//---------------------------------------------------------------
// llustration of Power Iteration for computing a prestige vector
//---------------------------------------------------------------
// Solving matrix equation lambda x P = A x P
// (find eigenvector P and eigenvalue lambda)
//
//           |p1|   | 0 0 1 |   |p1|
//  lambda x |p2| = | 1 0 0 | x |p2|
//           |p3|   | 1 1 0 |   |p3|
//
//---------------------------------------------------------------
public class PowerIteration
{
    static final double epsilon = 0.01;
    static double p1, p2, p3, q1, q2, q3, lambda;
    
    public static void main (String[] args)
    {
        p1=1;
        p2=1;
        p3=1;
        
        do
        {
            q1 = p1;
            q2 = p2;
            q3 = p3;
            
            p1 = 0*q1 + 0*q2 + 1*q3;
            p2 = 1*q1 + 0*q2 + 0*q3;
            p3 = 1*q1 + 1*q2 + 0*q3;
            
            lambda = norm(p1,p2,p3);
            p1 = p1/lambda;
            p2 = p2/lambda;
            p3 = p3/lambda;
            
            System.out.println(p1+"\t"+p2+"\t"+p3+"\t"+lambda);
            
        } while (norm(p1-q1,p2-q2,p3-q3)>epsilon);
   }
    
    private static double norm (double x,double y,double z) 
    { 
        return Math.sqrt(x*x+y*y+z*z);
    }
}