/* zlaqr1.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 zlaqr1_(integer *n, doublecomplex *h__, integer *ldh,
doublecomplex *s1, doublecomplex *s2, doublecomplex *v)
{
/* System generated locals */
integer h_dim1, h_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7, z__8;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
doublereal s;
doublecomplex h21s, h31s;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a */
/* scalar multiple of the first column of the product */
/* (*) K = (H - s1*I)*(H - s2*I) */
/* scaling to avoid overflows and most underflows. */
/* This is useful for starting double implicit shift bulges */
/* in the QR algorithm. */
/* N (input) integer */
/* Order of the matrix H. N must be either 2 or 3. */
/* H (input) COMPLEX*16 array of dimension (LDH,N) */
/* The 2-by-2 or 3-by-3 matrix H in (*). */
/* LDH (input) integer */
/* The leading dimension of H as declared in */
/* the calling procedure. LDH.GE.N */
/* S1 (input) COMPLEX*16 */
/* S2 S1 and S2 are the shifts defining K in (*) above. */
/* V (output) COMPLEX*16 array of dimension N */
/* A scalar multiple of the first column of the */
/* matrix K in (*). */
/* ================================================================ */
/* Based on contributions by */
/* Karen Braman and Ralph Byers, Department of Mathematics, */
/* University of Kansas, USA */
/* ================================================================ */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--v;
/* Function Body */
if (*n == 2) {
i__1 = h_dim1 + 1;
z__2.r = h__[i__1].r - s2->r, z__2.i = h__[i__1].i - s2->i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__2 = h_dim1 + 2;
s = (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), abs(d__2)) + (
(d__3 = h__[i__2].r, abs(d__3)) + (d__4 = d_imag(&h__[h_dim1
+ 2]), abs(d__4)));
if (s == 0.) {
v[1].r = 0., v[1].i = 0.;
v[2].r = 0., v[2].i = 0.;
} else {
i__1 = h_dim1 + 2;
z__1.r = h__[i__1].r / s, z__1.i = h__[i__1].i / s;
h21s.r = z__1.r, h21s.i = z__1.i;
i__1 = (h_dim1 << 1) + 1;
z__2.r = h21s.r * h__[i__1].r - h21s.i * h__[i__1].i, z__2.i =
h21s.r * h__[i__1].i + h21s.i * h__[i__1].r;
i__2 = h_dim1 + 1;
z__4.r = h__[i__2].r - s1->r, z__4.i = h__[i__2].i - s1->i;
i__3 = h_dim1 + 1;
z__6.r = h__[i__3].r - s2->r, z__6.i = h__[i__3].i - s2->i;
z__5.r = z__6.r / s, z__5.i = z__6.i / s;
z__3.r = z__4.r * z__5.r - z__4.i * z__5.i, z__3.i = z__4.r *
z__5.i + z__4.i * z__5.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
v[1].r = z__1.r, v[1].i = z__1.i;
i__1 = h_dim1 + 1;
i__2 = (h_dim1 << 1) + 2;
z__4.r = h__[i__1].r + h__[i__2].r, z__4.i = h__[i__1].i + h__[
i__2].i;
z__3.r = z__4.r - s1->r, z__3.i = z__4.i - s1->i;
z__2.r = z__3.r - s2->r, z__2.i = z__3.i - s2->i;
z__1.r = h21s.r * z__2.r - h21s.i * z__2.i, z__1.i = h21s.r *
z__2.i + h21s.i * z__2.r;
v[2].r = z__1.r, v[2].i = z__1.i;
}
} else {
i__1 = h_dim1 + 1;
z__2.r = h__[i__1].r - s2->r, z__2.i = h__[i__1].i - s2->i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__2 = h_dim1 + 2;
i__3 = h_dim1 + 3;
s = (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), abs(d__2)) + (
(d__3 = h__[i__2].r, abs(d__3)) + (d__4 = d_imag(&h__[h_dim1
+ 2]), abs(d__4))) + ((d__5 = h__[i__3].r, abs(d__5)) + (d__6
= d_imag(&h__[h_dim1 + 3]), abs(d__6)));
if (s == 0.) {
v[1].r = 0., v[1].i = 0.;
v[2].r = 0., v[2].i = 0.;
v[3].r = 0., v[3].i = 0.;
} else {
i__1 = h_dim1 + 2;
z__1.r = h__[i__1].r / s, z__1.i = h__[i__1].i / s;
h21s.r = z__1.r, h21s.i = z__1.i;
i__1 = h_dim1 + 3;
z__1.r = h__[i__1].r / s, z__1.i = h__[i__1].i / s;
h31s.r = z__1.r, h31s.i = z__1.i;
i__1 = h_dim1 + 1;
z__4.r = h__[i__1].r - s1->r, z__4.i = h__[i__1].i - s1->i;
i__2 = h_dim1 + 1;
z__6.r = h__[i__2].r - s2->r, z__6.i = h__[i__2].i - s2->i;
z__5.r = z__6.r / s, z__5.i = z__6.i / s;
z__3.r = z__4.r * z__5.r - z__4.i * z__5.i, z__3.i = z__4.r *
z__5.i + z__4.i * z__5.r;
i__3 = (h_dim1 << 1) + 1;
z__7.r = h__[i__3].r * h21s.r - h__[i__3].i * h21s.i, z__7.i =
h__[i__3].r * h21s.i + h__[i__3].i * h21s.r;
z__2.r = z__3.r + z__7.r, z__2.i = z__3.i + z__7.i;
i__4 = h_dim1 * 3 + 1;
z__8.r = h__[i__4].r * h31s.r - h__[i__4].i * h31s.i, z__8.i =
h__[i__4].r * h31s.i + h__[i__4].i * h31s.r;
z__1.r = z__2.r + z__8.r, z__1.i = z__2.i + z__8.i;
v[1].r = z__1.r, v[1].i = z__1.i;
i__1 = h_dim1 + 1;
i__2 = (h_dim1 << 1) + 2;
z__5.r = h__[i__1].r + h__[i__2].r, z__5.i = h__[i__1].i + h__[
i__2].i;
z__4.r = z__5.r - s1->r, z__4.i = z__5.i - s1->i;
z__3.r = z__4.r - s2->r, z__3.i = z__4.i - s2->i;
z__2.r = h21s.r * z__3.r - h21s.i * z__3.i, z__2.i = h21s.r *
z__3.i + h21s.i * z__3.r;
i__3 = h_dim1 * 3 + 2;
z__6.r = h__[i__3].r * h31s.r - h__[i__3].i * h31s.i, z__6.i =
h__[i__3].r * h31s.i + h__[i__3].i * h31s.r;
z__1.r = z__2.r + z__6.r, z__1.i = z__2.i + z__6.i;
v[2].r = z__1.r, v[2].i = z__1.i;
i__1 = h_dim1 + 1;
i__2 = h_dim1 * 3 + 3;
z__5.r = h__[i__1].r + h__[i__2].r, z__5.i = h__[i__1].i + h__[
i__2].i;
z__4.r = z__5.r - s1->r, z__4.i = z__5.i - s1->i;
z__3.r = z__4.r - s2->r, z__3.i = z__4.i - s2->i;
z__2.r = h31s.r * z__3.r - h31s.i * z__3.i, z__2.i = h31s.r *
z__3.i + h31s.i * z__3.r;
i__3 = (h_dim1 << 1) + 3;
z__6.r = h21s.r * h__[i__3].r - h21s.i * h__[i__3].i, z__6.i =
h21s.r * h__[i__3].i + h21s.i * h__[i__3].r;
z__1.r = z__2.r + z__6.r, z__1.i = z__2.i + z__6.i;
v[3].r = z__1.r, v[3].i = z__1.i;
}
}
return 0;
} /* zlaqr1_ */
