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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/math_fwd.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 Real, class T>
void test_inverses(const T& data)
{
using namespace std;
//typedef typename T::value_type row_type;
typedef Real value_type;
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
for(unsigned i = 0; i < data.size(); ++i)
{
//
// These inverse tests are thrown off if the output of the
// incomplete beta is too close to 1: basically there is insuffient
// information left in the value we're using as input to the inverse
// to be able to get back to the original value.
//
if(Real(data[i][5]) == 0)
BOOST_CHECK_EQUAL(boost::math::ibeta_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
else if((1 - Real(data[i][5]) > 0.001)
&& (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<value_type>())
&& (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<double>()))
{
value_type inv = boost::math::ibeta_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
BOOST_CHECK_CLOSE(Real(data[i][2]), inv, precision);
}
else if(1 == Real(data[i][5]))
BOOST_CHECK_EQUAL(boost::math::ibeta_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
if(Real(data[i][6]) == 0)
BOOST_CHECK_EQUAL(boost::math::ibetac_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][6])), value_type(1));
else if((1 - Real(data[i][6]) > 0.001)
&& (fabs(Real(data[i][6])) > 2 * boost::math::tools::min_value<value_type>())
&& (fabs(Real(data[i][6])) > 2 * boost::math::tools::min_value<double>()))
{
value_type inv = boost::math::ibetac_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][6]));
BOOST_CHECK_CLOSE(Real(data[i][2]), inv, precision);
}
else if(Real(data[i][6]) == 1)
BOOST_CHECK_EQUAL(boost::math::ibetac_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][6])), value_type(0));
}
}
template <class Real, class T>
void test_inverses2(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(IBETA_INV_FUNCTION_TO_TEST))
//typedef typename T::value_type row_type;
typedef Real value_type;
typedef value_type (*pg)(value_type, value_type, value_type);
#ifdef IBETA_INV_FUNCTION_TO_TEST
pg funcp = IBETA_INV_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::ibeta_inv<value_type, value_type, value_type>;
#else
pg funcp = boost::math::ibeta_inv;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test ibeta_inv(T, T, T) 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, "ibeta_inv", test_name);
//
// test ibetac_inv(T, T, T) against data:
//
#ifdef IBETAC_INV_FUNCTION_TO_TEST
funcp = IBETAC_INV_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::ibetac_inv<value_type, value_type, value_type>;
#else
funcp = boost::math::ibetac_inv;
#endif
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1, 2),
extract_result<Real>(4));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "ibetac_inv", test_name);
#endif
}
template <class T>
void test_beta(T, const char* name)
{
#if !defined(ERROR_REPORTING_MODE)
(void)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_small_data.ipp"
test_inverses<T>(ibeta_small_data);
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 2)
# include "ibeta_data.ipp"
test_inverses<T>(ibeta_data);
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 3)
# include "ibeta_large_data.ipp"
test_inverses<T>(ibeta_large_data);
#endif
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 4)
# include "ibeta_inv_data.ipp"
test_inverses2<T>(ibeta_inv_data, name, "Inverse incomplete beta");
#endif
}
template <class T>
void test_spots(T)
{
BOOST_MATH_STD_USING
//
// basic sanity checks, tolerance is 100 epsilon expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 10000;
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(1),
static_cast<T>(2),
static_cast<T>(0.5)),
static_cast<T>(0.29289321881345247559915563789515096071516406231153L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(3),
static_cast<T>(0.5),
static_cast<T>(0.5)),
static_cast<T>(0.92096723292382700385142816696980724853063433975470L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(20.125),
static_cast<T>(0.5),
static_cast<T>(0.5)),
static_cast<T>(0.98862133312917003480022776106012775747685870929920L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(40),
static_cast<T>(80),
static_cast<T>(0.5)),
static_cast<T>(0.33240456430025026300937492802591128972548660643778L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(40),
static_cast<T>(0.5),
ldexp(T(1), -30)),
static_cast<T>(0.624305407878048788716096298053941618358257550305573588792717L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(40),
static_cast<T>(0.5),
static_cast<T>(1 - ldexp(T(1), -30))),
static_cast<T>(0.99999999999999999998286262026583217516676792408012252456039L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(0.5),
static_cast<T>(40),
static_cast<T>(ldexp(T(1), -30))),
static_cast<T>(1.713737973416782483323207591987747543960774485649459249e-20L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(0.5),
static_cast<T>(0.75),
static_cast<T>(ldexp(T(1), -30))),
static_cast<T>(1.245132488513853853809715434621955746959615015005382639e-18L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(0.5),
static_cast<T>(0.5),
static_cast<T>(0.25)),
static_cast<T>(0.1464466094067262377995778189475754803575820311557629L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(0.5),
static_cast<T>(0.5),
static_cast<T>(0.75)),
static_cast<T>(0.853553390593273762200422181052424519642417968844237018294169L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(1),
static_cast<T>(5),
static_cast<T>(0.125)),
static_cast<T>(0.026352819384831863473794894078665766580641189002729204514544L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(5),
static_cast<T>(1),
static_cast<T>(0.125)),
static_cast<T>(0.659753955386447129687000985614820066516734506596709340752903L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(1),
static_cast<T>(0.125),
static_cast<T>(0.125)),
static_cast<T>(0.656391084194183349609374999999999999999999999999999999999999L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta_inv(
static_cast<T>(0.125),
static_cast<T>(1),
static_cast<T>(0.125)),
static_cast<T>(5.960464477539062500000e-8), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibetac_inv(
static_cast<T>(5),
static_cast<T>(1),
static_cast<T>(0.125)),
static_cast<T>(0.973647180615168136526205105921334233419358810997270795485455L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibetac_inv(
static_cast<T>(1),
static_cast<T>(5),
static_cast<T>(0.125)),
static_cast<T>(0.340246044613552870312999014385179933483265493403290659247096L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibetac_inv(
static_cast<T>(0.125),
static_cast<T>(1),
static_cast<T>(0.125)),
static_cast<T>(0.343608915805816650390625000000000000000000000000000000000000L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibetac_inv(
static_cast<T>(1),
static_cast<T>(0.125),
static_cast<T>(0.125)),
static_cast<T>(0.99999994039535522460937500000000000000000000000L), tolerance);
}
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