| // (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 function inverses |
| // ibeta_inv and ibetac_inv. There are three sets of tests: |
| // 1) Spot tests which compare our results with selected values |
| // computed using the online special function calculator at |
| // functions.wolfram.com, |
| // 2) TODO!!!! Accuracy tests use values generated with NTL::RR at |
| // 1000-bit precision and our generic versions of these functions. |
| // 3) Round trip sanity checks, use the test data for the forward |
| // functions, and verify that we can get (approximately) back |
| // where we started. |
| // |
| // 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. |
| // |
| // Note that permitted max errors are really pretty high |
| // at around 10000eps. The reason for this is that even |
| // if the forward function is off by 1eps, it's enough to |
| // throw out the inverse by ~7000eps. In other words the |
| // forward function may flatline, so that many x-values |
| // all map to about the same p. Trying to invert in this |
| // region is almost futile. |
| // |
| 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 |
| |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| // |
| // Linux etc, |
| // Extended exponent range of long double |
| // causes more extreme test cases to be executed: |
| // |
| if(std::numeric_limits<long double>::digits == 64) |
| { |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*", // test data group |
| ".*", 20, 10); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "long double", // test type(s) |
| ".*", // test data group |
| ".*", 200000, 100000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 5000000L, 500000); // test function |
| } |
| #endif |
| // |
| // MinGW, |
| // Extended exponent range of long double |
| // causes more extreme test cases to be executed: |
| // |
| add_expected_result( |
| ".*mingw.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*", // test data group |
| ".*", 10, 10); // test function |
| add_expected_result( |
| ".*mingw.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 300000, 20000); // test function |
| |
| // |
| // HP-UX and Solaris: |
| // Extended exponent range of long double |
| // causes more extreme test cases to be executed: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX|Sun Solaris", // platform |
| "long double", // test type(s) |
| ".*", // test data group |
| ".*", 200000, 100000); // test function |
| |
| // |
| // HP Tru64: |
| // Extended exponent range of long double |
| // causes more extreme test cases to be executed: |
| // |
| add_expected_result( |
| "HP Tru64.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "long double", // test type(s) |
| ".*", // test data group |
| ".*", 200000, 100000); // test function |
| |
| // |
| // Catch all cases come last: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 10000, 1000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 500000, 500000); // 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 test_inverses(const T& data) |
| { |
| using namespace std; |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type 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(data[i][5] == 0) |
| BOOST_CHECK_EQUAL(boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]), value_type(0)); |
| else if((1 - data[i][5] > 0.001) |
| && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<value_type>()) |
| && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<double>())) |
| { |
| value_type inv = boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]); |
| BOOST_CHECK_CLOSE(data[i][2], inv, precision); |
| } |
| else if(1 == data[i][5]) |
| BOOST_CHECK_EQUAL(boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]), value_type(1)); |
| |
| if(data[i][6] == 0) |
| BOOST_CHECK_EQUAL(boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]), value_type(1)); |
| else if((1 - data[i][6] > 0.001) |
| && (fabs(data[i][6]) > 2 * boost::math::tools::min_value<value_type>()) |
| && (fabs(data[i][6]) > 2 * boost::math::tools::min_value<double>())) |
| { |
| value_type inv = boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]); |
| BOOST_CHECK_CLOSE(data[i][2], inv, precision); |
| } |
| else if(data[i][6] == 1) |
| BOOST_CHECK_EQUAL(boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]), value_type(0)); |
| } |
| } |
| |
| template <class T> |
| void test_inverses2(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::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( |
| data, |
| bind_func(funcp, 0, 1, 2), |
| extract_result(3)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibeta_inv", test_name); |
| // |
| // test ibetac_inv(T, T, T) against data: |
| // |
| #if 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( |
| data, |
| bind_func(funcp, 0, 1, 2), |
| extract_result(4)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibetac_inv", test_name); |
| } |
| |
| |
| template <class T> |
| void test_beta(T, const char* name) |
| { |
| (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(ibeta_small_data); |
| #endif |
| |
| #if !defined(TEST_DATA) || (TEST_DATA == 2) |
| # include "ibeta_data.ipp" |
| |
| test_inverses(ibeta_data); |
| #endif |
| |
| #if !defined(TEST_DATA) || (TEST_DATA == 3) |
| # include "ibeta_large_data.ipp" |
| |
| test_inverses(ibeta_large_data); |
| #endif |
| |
| #if !defined(TEST_DATA) || (TEST_DATA == 4) |
| # include "ibeta_inv_data.ipp" |
| |
| test_inverses2(ibeta_inv_data, name, "Inverse incomplete beta"); |
| #endif |
| } |
| |
| template <class T> |
| void test_spots(T) |
| { |
| // |
| // 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); |
| } |
| |
| int test_main(int, char* []) |
| { |
| BOOST_MATH_CONTROL_FP; |
| expected_results(); |
| #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 |
| #ifdef TEST_REAL_CONCEPT |
| test_spots(boost::math::concepts::real_concept(0.1)); |
| #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; |
| } |
| |
| |
| |
| |
