code: ///////////////////////////////////////////////////////////////////////////////
  // For information as to what this class does, see the Javadoc, below.       //
  // Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,       //
  // 2007, 2008, 2009, 2010, 2014, 2015 by Peter Spirtes, Richard Scheines, Joseph   //
  // Ramsey, and Clark Glymour.                                                //
  //                                                                           //
  // This program is free software; you can redistribute it and/or modify      //
  // it under the terms of the GNU General Public License as published by      //
  // the Free Software Foundation; either version 2 of the License, or         //
  // (at your option) any later version.                                       //
  //                                                                           //
  // This program 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.                              //
  //                                                                           //
  // You should have received a copy of the GNU General Public License         //
  // along with this program; if not, write to the Free Software               //
  // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
  ///////////////////////////////////////////////////////////////////////////////
  
  package edu.cmu.tetrad.util;
  
  /**
   * Some extra mathematical functions not contained in java.lang.Math.
   *
   * @author Joseph Ramsey
   */
  public class MathUtils {
  
      /**
       * @param x a double value.
       * @return the logistic function of x = 1 / (1 + exp(-x)).
       */
      public static double logistic(double x) {
          return 1. / (1. + Math.exp(-x));
      }
  
      public static int factorial(int n) {
          int i = 1;
  
          for (int j = 1; j <= n; j++) {
              i *= j;
          }
  
          return i;
      }
  
      public static double logFactorial(int n) {
          double i = 0;
  
          for (int j = 1; j <= n; j++) {
              i += Math.log(j);
          }
  
          return i;
      }
  
      public static int choose(int a, int b) {
          if (a == 0 && b == 0) {
              return 1;
          } else if (a == 0 && b > 0) {
              return (int) Math.round(Math.exp(1 - (logFactorial(b) + logFactorial(a - b))));
          } else if (a > 0 && b == 0) {
              return (int) Math.round(Math.exp(logFactorial(a) - (1 + logFactorial(a - b))));
          } else if (a > 0 && b > 0) {
              return (int) Math.round(Math.exp(logFactorial(a) - (logFactorial(b) + logFactorial(a - b))));
          } else {
              throw new IllegalArgumentException();
          }
      }
  
      public static double logChoose(int a, int b) {
          return logFactorial(a) - (logFactorial(b) + logFactorial(a - b));
      }
  }
  
  
  
  