vendredi 12 août 2016

Monte Carlo calculation of pi using randomly generated data in Java

I'm working on a program that calculates pi based on randomly generated float numbers that represent x,y co-ordinates on a graph. Each x, y co-ordinate is raised by the power of 2 and stored in two separate arrays. The co-ordinates are distributed uniformly on a graph of interval of 0,1.

The program adds the x, y co-ordinates and if they are less than 1 then the points are located within a circle of diameter 1, illustrated in the diagram below.

enter image description here

I then used the formula,

π ≈ 4 w / n

to work out pi. Where, w is the count of the points within the circle and n is the number of x or y co-ordinates within the arrays.

When I set n up to 10,000,000 (the size of the array) it generates the most accurate calculation of pi of 15-16 decimal places. However after dedicating 4gb of ram to the run config and setting n to 100,000,000 pi ends up being 0.6710...

I was wondering why this may be happening? Sorry if this is a stupid question.. code is below.

import java.text.DecimalFormat;
import java.util.Random;

public class random_pi {

    public random_pi() {

        float x2_store[] = new float[10000000];
        float y2_store[] = new float[10000000];
        float w = 0;

        Random rand = new Random();
        DecimalFormat df2 = new DecimalFormat("#,###,###");

        for (int i = 0; i < x2_store.length; i++) {
            float x2 = (float) Math.pow(rand.nextFloat(), 2);
            x2_store[i] = x2;
            float y2 = (float) Math.pow(rand.nextFloat(), 2);
            y2_store[i] = y2;
        }

        for (int i = 0; i < x2_store.length; i++) {
            if (x2_store[i] + y2_store[i] < 1) {
                w++;
            }
        }

        System.out.println("w: "+w);
        float numerator = (4*w);
        System.out.printf("4*w: " + (numerator));
        System.out.println("\nn: " + df2.format(x2_store.length));
        float pi = numerator / x2_store.length;

        String fmt = String.format("%.20f", pi);
        System.out.println(fmt);

        String pi_string = Double.toString(Math.abs(pi));
        int intP = pi_string.indexOf('.');
        int decP = pi_string.length() - intP - 1;
        System.out.println("decimal places: " + decP);
    }

    public static void main(String[] args) {
        new random_pi();
    }
}




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