// Instructions:
// Compile and execute

public class PowerMethodExample {

    public static void main (String[] argv)
    {
	double[][] A = {
	    {5,-2},
	    {0,1}
	};

	// Now start with some initial vector u0
	double[] u0 = {1,1};

	int numIterations = 10;
	
	// We'll also compute powers of A for illustration.
	double[][] A_power_k = copy (A);            

	// Initialize:
	double[] u = {u0[0], u0[1]};

	for (int k=1; k<=numIterations; k++) {
	    u = MatrixTool.matrixVectorMult (A, u);
	    u = normalize (u);
	    MatrixTool.print (u);
	    A_power_k = MatrixTool.matrixMult (A, A_power_k);
	}

	// Compute lambda = (Au dot u) / (u dot u)
	double[] y = MatrixTool.matrixVectorMult (A, u);
	double lambda = MatrixTool.dotProduct (y,u) / MatrixTool.dotProduct (u,u);
	System.out.println ("lambda=" + lambda);

	// Compare with A^k * u
	double[] x = MatrixTool.matrixVectorMult (A_power_k, u0);
	MatrixTool.print (x);
    }


    static double[] normalize (double[] x)
    {
	double normX = MatrixTool.norm (x);
	double[] y = new double [x.length];
	for (int i=0; i<x.length; i++) {
	    y[i] = (1.0 / normX) * x[i];
	}
	return y;
    }

    static double[][] copy (double[][] A)
    {
	double[][] B = new double [A.length][A[0].length];
	for (int i=0; i<A.length; i++) {
	    for (int j=0; j<A[0].length; j++) {
		B[i][j] = A[i][j];
	    }
	}
	return B;
    }

}