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

#include <math.h>
#include <grass/gis.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];
    }
}