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/* dlaed5.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__,
doublereal *delta, doublereal *rho, doublereal *dlam)
{
/* System generated locals */
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal b, c__, w, del, tau, temp;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* This subroutine computes the I-th eigenvalue of a symmetric rank-one */
/* modification of a 2-by-2 diagonal matrix */
/* diag( D ) + RHO * Z * transpose(Z) . */
/* The diagonal elements in the array D are assumed to satisfy */
/* D(i) < D(j) for i < j . */
/* We also assume RHO > 0 and that the Euclidean norm of the vector */
/* Z is one. */
/* Arguments */
/* ========= */
/* I (input) INTEGER */
/* The index of the eigenvalue to be computed. I = 1 or I = 2. */
/* D (input) DOUBLE PRECISION array, dimension (2) */
/* The original eigenvalues. We assume D(1) < D(2). */
/* Z (input) DOUBLE PRECISION array, dimension (2) */
/* The components of the updating vector. */
/* DELTA (output) DOUBLE PRECISION array, dimension (2) */
/* The vector DELTA contains the information necessary */
/* to construct the eigenvectors. */
/* RHO (input) DOUBLE PRECISION */
/* The scalar in the symmetric updating formula. */
/* DLAM (output) DOUBLE PRECISION */
/* The computed lambda_I, the I-th updated eigenvalue. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ren-Cang Li, Computer Science Division, University of California */
/* at Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--delta;
--z__;
--d__;
/* Function Body */
del = d__[2] - d__[1];
if (*i__ == 1) {
w = *rho * 2. * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.;
if (w > 0.) {
b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
c__ = *rho * z__[1] * z__[1] * del;
/* B > ZERO, always */
tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1))));
*dlam = d__[1] + tau;
delta[1] = -z__[1] / tau;
delta[2] = z__[2] / (del - tau);
} else {
b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
c__ = *rho * z__[2] * z__[2] * del;
if (b > 0.) {
tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.));
} else {
tau = (b - sqrt(b * b + c__ * 4.)) / 2.;
}
*dlam = d__[2] + tau;
delta[1] = -z__[1] / (del + tau);
delta[2] = -z__[2] / tau;
}
temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
delta[1] /= temp;
delta[2] /= temp;
} else {
/* Now I=2 */
b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
c__ = *rho * z__[2] * z__[2] * del;
if (b > 0.) {
tau = (b + sqrt(b * b + c__ * 4.)) / 2.;
} else {
tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.));
}
*dlam = d__[2] + tau;
delta[1] = -z__[1] / (del + tau);
delta[2] = -z__[2] / tau;
temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
delta[1] /= temp;
delta[2] /= temp;
}
return 0;
/* End OF DLAED5 */
} /* dlaed5_ */
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