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79a8199f9c
Tidied up inverse code and moved files to detail directory. Updated docs and Jamfile. [SVN r3107]
200 lines
6.9 KiB
C++
200 lines
6.9 KiB
C++
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/concepts/real_concept.hpp>
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#include <boost/test/included/test_exec_monitor.hpp>
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/special_functions/beta.hpp>
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#include <boost/math/tools/stats.hpp>
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#include <boost/math/tools/test.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/type_traits/is_floating_point.hpp>
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#include <boost/array.hpp>
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#include <boost/lambda/lambda.hpp>
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#include <boost/lambda/bind.hpp>
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#include "test_beta_hooks.hpp"
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#include "handle_test_result.hpp"
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//
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// DESCRIPTION:
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// ~~~~~~~~~~~~
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//
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// This file tests the incomplete beta function inverses
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// ibeta_inv and ibetac_inv. There are three sets of tests:
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// 1) Spot tests which compare our results with selected values
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// computed using the online special function calculator at
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// functions.wolfram.com,
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// 2) TODO!!!! Accuracy tests use values generated with NTL::RR at
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// 1000-bit precision and our generic versions of these functions.
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// 3) Round trip sanity checks, use the test data for the forward
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// functions, and verify that we can get (approximately) back
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// where we started.
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//
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// Note that when this file is first run on a new platform many of
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// these tests will fail: the default accuracy is 1 epsilon which
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// is too tight for most platforms. In this situation you will
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// need to cast a human eye over the error rates reported and make
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// a judgement as to whether they are acceptable. Either way please
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// report the results to the Boost mailing list. Acceptable rates of
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// error are marked up below as a series of regular expressions that
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// identify the compiler/stdlib/platform/data-type/test-data/test-function
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// along with the maximum expected peek and RMS mean errors for that
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// test.
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//
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void expected_results()
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{
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//
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// Define the max and mean errors expected for
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// various compilers and platforms.
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//
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//
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// Catch all cases come last:
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//
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// TODO!!!!
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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".*", // test type(s)
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"Inverse Erf.*", // test data group
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"boost::math::erfc?_inv", 14, 4); // test function
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//
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// Finish off by printing out the compiler/stdlib/platform names,
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// we do this to make it easier to mark up expected error rates.
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//
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std::cout << "Tests run with " << BOOST_COMPILER << ", "
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<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
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}
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template <class T>
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void test_inverses(const T& data)
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{
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using namespace std;
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::tools::digits<value_type>()/2)) * 100;
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if(boost::math::tools::digits<value_type>() < 50)
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precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated
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for(unsigned i = 0; i < data.size(); ++i)
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{
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//
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// These inverse tests are thrown off if the output of the
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// incomplete beta is too close to 1: basically there is insuffient
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// information left in the value we're using as input to the inverse
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// to be able to get back to the original value.
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//
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if(data[i][5] == 0)
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BOOST_CHECK_EQUAL(boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]), value_type(0));
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else if((1 - data[i][5] > 0.001) && (fabs(data[i][5]) >= boost::math::tools::min_value<value_type>()))
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{
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value_type inv = boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]);
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BOOST_CHECK_CLOSE(data[i][2], inv, precision);
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}
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else if(1 == data[i][5])
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BOOST_CHECK_EQUAL(boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]), value_type(1));
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if(data[i][6] == 0)
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BOOST_CHECK_EQUAL(boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]), value_type(1));
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else if((1 - data[i][6] > 0.001) && (fabs(data[i][6]) >= boost::math::tools::min_value<value_type>()))
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{
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value_type inv = boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]);
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BOOST_CHECK_CLOSE(data[i][2], inv, precision);
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}
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else if(data[i][6] == 1)
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BOOST_CHECK_EQUAL(boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]), value_type(0));
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}
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}
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template <class T>
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void test_beta(T, const char* name)
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{
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//
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// The actual test data is rather verbose, so it's in a separate file
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//
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// The contents are as follows, each row of data contains
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// five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
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//
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# include "ibeta_small_data.ipp"
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test_inverses(ibeta_small_data);
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# include "ibeta_data.ipp"
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test_inverses(ibeta_data);
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# include "ibeta_large_data.ipp"
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test_inverses(ibeta_large_data);
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}
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template <class T>
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void test_spots(T)
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{
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//
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// basic sanity checks, tolerance is 100 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 10000;
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(1),
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static_cast<T>(2),
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static_cast<T>(0.5)),
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static_cast<T>(0.29289321881345247559915563789515096071516406231153L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(3),
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static_cast<T>(0.5),
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static_cast<T>(0.5)),
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static_cast<T>(0.92096723292382700385142816696980724853063433975470L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(20.125),
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static_cast<T>(0.5),
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static_cast<T>(0.5)),
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static_cast<T>(0.98862133312917003480022776106012775747685870929920L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(40),
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static_cast<T>(80),
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static_cast<T>(0.5)),
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static_cast<T>(0.33240456430025026300937492802591128972548660643778L), tolerance);
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}
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int test_main(int, char* [])
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{
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expected_results();
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#ifdef TEST_GSL
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gsl_set_error_handler_off();
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#endif
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test_spots(0.0F);
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test_spots(0.0);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L);
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test_spots(boost::math::concepts::real_concept(0.1));
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#endif
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test_beta(0.1F, "float");
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test_beta(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_beta(0.1L, "long double");
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test_beta(boost::math::concepts::real_concept(0.1), "real_concept");
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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"either because the long double overloads of the usual math functions are "
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"not available at all, or because they are too inaccurate for these tests "
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"to pass.</note>" << std::cout;
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#endif
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return 0;
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}
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