DiscL2Hickernell.java

/*
 * Class:        DiscL2Hickernell
 * Description:  computes the Hickernell L_2 star discrepancy
 * Environment:  Java
 * Software:     SSJ 
 * Copyright (C) 2001  Pierre L'Ecuyer and Universite de Montreal
 * Organization: DIRO, Universite de Montreal
 * @author       Richard Simard
 * @since        January 2009
 
 * SSJ is free software: you can redistribute it and/or modify it under
 * the terms of the GNU General Public License (GPL) as published by the
 * Free Software Foundation, either version 3 of the License, or
 * any later version.
 
 * SSJ is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 
 * A copy of the GNU General Public License is available at
   <a href="http://www.gnu.org/licenses">GPL licence site</a>.
 */
package umontreal.ssj.discrepancy;
 
import umontreal.ssj.hups.PointSet;

public class DiscL2Hickernell extends Discrepancy {
 
   public double compute(double[][] points, int n, int s, double[] gamma) {
      return compute(points, n, s);
   }

   public DiscL2Hickernell(double[][] points, int n, int s) {
      super(points, n, s);
   }

   public DiscL2Hickernell(int n, int s) {
      super(null, n, s);
   }

   public DiscL2Hickernell(PointSet set) {
      super(set);
   }

   public DiscL2Hickernell() {
      super();
   }

   public double compute(double[][] points, int n, int s) {
      final int N = n;
      final double RAC3 = 1.73205080756887729352; // sqrt(3)
      double sum = 0.0;
      for (int i = 0; i < N; ++i) {
         double prod = 1.0;
         for (int j = 0; j < s; ++j) {
            double u = points[i][j];
            prod *= (RAC3 - u) * (RAC3 + u);
         }
         sum += prod;
      }
      double disc = -Math.pow(0.5, (double) (s - 1)) * sum / N;
 
      sum = 0.0;
      for (int i = 0; i < N; ++i) {
         double prod = 1.0;
         for (int j = 0; j < s; ++j)
            prod *= 2.0 - points[i][j];
         sum += prod;
      }
 
      double sum2 = 0.0;
      for (int i = 0; i < N - 1; ++i) {
         for (int j = i + 1; j < N; ++j) {
            double prod = 1.0;
            for (int k = 0; k < s; ++k)
               prod *= 2.0 - Math.max(points[i][k], points[j][k]);
            sum2 += prod;
         }
      }
 
      disc += (sum + 2.0 * sum2) / ((long) N * N);
      disc += Math.pow(4.0 / 3.0, s);
      if (disc < 0.0)
         return -1.0;
      return Math.sqrt(disc);
   }

   public double compute(double[] T, int n) {
      // In 1 dimension, L2*Hickernell = L2*
      double sum = 0.0;
      for (int i = 0; i < n; ++i)
         sum += T[i] * T[i];
      double disc = sum / n;
 
      sum = 0.0;
      for (int i = 0; i < n; ++i)
         sum += T[i];
 
      double sum2 = 0.0;
      for (int i = 0; i < n - 1; ++i) {
         for (int j = i + 1; j < n; ++j)
            sum2 += Math.max(T[i], T[j]);
      }
 
      disc -= (sum + 2.0 * sum2) / ((long) n * n);
      disc += 1.0 / 3.0;
      if (disc < 0.0)
         return -1.0;
      return Math.sqrt(disc);
   }
 
}