#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "nrutil.h"
#define TINY 1.0e-20
// #define N 2


void ludcmp (float **a, int n, int *indx, float *d)
{
  int i, imax, j, k;
  float big, dum, sum, temp;
  float *vv;

  vv = vector (1,n);
  *d = 1.0;
  for (i=1; i<=n; i++) 
  {
    big = 0.0;
    for (j=1; j<=n; j++)
      if ((temp = fabs(a[i][j])) > big) big = temp;
    if (big == 0.0) nrerror("Singular matrix in routine ludcmp");
    vv[i] = 1.0 / big;
  }
  
  for (j=1; j<=n; j++) 
  {
    for (i=1; i<j; i++) 
    {
      sum = a[i][j];
      for (k=1; 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=1; 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=1; 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;
    }
  }
  free_vector (vv, 1, n);
}


void lubksb (float **a, int n, int *indx, float b[])
{
  int i, ii=0, ip, j;
  float sum;
  
  for (i=1; i<=n; i++)
  {
    ip = indx[i];
    sum = b[ip];
    b[ip] = b[i];
    if (ii)
      for (j=ii; j<=i-1; j++) sum -= a[i][j] * b[j];
    else if (sum) ii = i;
    b[i] = sum;
  }
  for (i=n; i>=1; i--) 
  {
    sum = b[i];
    for (j=i+1; j<=n; j++) sum -= a[i][j] * b[j];
    b[i] = sum / a[i][i];
  }
}


// int main ()
// {
//   float **a, d;
//   int i, j, *indx;
//   
//   float a_array[N][N] = {
//     { 1.0, 2.0 },
//     { 3.0, 4.0 }
//   };
//   a = matrix (1, N, 1, N);
//   for (i=1; i<N+1; i++)
//     for (j=1; j<N+1; j++)
//       a[i][j] = a_array[i-1][j-1];
//   indx = ivector (1, N);
//   ludcmp (a, N, indx, &d);
//   for(j=1; j<=N; j++) d *= a[j][j];
//   printf ("%lf\n", d);
// 
//   return 0;
// }