324 lines
9.7 KiB
C
324 lines
9.7 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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static real c_b22 = 1.f;
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static real c_b23 = 0.f;
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/* Subroutine */ int slaed3_(integer *k, integer *n, integer *n1, real *d__,
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real *q, integer *ldq, real *rho, real *dlamda, real *q2, integer *
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indx, integer *ctot, real *w, real *s, integer *info)
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{
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/* System generated locals */
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integer q_dim1, q_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, n2, n12, ii, n23, iq2;
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real temp;
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extern doublereal snrm2_(integer *, real *, integer *);
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extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
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integer *, real *, real *, integer *, real *, integer *, real *,
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real *, integer *), scopy_(integer *, real *,
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integer *, real *, integer *), slaed4_(integer *, integer *, real
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*, real *, real *, real *, real *, integer *);
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extern doublereal slamc3_(real *, real *);
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extern /* Subroutine */ int xerbla_(char *, integer *), slacpy_(
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char *, integer *, integer *, real *, integer *, real *, integer *
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), slaset_(char *, integer *, integer *, real *, real *,
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real *, 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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/* SLAED3 finds the roots of the secular equation, as defined by the */
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/* values in D, W, and RHO, between 1 and K. It makes the */
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/* appropriate calls to SLAED4 and then updates the eigenvectors by */
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/* multiplying the matrix of eigenvectors of the pair of eigensystems */
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/* being combined by the matrix of eigenvectors of the K-by-K system */
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/* which is solved here. */
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/* This code makes very mild assumptions about floating point */
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/* arithmetic. It will work on machines with a guard digit in */
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/* add/subtract, or on those binary machines without guard digits */
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/* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
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/* It could conceivably fail on hexadecimal or decimal machines */
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/* without guard digits, but we know of none. */
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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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/* N (input) INTEGER */
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/* The number of rows and columns in the Q matrix. */
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/* N >= K (deflation may result in N>K). */
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/* N1 (input) INTEGER */
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/* The location of the last eigenvalue in the leading submatrix. */
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/* min(1,N) <= N1 <= N/2. */
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/* D (output) REAL array, dimension (N) */
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/* D(I) contains the updated eigenvalues for */
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/* 1 <= I <= K. */
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/* Q (output) REAL array, dimension (LDQ,N) */
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/* Initially the first K columns are used as workspace. */
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/* On output the columns 1 to K contain */
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/* the updated eigenvectors. */
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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/output) 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. May be changed on output by */
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/* having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
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/* Cray-2, or Cray C-90, as described above. */
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/* Q2 (input) REAL array, dimension (LDQ2, N) */
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/* The first K columns of this matrix contain the non-deflated */
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/* eigenvectors for the split problem. */
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/* INDX (input) INTEGER array, dimension (N) */
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/* The permutation used to arrange the columns of the deflated */
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/* Q matrix into three groups (see SLAED2). */
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/* The rows of the eigenvectors found by SLAED4 must be likewise */
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/* permuted before the matrix multiply can take place. */
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/* CTOT (input) INTEGER array, dimension (4) */
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/* A count of the total number of the various types of columns */
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/* in Q, as described in INDX. The fourth column type is any */
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/* column which has been deflated. */
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/* W (input/output) 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. Destroyed on */
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/* output. */
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/* S (workspace) REAL array, dimension (N1 + 1)*K */
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/* Will contain the eigenvectors of the repaired matrix which */
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/* will be 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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/* Modified by Francoise Tisseur, University of Tennessee. */
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/* ===================================================================== */
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/* .. Parameters .. */
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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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--q2;
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--indx;
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--ctot;
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--w;
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--s;
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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 (*n < *k) {
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*info = -2;
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} else if (*ldq < max(1,*n)) {
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*info = -6;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SLAED3", &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 = *k;
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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 = *k;
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for (j = 1; 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) {
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goto L110;
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}
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if (*k == 2) {
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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w[1] = q[j * q_dim1 + 1];
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w[2] = q[j * q_dim1 + 2];
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ii = indx[1];
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q[j * q_dim1 + 1] = w[ii];
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ii = indx[2];
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q[j * q_dim1 + 2] = w[ii];
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/* L30: */
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}
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goto L110;
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}
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/* Compute updated W. */
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scopy_(k, &w[1], &c__1, &s[1], &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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/* L40: */
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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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/* L50: */
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}
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/* L60: */
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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__]);
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/* L70: */
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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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s[i__] = w[i__] / q[i__ + j * q_dim1];
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/* L80: */
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}
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temp = snrm2_(k, &s[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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ii = indx[i__];
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q[i__ + j * q_dim1] = s[ii] / temp;
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/* L90: */
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}
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/* L100: */
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}
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/* Compute the updated eigenvectors. */
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L110:
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n2 = *n - *n1;
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n12 = ctot[1] + ctot[2];
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n23 = ctot[2] + ctot[3];
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slacpy_("A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23);
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iq2 = *n1 * n12 + 1;
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if (n23 != 0) {
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sgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
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c_b23, &q[*n1 + 1 + q_dim1], ldq);
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} else {
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slaset_("A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq);
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}
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slacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12);
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if (n12 != 0) {
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sgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23,
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&q[q_offset], ldq);
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} else {
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slaset_("A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq);
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}
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L120:
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return 0;
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/* End of SLAED3 */
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} /* slaed3_ */
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