/* ---------------------------------------------------------------------- * * A Monte Carlo simulation to estimate the probability that the * determinant of a 3 by 3 matrix of random numbers is positive. * * Name              : Det.java * Author            : Larry Leemis * Translated by     : Richard Dutton * Language          : Java * Latest Revision   : 6-16-06 * ---------------------------------------------------------------------- */import java.io.*;import java.text.*;public class Det{    static long N = 200000000;                  /* number of replications    */    static Rng rng;    public static void main(String args[]){	rng = new Rng();	int    i;                              /* replication index         */	int    j;                              /* row index                 */	int    k;                              /* column index              */	double a[][] = new double[4][4];       /* matrix(9 elements used)   */	double temp1;                          /* first 2 by 2 determinant  */	double temp2;                          /* second 2 by 2 determinant */	double temp3;                          /* third 2 by 2 determinant  */	double x;                              /* determinant               */	int    count = 0;                      /* counts number of pos det  */  	rng.putSeed(0);	for (i = 0; i < N; i++) {	    for (j = 1; j <= 3; j++) {		for (k = 1; k <= 3; k++) {		    a[j][k] = rng.random();		    if (j != k)			a[j][k] = -a[j][k];		}	    }	    temp1 = a[2][2] * a[3][3] - a[3][2] * a[2][3];	    temp2 = a[2][1] * a[3][3] - a[3][1] * a[2][3];	    temp3 = a[2][1] * a[3][2] - a[3][1] * a[2][2];	    x = a[1][1] * temp1 - a[1][2] * temp2 + a[1][3] * temp3;	    if (x > 0)		count++;	}	//printf("\nbased on %ld replications ", N);	System.out.print("\nbased on " + N + " replications ");  	//printf("the estimated probability of a positive determinant is:\n");	System.out.println("the estimated probability of a positive determinant is:\n");	//printf("%11.9f", (double) count / N);	System.out.print((double) count / N);	//printf("\n");	System.out.println();    }}