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177 lines
4.9 KiB
C
177 lines
4.9 KiB
C
#include "clapack.h"
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/* Subroutine */ int slasd5_(integer *i__, real *d__, real *z__, real *delta,
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real *rho, real *dsigma, real *work)
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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, delsq;
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/* -- LAPACK auxiliary 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 square root of the I-th eigenvalue */
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/* of a positive symmetric rank-one modification of a 2-by-2 diagonal */
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/* matrix */
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/* diag( D ) * diag( D ) + RHO * Z * transpose(Z) . */
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/* The diagonal entries in the array D are assumed to satisfy */
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/* 0 <= 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 0 <= 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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/* Contains (D(j) - sigma_I) in its j-th component. */
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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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/* DSIGMA (output) REAL */
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/* The computed sigma_I, the I-th updated eigenvalue. */
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/* WORK (workspace) REAL array, dimension (2) */
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/* WORK contains (D(j) + sigma_I) in its j-th component. */
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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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--work;
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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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delsq = del * (d__[2] + d__[1]);
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if (*i__ == 1) {
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w = *rho * 4.f * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.f) - z__[1] *
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z__[1] / (d__[1] * 3.f + d__[2])) / del + 1.f;
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if (w > 0.f) {
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b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
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c__ = *rho * z__[1] * z__[1] * delsq;
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/* B > ZERO, always */
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/* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) */
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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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/* The following TAU is DSIGMA - D( 1 ) */
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tau /= d__[1] + sqrt(d__[1] * d__[1] + tau);
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*dsigma = d__[1] + tau;
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delta[1] = -tau;
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delta[2] = del - tau;
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work[1] = d__[1] * 2.f + tau;
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work[2] = d__[1] + tau + d__[2];
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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 = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
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c__ = *rho * z__[2] * z__[2] * delsq;
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/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */
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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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/* The following TAU is DSIGMA - D( 2 ) */
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tau /= d__[2] + sqrt((r__1 = d__[2] * d__[2] + tau, dabs(r__1)));
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*dsigma = d__[2] + tau;
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delta[1] = -(del + tau);
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delta[2] = -tau;
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work[1] = d__[1] + tau + d__[2];
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work[2] = d__[2] * 2.f + 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 ) = DELTA( 1 ) / TEMP */
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/* DELTA( 2 ) = DELTA( 2 ) / TEMP */
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} else {
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/* Now I=2 */
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b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
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c__ = *rho * z__[2] * z__[2] * delsq;
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/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */
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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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/* The following TAU is DSIGMA - D( 2 ) */
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tau /= d__[2] + sqrt(d__[2] * d__[2] + tau);
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*dsigma = d__[2] + tau;
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delta[1] = -(del + tau);
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delta[2] = -tau;
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work[1] = d__[1] + tau + d__[2];
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work[2] = d__[2] * 2.f + 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 ) = DELTA( 1 ) / TEMP */
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/* DELTA( 2 ) = DELTA( 2 ) / TEMP */
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}
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return 0;
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/* End of SLASD5 */
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} /* slasd5_ */
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