chiSquare.cpp

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 *       - Pierre-Henri WUILLEMIN(_at_LIP6)                                 *
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// =========================================================================
#include <agrum/FMDP/learning/core/chiSquare.h>
 
#include <agrum/base/core/math/math_utils.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;