lu.c

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#include <math.h>
#include <grass/gis.h>
#include <grass/gmath.h>
 
#define TINY 1.0e-20;
 
/*!
 * \brief LU decomposition
 *
 * \param a double **
 * \param n int
 * \param indx int *
 * \param d double *
 *
 * \return 0 on singular matrix, 1 on success
 */
int G_ludcmp(double **a, int n, int *indx, double *d)
{
    int i, imax = 0, j, k;
    double big, dum, sum, temp;
    double *vv;
    int is_singular = FALSE;
 
    vv = G_alloc_vector(n);
    *d = 1.0;
    /* this pragma works, but doesn't really help speed things up */
    /* #pragma omp parallel for private(i, j, big, temp) shared(n, a, vv,
     * is_singular) */
    for (i = 0; i < n; i++) {
        big = 0.0;
        for (j = 0; j < n; j++)
            if ((temp = fabs(a[i][j])) > big)
                big = temp;
 
        if (big == 0.0) {
            is_singular = TRUE;
            break;
        }
 
        vv[i] = 1.0 / big;
    }
    if (is_singular) {
        *d = 0.0;
        return 0; /* Singular matrix  */
    }
 
    for (j = 0; j < n; j++) {
        for (i = 0; i < j; i++) {
            sum = a[i][j];
            for (k = 0; k < i; k++)
                sum -= a[i][k] * a[k][j];
            a[i][j] = sum;
        }
 
        big = 0.0;
        /* not very efficient, but this pragma helps speed things up a bit */
#pragma omp parallel for private(i, k, sum, dum) shared(j, n, a, vv, big, imax)
        for (i = j; i < n; i++) {
            sum = a[i][j];
            for (k = 0; k < j; k++)
                sum -= a[i][k] * a[k][j];
            a[i][j] = sum;
            if ((dum = vv[i] * fabs(sum)) >= big) {
                big = dum;
                imax = i;
            }
        }
        if (j != imax) {
            for (k = 0; k < n; k++) {
                dum = a[imax][k];
                a[imax][k] = a[j][k];
                a[j][k] = dum;
            }
            *d = -(*d);
            vv[imax] = vv[j];
        }
        indx[j] = imax;
        if (a[j][j] == 0.0)
            a[j][j] = TINY;
        if (j != n) {
            dum = 1.0 / (a[j][j]);
            for (i = j + 1; i < n; i++)
                a[i][j] *= dum;
        }
    }
    G_free_vector(vv);
 
    return 1;
}
 
#undef TINY
 
/*!
 * \brief LU backward substitution
 *
 * \param a double **
 * \param n int
 * \param indx int *
 * \param b double []
 *
 * \return void
 */
void G_lubksb(double **a, int n, int *indx, double b[])
{
    int i, ii, ip, j;
    double sum;
 
    ii = -1;
    for (i = 0; i < n; i++) {
        ip = indx[i];
        sum = b[ip];
        b[ip] = b[i];
        if (ii >= 0)
            for (j = ii; j < i; j++)
                sum -= a[i][j] * b[j];
        else if (sum)
            ii = i;
        b[i] = sum;
    }
    for (i = n - 1; i >= 0; i--) {
        sum = b[i];
        for (j = i + 1; j < n; j++)
            sum -= a[i][j] * b[j];
        b[i] = sum / a[i][i];
    }
}