svdval.c

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/*  svdval.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 svdval(double *d, double *a, int m, int n)
{
    double *p, *p1, *q, *w, *v;

    double s, h, u;

    int i, j, k, mm, nm, ms;

    if (m < n)
        return -1;
    w = (double *)calloc(m, sizeof(double));
    for (i = 0, mm = m, nm = n - 1, p = a; i < n; ++i, --mm, --nm, p += n + 1) {
        if (mm > 1) {
            for (j = 0, q = p, s = 0.; j < mm; ++j, q += n) {
                w[j] = *q;
                s += *q * *q;
            }
            if (s > 0.) {
                h = sqrt(s);
                if (*p < 0.)
                    h = -h;
                s += *p * h;
                s = 1. / s;
                w[0] += h;
                for (k = 1, ms = n - i; k < ms; ++k) {
                    for (j = 0, q = p + k, u = 0.; j < mm; q += n)
                        u += w[j++] * *q;
                    u *= s;
                    for (j = 0, q = p + k; j < mm; q += n)
                        *q -= u * w[j++];
                }
                *p = -h;
            }
        }
        p1 = p + 1;
        if (nm > 1) {
            for (j = 0, q = p1, s = 0.; j < nm; ++j, ++q)
                s += *q * *q;
            if (s > 0.) {
                h = sqrt(s);
                if (*p1 < 0.)
                    h = -h;
                s += *p1 * h;
                s = 1. / s;
                *p1 += h;
                for (k = n, ms = n * (m - i); k < ms; k += n) {
                    for (j = 0, q = p1, v = p1 + k, u = 0.; j < nm; ++j)
                        u += *q++ * *v++;
                    u *= s;
                    for (j = 0, q = p1, v = p1 + k; j < nm; ++j)
                        *v++ -= u * *q++;
                }
                *p1 = -h;
            }
        }
    }

    for (j = 0, p = a; j < n; ++j, p += n + 1) {
        d[j] = *p;
        if (j != n - 1)
            w[j] = *(p + 1);
        else
            w[j] = 0.;
    }
    qrbdi(d, w, n);
    for (i = 0; i < n; ++i)
        if (d[i] < 0.)
            d[i] = -d[i];
    free(w);
    return 0;
}