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// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 2009
// 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)
#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/special_functions/beta.hpp>
#include <boost/math/tools/stats.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
#ifndef SC_
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#endif
template <class T>
T ibeta_forwarder(T a, T b, T x)
{
T derivative;
boost::math::detail::ibeta_imp(a, b, x, boost::math::policies::policy<>(), false, true, &derivative);
return derivative;
}
template <class Real, class T>
void do_test_beta(const T& data, const char* type_name, const char* test_name)
{
typedef Real value_type;
typedef value_type (*pg)(value_type, value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::ibeta_derivative<value_type, value_type, value_type>;
#else
pg funcp = boost::math::ibeta_derivative;
#endif
boost::math::tools::test_result<value_type> result;
#if !(defined(ERROR_REPORTING_MODE) && !defined(BETA_INC_FUNCTION_TO_TEST))
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test ibeta_derivative against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1, 2),
extract_result<Real>(3));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "beta (incomplete)", test_name);
#endif
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = ibeta_forwarder<value_type>;
#else
funcp = ibeta_forwarder;
#endif
if(boost::math::tools::digits<value_type>() > 40)
{
//
// test ibeta_derivative against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1, 2),
extract_result<Real>(3));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "beta (incomplete, internal call test)", test_name);
}
}
template <class T>
void test_beta(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
//
#if !defined(TEST_DATA) || (TEST_DATA == 1)
# include "ibeta_derivative_small_data.ipp"
do_test_beta<T>(ibeta_derivative_small_data, name, "Incomplete Beta Function Derivative: Small Values");
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 2)
# include "ibeta_derivative_data.ipp"
do_test_beta<T>(ibeta_derivative_data, name, "Incomplete Beta Function Derivative: Medium Values");
#endif
#ifndef __SUNPRO_CC
#if !defined(TEST_DATA) || (TEST_DATA == 3)
# include "ibeta_derivative_large_data.ipp"
do_test_beta<T>(ibeta_derivative_large_data, name, "Incomplete Beta Function Derivative: Large and Diverse Values");
#endif
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 4)
# include "ibeta_derivative_int_data.ipp"
do_test_beta<T>(ibeta_derivative_int_data, name, "Incomplete Beta Function Derivative: Small Integer Values");
#endif
}
template <class T>
void test_spots(T)
{
using std::ldexp;
T tolerance = boost::math::tools::epsilon<T>() * 40000;
BOOST_CHECK_CLOSE(
::boost::math::ibeta_derivative(
static_cast<T>(2),
static_cast<T>(4),
ldexp(static_cast<T>(1), -557)),
static_cast<T>(4.23957586190238472641508753637420672781472122471791800210e-167L), tolerance * 4);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_derivative(
static_cast<T>(2),
static_cast<T>(4.5),
ldexp(static_cast<T>(1), -557)),
static_cast<T>(5.24647512910420109893867082626308082567071751558842352760e-167L), tolerance * 4);
BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_quiet_NaN)
{
T n = std::numeric_limits<T>::quiet_NaN();
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(n, static_cast<T>(2.125), static_cast<T>(0.125)), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(static_cast<T>(2.125), n, static_cast<T>(0.125)), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(static_cast<T>(2.125), static_cast<T>(1.125), n), std::domain_error);
}
BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity)
{
T n = std::numeric_limits<T>::infinity();
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(n, static_cast<T>(2.125), static_cast<T>(0.125)), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(static_cast<T>(2.125), n, static_cast<T>(0.125)), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(static_cast<T>(2.125), static_cast<T>(1.125), n), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(-n, static_cast<T>(2.125), static_cast<T>(0.125)), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(static_cast<T>(2.125), -n, static_cast<T>(0.125)), std::domain_error);
BOOST_MATH_CHECK_THROW(::boost::math::ibeta_derivative(static_cast<T>(2.125), static_cast<T>(1.125), -n), std::domain_error);
}
//
// Some additional tests: some of our internal root finding code uses a "back door" into
// ibeta in order to compute ibeta and it's derivative at the same time, we need to
// exercise the special case handling in there as well as in the public interface
// tested above.
//
T derivative = 0;
boost::math::detail::ibeta_imp(T(1), T(2), T(0), boost::math::policies::policy<>(), false, true, &derivative);
BOOST_CHECK_EQUAL(derivative, T(1));
boost::math::detail::ibeta_imp(T(0.5), T(2), T(0), boost::math::policies::policy<>(), false, true, &derivative);
BOOST_CHECK_GT(derivative, boost::math::tools::max_value<T>() / 3); // any large value will do
BOOST_CHECK_LT(derivative, boost::math::tools::max_value<T>()); // But not so large that arithmetic overflows.
boost::math::detail::ibeta_imp(T(2.5), T(2), T(0), boost::math::policies::policy<>(), false, true, &derivative);
BOOST_CHECK_LT(derivative, boost::math::tools::min_value<T>() * 3); // any small value will do
BOOST_CHECK_GT(derivative, T(0)); // But not zero.
T val = boost::math::detail::ibeta_imp(T(0.5f), T(0.5f), T(0.25), boost::math::policies::policy<>(), false, true, &derivative);
BOOST_CHECK_CLOSE(derivative, static_cast<T>(0.7351051938957227326817686644172925885298486404888542037324880270L), tolerance);
BOOST_CHECK_CLOSE(val, static_cast<T>(0.3333333333333333333333333333333333333333333333333333333333333333L), tolerance);
BOOST_CHECK_CLOSE(boost::math::beta(T(0.5f), T(0.5f), T(0.25)), static_cast<T>(1.0471975511965977461542144610931676280657231331250352736583148641L), tolerance);
//
// Error handling:
//
BOOST_CHECK_THROW(boost::math::ibeta_derivative(T(0), T(2), T(0.5)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ibeta_derivative(T(-1), T(2), T(0.5)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ibeta_derivative(T(1), T(0), T(0.5)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ibeta_derivative(T(1), T(-1), T(0.5)), std::domain_error);
}
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