DiscShiftBaker1.java

/*
 * Class:        DiscShiftBaker1
 * Description:  computes a discrepancy for a randomly shifted, then baker
                 folded point 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 DiscShiftBaker1 extends Discrepancy {
 
   static protected double[] setC(double gam) { // dimension = 1
      double[] C = new double[3];
      double v = gam * gam;
      C[0] = v * 4.0 / 3.0;
      v = v * v;
      C[1] = v / 9.0;
      C[2] = v * 16.0 / 45.0;
      return C;
   }
 
   static protected void setC(double[] C1, double[] C2, double[] C3, double[] gam, int s) {
      for (int i = 0; i < s; i++) {
         double v = gam[i] * gam[i];
         C1[i] = v * 4.0 / 3.0;
         v = v * v;
         C2[i] = v / 9.0;
         C3[i] = v * 16.0 / 45.0;
      }
   }

   public DiscShiftBaker1(double[][] points, int n, int s) {
      super(points, n, s);
   }

   public DiscShiftBaker1(double[][] points, int n, int s, double[] gamma) {
      super(points, n, s, gamma);
   }

   public DiscShiftBaker1(int n, int s, double[] gamma) {
      super(n, s, gamma);
   }

   public DiscShiftBaker1(PointSet set) {
      super(set);
   }

   public DiscShiftBaker1() {
   }

   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];
      double[] C3 = new double[s];
      setC(C1, C2, C3, gamma, s);
 
      double pol1 = -1.0 / 30.0; // BernoulliPoly(4, 0);
      double pol2 = 7.0 / 240.0; // BernoulliPoly(4, 0.5);
      double pol3 = 1.0 / 42.0; // BernoulliPoly(6, 0);
      double pol4 = -31.0 / 1344.0; // BernoulliPoly(6, 0.5);
 
      double prod = 1.0;
      double temp;
      for (int r = 0; r < s; ++r) {
         temp = C1[r] * (pol1 - pol2) + C2[r] * (7.0 * pol1 - 2.0 * pol2) + C3[r] * (pol3 - pol4);
         prod *= 1.0 - temp;
      }
      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 - 2.0) * u + 1.0) * u * u - UNTRENTE; // Bernoulli(4,u)
               double v = u - 0.5;
               if (v < 0.0)
                  v += 1.0;
               pol2 = ((v - 2.0) * v + 1.0) * v * v - UNTRENTE; // Bernoulli(4,v)
 
               // Bernoulli (6, u) and Bernoulli (6, v)
               pol3 = (((u - 3.0) * u + 2.5) * u * u - 0.5) * u * u + QUARAN;
               pol4 = (((v - 3.0) * v + 2.5) * v * v - 0.5) * v * v + QUARAN;
 
               temp = C1[r] * (pol1 - pol2) + C2[r] * (7.0 * pol1 - 2.0 * pol2) + C3[r] * (pol3 - pol4);
               prod *= 1.0 - temp;
            }
            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[] C = setC(gamma);
      double C1 = C[0];
      double C2 = C[1];
      double C3 = C[2];
 
      double pol1 = -1.0 / 30.0; // BernoulliPoly(4, 0);
      double pol2 = 7.0 / 240.0; // BernoulliPoly(4, 0.5);
      double temp = C1 * (pol1 - pol2) + C2 * (7.0 * pol1 - 2.0 * pol2) + C3 * (1.0 / 42.0 + 31.0 / 1344.0);
      double disc = -temp / n;
 
      double sum = 0.0;
      for (int i = 0; i < n - 1; ++i) {
         for (int j = i + 1; j < n; ++j) {
            double h = T[i] - T[j];
            if (h < 0.0)
               h += 1.0;
            pol1 = ((h - 2.0) * h + 1.0) * h * h - UNTRENTE; // Bernoulli(4,h)
            double v = h - 0.5;
            if (v < 0.0)
               v += 1.0;
            pol2 = ((v - 2.0) * v + 1.0) * v * v - UNTRENTE; // Bernoulli(4,v)
            temp = C1 * (pol1 - pol2) + C2 * (7.0 * pol1 - 2.0 * pol2);
            // Bernoulli (6, h) and Bernoulli (6, v)
            pol1 = (((h - 3.0) * h + 2.5) * h * h - 0.5) * h * h + QUARAN;
            pol2 = (((v - 3.0) * v + 2.5) * v * v - 0.5) * v * v + QUARAN;
            temp += C3 * (pol1 - pol2);
            sum -= temp;
         }
      }
 
      disc += 2.0 * sum / ((long) n * n);
      if (disc < 0.0)
         return -1.0;
      return Math.sqrt(disc);
   }
 
}