chiSquare.cpp

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/***************************************************************************
 *   Copyright (C) 2005 by Christophe GONZALES and Pierre-Henri WUILLEMIN  *
 *   {prenom.nom}_at_lip6.fr                                               *
 *                                                                         *
 *   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.             *
 ***************************************************************************/
// =========================================================================
#include <agrum/core/math/math.h>
#include <agrum/FMDP/learning/core/chiSquare.h>
// =========================================================================


// constants used by Gary Perlman for his code for computing chi2 critical
// values

namespace gum {

  // ==========================================================================
  // ==========================================================================
  double ChiSquare::__probaZValue(double z) {
    //      ++nbZt;

    //      z = std::round(z * std::pow(10, 3)) / std::pow(10, 3);
    //      if( !__ZCache.exists(z) ){

    double y, x, w;

    if (z == 0.0)
      x = 0.0;
    else {
      y = 0.5 * fabs(z);

      if (y >= (__Z_MAX * 0.5))
        x = 1.0;
      else if (y < 1.0) {
        w = y * y;
        x = ((((((((0.000124818987 * w - 0.001075204047) * w + 0.005198775019) * w
                  - 0.019198292004)
                    * w
                 + 0.059054035642)
                   * w
                - 0.151968751364)
                  * w
               + 0.319152932694)
                 * w
              - 0.531923007300)
                * w
             + 0.797884560593)
            * y * 2.0;
      } else {
        y -= 2.0;
        x =
           (((((((((((((-0.000045255659 * y + 0.000152529290) * y - 0.000019538132)
                         * y
                      - 0.000676904986)
                        * y
                     + 0.001390604284)
                       * y
                    - 0.000794620820)
                      * y
                   - 0.002034254874)
                     * y
                  + 0.006549791214)
                    * y
                 - 0.010557625006)
                   * y
                + 0.011630447319)
                  * y
               - 0.009279453341)
                 * y
              + 0.005353579108)
                * y
             - 0.002141268741)
               * y
            + 0.000535310849)
              * y
           + 0.999936657524;
      }
    }

    //        __ZCache.insert(z, ( z > 0.0 ? (( x + 1.0 ) * 0.5 ) : (( 1.0 - x )
    //        * 0.5 ) ) );
    //      } else {
    //          ++nbZ;
    //        }

    //      return __ZCache[z];
    return (z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5));
  }


  // ==========================================================================
  // ==========================================================================
  double ChiSquare::probaChi2(double x, Size df) {
    double retVal = 0.0;
    //      ++nbChit;

    //      std::pair<double, unsigned long> conty(x, df);
    //      if( !__chi2Cache.exists(conty) ){

    double a, y = 0, s;
    double e, c, z;
    int    even; /* true if df is an even number */

    if ((x <= 0.0) || (df < 1)) {
      //          __chi2Cache.insert(conty,1.0);
      retVal = 1.0;
    } else {
      a = 0.5 * x;

      even = (2 * (df / 2)) == df;

      if (df > 1) y = __exp(-a);

      s = (even ? y : (2.0 * __probaZValue(-sqrt(x))));

      if (df > 2) {
        x = 0.5 * (df - 1.0);
        z = (even ? 1.0 : 0.5);

        if (a > __BIGX) {
          e = (even ? 0.0 : __LOG_SQRT_PI);
          c = log(a);

          while (z <= x) {
            e = log(z) + e;
            s += __exp(c * z - a - e);
            z += 1.0;
          }

          //              __chi2Cache.insert(conty,s);
          retVal = s;

        } else {
          e = (even ? 1.0 : (__I_SQRT_PI / sqrt(a)));
          c = 0.0;

          while (z <= x) {
            e = e * (a / z);
            c = c + e;
            z += 1.0;
          }

          //              __chi2Cache.insert(conty,( c * y + s ));
          retVal = (c * y + s);
        }
      } else {
        //            __chi2Cache.insert(conty,s);
        retVal = s;
      }
    }
    //      } else {
    //          ++nbChi;
    //        }
    //      std::cout << "Z avoid : " << nbZ << " / " << nbZt << ". Chi avoid :
    //      " << nbChi << " / " << nbChit << "." << std::endl;
    //      return __chi2Cache[conty];
    return retVal;
  }

}   // End of namespace gum

// HashTable<std::pair<double, unsigned long>, double> ChiSquare::__chi2Cache;
// HashTable<double, double> ChiSquare::__ZCache;
// Idx ChiSquare::nbZ = 0;
// Idx ChiSquare::nbChi = 0;
// Idx ChiSquare::nbZt = 0;
// Idx ChiSquare::nbChit = 0;