sv2uv.c

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/*  sv2uv.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 sv2uv(double *d, double *a, double *u, int m, double *v, int n)
{
    double *p, *p1, *q, *pp, *w, *e;

    double s, t, h, r, sv;

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

    if (m < n)
        return -1;
    w = (double *)calloc(m + n, sizeof(double));
    e = w + m;
    for (i = 0, mm = m, p = a; i < n; ++i, --mm, p += n + 1) {
        if (mm > 1) {
            sv = h = 0.;
            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;
                t = 1. / (w[0] += h);
                sv = 1. + fabs(*p / h);
                for (k = 1, ms = n - i; k < ms; ++k) {
                    for (j = 0, q = p + k, r = 0.; j < mm; q += n)
                        r += w[j++] * *q;
                    r = r * s;
                    for (j = 0, q = p + k; j < mm; q += n)
                        *q -= r * w[j++];
                }
                for (j = 1, q = p; j < mm;)
                    *(q += n) = w[j++] * t;
            }
            *p = sv;
            d[i] = -h;
        }
        if (mm == 1)
            d[i] = *p;
    }
    ldumat(a, u, m, n);
    for (i = 0, q = a; i < n; ++i) {
        for (j = 0; j < n; ++j, ++q) {
            if (j < i)
                *q = 0.;
            else if (j == i)
                *q = d[i];
        }
    }
    for (i = 0, mm = n, nm = n - 1, p = a; i < n; ++i, --mm, --nm, p += n + 1) {
        if (i && mm > 1) {
            sv = h = 0.;
            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;
                t = 1. / (w[0] += h);
                sv = 1. + fabs(*p / h);
                for (k = 1, ms = n - i; k < ms; ++k) {
                    for (j = 0, q = p + k, r = 0.; j < mm; q += n)
                        r += w[j++] * *q;
                    for (j = 0, q = p + k, r *= s; j < mm; q += n)
                        *q -= r * w[j++];
                }
                for (k = 0, p1 = u + i; k < m; ++k, p1 += m) {
                    for (j = 0, q = p1, r = 0.; j < mm;)
                        r += w[j++] * *q++;
                    for (j = 0, q = p1, r *= s; j < mm;)
                        *q++ -= r * w[j++];
                }
            }
            *p = sv;
            d[i] = -h;
        }
        if (mm == 1)
            d[i] = *p;
        p1 = p + 1;
        if (nm > 1) {
            sv = h = 0.;
            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;
                sv = 1. + fabs(*p1 / h);
                s += *p1 * h;
                s = 1. / s;
                t = 1. / (*p1 += h);
                for (k = n, ms = n * (n - i); k < ms; k += n) {
                    for (j = 0, q = p1, pp = p1 + k, r = 0.; j < nm; ++j)
                        r += *q++ * *pp++;
                    for (j = 0, q = p1, pp = p1 + k, r *= s; j < nm; ++j)
                        *pp++ -= r * *q++;
                }
                for (j = 1, q = p1 + 1; j < nm; ++j)
                    *q++ *= t;
            }
            *p1 = sv;
            e[i] = -h;
        }
        if (nm == 1)
            e[i] = *p1;
    }
    ldvmat(a, v, n);
    qrbdv(d, e, u, m, v, n);
    for (i = 0; i < n; ++i) {
        if (d[i] < 0.) {
            d[i] = -d[i];
            for (j = 0, p = v + i; j < n; ++j, p += n)
                *p = -*p;
        }
    }
    free(w);
    return 0;
}