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eec6aaf0a0
Added elliptic integrals plus tests (no docs yet). Added some refs to Remez docs. Added comment about Erlang=gamma distribution. [SVN r3559]
326 lines
12 KiB
C++
326 lines
12 KiB
C++
// Copyright (c) 2006 Xiaogang Zhang
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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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#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
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#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
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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/ellint_rf.hpp>
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#include <boost/math/special_functions/ellint_rc.hpp>
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#include <boost/math/special_functions/ellint_rj.hpp>
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#include <boost/math/special_functions/ellint_rd.hpp>
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#include <boost/math/constants/constants.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 <boost/tr1/random.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 Carlson Elliptic Integrals.
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// There are two sets of tests, spot
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// tests which compare our results with the published test values,
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// in Numerical Computation of Real or Complex Elliptic Integrals,
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// B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
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// However, 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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// HP-UX:
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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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"HP-UX", // platform
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largest_type, // test type(s)
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".*RJ.*", // test data group
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".*", 250, 50); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"HP-UX", // platform
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"real_concept", // test type(s)
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".*RJ.*", // test data group
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".*", 250, 50); // test function
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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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".*RJ.*", // 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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"real_concept", // test type(s)
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".*RJ.*", // 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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".*", // test data group
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".*", 15, 8); // 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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".*", // test data group
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".*", 15, 8); // 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 <typename T>
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void do_test_ellint_rf(T& data, const char* type_name, const char* test)
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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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std::cout << "Testing: " << test << std::endl;
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value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf;
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boost::math::tools::test_result<value_type> result;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp,
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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(),
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type_name, "boost::math::ellint_rf", test);
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std::cout << std::endl;
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}
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template <typename T>
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void do_test_ellint_rc(T& data, const char* type_name, const char* test)
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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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std::cout << "Testing: " << test << std::endl;
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value_type (*fp)(value_type, value_type) = boost::math::ellint_rc;
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boost::math::tools::test_result<value_type> result;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp,
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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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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "boost::math::ellint_rc", test);
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std::cout << std::endl;
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}
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template <typename T>
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void do_test_ellint_rj(T& data, const char* type_name, const char* test)
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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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std::cout << "Testing: " << test << std::endl;
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value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj;
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boost::math::tools::test_result<value_type> result;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp,
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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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boost::lambda::ret<value_type>(boost::lambda::_1[4]));
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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "boost::math::ellint_rf", test);
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std::cout << std::endl;
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}
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template <typename T>
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void do_test_ellint_rd(T& data, const char* type_name, const char* test)
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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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std::cout << "Testing: " << test << std::endl;
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value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd;
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boost::math::tools::test_result<value_type> result;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp,
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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(),
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type_name, "boost::math::ellint_rd", test);
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std::cout << std::endl;
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}
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template <typename T>
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void test_spots(T, const char* type_name)
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{
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using namespace boost::math;
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using namespace std;
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// Spot values from Numerical Computation of Real or Complex
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// Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
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// RF:
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T tolerance = (std::max)(T(1e-13f), tools::epsilon<T>() * 5) * 100; // Note 5eps expressed as a persentage!!!
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T eps2 = 2 * tools::epsilon<T>();
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BOOST_CHECK_CLOSE(ellint_rf(T(1), T(2), T(0)), T(1.3110287771461), tolerance);
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BOOST_CHECK_CLOSE(ellint_rf(T(0.5), T(1), T(0)), T(1.8540746773014), tolerance);
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BOOST_CHECK_CLOSE(ellint_rf(T(2), T(3), T(4)), T(0.58408284167715), tolerance);
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// RC:
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BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(0), T(1)/4), boost::math::constants::pi<T>(), eps2);
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BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(9)/4, T(2)), log(T(2)), eps2);
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BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(1)/4, T(-2)), log(T(2))/3, eps2);
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// RJ:
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BOOST_CHECK_CLOSE(ellint_rj(T(0), T(1), T(2), T(3)), T(0.77688623778582), tolerance);
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BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(5)), T(0.14297579667157), tolerance);
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BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-0.5)), T(0.24723819703052), tolerance);
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BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-5)), T(-0.12711230042964), tolerance);
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// RD:
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BOOST_CHECK_CLOSE(ellint_rd(T(0), T(2), T(1)), T(1.7972103521034), tolerance);
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BOOST_CHECK_CLOSE(ellint_rd(T(2), T(3), T(4)), T(0.16510527294261), tolerance);
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// Sanity/consistency checks from Numerical Computation of Real or Complex
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// Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
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std::tr1::mt19937 ran;
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std::tr1::uniform_real<float> ur(0, 1000);
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T eps40 = 40 * tools::epsilon<T>();
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for(unsigned i = 0; i < 1000; ++i)
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{
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T x = ur(ran);
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T y = ur(ran);
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T z = ur(ran);
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T lambda = ur(ran);
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T mu = x * y / lambda;
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// RF, eq 49:
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T s1 = ellint_rf(x+lambda, y+lambda, lambda) +
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ellint_rf(x + mu, y + mu, mu);
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T s2 = ellint_rf(x, y, T(0));
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BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
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// RC is degenerate case of RF:
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s1 = ellint_rc(x, y);
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s2 = ellint_rf(x, y, y);
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BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
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// RC, eq 50 (Note have to assume y = x):
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T mu2 = x * x / lambda;
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s1 = ellint_rc(lambda, x+lambda)
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+ ellint_rc(mu2, x + mu2);
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s2 = ellint_rc(T(0), x);
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BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
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/*
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T p = ????; // no closed form for a, b and p???
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s1 = ellint_rj(x+lambda, y+lambda, lambda, p+lambda)
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+ ellint_rj(x+mu, y+mu, mu, p+mu);
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s2 = ellint_rj(x, y, T(0), p)
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- 3 * ellint_rc(a, b);
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*/
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// RD, eq 53:
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s1 = ellint_rd(lambda, x+lambda, y+lambda)
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+ ellint_rd(mu, x+mu, y+mu);
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s2 = ellint_rd(T(0), x, y)
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- 3 / (y * sqrt(x+y+lambda+mu));
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BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
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// RD is degenerate case of RJ:
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s1 = ellint_rd(x, y, z);
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s2 = ellint_rj(x, y, z, z);
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BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
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}
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//
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// Now random spot values:
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//
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#include "ellint_rf_data.ipp"
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do_test_ellint_rf(ellint_rf_data, type_name, "RF: Random data");
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#include "ellint_rc_data.ipp"
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do_test_ellint_rc(ellint_rc_data, type_name, "RC: Random data");
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#include "ellint_rj_data.ipp"
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do_test_ellint_rj(ellint_rj_data, type_name, "RJ: Random data");
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#include "ellint_rd_data.ipp"
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do_test_ellint_rd(ellint_rd_data, type_name, "RD: Random data");
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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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test_spots(0.0F, "float");
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test_spots(0.0, "double");
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test_spots(0.0L, "long double");
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test_spots(boost::math::concepts::real_concept(0), "real_concept");
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return 0;
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}
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