
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/* L80: */
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}
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/* Compute eigenvectors of the modified rank-1 modification. */
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *k;
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for (i__ = 1; i__ <= i__2; ++i__) {
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q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1];
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/* L90: */
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}
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temp = snrm2_(k, &q[j * q_dim1 + 1], &c__1);
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i__2 = *k;
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for (i__ = 1; i__ <= i__2; ++i__) {
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s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp;
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/* L100: */
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}
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/* L110: */
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}
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L120:
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return 0;
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/* End of SLAED9 */
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} /* slaed9_ */
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