DiscShiftBaker1Lattice.java

/*
 * Class:        DiscShiftBaker1Lattice
 * Description:  computes a discrepancy for the randomly shifted, then baker
                 folded points of an integration lattice
 * 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.Rank1Lattice;

public class DiscShiftBaker1Lattice extends DiscShiftBaker1 {
   static final double TRENTEUN24 = 31.0 / 24.0;
   static final double SEPT24 = 7.0 / 24.0;
 
   private static double computeFactor(double x, double C1, double C2, double C3) {
      // Compute 1 factor of the product with Cr = C[r], r = 1,2,3, and x =
      // Point[i][r]
      // This is a simplified form of computeFactor1.
 
      double pol1; // Bernoulli(4, u) - Bernoulli(4, v)
      double pol2; // 7*Bernoulli(4, u) - 2*Bernoulli(4, v)
      double pol3; // Bernoulli(6, u) - Bernoulli(6, v)
      double temp;
 
      if (x >= 0.5) {
         // v = x - 0.5;
         pol1 = -0.5625 + x * (3.0 - x * (4.5 - 2.0 * x));
         pol2 = -TRENTEUN24 + x * (6.0 - x * (4.0 + x * (6.0 - 5.0 * x)));
         temp = 1.0 + x * (-6.0 + 4.0 * x);
         pol3 = 0.046875 * temp * temp * (4.0 * x - 3.0);
      } else {
         // v = x + 0.5;
         pol1 = -0.0625 + x * x * (1.5 - 2.0 * x);
         pol2 = -SEPT24 + x * x * (8.0 - x * (14.0 - 5.0 * x));
         temp = 1.0 + x * (2.0 - 4.0 * x);
         pol3 = -0.046875 * temp * temp * (4.0 * x - 1.0);
      }
 
      temp = C1 * pol1 + C2 * pol2 + C3 * pol3;
      return temp;
   }

   public DiscShiftBaker1Lattice(double[][] points, int n, int s) {
      super(points, n, s);
   }

   public DiscShiftBaker1Lattice(double[][] points, int n, int s, double[] gamma) {
      super(points, n, s, gamma);
   }

   public DiscShiftBaker1Lattice(int n, int s, double[] gamma) {
      super(n, s, gamma);
   }

   public DiscShiftBaker1Lattice(Rank1Lattice set) {
      super(set);
   }

   public DiscShiftBaker1Lattice() {
   }

   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 prod, fact;
      int r;
 
      double sum = 0.0;
      for (int i = 0; i < n; ++i) {
         prod = 1.0;
         for (r = 0; r < s; ++r) {
            fact = computeFactor(points[i][r], C1[r], C2[r], C3[r]);
            prod *= 1.0 - fact;
         }
         sum += prod;
      }
      double disc = sum / n - 1.0;
      if (disc < 0.0) // Lost all precision: result meaningless
         return -1.0;
      return Math.sqrt(disc);
   }

   public double compute(double[] T, int n) {
      return compute(T, n, 1.);
   }

   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 sum = 0.0;
      for (int i = 0; i < n; ++i) {
         double h = T[i];
         double 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;
         double pol2 = ((v - 2.0) * v + 1.0) * v * v - UNTRENTE; // Bernoulli(4,v)
         double 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;
      }
 
      double disc = sum / n;
      if (disc < 0.0)
         return -1.0;
      return Math.sqrt(disc);
   }
 
}