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chousv.c
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/* chousv.c CCMATH mathematics library source code.
*
* Copyright (C) 2000 Daniel A. Atkinson All rights reserved.
* This code may be redistributed under the terms of the GNU library
* public license (LGPL). ( See the lgpl.license file for details.)
* ------------------------------------------------------------------------
*/
#include <stdlib.h>
#include "ccmath.h"
void chousv(Cpx *a, double *d, double *dp, int n)
{
double sc, x, y;
Cpx cc, u, *qs;
int i, j, k, m, e;
Cpx *qw, *pc, *p, *q;
qs = (Cpx *)calloc(2 * n, sizeof(Cpx));
q = qs + n;
for (j = 0, pc = a; j < n - 2; ++j, pc += n + 1, ++q) {
m = n - j - 1;
for (i = 1, sc = 0.; i <= m; ++i)
sc += pc[i].re * pc[i].re + pc[i].im * pc[i].im;
if (sc > 0.) {
sc = sqrt(sc);
p = pc + 1;
y = sc + (x = sqrt(p->re * p->re + p->im * p->im));
if (x > 0.) {
cc.re = p->re / x;
cc.im = p->im / x;
}
else {
cc.re = 1.;
cc.im = 0.;
}
q->re = -cc.re;
q->im = -cc.im;
x = 1. / sqrt(2. * sc * y);
y *= x;
for (i = 0, qw = pc + 1; i < m; ++i) {
qs[i].re = qs[i].im = 0.;
if (i) {
qw[i].re *= x;
qw[i].im *= -x;
}
else {
qw[0].re = y * cc.re;
qw[0].im = -y * cc.im;
}
}
for (i = 0, e = j + 2, p = pc + n + 1, y = 0.; i < m;
++i, p += e++) {
qs[i].re +=
(u.re = qw[i].re) * p->re - (u.im = qw[i].im) * p->im;
qs[i].im += u.re * p->im + u.im * p->re;
++p;
for (k = i + 1; k < m; ++k, ++p) {
qs[i].re += qw[k].re * p->re - qw[k].im * p->im;
qs[i].im += qw[k].im * p->re + qw[k].re * p->im;
qs[k].re += u.re * p->re + u.im * p->im;
qs[k].im += u.im * p->re - u.re * p->im;
}
y += u.re * qs[i].re + u.im * qs[i].im;
}
for (i = 0; i < m; ++i) {
qs[i].re -= y * qw[i].re;
qs[i].re += qs[i].re;
qs[i].im -= y * qw[i].im;
qs[i].im += qs[i].im;
}
for (i = 0, e = j + 2, p = pc + n + 1; i < m; ++i, p += e++) {
for (k = i; k < m; ++k, ++p) {
p->re -= qw[i].re * qs[k].re + qw[i].im * qs[k].im +
qs[i].re * qw[k].re + qs[i].im * qw[k].im;
p->im -= qw[i].im * qs[k].re - qw[i].re * qs[k].im +
qs[i].im * qw[k].re - qs[i].re * qw[k].im;
}
}
}
d[j] = pc->re;
dp[j] = sc;
}
d[j] = pc->re;
cc = *(pc + 1);
d[j + 1] = (pc += n + 1)->re;
dp[j] = sc = sqrt(cc.re * cc.re + cc.im * cc.im);
q->re = cc.re /= sc;
q->im = cc.im /= sc;
for (i = 0, m = n + n, p = pc; i < m; ++i, --p)
p->re = p->im = 0.;
pc->re = 1.;
(pc -= n + 1)->re = 1.;
qw = pc - n;
for (m = 2; m < n; ++m, qw -= n + 1) {
for (j = 0, p = pc, pc->re = 1.; j < m; ++j, p += n) {
for (i = 0, q = p, u.re = u.im = 0.; i < m; ++i, ++q) {
u.re += qw[i].re * q->re - qw[i].im * q->im;
u.im += qw[i].re * q->im + qw[i].im * q->re;
}
for (i = 0, q = p, u.re += u.re, u.im += u.im; i < m; ++i, ++q) {
q->re -= u.re * qw[i].re + u.im * qw[i].im;
q->im -= u.im * qw[i].re - u.re * qw[i].im;
}
}
for (i = 0, p = qw + m - 1; i < n; ++i, --p)
p->re = p->im = 0.;
(pc -= n + 1)->re = 1.;
}
for (j = 1, p = a + n + 1, q = qs + n, u.re = 1., u.im = 0.; j < n;
++j, ++p, ++q) {
sc = u.re * q->re - u.im * q->im;
u.im = u.im * q->re + u.re * q->im;
u.re = sc;
for (i = 1; i < n; ++i, ++p) {
sc = u.re * p->re - u.im * p->im;
p->im = u.re * p->im + u.im * p->re;
p->re = sc;
}
}
free(qs);
}
ccmath.h
Cpx
struct complex Cpx
Definition ccmath.h:41
chousv
void chousv(Cpx *a, double *d, double *dp, int n)
Definition chousv.c:12
complex::re
double re
Definition ccmath.h:39
complex::im
double im
Definition ccmath.h:39
x
#define x