Example: LU Factorization of a Matrix

using System;
using Imsl.Math;

public class LUEx1
{
   public static void Main(String[] args)
   {
      double[,] a = {
            {1, 3, 3}, 
            {1, 3, 4},
            {1, 4, 3}
        };
      double[] b = new double[] { 12, 13, 14 };

      // Compute the LU factorization of A
      LU lu = new LU(a);

      // Solve Ax = b
      double[] x = lu.Solve(b);
      new PrintMatrix("x").Print(x);

      // Find the inverse of A.
      double[,] ainv = lu.Inverse();
      new PrintMatrix("ainv").Print(ainv);

      // Find the condition number of A.
      double condition = lu.Condition(a);
      Console.Out.WriteLine("condition number = " + condition);
      Console.Out.WriteLine();

      // Find the determinant of A.
      double determinant = lu.Determinant();
      Console.Out.WriteLine("determinant = " + determinant);
   }
}

Output

  x
   0  
0  3  
1  2  
2  1  

               ainv
   0             1            2   
0   7  -3                     -3  
1  -1   2.22044604925031E-16   1  
2  -1   1                      0  

condition number = 0.0151202749140893

determinant = -1