minv.c

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/*  minv.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 minv(double *a, int n)
{
    int lc, *le;
 
    double s, t, tq = 0., zr = 1.e-15;
 
    double *pa, *pd, *ps, *p, *q, *q0;
 
    int i, j, k, m;
 
    le = (int *)malloc(n * sizeof(int));
    q0 = (double *)malloc(n * sizeof(double));
    for (j = 0, pa = pd = a; j < n; ++j, ++pa, pd += n + 1) {
        if (j > 0) {
            for (i = 0, q = q0, p = pa; i < n; ++i, p += n)
                *q++ = *p;
            for (i = 1; i < n; ++i) {
                lc = i < j ? i : j;
                for (k = 0, p = pa + i * n - j, q = q0, t = 0.; k < lc; ++k)
                    t += *p++ * *q++;
                q0[i] -= t;
            }
            for (i = 0, q = q0, p = pa; i < n; ++i, p += n)
                *p = *q++;
        }
        s = fabs(*pd);
        lc = j;
        for (k = j + 1, ps = pd; k < n; ++k) {
            if ((t = fabs(*(ps += n))) > 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) {
            for (k = 0, p = a + n * j, q = a + n * lc; k < n; ++k) {
                t = *p;
                *p++ = *q;
                *q++ = t;
            }
        }
        for (k = j + 1, ps = pd, t = 1. / *pd; k < n; ++k)
            *(ps += n) *= t;
        *pd = t;
    }
    for (j = 1, pd = ps = a; j < n; ++j) {
        for (k = 0, pd += n + 1, q = ++ps; k < j; ++k, q += n)
            *q *= *pd;
    }
    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) {
            t = 0.;
            for (i = k, p = pa + k * n + k - j, q = q0 + k; i < j; ++i)
                t -= *p++ * *q++;
            q0[k] = t;
        }
        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) {
            t = -(*ps);
            for (i = j + 1, p = ps, q = q0; i < k; ++i)
                t -= *++p * *q++;
            q0[--m] = t;
        }
        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) {
                t = 0.;
                p = ps + j;
                i = j;
            }
            else {
                t = q0[j];
                p = ps + k + 1;
                i = k + 1;
            }
            for (; i < n;)
                t += *p++ * q0[i++];
            q0[j] = t;
        }
        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) {
            t = *p;
            *p = *q;
            *q = t;
        }
    }
    free(le);
    free(q0);
    return 0;
}