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137 lines
3.5 KiB
C
137 lines
3.5 KiB
C
#include "clapack.h"
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/* Subroutine */ int slaed5_(integer *i__, real *d__, real *z__, real *delta,
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real *rho, real *dlam)
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{
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/* System generated locals */
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real r__1;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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real b, c__, w, del, tau, temp;
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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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/* This subroutine computes the I-th eigenvalue of a symmetric rank-one */
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/* modification of a 2-by-2 diagonal matrix */
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/* diag( D ) + RHO * Z * transpose(Z) . */
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/* The diagonal elements in the array D are assumed to satisfy */
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/* D(i) < D(j) for i < j . */
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/* We also assume RHO > 0 and that the Euclidean norm of the vector */
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/* Z is one. */
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/* Arguments */
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/* ========= */
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/* I (input) INTEGER */
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/* The index of the eigenvalue to be computed. I = 1 or I = 2. */
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/* D (input) REAL array, dimension (2) */
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/* The original eigenvalues. We assume D(1) < D(2). */
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/* Z (input) REAL array, dimension (2) */
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/* The components of the updating vector. */
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/* DELTA (output) REAL array, dimension (2) */
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/* The vector DELTA contains the information necessary */
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/* to construct the eigenvectors. */
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/* RHO (input) REAL */
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/* The scalar in the symmetric updating formula. */
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/* DLAM (output) REAL */
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/* The computed lambda_I, the I-th updated eigenvalue. */
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/* Further Details */
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/* =============== */
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/* Based on contributions by */
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/* Ren-Cang Li, Computer Science Division, University of California */
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/* at Berkeley, USA */
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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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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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--delta;
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--z__;
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--d__;
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/* Function Body */
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del = d__[2] - d__[1];
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if (*i__ == 1) {
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w = *rho * 2.f * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.f;
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if (w > 0.f) {
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b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
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c__ = *rho * z__[1] * z__[1] * del;
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/* B > ZERO, always */
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tau = c__ * 2.f / (b + sqrt((r__1 = b * b - c__ * 4.f, dabs(r__1))
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));
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*dlam = d__[1] + tau;
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delta[1] = -z__[1] / tau;
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delta[2] = z__[2] / (del - tau);
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} else {
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b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
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c__ = *rho * z__[2] * z__[2] * del;
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if (b > 0.f) {
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tau = c__ * -2.f / (b + sqrt(b * b + c__ * 4.f));
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} else {
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tau = (b - sqrt(b * b + c__ * 4.f)) / 2.f;
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}
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*dlam = d__[2] + tau;
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delta[1] = -z__[1] / (del + tau);
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delta[2] = -z__[2] / tau;
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}
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temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
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delta[1] /= temp;
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delta[2] /= temp;
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} else {
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/* Now I=2 */
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b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
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c__ = *rho * z__[2] * z__[2] * del;
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if (b > 0.f) {
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tau = (b + sqrt(b * b + c__ * 4.f)) / 2.f;
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} else {
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tau = c__ * 2.f / (-b + sqrt(b * b + c__ * 4.f));
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}
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*dlam = d__[2] + tau;
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delta[1] = -z__[1] / (del + tau);
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delta[2] = -z__[2] / tau;
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temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
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delta[1] /= temp;
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delta[2] /= temp;
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}
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return 0;
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/* End OF SLAED5 */
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} /* slaed5_ */
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