Geografic-Information-System/lib/gmath/lu.c

#include <math.h>
#include <grass/gis.h>
#include <grass/gmath.h>


#define TINY 1.0e-20;


int G_ludcmp(double **a, int n, int *indx, double *d)
{
    int i, imax = 0, j, k;
    double big, dum, sum, temp;
    double *vv;

    vv = G_alloc_vector(n);
    *d = 1.0;
    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) {
	    *d = 0.0;
	    return 0;		/* Singular matrix  */
	}
	vv[i] = 1.0 / big;
    }
    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;
	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

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];
    }
}