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);
}