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91 lines
3.5 KiB
91 lines
3.5 KiB
/*
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* Copyright(C) 1999-2020, 2023 National Technology & Engineering Solutions
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* of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with
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* NTESS, the U.S. Government retains certain rights in this software.
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*
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* See packages/seacas/LICENSE for details
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*/
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#include "prototypes.h"
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#include <math.h>
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#include <stdio.h>
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/* Finds first extended eigenpair of system corresponding to
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tridiagonal T using using Rafael's bisection technique. */
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void get_extval(double *alpha, /* j-vector of Lanczos scalars (using elements 1 to j) */
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double *beta, /* (j+1)-vector of " " (has 0 element but using 1 to j-1) */
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int j, /* number of Lanczos iterations taken */
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double ritzval, /* Ritz value */
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double *s, /* Ritz vector (length n, re-computed in this routine) */
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double eigtol, /* tolerance on eigenpair */
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double wnorm_g, /* W-norm of n-vector g, the rhs in the extended eig. problem */
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double sigma, /* the norm constraint on the extended eigenvector */
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double *extval, /* the extended eigenvalue this routine computes */
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double *v, /* the j-vector solving the extended eig problem in T */
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double *work1, /* j-vector of workspace */
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double *work2 /* j-vector of workspace */
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)
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{
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extern int DEBUG_EVECS; /* debug flag for eigen computation */
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double lambda_low; /* lower bound on extended eval */
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double lambda_high; /* upper bound on extended eval */
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double tol; /* bisection tolerance */
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double norm_v; /* norm of the extended T eigenvector v */
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double lambda; /* the parameter that iterates to extval */
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int cnt; /* debug iteration counter */
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double diff; /* distance between lambda limits */
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/* Compute the Ritz vector */
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Tevec(alpha, beta - 1, j, ritzval, s);
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/* Shouldn't happen, but just in case ... */
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if (wnorm_g == 0.0) {
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*extval = ritzval;
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cpvec(v, 1, j, s);
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if (DEBUG_EVECS > 0) {
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printf("Degenerate extended eigenvector problem (g = 0).\n");
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}
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return;
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/* ... not really an extended eigenproblem; just return Ritz pair */
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}
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/* Set up the bisection parameters */
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lambda_low = ritzval - wnorm_g / sigma;
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lambda_high = ritzval - (wnorm_g / sigma) * s[1];
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lambda = 0.5 * (lambda_low + lambda_high);
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tol = eigtol * eigtol * (1 + fabs(lambda_low) + fabs(lambda_high));
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if (DEBUG_EVECS > 2) {
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printf("Computing extended eigenpairs of T\n");
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printf(" target norm_v (= sigma) %g\n", sigma);
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printf(" bisection tolerance %g\n", tol);
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}
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if (DEBUG_EVECS > 3) {
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printf(" lambda iterates to the extended eigenvalue\n");
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printf(" lambda_low lambda lambda_high norm_v\n");
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}
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/* Bisection loop - iterate until norm constraint is satisfied */
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cnt = 1;
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diff = 2 * tol;
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while (diff > tol) {
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lambda = 0.5 * (lambda_low + lambda_high);
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tri_solve(alpha, beta, j, lambda, v, wnorm_g, work1, work2);
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norm_v = ch_norm(v, 1, j);
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if (DEBUG_EVECS > 3) {
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printf("%2i %18.16f %18.16f %18.16f %g\n", cnt++, lambda_low, lambda, lambda_high,
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norm_v);
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}
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if (norm_v <= sigma) {
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lambda_low = lambda;
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}
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if (norm_v >= sigma) {
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lambda_high = lambda;
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}
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diff = lambda_high - lambda_low;
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}
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/* Return the extended eigenvalue (eigvec is automatically returned) */
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*extval = lambda;
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}
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