mirror of
https://github.com/boostorg/math.git
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46d9b33645
Added docs for roots without derivatives. Added derivatives of incomplete gamma and beta. [SVN r3112]
364 lines
14 KiB
C++
364 lines
14 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 functions beta,
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// betac, ibeta and ibetac. There are two sets of tests, spot
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// tests which compare our results with selected values computed
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// using the online special function calculator at
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// functions.wolfram.com, while the bulk of the accuracy tests
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// use values generated with NTL::RR at 1000-bit precision
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// and our generic versions of these functions.
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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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const char* largest_type;
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
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{
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largest_type = "(long\\s+)?double";
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}
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else
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{
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largest_type = "long double";
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}
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#else
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largest_type = "(long\\s+)?double";
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#endif
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//
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// Catch all cases come last:
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//
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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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largest_type, // test type(s)
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"(?i).*small.*", // test data group
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".*", 20, 10); // test function
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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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largest_type, // test type(s)
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"(?i).*medium.*", // test data group
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".*", 150, 50); // test function
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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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largest_type, // test type(s)
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"(?i).*large.*", // test data group
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".*", 5000, 500); // test function
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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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"real_concept", // test type(s)
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"(?i).*small.*", // test data group
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".*", 30, 15); // test function
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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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"real_concept", // test type(s)
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"(?i).*medium.*", // test data group
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".*", 100, 50); // test function
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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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"real_concept", // test type(s)
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"(?i).*large.*", // test data group
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".*", 200000, 50000); // 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 do_test_beta(const T& data, const char* type_name, const char* test_name)
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{
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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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typedef value_type (*pg)(value_type, value_type, value_type);
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pg funcp = boost::math::beta;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test beta against data:
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//
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]),
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boost::lambda::ret<value_type>(boost::lambda::_1[1]),
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boost::lambda::ret<value_type>(boost::lambda::_1[2])),
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boost::lambda::ret<value_type>(boost::lambda::_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::beta", test_name);
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funcp = boost::math::betac;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]),
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boost::lambda::ret<value_type>(boost::lambda::_1[1]),
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boost::lambda::ret<value_type>(boost::lambda::_1[2])),
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boost::lambda::ret<value_type>(boost::lambda::_1[4]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::betac", test_name);
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funcp = boost::math::ibeta;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]),
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boost::lambda::ret<value_type>(boost::lambda::_1[1]),
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boost::lambda::ret<value_type>(boost::lambda::_1[2])),
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boost::lambda::ret<value_type>(boost::lambda::_1[5]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibeta", test_name);
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funcp = boost::math::ibetac;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]),
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boost::lambda::ret<value_type>(boost::lambda::_1[1]),
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boost::lambda::ret<value_type>(boost::lambda::_1[2])),
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boost::lambda::ret<value_type>(boost::lambda::_1[6]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibetac", test_name);
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#ifdef TEST_OTHER
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if(::boost::is_floating_point<value_type>::value){
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funcp = other::ibeta;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]),
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boost::lambda::ret<value_type>(boost::lambda::_1[1]),
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boost::lambda::ret<value_type>(boost::lambda::_1[2])),
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boost::lambda::ret<value_type>(boost::lambda::_1[5]));
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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::ibeta");
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}
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#endif
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std::cout << std::endl;
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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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do_test_beta(ibeta_small_data, name, "Incomplete Beta Function: Small Values");
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# include "ibeta_data.ipp"
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do_test_beta(ibeta_data, name, "Incomplete Beta Function: Medium Values");
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# include "ibeta_large_data.ipp"
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do_test_beta(ibeta_large_data, name, "Incomplete Beta Function: Large and Diverse Values");
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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 30 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 3000;
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(0.015964560210704803),
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static_cast<T>(1.1846856068586931e-005),
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static_cast<T>(0.69176378846168518)),
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static_cast<T>(0.0007508604820642986204162462167319506309750L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(42.434902191162109),
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static_cast<T>(0.30012050271034241),
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static_cast<T>(0.91574394702911377)),
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static_cast<T>(0.002844243156314242058287766324242276991912L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(9.7131776809692383),
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static_cast<T>(99.406852722167969),
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static_cast<T>(0.083912998437881470)),
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static_cast<T>(0.4612716118626361034813232775095335302198L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(72.5),
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static_cast<T>(1.125),
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static_cast<T>(0.75)),
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static_cast<T>(1.3423066982487051710597194786268004978931316494920e-9L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(4.9854421615600586),
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static_cast<T>(1.0665277242660522),
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static_cast<T>(0.75997146964073181)),
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static_cast<T>(0.2755954254731642667260071858810487404614L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(6.8127136230468750),
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static_cast<T>(1.0562920570373535),
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static_cast<T>(0.17416560649871826)),
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static_cast<T>(7.702362015088558153029455563361002570531e-6L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(0.48983201384544373),
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static_cast<T>(0.22512593865394592),
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static_cast<T>(0.20032680034637451)),
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static_cast<T>(0.170905142698145967653807992508983970176L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(4.0498137474060059),
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static_cast<T>(0.15403440594673157),
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static_cast<T>(0.65370121598243713)),
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static_cast<T>(0.0172702040689452906446803217247250156007L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(7.2695474624633789),
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static_cast<T>(0.11902070045471191),
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static_cast<T>(0.80036874115467072)),
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static_cast<T>(0.013346136714187857821168127038816508028L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(2.7266697883605957),
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static_cast<T>(0.011510574258863926),
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static_cast<T>(0.086654007434844971)),
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static_cast<T>(5.812020420972734916187451486321162137375e-6L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(0.34317314624786377),
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static_cast<T>(0.046342257410287857),
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static_cast<T>(0.75823287665843964)),
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static_cast<T>(0.151317265120184850887504097401768195067L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(0.34317314624786377),
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static_cast<T>(0.046342257410287857),
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static_cast<T>(0)),
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static_cast<T>(0), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibetac(
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static_cast<T>(0.34317314624786377),
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static_cast<T>(0.046342257410287857),
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static_cast<T>(0)),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(0.34317314624786377),
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static_cast<T>(0.046342257410287857),
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static_cast<T>(1)),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibetac(
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static_cast<T>(0.34317314624786377),
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static_cast<T>(0.046342257410287857),
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static_cast<T>(1)),
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static_cast<T>(0), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(1),
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static_cast<T>(0.046342257410287857),
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static_cast<T>(0.32)),
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static_cast<T>(0.0177137046180187568703202426065033413304L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta(
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static_cast<T>(0.046342257410287857),
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static_cast<T>(1),
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static_cast<T>(0.32)),
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static_cast<T>(0.948565954109602496577407403168592262389L), tolerance);
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// very naive check on derivative:
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using namespace std; // For ADL of std functions
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tolerance = boost::math::tools::epsilon<T>() * 10000; // 100 eps
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_derivative(
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static_cast<T>(2),
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static_cast<T>(3),
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static_cast<T>(0.5)),
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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);
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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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