cminv.c

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/*  cminv.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 cminv(Cpx * a, int n)
{
    int i, j, k, m, lc, *le;

    Cpx *ps, *p, *q, *pa, *pd;

    Cpx z, h, *q0;

    double s, t, tq = 0., zr = 1.e-15;

    le = (int *)calloc(n, sizeof(int));
    q0 = (Cpx *) calloc(n, sizeof(Cpx));
    pa = 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(le - j);
            free(q0);
            return -1;
        }
        *le++ = lc;
        if (lc != j) {
            p = a + n * j;
            q = a + n * lc;
            for (k = 0; k < n; ++k, ++p, ++q) {
                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;
        }
        *pd = h;
    }
    for (j = 1, pd = ps = a; j < n; ++j) {
        for (k = 0, pd += n + 1, q = ++ps; k < j; ++k, q += n) {
            z.re = q->re * pd->re - q->im * pd->im;
            z.im = q->im * pd->re + q->re * pd->im;
            *q = z;
        }
    }
    for (j = 1, pa = a; j < n; ++j) {
        ++pa;
        for (i = 0, q = q0, p = pa; i < j; ++i, p += n)
            *q++ = *p;
        for (k = 0; k < j; ++k) {
            h.re = h.im = 0.;
            for (i = k, p = pa + k * n + k - j, q = q0 + k; i < j; ++i) {
                h.re -= p->re * q->re - p->im * q->im;
                h.im -= p->im * q->re + p->re * q->im;
                ++p;
                ++q;
            }
            q0[k] = h;
        }
        for (i = 0, q = q0, p = pa; i < j; ++i, p += n)
            *p = *q++;
    }
    for (j = n - 2, pd = pa = a + n * n - 1; j >= 0; --j) {
        --pa;
        pd -= n + 1;
        for (i = 0, m = n - j - 1, q = q0, p = pd + n; i < m; ++i, p += n)
            *q++ = *p;
        for (k = n - 1, ps = pa; k > j; --k, ps -= n) {
            z.re = -ps->re;
            z.im = -ps->im;
            for (i = j + 1, p = ps + 1, q = q0; i < k; ++i, ++p, ++q) {
                z.re -= p->re * q->re - p->im * q->im;
                z.im -= p->im * q->re + p->re * q->im;
            }
            q0[--m] = z;
        }
        for (i = 0, m = n - j - 1, q = q0, p = pd + n; i < m; ++i, p += n)
            *p = *q++;
    }
    for (k = 0, pa = a; k < n - 1; ++k, ++pa) {
        for (i = 0, q = q0, p = pa; i < n; ++i, p += n)
            *q++ = *p;
        for (j = 0, ps = a; j < n; ++j, ps += n) {
            if (j > k) {
                h.re = h.im = 0.;
                p = ps + j;
                i = j;
            }
            else {
                h = q0[j];
                p = ps + k + 1;
                i = k + 1;
            }
            for (; i < n; ++i, ++p) {
                h.re += p->re * q0[i].re - p->im * q0[i].im;
                h.im += p->im * q0[i].re + p->re * q0[i].im;
            }
            q0[j] = h;
        }
        for (i = 0, q = q0, p = pa; i < n; ++i, p += n)
            *p = *q++;
    }
    for (j = n - 2, le--; j >= 0; --j) {
        for (k = 0, p = a + j, q = a + *(--le); k < n; ++k, p += n, q += n) {
            h = *p;
            *p = *q;
            *q = h;
        }
    }
    free(le);
    free(q0);
    return 0;
}