csolv.c

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/*  csolv.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"
 
int csolv(Cpx *a, Cpx *b, int n)
{
    int i, j, k, lc;
 
    Cpx *ps, *p, *q, *pa, *pd;
 
    Cpx z, h, *q0;
 
    double s, t, tq = 0., zr = 1.e-15;
 
    q0 = (Cpx *)calloc(n, sizeof(Cpx));
    pa = a;
    pd = a;
    for (j = 0; j < n; ++j, ++pa, pd += n + 1) {
        if (j > 0) {
            for (i = 0, p = pa, q = q0; i < n; ++i, p += n)
                *q++ = *p;
            for (i = 1; i < n; ++i) {
                lc = i < j ? i : j;
                z.re = z.im = 0.;
                for (k = 0, p = pa + i * n - j, q = q0; k < lc; ++k, ++q, ++p) {
                    z.re += p->re * q->re - p->im * q->im;
                    z.im += p->im * q->re + p->re * q->im;
                }
                q0[i].re -= z.re;
                q0[i].im -= z.im;
            }
            for (i = 0, p = pa, q = q0; i < n; ++i, p += n)
                *p = *q++;
        }
        s = fabs(pd->re) + fabs(pd->im);
        lc = j;
        for (k = j + 1, ps = pd; k < n; ++k) {
            ps += n;
            if ((t = fabs(ps->re) + fabs(ps->im)) > s) {
                s = t;
                lc = k;
            }
        }
        tq = tq > s ? tq : s;
        if (s < zr * tq) {
            free(q0);
            return -1;
        }
        if (lc != j) {
            h = b[j];
            b[j] = b[lc];
            b[lc] = h;
            p = a + n * j;
            q = a + n * lc;
            for (k = 0; k < n; ++k) {
                h = *p;
                *p++ = *q;
                *q++ = h;
            }
        }
        t = pd->re * pd->re + pd->im * pd->im;
        h.re = pd->re / t;
        h.im = -(pd->im) / t;
        for (k = j + 1, ps = pd + n; k < n; ++k, ps += n) {
            z.re = ps->re * h.re - ps->im * h.im;
            z.im = ps->im * h.re + ps->re * h.im;
            *ps = z;
        }
    }
    for (j = 1, ps = b + 1; j < n; ++j, ++ps) {
        for (k = 0, p = a + n * j, q = b, z.re = z.im = 0.; k < j; ++k) {
            z.re += p->re * q->re - p->im * q->im;
            z.im += p->im * q->re + p->re * q->im;
            ++p;
            ++q;
        }
        ps->re -= z.re;
        ps->im -= z.im;
    }
    for (j = n - 1, --ps, pd = a + n * n - 1; j >= 0; --j, pd -= n + 1) {
        for (k = j + 1, p = pd + 1, q = b + j + 1, z.re = z.im = 0.; k < n;
             ++k) {
            z.re += p->re * q->re - p->im * q->im;
            z.im += p->im * q->re + p->re * q->im;
            ++p;
            ++q;
        }
        h.re = ps->re - z.re;
        h.im = ps->im - z.im;
        t = pd->re * pd->re + pd->im * pd->im;
        ps->re = (h.re * pd->re + h.im * pd->im) / t;
        ps->im = (h.im * pd->re - h.re * pd->im) / t;
        --ps;
    }
    free(q0);
    return 0;
}