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/* zlaesy.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"
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__2 = 2;
/* Subroutine */ int zlaesy_(doublecomplex *a, doublecomplex *b,
doublecomplex *c__, doublecomplex *rt1, doublecomplex *rt2,
doublecomplex *evscal, doublecomplex *cs1, doublecomplex *sn1)
{
/* System generated locals */
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7;
/* Builtin functions */
double z_abs(doublecomplex *);
void pow_zi(doublecomplex *, doublecomplex *, integer *), z_sqrt(
doublecomplex *, doublecomplex *), z_div(doublecomplex *,
doublecomplex *, doublecomplex *);
/* Local variables */
doublecomplex s, t;
doublereal z__;
doublecomplex tmp;
doublereal babs, tabs, evnorm;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix */
/* ( ( A, B );( B, C ) ) */
/* provided the norm of the matrix of eigenvectors is larger than */
/* some threshold value. */
/* RT1 is the eigenvalue of larger absolute value, and RT2 of */
/* smaller absolute value. If the eigenvectors are computed, then */
/* on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence */
/* [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ] */
/* [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ] */
/* Arguments */
/* ========= */
/* A (input) COMPLEX*16 */
/* The ( 1, 1 ) element of input matrix. */
/* B (input) COMPLEX*16 */
/* The ( 1, 2 ) element of input matrix. The ( 2, 1 ) element */
/* is also given by B, since the 2-by-2 matrix is symmetric. */
/* C (input) COMPLEX*16 */
/* The ( 2, 2 ) element of input matrix. */
/* RT1 (output) COMPLEX*16 */
/* The eigenvalue of larger modulus. */
/* RT2 (output) COMPLEX*16 */
/* The eigenvalue of smaller modulus. */
/* EVSCAL (output) COMPLEX*16 */
/* The complex value by which the eigenvector matrix was scaled */
/* to make it orthonormal. If EVSCAL is zero, the eigenvectors */
/* were not computed. This means one of two things: the 2-by-2 */
/* matrix could not be diagonalized, or the norm of the matrix */
/* of eigenvectors before scaling was larger than the threshold */
/* value THRESH (set below). */
/* CS1 (output) COMPLEX*16 */
/* SN1 (output) COMPLEX*16 */
/* If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector */
/* for RT1. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Special case: The matrix is actually diagonal. */
/* To avoid divide by zero later, we treat this case separately. */
if (z_abs(b) == 0.) {
rt1->r = a->r, rt1->i = a->i;
rt2->r = c__->r, rt2->i = c__->i;
if (z_abs(rt1) < z_abs(rt2)) {
tmp.r = rt1->r, tmp.i = rt1->i;
rt1->r = rt2->r, rt1->i = rt2->i;
rt2->r = tmp.r, rt2->i = tmp.i;
cs1->r = 0., cs1->i = 0.;
sn1->r = 1., sn1->i = 0.;
} else {
cs1->r = 1., cs1->i = 0.;
sn1->r = 0., sn1->i = 0.;
}
} else {
/* Compute the eigenvalues and eigenvectors. */
/* The characteristic equation is */
/* lambda **2 - (A+C) lambda + (A*C - B*B) */
/* and we solve it using the quadratic formula. */
z__2.r = a->r + c__->r, z__2.i = a->i + c__->i;
z__1.r = z__2.r * .5, z__1.i = z__2.i * .5;
s.r = z__1.r, s.i = z__1.i;
z__2.r = a->r - c__->r, z__2.i = a->i - c__->i;
z__1.r = z__2.r * .5, z__1.i = z__2.i * .5;
t.r = z__1.r, t.i = z__1.i;
/* Take the square root carefully to avoid over/under flow. */
babs = z_abs(b);
tabs = z_abs(&t);
z__ = max(babs,tabs);
if (z__ > 0.) {
z__5.r = t.r / z__, z__5.i = t.i / z__;
pow_zi(&z__4, &z__5, &c__2);
z__7.r = b->r / z__, z__7.i = b->i / z__;
pow_zi(&z__6, &z__7, &c__2);
z__3.r = z__4.r + z__6.r, z__3.i = z__4.i + z__6.i;
z_sqrt(&z__2, &z__3);
z__1.r = z__ * z__2.r, z__1.i = z__ * z__2.i;
t.r = z__1.r, t.i = z__1.i;
}
/* Compute the two eigenvalues. RT1 and RT2 are exchanged */
/* if necessary so that RT1 will have the greater magnitude. */
z__1.r = s.r + t.r, z__1.i = s.i + t.i;
rt1->r = z__1.r, rt1->i = z__1.i;
z__1.r = s.r - t.r, z__1.i = s.i - t.i;
rt2->r = z__1.r, rt2->i = z__1.i;
if (z_abs(rt1) < z_abs(rt2)) {
tmp.r = rt1->r, tmp.i = rt1->i;
rt1->r = rt2->r, rt1->i = rt2->i;
rt2->r = tmp.r, rt2->i = tmp.i;
}
/* Choose CS1 = 1 and SN1 to satisfy the first equation, then */
/* scale the components of this eigenvector so that the matrix */
/* of eigenvectors X satisfies X * X' = I . (No scaling is */
/* done if the norm of the eigenvalue matrix is less than THRESH.) */
z__2.r = rt1->r - a->r, z__2.i = rt1->i - a->i;
z_div(&z__1, &z__2, b);
sn1->r = z__1.r, sn1->i = z__1.i;
tabs = z_abs(sn1);
if (tabs > 1.) {
/* Computing 2nd power */
d__2 = 1. / tabs;
d__1 = d__2 * d__2;
z__5.r = sn1->r / tabs, z__5.i = sn1->i / tabs;
pow_zi(&z__4, &z__5, &c__2);
z__3.r = d__1 + z__4.r, z__3.i = z__4.i;
z_sqrt(&z__2, &z__3);
z__1.r = tabs * z__2.r, z__1.i = tabs * z__2.i;
t.r = z__1.r, t.i = z__1.i;
} else {
z__3.r = sn1->r * sn1->r - sn1->i * sn1->i, z__3.i = sn1->r *
sn1->i + sn1->i * sn1->r;
z__2.r = z__3.r + 1., z__2.i = z__3.i + 0.;
z_sqrt(&z__1, &z__2);
t.r = z__1.r, t.i = z__1.i;
}
evnorm = z_abs(&t);
if (evnorm >= .1) {
z_div(&z__1, &c_b1, &t);
evscal->r = z__1.r, evscal->i = z__1.i;
cs1->r = evscal->r, cs1->i = evscal->i;
z__1.r = sn1->r * evscal->r - sn1->i * evscal->i, z__1.i = sn1->r
* evscal->i + sn1->i * evscal->r;
sn1->r = z__1.r, sn1->i = z__1.i;
} else {
evscal->r = 0., evscal->i = 0.;
}
}
return 0;
/* End of ZLAESY */
} /* zlaesy_ */
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