test_nc_beta.cpp

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     RealType(1),                   // non-centrality param
     RealType(0.25),                // Chi Square statistic
     RealType(0.3658349),           // CDF
     RealType(1-0.3658349),         // Complement of CDF
     RealType(2.184465),            // PDF
     RealType(tolerance));
   test_spot(
     RealType(20),                  // alpha
     RealType(15),                  // beta
     RealType(35),                  // non-centrality param
     RealType(0.75),                // Chi Square statistic
     RealType(0.6994175),           // CDF
     RealType(1-0.6994175),         // Complement of CDF
     RealType(5.576146),            // PDF
     RealType(tolerance));
   test_spot(
     RealType(100),                 // alpha
     RealType(3),                   // beta
     RealType(63),                  // non-centrality param
     RealType(0.95),                // Chi Square statistic
     RealType(0.03529306),          // CDF
     RealType(1-0.03529306),        // Complement of CDF
     RealType(3.637894),            // PDF
     RealType(tolerance));
   test_spot(
     RealType(0.25),                // alpha
     RealType(0.75),                // beta
     RealType(150),                 // non-centrality param
     RealType(0.975),               // Chi Square statistic
     RealType(0.09752216),          // CDF
     RealType(1-0.09752216),        // Complement of CDF
     RealType(8.020935),            // PDF
     RealType(tolerance));

} // template <class RealType>void test_spots(RealType)

template <class T>
T nc_beta_cdf(T a, T b, T nc, T x)
{
   return cdf(boost::math::non_central_beta_distribution<T>(a, b, nc), x);
}

template <class T>
T nc_beta_ccdf(T a, T b, T nc, T x)
{
   return cdf(complement(boost::math::non_central_beta_distribution<T>(a, b, nc), x));
}

template <typename T>
void do_test_nc_chi_squared(T& data, const char* type_name, const char* test)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   std::cout << "Testing: " << test << std::endl;

   value_type (*fp1)(value_type, value_type, value_type, value_type) = nc_beta_cdf;
   boost::math::tools::test_result<value_type> result;

   result = boost::math::tools::test(
      data,
      bind_func(fp1, 0, 1, 2, 3),
      extract_result(4));
   handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "CDF", test);

   fp1 = nc_beta_ccdf;
   result = boost::math::tools::test(
      data,
      bind_func(fp1, 0, 1, 2, 3),
      extract_result(5));
   handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "CCDF", test);

#ifdef TEST_OTHER
   fp1 = other::ncbeta_cdf;
   result = boost::math::tools::test(
      data,
      bind_func(fp1, 0, 1, 2, 3),
      extract_result(4));
   handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "Other::CDF", test);
#endif
   std::cout << std::endl;

}

template <typename T>
void quantile_sanity_check(T& data, const char* type_name, const char* test)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   //
   // Tests with type real_concept take rather too long to run, so
   // for now we'll disable them:
   //
   if(!boost::is_floating_point<value_type>::value)
      return;

   std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;

   //
   // These sanity checks test for a round trip accuracy of one half
   // of the bits in T, unless T is type float, in which case we check
   // for just one decimal digit.  The problem here is the sensitivity
   // of the functions, not their accuracy.  This test data was generated
   // for the forward functions, which means that when it is used as
   // the input to the inverses then it is necessarily inexact.  This rounding
   // of the input is what makes the data unsuitable for use as an accuracy check,
   // and also demonstrates that you can't in general round-trip these functions.
   // It is however a useful sanity check.
   //
   value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
   if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
      precision = 1;   // 1% or two decimal digits, all we can hope for when the input is truncated to float

   for(unsigned i = 0; i < data.size(); ++i)
   {
      //
      // Test case 493 fails at float precision: not enough bits to get
      // us back where we started:
      //
      if((i == 493) && boost::is_same<float, value_type>::value)
         continue;

      if(data[i][4] == 0)
      {
         BOOST_CHECK(0 == quantile(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][4]));
      }
      else if(data[i][4] < 0.9999f)
      {
         value_type p = quantile(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][4]);
         value_type pt = data[i][3];
         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
      }
      if(data[i][5] == 0)
      {
         BOOST_CHECK(1 == quantile(complement(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][5])));
      }
      else if(data[i][5] < 0.9999f)
      {
         value_type p = quantile(complement(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][5]));
         value_type pt = data[i][3];
         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
      }
      if(boost::math::tools::digits<value_type>() > 50)
      {
         //
         // Sanity check mode, accuracy of
         // the mode is at *best* the square root of the accuracy of the PDF:
         //
         value_type m = mode(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]));
         if((m == 1) || (m == 0))
            break;
         value_type p = pdf(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), m);
         if(m * (1 + sqrt(precision) * 10) < 1)
         {
            BOOST_CHECK_EX(pdf(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), m * (1 + sqrt(precision) * 10)) <= p, i);
         }
         if(m * (1 - sqrt(precision)) * 10 > boost::math::tools::min_value<value_type>())
         {
            BOOST_CHECK_EX(pdf(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), m * (1 - sqrt(precision)) * 10) <= p, i);
         }
      }
   }
}

template <typename T>
void test_accuracy(T, const char* type_name)
{
#include "ncbeta.ipp"
    do_test_nc_chi_squared(ncbeta, type_name, "Non Central Beta, medium parameters");
    quantile_sanity_check(ncbeta, type_name, "Non Central Beta, medium parameters");

#include "ncbeta_big.ipp"
    do_test_nc_chi_squared(ncbeta_big, type_name, "Non Central Beta, large parameters");
    // Takes too long to run:
    // quantile_sanity_check(ncbeta_big, type_name, "Non Central Beta, large parameters");
}

int test_main(int, char* [])
{
   BOOST_MATH_CONTROL_FP;
   // Basic sanity-check spot values.
   expected_results();
   // (Parameter value, arbitrarily zero, only communicates the floating point type).
#ifdef TEST_FLOAT
   test_spots(0.0F); // Test float.
#endif
#ifdef TEST_DOUBLE
   test_spots(0.0); // Test double.
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
   test_spots(0.0L); // Test long double.
#endif
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
#ifdef TEST_REAL_CONCEPT
   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
#endif
#endif
#endif

#ifdef TEST_FLOAT
   test_accuracy(0.0F, "float"); // Test float.
#endif
#ifdef TEST_DOUBLE
   test_accuracy(0.0, "double"); // Test double.
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
   test_accuracy(0.0L, "long double"); // Test long double.
#endif
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
#ifdef TEST_REAL_CONCEPT
   test_accuracy(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
#endif
#endif
#endif
   return 0;
} // int test_main(int, char* [])