// crout.java  solve simultaneous equation  A x = y  by Crout method
//             converted from crout.ada, 1 based to zero based, c to y

class crout
{
  crout(int n, double A[][], double y[], double x[])
  {
    double sum;

    for(int m=0; m<n; m++)
    {
      // below diagonal computations
      for(int i=m; i<n; i++)
      {
        sum = 0.0;
        for(int k=0; k<m; k++)
	{
          sum = sum + A[i][k]*A[k][m];
        } // k
        A[i][m] = A[i][m] - sum;
      } // i

      // above diagonal computations
      for(int j=m+1; j<n; j++)
      {
        sum = 0.0;
        for(int k=0; k<m; k++)
	{
          sum = sum + A[m][k]*A[k][j];
        } // k
        A[m][j] = (A[m][j]-sum)/A[m][m];
      } // j
      sum = 0.0;
      for(int k=0; k<m; k++)
      {
        sum = sum + A[m][k]*y[k];
      } // k
      y[m] = (y[m]-sum)/A[m][m];
    } // m

    // back substitute
    x[0] = 0.0;
    for(int i=n-1; i>=0; i--)
    {
      sum = 0.0;
      for(int k=i+1; k<n; k++)
      {
        sum = sum + A[i][k]*x[k];
      } // k
      x[i] = y[i] - sum;
    } // i
  } // end crout
} // end class crout