#include <stdio.h>
#include <math.h>
/* lu : 1999 3 8 by Oguni */
#define N 3
main(){
  double A[N][N]={1., 4., 3., 2., 5., 4., 1., -3., -2.};
  double L[N][N], U[N][N];
  double b[N]={1.,4.,5.}, x[N];
  double tol=0.000001;
  int n=3, i, j;
  lu(A,L,U,tol,n);
  for (i=0; i<n; i++){
    for (j=0; j<n; j++){
      printf("%f", L[i][j]); }
    printf("\n");
  }
  for (i=0; i<n; i++){
    for (j=0; j<n; j++){
      printf("%f", U[i][j]); }
    printf("\n");
  }
  printf("Solution\n");
  subs(L,U,b,x,tol,n);
  for (i=0; i<n; i++){
    printf("%f\n", x[i]); }
}
/* function lu */
lu(A,L,U,tol,n)
double A[N][N], L[N][N], U[N][N], tol;
int n;
{
  double akk, aik;
  int i, j, k;
  for (k=0; k<n-1; k++){
    if (fabs(A[k][k])<tol) {
      printf("The pivot is too small at step # %d", k); }
    akk=1.0/A[k][k];
    for (i=k+1; i<n; i++){
      aik=-A[i][k]*akk;
      for (j=k+1; j<n; j++){ A[i][j]+=aik*A[k][j]; }
    }
    for (j=k+1; j<n; j++){ A[k][j]*=akk; }
  }
  for (i=0; i<n-1; i++){
    for (j=0; j<=i; j++){ L[i][j]=A[i][j]; }
    for (j=i+1; j<n; j++){ U[i][j]=A[i][j]; }
    U[i][i]=1.0;
  }
  U[n-1][n-1]=1.0;
  for (j=0; j<n; j++){ L[n-1][j]=A[n-1][j]; }
}
/* function subs */
subs(L,U,b,x,tol,n)
double L[N][N], U[N][N], b[N], x[N], tol;
int n;
{
  double y[N], s;
  int i, j, k;
  y[0]=b[0]/L[0][0];
  for (i=1; i<=n-1; i++){
    if (fabs(L[i][i])<tol) {
      printf("The pivot is too small at step #%d", i); }
    s=0.0;
    for (j=0; j<=i-1; j++){
      s+=L[i][j]*y[j]; }
    y[i]=(b[i]-s)/L[i][i];
  }
  x[n-1]=y[n-1]/U[n-1][n-1];
  for (k=n-2; k>=0; k--){
    s=0.0;
    for (j=k+1; j<n; j++){ s+=U[k][j]*x[j]; }
    x[k]=(y[k]-s)/U[k][k];
  }
}