testStatFunc.cxx

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/// test of the statistical functions cdf and quantiles 

//#define NO_MATHCORE

#include "Math/DistFuncMathMore.h"
#ifndef NO_MATHCORE
#include "Math/GSLIntegrator.h"
#include "Math/WrappedFunction.h"
#include "Math/DistFuncMathCore.h"
#endif


#include <iostream>
#include <limits>

using namespace ROOT::Math; 

int compare( std::string name, double v1, double v2, double scale = 2.0) {
  //  ntest = ntest + 1; 

   //std::cout << std::setw(50) << std::left << name << ":\t";   
   
  // numerical double limit for epsilon 
   double eps = scale* std::numeric_limits<double>::epsilon();
   int iret = 0; 
   double delta = v2 - v1;
   double d = 0;
   if (delta < 0 ) delta = - delta; 
   if (v1 == 0 || v2 == 0) { 
      if  (delta > eps ) { 
         iret = 1; 
      }
   }
   // skip case v1 or v2 is infinity
   else { 
      d = v1; 

      if ( v1 < 0) d = -d; 
      // add also case when delta is small by default
      if ( delta/d  > eps && delta > eps ) 
         iret =  1; 
   }

   if (iret == 0) 
      std::cout <<".";
   else { 
      int pr = std::cout.precision (18);
      std::cout << "\nDiscrepancy in " << name.c_str() << "() :\n  " << v1 << " != " << v2 << " discr = " << int(delta/d/eps) 
                << "   (Allowed discrepancy is " << eps  << ")\n\n";
      std::cout.precision (pr);
      //nfail = nfail + 1;
   }
   return iret; 
}



// for functions with one parameters

struct TestFunc1 { 

   typedef double ( * Pdf) ( double, double, double); 
   typedef double ( * Cdf) ( double, double, double); 
   typedef double ( * Quant) ( double, double); 

   // wrappers to pdf to be integrated 
   struct PdfFunction { 
      PdfFunction( Pdf pdf, double p1 ) : fPdf(pdf), fP1(p1) {}
      double operator() ( double x) const { return fPdf(x,fP1,0.0); }
      
      Pdf fPdf; 
      double fP1; 
   };


   TestFunc1( double p1, double s = 2) : 
      scale(s)
   {
      p[0] = p1;
   }

#ifndef NO_MATHCORE // skip cdf test when Mathcore is missing
 
   int testCdf( Pdf f_pdf, Cdf f_cdf, bool c = false) {
      int iret = 0; 
      double val = 1.0; // value used  for testing
      double q1 = f_cdf(val, p[0],0.0);
      // calculate integral of pdf
      PdfFunction f(f_pdf,p[0]); 
      WrappedFunction<PdfFunction> wf(f);
      GSLIntegrator ig(1.E-12,1.E-12,100000);
      ig.SetFunction(wf);
      if (!c) { 
         // lower intergal (cdf) 
         double q2 = ig.IntegralLow(val); 
         // use a larger scale (integral error is 10-9)
         iret |= compare("test _cdf", q1, q2, 1.0E6);
      }
      else { 
         // upper integral (cdf_c)
         double q2 = ig.IntegralUp(val); 
         iret |= compare("test _cdf_c", q1, q2, 1.0E6);
      }
      return iret; 
   }

#endif
   
   int testQuantile (Cdf f_cdf, Quant f_quantile, bool c= false) {
      int iret = 0; 
      double z1,z2,q; 
      z1 = 1.0E-6; 
      for (int i = 0; i < 10; ++i) { 
         q = f_quantile(z1,p[0]); 
         z2 = f_cdf(q, p[0],0.); 
         if (!c) 
            iret |= compare("test quantile", z1, z2, scale);
         else 
            iret |= compare("test quantile_c", z1, z2, scale);
         z1 += 0.1; 
      }
      return iret; 
   } 

   double p[1]; // parameters 
   double scale; 
};

// for functions with two parameters


struct TestFunc2 { 

   typedef double ( * Pdf) ( double, double, double, double); 
   typedef double ( * Cdf) ( double, double, double, double); 
   typedef double ( * Quant) ( double, double, double); 


   struct PdfFunction { 
      PdfFunction( Pdf pdf, double p1, double p2 ) : fPdf(pdf), fP1(p1), fP2(p2) {}
      double operator() ( double x) const { return fPdf(x,fP1,fP2,0.0); }
      
      Pdf fPdf; 
      double fP1; 
      double fP2; 
   };

   TestFunc2( double p1, double p2, double s = 2) : 
      scale(s)
   {
      p[0] = p1,
      p[1] = p2; 
   }

#ifndef NO_MATHCORE // skip cdf test when Mathcore is missing

    int testCdf( Pdf f_pdf, Cdf f_cdf, bool c = false) {
      int iret = 0; 
      double val = 1.0; // value used  for testing
      double q1 = f_cdf(val, p[0],p[1],0.0);
      // calculate integral of pdf
      PdfFunction f(f_pdf,p[0],p[1]); 
      WrappedFunction<PdfFunction> wf(f);
      GSLIntegrator ig(1.E-12,1.E-12,100000);
      ig.SetFunction(wf);
      if (!c) { 
         // lower intergal (cdf) 
         double q2 = ig.IntegralLow(val); 
         // use a larger scale (integral error is 10-9)
         iret |= compare("test _cdf", q1, q2, 1.0E6);
      }
      else { 
         // upper integral (cdf_c)
         double q2 = ig.IntegralUp(val); 
         iret |= compare("test _cdf_c", q1, q2, 1.0E6);
      }
      return iret; 
   }

#endif
   
    int testQuantile (Cdf f_cdf, Quant f_quantile, bool c=false) {
      int iret = 0; 
      double z1,z2,q; 
      z1 = 1.0E-6; 
      for (int i = 0; i < 10; ++i) { 
         q = f_quantile(z1,p[0],p[1]); 
         z2 = f_cdf(q, p[0],p[1],0.0); 
         if (!c) 
            iret |= compare("test quantile", z1, z2, scale);
         else 
            iret |= compare("test quantile_c", z1, z2, scale);
         z1 += 0.1; 
      }
      return iret; 
   } 

   double p[2]; // parameters 
   double scale; 
}; 

void printStatus(int iret) { 
   if (iret == 0) 
      std::cout <<"\t\t\t\t OK" << std::endl;
   else  
      std::cout <<"\t\t\t\t FAILED " << std::endl;
}

#ifndef NO_MATHCORE

#define TESTDIST1(name, p1, s) {\
      int ir = 0; \
      TestFunc1 t(p1,s);\
      ir |= t.testCdf( name ## _pdf , name ## _cdf );\
      ir |= t.testCdf( name ##_pdf , name ##_cdf_c,true);\
      ir |= t.testQuantile( name ## _cdf, name ##_quantile);\
      ir |= t.testQuantile( name ##_cdf_c, name ##_quantile_c,true);\
      printStatus(ir);\
      iret |= ir; }  

#define TESTDIST2(name, p1, p2, s) {\
      int ir = 0; \
      TestFunc2 t(p1,p2,s);\
      ir |= t.testCdf( name ## _pdf , name ## _cdf );\
      ir |= t.testCdf( name ##_pdf , name ##_cdf_c,true);\
      ir |= t.testQuantile( name ## _cdf, name ##_quantile);\
      ir |= t.testQuantile( name ##_cdf_c, name ##_quantile_c,true);\
      printStatus(ir);\
      iret |= ir; }  




#else
// without mathcore pdf are missing so skip cdf test
#define TESTDIST1(name, p1, s) {\
      int ir = 0; \
      TestFunc1 t(p1,s);\
      ir |= t.testQuantile( name ## _cdf, name ##_quantile);\
      ir |= t.testQuantile( name ##_cdf_c, name ##_quantile_c,true);\
      printStatus(ir);\
      iret |= ir; }  

#define TESTDIST2(name, p1, p2, s) {\
      int ir = 0; \
      TestFunc2 t(p1,p2,s);\
      ir |= t.testQuantile( name ## _cdf, name ##_quantile);\
      ir |= t.testQuantile( name ##_cdf_c, name ##_quantile_c,true);\
      printStatus(ir);\
      iret |= ir; }  

#endif

// wrapper for the beta 
double mbeta_pdf(double x, double a, double b, double){ 
   return beta_pdf(x,a,b);
}
double mbeta_cdf(double x, double a, double b, double){ 
   return beta_cdf(x,a,b);
}
double mbeta_cdf_c(double x, double a, double b, double){ 
   return beta_cdf_c(x,a,b);
}
double mbeta_quantile(double x, double a, double b){ 
   return beta_quantile(x,a,b);
}
double mbeta_quantile_c(double x, double a, double b){ 
   return beta_quantile_c(x,a,b);
}


#ifndef NO_MATHCORE

int testPoissonCdf(double mu,double tol) { 
   int iret = 0; 
   for (int i = 0; i < 12; ++i) { 
      double q1 = poisson_cdf(i,mu); 
      double q1c = 1.- poisson_cdf_c(i,mu); 
      double q2 = 0; 
      for (int j = 0; j <= i; ++j) {
         q2 += poisson_pdf(j,mu); 
      }
      iret |= compare("test cdf",q1,q2,tol);
      iret |= compare("test cdf_c",q1c,q2,tol);
   }
   printStatus(iret);   
   return iret; 
}

int testBinomialCdf(double p, int n, double tol) { 
   int iret = 0; 
   for (int i = 0; i < 12; ++i) { 
      double q1 = binomial_cdf(i,p,n); 
      double q1c = 1.- binomial_cdf_c(i,p,n); 
      double q2 = 0; 
      for (int j = 0; j <= i; ++j) {
         q2 += binomial_pdf(j,p,n); 
      }
      iret |= compare("test cdf",q1,q2,tol);
      iret |= compare("test cdf_c",q1c,q2,tol);
   }
   printStatus(iret);   
   return iret; 
}

#endif

int testStatFunc() { 

   int iret = 0; 
   double tol = 2; 


#ifndef NO_MATHCORE

   tol = 8; 
   std::cout << "Poisson distrib. \t: "; 
   double mu = 5; 
   iret |= testPoissonCdf(mu,tol); 

   tol = 32;
   std::cout << "Binomial distrib. \t: "; 
   double p = 0.5; int nt = 9;  
   iret |= testBinomialCdf(p,nt,tol); 

   tol = 2; 
   std::cout << "BreitWigner distrib\t: "; 
   TESTDIST1(breitwigner,1.0,tol);

   std::cout << "Cauchy distribution\t: "; 
   TESTDIST1(cauchy,2.0,tol);

   std::cout << "Exponential distrib\t: "; 
   TESTDIST1(exponential,1.0,tol);

   std::cout << "Gaussian distribution\t: "; 
   TESTDIST1(gaussian,1.0,tol);

   std::cout << "Log-normal distribution\t: "; 
   TESTDIST2(lognormal,1.0,1.0,tol);

   std::cout << "Normal distribution\t: "; 
   TESTDIST1(normal,1.0,tol);

   std::cout << "Uniform distribution\t: "; 
   TESTDIST2(uniform,0.0,10.0,tol);


         
#endif

   std::cout << "Chisquare distribution\t: "; 
   tol = 8; 
   TESTDIST1(chisquared,9.,tol);

   tol = 2; 
   
   std::cout << "F distribution\t\t: "; 
   double n = 5; double m = 6;  
   TESTDIST2(fdistribution,n,m,tol);
   
   std::cout << "Gamma distribution\t: "; 
   double a = 1; double b = 2;  
   TESTDIST2(gamma,a,b,tol);

   std::cout << "t distribution\t\t: "; 
   double nu = 10; 
   TESTDIST1(tdistribution,nu,tol);

   std::cout << "Beta distribution\t: "; 
   a = 2; b = 1;  
   TESTDIST2(mbeta,a,b,tol);



   return iret; 
}
int main() { 

   return testStatFunc();
}

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