chi2.cpp

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 *       - Pierre-Henri WUILLEMIN(_at_LIP6)                                 *
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#include <agrum/base/core/math/chi2.h>
 
#ifndef DOXYGEN_SHOULD_SKIP_THIS
 
// constants used by Gary Perlman for his code for computing chi2 critical
// values
#  define GUM_Z_MAX       6.0                           // maximum meaningful z value
#  define GUM_CHI_EPSILON 0.000001                      // accuracy of critchi approximation
#  define GUM_CHI_MAX     99999.0                       // maximum chi square value
#  define GUM_LOG_SQRT_PI 0.5723649429247000870717135   // std::log (std::sqrt (pi))
#  define GUM_I_SQRT_PI   0.5641895835477562869480795   // 1 / std::sqrt (pi)
#  define GUM_BIGX        20.0                          // max value to represent exp (x)
#  define _gum_ex(x)      (((x) < -GUM_BIGX) ? 0.0 : std::exp(x))
 
#endif                                                  /* DOXYGEN_SHOULD_SKIP_THIS */
 
 
namespace gum {
 
  // computes the probability of normal z value (used by the cache)
  double Chi2::_probaZValue_(double z) {
    double y, x, w;
 
    if (z == 0.0) x = 0.0;
    else {
      y = 0.5 * std::fabs(z);
 
      if (y >= (GUM_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;
      }
    }
 
    return (z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5));
  }
 
  // computes the probability of chi2 value (used by the cache)
  double Chi2::probaChi2(double x, Size df) {
    double a, y = 0, s;
    double e, c, z;
    int    even; /* true if df is an even number */
 
    if ((x <= 0.0) || (df < 1)) return (1.0);
 
    a = 0.5 * x;
 
    even = (2 * (df / 2)) == df;
 
    if (df > 1) y = _gum_ex(-a);
 
    s = (even ? y : (2.0 * _probaZValue_(-std::sqrt(x))));
 
    if (df > 2) {
      x = 0.5 * (df - 1.0);
      z = (even ? 1.0 : 0.5);
 
      if (a > GUM_BIGX) {
        e = (even ? 0.0 : GUM_LOG_SQRT_PI);
        c = std::log(a);
 
        while (z <= x) {
          e = std::log(z) + e;
          s += _gum_ex(c * z - a - e);
          z += 1.0;
        }
 
        return (s);
      } else {
        e = (even ? 1.0 : (GUM_I_SQRT_PI / std::sqrt(a)));
        c = 0.0;
 
        while (z <= x) {
          e = e * (a / z);
          c = c + e;
          z += 1.0;
        }
 
        return (c * y + s);
      }
    } else return (s);
  }
 
  // computes the critical value of a given chi2 test
  double Chi2::criticalValue(double proba, Size df) {
    double minchisq = 0.0;
    double maxchisq = GUM_CHI_MAX;
    double chisqval;
 
    if (df == 0) return (0.0);
 
    if (proba <= 0.0) return (maxchisq);
    else if (proba >= 1.0) return (0.0);
 
    chisqval = df / std::sqrt(proba); /* fair first value */
 
    while (maxchisq - minchisq > GUM_CHI_EPSILON) {
      if (probaChi2(chisqval, df) < proba) maxchisq = chisqval;
      else minchisq = chisqval;
 
      chisqval = (maxchisq + minchisq) * 0.5;
    }
 
    return (chisqval);
  }
 
} /* namespace gum */