| // 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/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 "test_beta_hooks.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 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::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_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, "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_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, "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_hetero<Real>( |
| data, |
| bind_func<Real>(funcp, 0, 1, 2), |
| extract_result<Real>(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_hetero<Real>( |
| data, |
| bind_func<Real>(funcp, 0, 1, 2), |
| extract_result<Real>(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_hetero<Real>( |
| data, |
| bind_func<Real>(funcp, 0, 1, 2), |
| extract_result<Real>(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<T>(ibeta_small_data, name, "Incomplete Beta Function: Small Values"); |
| #endif |
| |
| #if !defined(TEST_DATA) || (TEST_DATA == 2) |
| # include "ibeta_data.ipp" |
| |
| do_test_beta<T>(ibeta_data, name, "Incomplete Beta Function: Medium Values"); |
| |
| #endif |
| #if !defined(TEST_DATA) || (TEST_DATA == 3) |
| # include "ibeta_large_data.ipp" |
| |
| do_test_beta<T>(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<T>(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: |
| // Spot values are from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized |
| // using precision of 50 decimal digits. |
| 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); |
| |
| // |
| // a = b = 0.5 is a special case: |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(0.5f), |
| static_cast<T>(0.5f), |
| static_cast<T>(0.25)), |
| static_cast<T>(1) / 3, tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibetac( |
| static_cast<T>(0.5f), |
| static_cast<T>(0.5f), |
| static_cast<T>(0.25)), |
| static_cast<T>(2) / 3, tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(0.5f), |
| static_cast<T>(0.5f), |
| static_cast<T>(0.125)), |
| static_cast<T>(0.230053456162615885213780567705142893009911395270714102055874L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibetac( |
| static_cast<T>(0.5f), |
| static_cast<T>(0.5f), |
| static_cast<T>(0.125)), |
| static_cast<T>(0.769946543837384114786219432294857106990088604729285897944125L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(0.5f), |
| static_cast<T>(0.5f), |
| static_cast<T>(0.825L)), |
| static_cast<T>(0.725231121519469565327291851560156562956885802608457839260161L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibetac( |
| static_cast<T>(0.5f), |
| static_cast<T>(0.5f), |
| static_cast<T>(0.825L)), |
| static_cast<T>(0.274768878480530434672708148439843437043114197391542160739838L), tolerance); |
| // |
| // Second argument is 1 is a special case, see http://functions.wolfram.com/GammaBetaErf/BetaRegularized/03/01/01/ |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(0.5f), |
| static_cast<T>(1), |
| static_cast<T>(0.825L)), |
| static_cast<T>(0.908295106229247499626759842915458109758420750043003849691665L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibetac( |
| static_cast<T>(0.5f), |
| static_cast<T>(1), |
| static_cast<T>(0.825L)), |
| static_cast<T>(0.091704893770752500373240157084541890241579249956996150308334L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(30), |
| static_cast<T>(1), |
| static_cast<T>(0.825L)), |
| static_cast<T>(0.003116150729395132012981654047222541793435357905008020740211L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibetac( |
| static_cast<T>(30), |
| static_cast<T>(1), |
| static_cast<T>(0.825L)), |
| static_cast<T>(0.996883849270604867987018345952777458206564642094991979259788L), tolerance); |
| |
| // |
| // Bug cases from Rocco Romeo: |
| // |
| BOOST_CHECK_CLOSE( |
| ::boost::math::beta( |
| static_cast<T>(2), |
| static_cast<T>(24), |
| ldexp(static_cast<T>(1), -52)), |
| static_cast<T>(2.46519032881565349871772482100516780410072110983579277754743e-32L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(2), |
| static_cast<T>(24), |
| ldexp(static_cast<T>(1), -52)), |
| static_cast<T>(1.47911419728939209923063489260310068246043266590147566652846e-29L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::beta( |
| static_cast<T>(3), |
| static_cast<T>(2), |
| ldexp(static_cast<T>(1), -270)), |
| static_cast<T>(4.88182556606650701438035298707052523938789614661168065734809e-245L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::beta( |
| static_cast<T>(2), |
| static_cast<T>(31), |
| ldexp(static_cast<T>(1), -373)), |
| static_cast<T>(1.35080680244581673116149460571129957689952846520037541640260e-225L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(3), |
| static_cast<T>(2), |
| ldexp(static_cast<T>(1), -270)), |
| static_cast<T>(5.85819067927980841725642358448463028726547537593401678881771e-244L), tolerance); |
| BOOST_CHECK_CLOSE( |
| ::boost::math::ibeta( |
| static_cast<T>(2), |
| static_cast<T>(31), |
| ldexp(static_cast<T>(1), -373)), |
| static_cast<T>(1.34000034802625019731220264886560918028433223747877241307138e-222L), tolerance); |
| } |
| |
