#ifndef __APPLE__
#include <malloc.h>
#else
#include <stdlib.h>
#endif
#include <limits.h>
#include <float.h>

#include "mathlib.h"

#define TINY FLT_MIN

void lubksb( float **a, int n, int *indx, float b[] ){
// Solves the set of n linear equations A.X=B. Here a[n][n] is input, not as the matrix
// A but rather as its LU decomposition determined by the routine ludcmp. indx[n] is input
// as the permutation vector returned by ludcmp. b[n] is input as the right-hand side vector
// B, and returns with the solution vector X. a, n and indx are not modified by this routine
// and can be left in place for successive calls with different right-hand sides b. This routine takes
// into account the possibility that b will begin with many zero elements, so it is efficient for use
// in matrix inversion
	int i,ii = -1,ip,j;
	float sum;

	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];
	}
}
/* (C) Copr. 1986-92 Numerical Recipes Software */


int ludcmp( float **a, int n, int *indx, float *d ){
// given a matrix a[n][n] this routine replaces it with the LU decomposition of a rowwise
// permutation of itself. a and n are input. a is output, arranged as in above equation;
// indx[n] is an output vector that records the row permutation effected by the partial
// pivoting; d is output as +/-1 depending on whether the number of row interchanges was even
// or odd, respectively. This routine is used in combination with lubksb to solve linear
// equations or invert a matrix.
	int i,imax,j,k;
	float big,dum,sum,temp;
	float *vv;

	imax = 0;
	vv = (float*)malloc( sizeof( float ) * n );
	*d = 1.0;
	for ( i = 0; i < n; i++ ) {
		big = 0.0;
		for ( j = 0; j < n; j++ )
			if ( ( temp = (float)fabs( a[i][j] ) ) > big ) {
				big = temp;
			}
		if ( big == 0.0 ) {
			return 1;
		}
		vv[i] = 1.0f / 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] * (float)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 = 1.0f / ( a[j][j] );
			for ( i = j + 1; i < n; i++ ) a[i][j] *= dum;
		}
	}
	free( vv );
	return 0;
}
/* (C) Copr. 1986-92 Numerical Recipes Software */