PiEstimator.java

package org.drip.zen.juice;

/*
 * 1) Introduce Probability
 * 2) Motivate the Lesson
 * 3) Outline the Approach
 * 4) Write Down the Formula
 * 5) Random Numbers Between -1 and 1
 * 6) Is Inside Circle
 * 7) Count of Inside Circle
 * 8) Probability To PI
 * 9) Generate Random Numbers
 * 10) Bring them all together
 */

public class PiEstimator {

    static double RandomNumber()
    {
        double random = Math.random();

        double randomBetweenMinus1AndPlus1 = 2. * random - 1;

        return randomBetweenMinus1AndPlus1;
    }

    static boolean IsPointInsideCircle (double x, double y)
    {
        double distanceFromOrigin = Math.sqrt (x * x + y * y);

        boolean insideCircle = false;

        if (distanceFromOrigin < 1.)
        {
            insideCircle = true;
        }
        else
        {
            insideCircle = false;
        }

        return insideCircle;
    }

    static double InsideCircleCount (double[] xArray, double[] yArray)
    {
        double numberInsideCircle = 0.;
        int numberOfPoints = xArray.length;

        for (int counter = 0; counter < numberOfPoints; counter = counter + 1)
        {
            if (IsPointInsideCircle (xArray[counter], yArray[counter]))
            {
                numberInsideCircle = numberInsideCircle + 1;
            }
        }

        return numberInsideCircle;
    }

    static double ProbabilityToPI (double probability)
    {
        double pi = 4. * probability;
        return pi;
    }

    public static void main (String[] input)
    {
        int totalNumberOfPoints = 10000000;

        double[] xPoints = new double[totalNumberOfPoints];
        double[] yPoints = new double[totalNumberOfPoints];

        for (int pointCounter = 0; pointCounter < totalNumberOfPoints; pointCounter = pointCounter + 1)
        {
            xPoints[pointCounter] = RandomNumber();
            yPoints[pointCounter] = RandomNumber();
        }

        double pointsInsideCircle = InsideCircleCount (xPoints, yPoints);

        double probabilityOfPointsInsideCircle = pointsInsideCircle / totalNumberOfPoints;

        double estimatedPI = ProbabilityToPI (probabilityOfPointsInsideCircle);

        System.out.println ("\tNumber of Points Inside Square    : " + totalNumberOfPoints);

        System.out.println ("\tNumber of Points Inside Circle    : " + pointsInsideCircle);

        System.out.println ("\tProbability Of Points in a Circle : " + probabilityOfPointsInsideCircle);

        System.out.println ("\tEstimated PI                      : " + estimatedPI);

        System.out.println ("\tActual PI                         : " + Math.PI);
    }
}