// test_nc_beta.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)
//
// This must appear *before* any #includes, and precludes pch usage:
//
#define BOOST_MATH_ASSERT_UNDEFINED_POLICY false
#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_beta.hpp> // for chi_squared_distribution
#include <boost/math/distributions/poisson.hpp> // for poisson_distribution
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // for test_main
#include <boost/test/results_collector.hpp>
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "test_ncbeta_hooks.hpp"
#include "table_type.hpp"
#include "test_nc_beta.hpp"
#include <iostream>
using std::cout;
using std::endl;
#include <limits>
using std::numeric_limits;
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
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::tools::digits<long double>() == 64)
{
//
// Allow a small amount of error leakage from long double to double:
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"double", // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 5, 5); // test function
}
if(boost::math::tools::digits<long double>() == 64)
{
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*medium[^|]*", // test data group
"[^|]*", 1200, 500); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 40000, 6000); // test function
}
#endif
//
// Catch all cases come last:
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*medium[^|]*", // test data group
"[^|]*", 1500, 500); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"real_concept", // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 30000, 4000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 20000, 2000); // 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 a, RealType b, RealType lam, RealType x)
{
using namespace boost::math;
RealType term = pdf(poisson_distribution<RealType>(lam/2), 0)
* ibeta_derivative(a, b, x);
RealType sum = term;
int i = 1;
while(term / sum > tools::epsilon<RealType>())
{
term = pdf(poisson_distribution<RealType>(lam/2), i)
* ibeta_derivative(a + i, b, x);
++i;
sum += term;
}
return sum;
}
template <class RealType>
void test_spot(
RealType a, // alpha
RealType b, // beta
RealType ncp, // non-centrality param
RealType cs, // Chi Square statistic
RealType P, // CDF
RealType Q, // Complement of CDF
RealType D, // PDF
RealType tol) // Test tolerance
{
boost::math::non_central_beta_distribution<RealType> dist(a, b, ncp);
BOOST_CHECK_CLOSE(
cdf(dist, cs), P, tol);
//
// Sanity checking using the naive PDF calculation above fails at
// float precision:
//
if(!boost::is_same<float, RealType>::value)
{
BOOST_CHECK_CLOSE(
pdf(dist, cs), naive_pdf(dist.alpha(), dist.beta(), ncp, cs), tol);
}
BOOST_CHECK_CLOSE(
pdf(dist, cs), D, tol);
if((P < 0.99) && (Q < 0.99))
{
//
// We can only check this if P is not too close to 1,
// so that we can guarantee Q is reasonably free of error:
//
BOOST_CHECK_CLOSE(
cdf(complement(dist, cs)), Q, tol);
BOOST_CHECK_CLOSE(
quantile(dist, P), cs, tol * 10);
BOOST_CHECK_CLOSE(
quantile(complement(dist, Q)), cs, tol * 10);
}
}
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
RealType tolerance = (std::max)(
boost::math::tools::epsilon<RealType>() * 100,
(RealType)1e-6) * 100;
RealType abs_tolerance = boost::math::tools::epsilon<RealType>() * 100;
cout << "Tolerance = " << tolerance << "%." << endl;
//
// Spot tests use values computed by the R statistical
// package and the pbeta and dbeta functions:
//
test_spot(
RealType(2), // alpha
RealType(5), // beta
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));
BOOST_MATH_STD_USING
boost::math::non_central_beta_distribution<RealType> dist(100, 3, 63);
BOOST_CHECK_CLOSE(mean(dist), RealType(4.82280451915522329944315287538684030781836554279474240490936e13L) * exp(-RealType(31.5)) * 100 / 103, tolerance);
// Variance only guarantees small absolute error:
BOOST_CHECK_SMALL(variance(dist)
- static_cast<RealType>(RealType(4.85592267707818899235900237275021938334418424134218087127572e13L)
* exp(RealType(-31.5)) * 100 * 101 / (103 * 104) -
RealType(4.82280451915522329944315287538684030781836554279474240490936e13L) * RealType(4.82280451915522329944315287538684030781836554279474240490936e13L)
* exp(RealType(-63)) * 10000 / (103 * 103)), abs_tolerance);
BOOST_MATH_CHECK_THROW(skewness(dist), boost::math::evaluation_error);
BOOST_MATH_CHECK_THROW(kurtosis(dist), boost::math::evaluation_error);
BOOST_MATH_CHECK_THROW(kurtosis_excess(dist), boost::math::evaluation_error);
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
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
} // BOOST_AUTO_TEST_CASE( test_main )