DiscShift2.java

/*
 * Class:        DiscShift2
 * Description:  computes a discrepancy for the randomly shifted points of a set
 * 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;
import umontreal.ssj.util.Num;

public class DiscShift2 extends Discrepancy {
 
   protected static double[] setC(double gam) {
      // 1 dimension
      double[] C = new double[2];
      double v = gam * gam;
      C[0] = 0.5 * v;
      v = v * v;
      C[1] = v / 12.0;
      return C;
   }
 
   protected static void setC(double[] C1, double[] C2, double[] gam, int s) {
      for (int i = 0; i < s; i++) {
         double v = gam[i] * gam[i];
         C1[i] = 0.5 * v;
         v = v * v;
         C2[i] = v / 12.0;
      }
   }

   public DiscShift2(double[][] points, int n, int s) {
      super(points, n, s);
   }

   public DiscShift2(double[][] points, int n, int s, double[] gamma) {
      super(points, n, s, gamma);
   }

   public DiscShift2(int n, int s, double[] gamma) {
      super(n, s, gamma);
   }

   public DiscShift2(PointSet set) {
      super(set);
   }

   public DiscShift2() {
   }

   public double compute(double[][] points, int n, int s) {
      setONES(s);
      return compute(points, n, s, ONES);
   }

   public double compute(double[][] points, int n, int s, double[] gamma) {
      double[] C1 = new double[s];
      double[] C2 = new double[s];
      setC(C1, C2, gamma, s);
 
      double pol1 = UNSIX; // BernoulliPoly(2, 0);
      double pol2 = -UNTRENTE; // BernoulliPoly(4, 0);
      double prod = 1.0;
      for (int r = 0; r < s; ++r)
         prod *= (1.0 + C1[r] * pol1 - C2[r] * pol2);
      double disc = prod / n;
 
      double sum = 0.0;
      for (int i = 0; i < n - 1; ++i) {
         for (int j = i + 1; j < n; ++j) {
            prod = 1.0;
            for (int r = 0; r < s; ++r) {
               double u = points[i][r] - points[j][r];
               if (u < 0.0)
                  u += 1.0;
               pol1 = u * (u - 1.0) + UNSIX; // Bernoulli(2, u)
               pol2 = ((u - 2.0) * u + 1.0) * u * u - UNTRENTE; // Bernoulli(4,h)
               prod *= 1.0 + C1[r] * pol1 - C2[r] * pol2;
            }
            sum += prod;
         }
      }
 
      disc += 2.0 * sum / ((long) n * n) - 1.0;
      if (disc < 0.0)
         return -1.0;
      return Math.sqrt(disc);
   }

   public double compute(double[] T, int n) {
      return compute(T, n, 1.0);
   }

   public double compute(double[] T, int n, double gamma) {
      double pol1 = UNSIX; // BernoulliPoly(2, 0);
      double pol2 = -UNTRENTE; // BernoulliPoly(4, 0);
      double[] C = setC(gamma);
      double C1 = C[0];
      double C2 = C[1];
      double disc = (C1 * pol1 - C2 * pol2) / n;
 
      double sum = 0.0;
      for (int i = 0; i < n - 1; ++i) {
         for (int j = i + 1; j < n; ++j) {
            double u = T[i] - T[j];
            if (u < 0.0)
               u += 1.0;
            pol1 = u * (u - 1.0) + UNSIX; // Bernoulli(2, u)
            pol2 = ((u - 2.0) * u + 1.0) * u * u - UNTRENTE; // Bernoulli(4,h)
            sum += (C1 * pol1 - C2 * pol2);
         }
      }
 
      disc += 2.0 * sum / ((long) n * n);
      if (disc < 0.0)
         return -1.0;
      return Math.sqrt(disc);
   }
 
}