qrbdv.c

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/*  qrbdv.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 "ccmath.h"
int qrbdv(double *dm, double *em, double *um, int mm, double *vm, int m)
{
    int i, j, k, n, jj, nm;
 
    double u, x, y, a, b, c, s, t, w, *p, *q;
 
    for (j = 1, t = fabs(dm[0]); j < m; ++j)
        if ((s = fabs(dm[j]) + fabs(em[j - 1])) > t)
            t = s;
    t *= 1.e-15;
    n = 100 * m;
    nm = m;
    for (j = 0; m > 1 && j < n; ++j) {
        for (k = m - 1; k > 0; --k) {
            if (fabs(em[k - 1]) < t)
                break;
            if (fabs(dm[k - 1]) < t) {
                for (i = k, s = 1., c = 0.; i < m; ++i) {
                    a = s * em[i - 1];
                    b = dm[i];
                    em[i - 1] *= c;
                    dm[i] = u = sqrt(a * a + b * b);
                    s = -a / u;
                    c = b / u;
                    for (jj = 0, p = um + k - 1; jj < mm; ++jj, p += mm) {
                        q = p + i - k + 1;
                        w = c * *p + s * *q;
                        *q = c * *q - s * *p;
                        *p = w;
                    }
                }
                break;
            }
        }
        y = dm[k];
        x = dm[m - 1];
        u = em[m - 2];
        a = (y + x) * (y - x) - u * u;
        s = y * em[k];
        b = s + s;
        u = sqrt(a * a + b * b);
        if (u != 0.) {
            c = sqrt((u + a) / (u + u));
            if (c != 0.)
                s /= (c * u);
            else
                s = 1.;
            for (i = k; i < m - 1; ++i) {
                b = em[i];
                if (i > k) {
                    a = s * em[i];
                    b *= c;
                    em[i - 1] = u = sqrt(x * x + a * a);
                    c = x / u;
                    s = a / u;
                }
                a = c * y + s * b;
                b = c * b - s * y;
                for (jj = 0, p = vm + i; jj < nm; ++jj, p += nm) {
                    w = c * *p + s * *(p + 1);
                    *(p + 1) = c * *(p + 1) - s * *p;
                    *p = w;
                }
                s *= dm[i + 1];
                dm[i] = u = sqrt(a * a + s * s);
                y = c * dm[i + 1];
                c = a / u;
                s /= u;
                x = c * b + s * y;
                y = c * y - s * b;
                for (jj = 0, p = um + i; jj < mm; ++jj, p += mm) {
                    w = c * *p + s * *(p + 1);
                    *(p + 1) = c * *(p + 1) - s * *p;
                    *p = w;
                }
            }
        }
        em[m - 2] = x;
        dm[m - 1] = y;
        if (fabs(x) < t)
            --m;
        if (m == k + 1)
            --m;
    }
    return j;
}