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/* dlasd5.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 dlasd5_(integer *i__, doublereal *d__, doublereal *z__,
doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal *
work)
{
/* System generated locals */
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal b, c__, w, del, tau, delsq;
/* -- LAPACK auxiliary 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 square root of the I-th eigenvalue */
/* of a positive symmetric rank-one modification of a 2-by-2 diagonal */
/* matrix */
/* diag( D ) * diag( D ) + RHO * Z * transpose(Z) . */
/* The diagonal entries in the array D are assumed to satisfy */
/* 0 <= 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 0 <= D(1) < D(2). */
/* Z (input) DOUBLE PRECISION array, dimension ( 2 ) */
/* The components of the updating vector. */
/* DELTA (output) DOUBLE PRECISION array, dimension ( 2 ) */
/* Contains (D(j) - sigma_I) in its j-th component. */
/* The vector DELTA contains the information necessary */
/* to construct the eigenvectors. */
/* RHO (input) DOUBLE PRECISION */
/* The scalar in the symmetric updating formula. */
/* DSIGMA (output) DOUBLE PRECISION */
/* The computed sigma_I, the I-th updated eigenvalue. */
/* WORK (workspace) DOUBLE PRECISION array, dimension ( 2 ) */
/* WORK contains (D(j) + sigma_I) in its j-th component. */
/* 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 */
--work;
--delta;
--z__;
--d__;
/* Function Body */
del = d__[2] - d__[1];
delsq = del * (d__[2] + d__[1]);
if (*i__ == 1) {
w = *rho * 4. * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - z__[1] *
z__[1] / (d__[1] * 3. + d__[2])) / del + 1.;
if (w > 0.) {
b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
c__ = *rho * z__[1] * z__[1] * delsq;
/* B > ZERO, always */
/* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) */
tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1))));
/* The following TAU is DSIGMA - D( 1 ) */
tau /= d__[1] + sqrt(d__[1] * d__[1] + tau);
*dsigma = d__[1] + tau;
delta[1] = -tau;
delta[2] = del - tau;
work[1] = d__[1] * 2. + tau;
work[2] = d__[1] + tau + d__[2];
/* DELTA( 1 ) = -Z( 1 ) / TAU */
/* DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) */
} else {
b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
c__ = *rho * z__[2] * z__[2] * delsq;
/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */
if (b > 0.) {
tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.));
} else {
tau = (b - sqrt(b * b + c__ * 4.)) / 2.;
}
/* The following TAU is DSIGMA - D( 2 ) */
tau /= d__[2] + sqrt((d__1 = d__[2] * d__[2] + tau, abs(d__1)));
*dsigma = d__[2] + tau;
delta[1] = -(del + tau);
delta[2] = -tau;
work[1] = d__[1] + tau + d__[2];
work[2] = d__[2] * 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 ) = DELTA( 1 ) / TEMP */
/* DELTA( 2 ) = DELTA( 2 ) / TEMP */
} else {
/* Now I=2 */
b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
c__ = *rho * z__[2] * z__[2] * delsq;
/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */
if (b > 0.) {
tau = (b + sqrt(b * b + c__ * 4.)) / 2.;
} else {
tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.));
}
/* The following TAU is DSIGMA - D( 2 ) */
tau /= d__[2] + sqrt(d__[2] * d__[2] + tau);
*dsigma = d__[2] + tau;
delta[1] = -(del + tau);
delta[2] = -tau;
work[1] = d__[1] + tau + d__[2];
work[2] = d__[2] * 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 ) = DELTA( 1 ) / TEMP */
/* DELTA( 2 ) = DELTA( 2 ) / TEMP */
}
return 0;
/* End of DLASD5 */
} /* dlasd5_ */
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