blob: 550e2087e58b04f5a5dce459c19b24da074c77b7 [file] [log] [blame]
// (C) Copyright John Maddock 2006.
// 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 <pch.hpp>
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/test_exec_monitor.hpp>
#include <boost/test/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 "test_beta_hooks.hpp"
#include "handle_test_result.hpp"
#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
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the incomplete beta functions beta,
// betac, ibeta and ibetac. There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
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";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// Darwin: just one special case for real_concept:
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"Mac OS", // platform
"real_concept", // test type(s)
"(?i).*large.*", // test data group
".*", 400000, 50000); // test function
//
// Linux - results depend quite a bit on the
// processor type, and how good the std::pow
// function is for that processor.
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"linux", // platform
largest_type, // test type(s)
"(?i).*small.*", // test data group
".*", 350, 100); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"linux", // platform
largest_type, // test type(s)
"(?i).*medium.*", // test data group
".*", 300, 80); // test function
//
// Deficiencies in pow function really kick in here for
// large arguments. Note also that the tests here get
// *very* extreme due to the increased exponent range
// of 80-bit long doubles. Also effect Mac OS.
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"linux|Mac OS", // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 200000, 10000); // test function
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"linux|Mac OS|Sun.*", // platform
"double", // test type(s)
"(?i).*large.*", // test data group
".*", 40, 20); // test function
#endif
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"linux|Mac OS", // platform
"real_concept", // test type(s)
"(?i).*medium.*", // test data group
".*", 350, 100); // test function
//
// HP-UX:
//
// Large value tests include some with *very* extreme
// results, thanks to the large exponent range of
// 128-bit long doubles.
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 200000, 10000); // test function
//
// Tru64:
//
add_expected_result(
".*Tru64.*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 130000, 10000); // test function
//
// Sun OS:
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"Sun.*", // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 130000, 10000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"Sun.*", // platform
largest_type, // test type(s)
"(?i).*small.*", // test data group
".*", 130, 30); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"Sun.*", // platform
largest_type, // test type(s)
"(?i).*medium.*", // test data group
".*", 200, 40); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"Sun.*", // platform
"real_concept", // test type(s)
"(?i).*medium.*", // test data group
".*", 200, 40); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"Sun.*", // platform
"real_concept", // test type(s)
"(?i).*small.*", // test data group
".*", 130, 30); // test function
//
// MinGW:
//
add_expected_result(
"[^|]*mingw[^|]*", // compiler
"[^|]*", // stdlib
".*", // platform
"double", // test type(s)
"(?i).*large.*", // test data group
".*", 20, 10); // test function
add_expected_result(
"[^|]*mingw[^|]*", // compiler
"[^|]*", // stdlib
".*", // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 200000, 10000); // test function
#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
//
// No long doubles:
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
BOOST_PLATFORM, // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 13000, 500); // test function
#endif
//
// Catch all cases come last:
//
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"(?i).*small.*", // test data group
".*", 90, 25); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"(?i).*medium.*", // test data group
".*", 150, 50); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"(?i).*large.*", // test data group
".*", 5000, 500); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"real_concept", // test type(s)
"(?i).*small.*", // test data group
".*", 90, 25); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"real_concept", // test type(s)
"(?i).*medium.*", // test data group
".*", 200, 50); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"real_concept", // test type(s)
"(?i).*large.*", // test data group
".*", 200000, 50000); // test function
// catch all default is 2eps for all types:
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"[^|]*", // test type(s)
"[^|]*", // test data group
".*", 2, 2); // 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 T>
void do_test_beta(const T& data, const char* type_name, const char* test_name)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(value_type, value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::beta<value_type, value_type, value_type>;
#else
pg funcp = boost::math::beta;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test beta against data:
//
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1, 2),
extract_result(3));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::beta", test_name);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::betac<value_type, value_type, value_type>;
#else
funcp = boost::math::betac;
#endif
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1, 2),
extract_result(4));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::betac", test_name);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::ibeta<value_type, value_type, value_type>;
#else
funcp = boost::math::ibeta;
#endif
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1, 2),
extract_result(5));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibeta", test_name);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::ibetac<value_type, value_type, value_type>;
#else
funcp = boost::math::ibetac;
#endif
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1, 2),
extract_result(6));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibetac", test_name);
#ifdef TEST_OTHER
if(::boost::is_floating_point<value_type>::value){
funcp = other::ibeta;
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1, 2),
extract_result(5));
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::ibeta");
}
#endif
std::cout << std::endl;
}
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_small_data.ipp"
do_test_beta(ibeta_small_data, name, "Incomplete Beta Function: Small Values");
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 2)
# include "ibeta_data.ipp"
do_test_beta(ibeta_data, name, "Incomplete Beta Function: Medium Values");
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 3)
# include "ibeta_large_data.ipp"
do_test_beta(ibeta_large_data, name, "Incomplete Beta Function: Large and Diverse Values");
#endif
#if !defined(TEST_DATA) || (TEST_DATA == 4)
# include "ibeta_int_data.ipp"
do_test_beta(ibeta_int_data, name, "Incomplete Beta Function: Small Integer Values");
#endif
}
template <class T>
void test_spots(T)
{
//
// basic sanity checks, tolerance is 30 epsilon expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 3000;
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(159) / 10000, //(0.015964560210704803L),
static_cast<T>(1184) / 1000000000L,//(1.1846856068586931e-005L),
static_cast<T>(6917) / 10000),//(0.69176378846168518L)),
static_cast<T>(0.000075393541456247525676062058821484095548666733251733L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(4243) / 100,//(42.434902191162109L),
static_cast<T>(3001) / 10000, //(0.30012050271034241L),
static_cast<T>(9157) / 10000), //(0.91574394702911377L)),
static_cast<T>(0.0028387319012616013434124297160711532419664289474798L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(9713) / 1000, //(9.7131776809692383L),
static_cast<T>(9940) / 100, //(99.406852722167969L),
static_cast<T>(8391) / 100000), //(0.083912998437881470L)),
static_cast<T>(0.46116895440368248909937863372410093344466819447476L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(72.5),
static_cast<T>(1.125),
static_cast<T>(0.75)),
static_cast<T>(1.3423066982487051710597194786268004978931316494920e-9L), tolerance*3); // extra tolerance needed on linux X86EM64
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(4985)/1000, //(4.9854421615600586L),
static_cast<T>(1066)/1000, //(1.0665277242660522L),
static_cast<T>(7599)/10000), //(0.75997146964073181L)),
static_cast<T>(0.27533431334486812211032939156910472371928659321347L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(6813)/1000, //(6.8127136230468750L),
static_cast<T>(1056)/1000, //(1.0562920570373535L),
static_cast<T>(1741)/10000), //(0.17416560649871826L)),
static_cast<T>(7.6736128722762245852815040810349072461658078840945e-6L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(4898)/10000, //(0.48983201384544373L),
static_cast<T>(2251)/10000, //(0.22512593865394592L),
static_cast<T>(2003)/10000), //(0.20032680034637451L)),
static_cast<T>(0.17089223868046209692215231702890838878342349377008L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(4049)/1000, //(4.0498137474060059L),
static_cast<T>(1540)/10000, //(0.15403440594673157L),
static_cast<T>(6537)/10000), //(0.65370121598243713L)),
static_cast<T>(0.017273988301528087878279199511703371301647583919670L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(7269)/1000, //(7.2695474624633789L),
static_cast<T>(1190)/10000, //(0.11902070045471191L),
static_cast<T>(8003)/10000), //(0.80036874115467072L)),
static_cast<T>(0.013334694467796052900138431733772122625376753696347L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(2726)/1000, //(2.7266697883605957L),
static_cast<T>(1151)/100000, //(0.011510574258863926L),
static_cast<T>(8665)/100000), //(0.086654007434844971L)),
static_cast<T>(5.8218877068298586420691288375690562915515260230173e-6L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(3431)/10000, //(0.34317314624786377L),
static_cast<T>(4634)/100000, //0.046342257410287857L),
static_cast<T>(7582)/10000), //(0.75823287665843964L)),
static_cast<T>(0.15132819929418661038699397753916091907278005695387L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(0.34317314624786377L),
static_cast<T>(0.046342257410287857L),
static_cast<T>(0)),
static_cast<T>(0), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibetac(
static_cast<T>(0.34317314624786377L),
static_cast<T>(0.046342257410287857L),
static_cast<T>(0)),
static_cast<T>(1), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(0.34317314624786377L),
static_cast<T>(0.046342257410287857L),
static_cast<T>(1)),
static_cast<T>(1), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibetac(
static_cast<T>(0.34317314624786377L),
static_cast<T>(0.046342257410287857L),
static_cast<T>(1)),
static_cast<T>(0), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(1),
static_cast<T>(4634)/100000, //(0.046342257410287857L),
static_cast<T>(32)/100),
static_cast<T>(0.017712849440718489999419956301675684844663359595318L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(4634)/100000, //(0.046342257410287857L),
static_cast<T>(1),
static_cast<T>(32)/100),
static_cast<T>(0.94856839398626914764591440181367780660208493234722L), tolerance);
// try with some integer arguments:
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(3),
static_cast<T>(8),
static_cast<T>(0.25)),
static_cast<T>(0.474407196044921875000000000000000000000000000000000000000000L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(6),
static_cast<T>(8),
static_cast<T>(0.25)),
static_cast<T>(0.0802125930786132812500000000000000000000000000000000000000000L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(12),
static_cast<T>(1),
static_cast<T>(0.25)),
static_cast<T>(5.96046447753906250000000000000000000000000000000000000000000e-8L), tolerance);
BOOST_CHECK_CLOSE(
::boost::math::ibeta(
static_cast<T>(1),
static_cast<T>(8),
static_cast<T>(0.25)),
static_cast<T>(0.899887084960937500000000000000000000000000000000000000000000L), tolerance);
// very naive check on derivative:
using namespace std; // For ADL of std functions
tolerance = boost::math::tools::epsilon<T>() * 10000; // 100 eps
BOOST_CHECK_CLOSE(
::boost::math::ibeta_derivative(
static_cast<T>(2),
static_cast<T>(3),
static_cast<T>(0.5)),
pow(static_cast<T>(0.5), static_cast<T>(2)) * pow(static_cast<T>(0.5), static_cast<T>(1)) / boost::math::beta(static_cast<T>(2), static_cast<T>(3)), tolerance);
//
// Special cases and error handling:
//
BOOST_CHECK_EQUAL(::boost::math::ibeta(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), static_cast<T>(1));
BOOST_CHECK_EQUAL(::boost::math::ibeta(static_cast<T>(3), static_cast<T>(0), static_cast<T>(0.5)), static_cast<T>(0));
BOOST_CHECK_EQUAL(::boost::math::ibetac(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), static_cast<T>(0));
BOOST_CHECK_EQUAL(::boost::math::ibetac(static_cast<T>(4), static_cast<T>(0), static_cast<T>(0.5)), static_cast<T>(1));
BOOST_CHECK_THROW(::boost::math::beta(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::beta(static_cast<T>(3), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::betac(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::betac(static_cast<T>(4), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(0), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(-1), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(-2), static_cast<T>(0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(2), static_cast<T>(-0.5)), std::domain_error);
BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(2), static_cast<T>(1.5)), std::domain_error);
}
int test_main(int, char* [])
{
expected_results();
BOOST_MATH_CONTROL_FP;
#ifdef TEST_GSL
gsl_set_error_handler_off();
#endif
#ifdef TEST_FLOAT
test_spots(0.0F);
#endif
#ifdef TEST_DOUBLE
test_spots(0.0);
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
test_spots(0.0L);
#endif
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
#ifdef TEST_REAL_CONCEPT
test_spots(boost::math::concepts::real_concept(0.1));
#endif
#endif
#endif
#ifdef TEST_FLOAT
test_beta(0.1F, "float");
#endif
#ifdef TEST_DOUBLE
test_beta(0.1, "double");
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
test_beta(0.1L, "long double");
#endif
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#ifdef TEST_REAL_CONCEPT
test_beta(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::cout;
#endif
return 0;
}