/**  * file: Covariance.java * * Last editted: Ryan Irwin * */// import necessary java libraries////These imports are not needed - Phil T. 6-23-03//import java.awt.*;//import java.applet.*;//import javax.swing.*;/** * Covariance as the name sggests computes the covariance matrix given  * two random vectors i.e., the X = (x1, x2, x3 ...) and Y = (y1, y2, y3 ...) */public class Covariance {    // *********************************************************************    //    // declare class methods    //    // *********************************************************************        /**     * The method normalizes the covariance matrix based on the the range of      * the values within the covariance matrix     *     * @param   M covariance matrix     */    public void normalizeCovariance(double[][] M)     {		// declare local variables	//	double min = Double.MAX_VALUE;	double max = -Double.MAX_VALUE;		// obtain the minimum and maximum value from the covariance matrix	//	for(int i=0; i < M.length; i++) 	{	    for(int j=0; j < M.length; j++) 	    {		if (M[i][j] < min) 		{		    min = M[i][j];		}		if (M[i][j] > max) 		{		    max = M[i][j];		}	    }	}		// normalize the covariance matrix	//	for(int i=0; i < M.length; i++) 	{	    for(int j=0; j < M.length; j++) 	    {		M[i][j] = (M[i][j] - min) / (max - min);	    }	}    }        /**     * computes the covariance matrix given two discrete random variables     *     * @param   x random vector X = (x1, x2, x3 ...)     * @param   y random vector Y = (y1, y2, y3 ...)     *     * @return  covariance matrix     */    public double[][] computeCovariance(double[] x, double[] y)     {		// declare local variables	//	double sum11 = 0.0;	double sum12 = 0.0;	double sum21 = 0.0;	double sum22 = 0.0;		double sum1 = 0.0;	double mean1 = 0.0;	double sum2 = 0.0;	double mean2 = 0.0;		// declare the covariance matrix	//	double[][] cov = new double[2][2];		// compute the mean of the first random variable	//	for(int i = 0; i < x.length; i++) 	{ 	    sum1 += x[i]; 	}	mean1 = sum1 / x.length;	// compute the mean of the second random variable	//	for(int i = 0; i < y.length; i++) 	{ 	    sum2 += y[i]; 	}	mean2 = sum2 / y.length;		// compute the c11 component of the covariance matrix	//	for(int i = 0; i < x.length; i++) 	{	    sum11 += (x[i] - mean1) * (x[i] - mean1);	}	cov[0][0] = sum11 / (x.length - 1);	// compute the c12 component of the covariance matrix	//	for(int i = 0; i < x.length; i++) 	{	    sum12 += (x[i] - mean1) * (y[i] - mean2);	}	cov[0][1] = sum12 / (x.length - 1);	// compute the c21 component of the covariance matrix	//	for(int i = 0; i < x.length; i++) 	{    	    sum21 += (y[i] - mean2) * (x[i] - mean1);	}	cov[1][0] = sum21 / (x.length - 1);	// compute the c22 component of the covariance matrix	//	for(int i = 0; i < x.length; i++) 	{	    sum22 += (y[i] - mean2) * (y[i] - mean2);	}	cov[1][1] = sum22 / (x.length - 1);	// return the covariance matrix	//	return cov;    }}