I have the next code, which multiplies the probability matrix p the certain number of times. For the first 50 iterations everything is ok, the sum of probabilities in each row is equal to 1, but then I recieve the sum > 1 and approximately on the 70th iteration I recieve infinity values. And I do not understand why.
The sum of probabilities in each row must be equal to 1. This is the classic Markov's chain model. And regardless of num of multiplications you must receive the sum = 1 in each row. I suppose there is a problem in a floating-point calculation.
public class Test {
public static void main(String[] args) {
int trials = Integer.parseInt(args[0]);
double[][] p = {
{0.02, 0.92, 0.02, 0.02, 0.02},
{0.02, 0.02, 0.38, 0.38, 0.2},
{0.02, 0.02, 0.02, 0.92, 0.02},
{0.92, 0.02, 0.02, 0.02, 0.02},
{0.47, 0.02, 0.47, 0.02, 0.02}};
for (int t = 0; t < trials; t++) {
p = multiply(p, p);
}
for (int i = 0; i < p.length; i++) {
for (int j = 0; j < p[i].length; j++) {
System.out.printf("%9.4f", p[i][j]);
}
System.out.println();
}
}
public static double[][] multiply(double[][] a, double[][] b) {
int w = a[0].length;
int l = b.length;
if (w != l) {
throw new IllegalArgumentException("The number of columns " +
"in the first matrix must be equal to the number " +
"of rows in second matrix!" + w + " " + l);
}
double[][] result = new double[a.length][b[0].length];
for (int i = 0; i < a.length; i++) {
for (int j = 0; j < b[0].length; j++) {
for (int k = 0; k < b.length; k++) {
result[i][j] += a[i][k] * b[k][j];
}
}
}
return result;
}
}
/*
output for the trials = 30:
0,2730 0,2657 0,1462 0,2472 0,0678
0,2730 0,2657 0,1462 0,2472 0,0678
0,2730 0,2657 0,1462 0,2472 0,0678
0,2730 0,2657 0,1462 0,2472 0,0678
0,2730 0,2657 0,1462 0,2472 0,0678
output for the trials = 45:
0,2732 0,2659 0,1463 0,2474 0,0679
0,2732 0,2659 0,1463 0,2474 0,0679
0,2732 0,2659 0,1463 0,2474 0,0679
0,2732 0,2659 0,1463 0,2474 0,0679
0,2732 0,2659 0,1463 0,2474 0,0679
output for the trials = 55:
0,5183 0,5044 0,2775 0,4693 0,1288
0,5183 0,5044 0,2775 0,4693 0,1288
0,5183 0,5044 0,2775 0,4693 0,1288
0,5183 0,5044 0,2775 0,4693 0,1288
0,5183 0,5044 0,2775 0,4693 0,1288
output for the trials = 70:
Infinity Infinity Infinity Infinity Infinity
Infinity Infinity Infinity Infinity Infinity
Infinity Infinity Infinity Infinity Infinity
Infinity Infinity Infinity Infinity Infinity
Infinity Infinity Infinity Infinity Infinity
*/
