housev.c

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/*  housev.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"
void housev(double *a, double *d, double *dp, int n)
{
    double sc, x, y, h;
 
    int i, j, k, m, e;
 
    double *qw, *qs, *pc, *p;
 
    qs = (double *)calloc(n, sizeof(double));
    for (j = 0, pc = a; j < n - 2; ++j, pc += n + 1) {
        m = n - j - 1;
        for (i = 1, sc = 0.; i <= m; ++i)
            sc += pc[i] * pc[i];
        if (sc > 0.) {
            sc = sqrt(sc);
            if ((x = *(pc + 1)) < 0.) {
                y = x - sc;
                h = 1. / sqrt(-2. * sc * y);
            }
            else {
                y = x + sc;
                h = 1. / sqrt(2. * sc * y);
                sc = -sc;
            }
            for (i = 0, qw = pc + 1; i < m; ++i) {
                qs[i] = 0.;
                if (i)
                    qw[i] *= h;
                else
                    qw[i] = y * h;
            }
            for (i = 0, e = j + 2, p = pc + n + 1, h = 0.; i < m;
                 ++i, p += e++) {
                qs[i] += (y = qw[i]) * *p++;
                for (k = i + 1; k < m; ++k) {
                    qs[i] += qw[k] * *p;
                    qs[k] += y * *p++;
                }
                h += y * qs[i];
            }
            for (i = 0; i < m; ++i) {
                qs[i] -= h * qw[i];
                qs[i] += qs[i];
            }
            for (i = 0, e = j + 2, p = pc + n + 1; i < m; ++i, p += e++) {
                for (k = i; k < m; ++k)
                    *p++ -= qw[i] * qs[k] + qs[i] * qw[k];
            }
        }
        d[j] = *pc;
        dp[j] = sc;
    }
    d[j] = *pc;
    dp[j] = *(pc + 1);
    d[j + 1] = *(pc += n + 1);
    free(qs);
    for (i = 0, m = n + n, p = pc; i < m; ++i)
        *p-- = 0.;
    *pc = 1.;
    *(pc -= n + 1) = 1.;
    qw = pc - n;
    for (m = 2; m < n; ++m, qw -= n + 1) {
        for (j = 0, p = pc, *pc = 1.; j < m; ++j, p += n) {
            for (i = 0, qs = p, h = 0.; i < m;)
                h += qw[i++] * *qs++;
            for (i = 0, qs = p, h += h; i < m;)
                *qs++ -= h * qw[i++];
        }
        for (i = 0, p = qw + m; i < n; ++i)
            *(--p) = 0.;
        *(pc -= n + 1) = 1.;
    }
}