test_nc_t.cpp

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// test_nc_t.cpp

// Copyright John Maddock 2008.

// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifdef _MSC_VER
#pragma warning (disable:4127 4512)
#endif

#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
#  define TEST_FLOAT
#  define TEST_DOUBLE
#  define TEST_LDOUBLE
#  define TEST_REAL_CONCEPT
#endif

#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/distributions/non_central_t.hpp> // for chi_squared_distribution
#include <boost/test/included/test_exec_monitor.hpp> // for test_main
#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE

#include "functor.hpp"
#include "handle_test_result.hpp"

#include <iostream>
using std::cout;
using std::endl;
#include <limits>
using std::numeric_limits;

#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
   {\
      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
      BOOST_CHECK_CLOSE(a, b, prec); \
      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
      {\
         std::cerr << "Failure was at row " << i << std::endl;\
         std::cerr << std::setprecision(35); \
         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
      }\
   }

#define BOOST_CHECK_EX(a, i) \
   {\
      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
      BOOST_CHECK(a); \
      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
      {\
         std::cerr << "Failure was at row " << i << std::endl;\
         std::cerr << std::setprecision(35); \
         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
      }\
   }

void expected_results()
{
   //
   // Define the max and mean errors expected for
   // various compilers and platforms.
   //
   const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
   {
      largest_type = "(long\\s+)?double|real_concept";
   }
   else
   {
      largest_type = "long double|real_concept";
   }
#else
   largest_type = "(long\\s+)?double|real_concept";
#endif

   //
   // Catch all cases come last:
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "[^|]*",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*",                          // test data group
      "[^|]*", 300000, 100000);                // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "[^|]*",                          // platform
      largest_type,                     // test type(s)
      "[^|]*",                          // test data group
      "[^|]*", 250, 50);                // test function

   //
   // Finish off by printing out the compiler/stdlib/platform names,
   // we do this to make it easier to mark up expected error rates.
   //
   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}

template <class RealType>
RealType naive_pdf(RealType v, RealType delta, RealType x)
{
}

template <class RealType>
RealType naive_mean(RealType v, RealType delta)
{
   using boost::math::tgamma;
   return delta * sqrt(v / 2) * tgamma((v-1)/2) / tgamma(v/2);
}

float naive_mean(float v, float delta)
{
   return (float)naive_mean((double)v, (double)delta);
}

template <class RealType>
RealType naive_variance(RealType v, RealType delta)
{
   using boost::math::tgamma;
   RealType r = tgamma((v-1)/2) / tgamma(v/2);
   r *= r;
   r *= -delta * delta * v / 2;
   r += (1 + delta * delta) * v / (v - 2);
   return r;
}

float naive_variance(float v, float delta)
{
   return (float)naive_variance((double)v, (double)delta);
}

template <class RealType>
RealType naive_skewness(RealType v, RealType delta)
{
   using boost::math::tgamma;
   RealType tgr = tgamma((v-1)/2) / tgamma(v / 2);
   RealType r = delta * sqrt(v) * tgamma((v-1)/2)
      * (v * (-3 + delta * delta + 2 * v) / ((-3 + v) * (-2 + v)) 
         - 2 * ((1 + delta * delta) * v / (-2 + v) - delta * delta * v * tgr * tgr / 2));
   r /= boost::math::constants::root_two<RealType>()
      * pow(((1+delta*delta) * v / (-2+v) - delta*delta*v*tgr*tgr/2), RealType(1.5f))
      * tgamma(v/2);
   return r;
}

float naive_skewness(float v, float delta)
{
   return (float)naive_skewness((double)v, (double)delta);
}

template <class RealType>
RealType naive_kurtosis_excess(RealType v, RealType delta)
{
   using boost::math::tgamma;
   RealType tgr = tgamma((v-1)/2) / tgamma(v / 2);
   RealType r = -delta * delta * v * tgr * tgr / 2;
   r *= v * (delta * delta * (1 + v) + 3 * (-5 + 3 * v)) / ((-3 + v)*(-2+v))
      - 3 * ((1 + delta * delta) * v / (-2 + v) - delta * delta * v * tgr * tgr / 2);
   r += (3 + 6 * delta * delta + delta * delta * delta * delta)* v * v 
      / ((-4+v) * (-2+v));
   r /= (1+delta*delta)*v / (-2+v) - delta*delta*v *tgr*tgr/2;
   r /= (1+delta*delta)*v / (-2+v) - delta*delta*v *tgr*tgr/2;
   return r;
}

float naive_kurtosis_excess(float v, float delta)
{
   return (float)naive_kurtosis_excess((double)v, (double)delta);
}

template <class RealType>
void test_spot(
     RealType df,    // Degrees of freedom
     RealType ncp,   // non-centrality param
     RealType t,     // T statistic
     RealType P,     // CDF
     RealType Q,     // Complement of CDF
     RealType tol)   // Test tolerance
{
   boost::math::non_central_t_distribution<RealType> dist(df, ncp);
   BOOST_CHECK_CLOSE(
      cdf(dist, t), P, tol);
   try{
      BOOST_CHECK_CLOSE(
         mean(dist), naive_mean(df, ncp), tol);
      BOOST_CHECK_CLOSE(
         variance(dist), naive_variance(df, ncp), tol);
      BOOST_CHECK_CLOSE(
         skewness(dist), naive_skewness(df, ncp), tol * 10);
      BOOST_CHECK_CLOSE(
         kurtosis_excess(dist), naive_kurtosis_excess(df, ncp), tol * 50);
      BOOST_CHECK_CLOSE(
         kurtosis(dist), 3 + naive_kurtosis_excess(df, ncp), tol * 50);
   }
   catch(const std::domain_error&)
   {
   }
   /*
   BOOST_CHECK_CLOSE(
      pdf(dist, t), naive_pdf(dist.degrees_of_freedom(), ncp, t), tol * 50);
   */
   if((P < 0.99) && (Q < 0.99))
   {
      //
      // We can only check this if P is not too close to 1,
      // so that we can guarentee Q is reasonably free of error:
      //
      BOOST_CHECK_CLOSE(
         cdf(complement(dist, t)), Q, tol);
      BOOST_CHECK_CLOSE(
            quantile(dist, P), t, tol * 10);
      BOOST_CHECK_CLOSE(
            quantile(complement(dist, Q)), t, tol * 10);
      /*
      BOOST_CHECK_CLOSE(
         dist.find_degrees_of_freedom(ncp, t, P), df, tol * 10);
      BOOST_CHECK_CLOSE(
         dist.find_degrees_of_freedom(boost::math::complement(ncp, t, Q)), df, tol * 10);
      BOOST_CHECK_CLOSE(
         dist.find_non_centrality(df, t, P), ncp, tol * 10);
      BOOST_CHECK_CLOSE(
         dist.find_non_centrality(boost::math::complement(df, t, Q)), ncp, tol * 10);
         */
   }
}

template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
   //
   // Approx limit of test data is 12 digits expressed here as a persentage:
   //
   RealType tolerance = (std::max)(
      boost::math::tools::epsilon<RealType>(),
      (RealType)5e-12f) * 100;
   //
   // At float precision we need to up the tolerance, since 
   // the input values are rounded off to inexact quantities
   // the results get thrown off by a noticeable amount.
   //
   if(boost::math::tools::digits<RealType>() < 50)
      tolerance *= 50;
   if(boost::is_floating_point<RealType>::value != 1)
      tolerance *= 20; // real_concept special functions are less accurate

   cout << "Tolerance = " << tolerance << "%." << endl;

   //
   // Test data is taken from:
   //
   // Computing discrete mixtures of continuous
   // distributions: noncentral chisquare, noncentral t
   // and the distribution of the square of the sample
   // multiple correlation coeficient.