org.powertac.householdcustomer.configurations.Gaussian Maven / Gradle / Ivy

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Bottom-up model of a household energy customer

There is a newer version: 1.9.0

/*************************************************************************
 * Compilation: javac Gaussian.java Execution: java Gaussian x mu sigma
 * 
 * Function to compute the Gaussian pdf (probability density function) and the
 * Gaussian cdf (cumulative density function)
 * 
 * % java Gaussian 820 1019 209 0.17050966869132111
 * 
 * % java Gaussian 1500 1019 209 0.9893164837383883
 * 
 * % java Gaussian 1500 1025 231 0.9801220907365489
 * 
 * The approximation is accurate to absolute error less than 8 * 10^(-16).
 * Reference: Evaluating the Normal Distribution by George Marsaglia.
 * http://www.jstatsoft.org/v11/a04/paper
 * 
 *************************************************************************/

package org.powertac.householdcustomer.configurations;

public class Gaussian
{

  // return phi(x) = standard Gaussian pdf
  public static double phi (double x)
  {
    return Math.exp(-x * x / 2) / Math.sqrt(2 * Math.PI);
  }

  // return phi(x, mu, signma) = Gaussian pdf with mean mu and stddev sigma
  public static double phi (double x, double mu, double sigma)
  {
    return phi((x - mu) / sigma) / sigma;
  }

  // return Phi(z) = standard Gaussian cdf using Taylor approximation
  public static double Phi (double z)
  {
    if (z < -8.0)
      return 0.0;
    if (z > 8.0)
      return 1.0;
    double sum = 0.0, term = z;
    for (int i = 3; sum + term != sum; i += 2) {
      sum = sum + term;
      term = term * z * z / i;
    }
    return 0.5 + sum * phi(z);
  }

  // return Phi(z, mu, sigma) = Gaussian cdf with mean mu and stddev sigma
  public static double Phi (double z, double mu, double sigma)
  {
    return Phi((z - mu) / sigma);
  }

  // Compute z such that Phi(z) = y via bisection search
  public static double PhiInverse (double y)
  {
    return PhiInverse(y, .00000001, -8, 8);
  }

  // bisection search
  private static double PhiInverse (double y, double delta, double lo, double hi)
  {
    double mid = lo + (hi - lo) / 2;
    if (hi - lo < delta)
      return mid;
    if (Phi(mid) > y)
      return PhiInverse(y, delta, lo, mid);
    else
      return PhiInverse(y, delta, mid, hi);
  }

  // test client
  public static void main (String[] args)
  {
    double z = Double.parseDouble(args[0]);
    double mu = Double.parseDouble(args[1]);
    double sigma = Double.parseDouble(args[2]);
    System.out.println(Phi(z, mu, sigma));
    double y = Phi(z);
    System.out.println(PhiInverse(y));
  }

}