| // Copyright 2006 John Maddock |
| // Copyright Paul A. Bristow 2007. |
| |
| // 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/ellint_rf.hpp> |
| #include <boost/math/special_functions/ellint_rc.hpp> |
| #include <boost/math/special_functions/ellint_rj.hpp> |
| #include <boost/math/special_functions/ellint_rd.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <boost/array.hpp> |
| #include <boost/tr1/random.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the Carlson Elliptic Integrals. |
| // There are two sets of tests, spot |
| // tests which compare our results with the published test values, |
| // in Numerical Computation of Real or Complex Elliptic Integrals, |
| // B. C. Carlson: http://arxiv.org/abs/math.CA/9409227 |
| // However, the bulk of the accuracy tests |
| // use values generated with NTL::RR at 1000-bit precision |
| // and our generic versions of these functions. |
| // |
| // 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. |
| // |
| 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 |
| // |
| // real long doubles: |
| // |
| if(boost::math::policies::digits<long double, boost::math::policies::policy<> >() > 53) |
| { |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| BOOST_PLATFORM, // platform |
| largest_type, // test type(s) |
| ".*RJ.*", // test data group |
| ".*", 1000, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| BOOST_PLATFORM, // platform |
| "real_concept", // test type(s) |
| ".*RJ.*", // test data group |
| ".*", 1000, 50); // test function |
| } |
| // |
| // Catch all cases come last: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*RJ.*", // test data group |
| ".*", 180, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*RJ.*", // test data group |
| ".*", 180, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 15, 8); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 15, 8); // 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 <typename T> |
| void do_test_ellint_rf(T& data, const char* type_name, const char* test) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| std::cout << "Testing: " << test << std::endl; |
| |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf<value_type, value_type, value_type>; |
| #else |
| value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf; |
| #endif |
| boost::math::tools::test_result<value_type> result; |
| |
| result = boost::math::tools::test( |
| data, |
| bind_func(fp, 0, 1, 2), |
| extract_result(3)); |
| handle_test_result(result, data[result.worst()], result.worst(), |
| type_name, "boost::math::ellint_rf", test); |
| |
| std::cout << std::endl; |
| |
| } |
| |
| template <typename T> |
| void do_test_ellint_rc(T& data, const char* type_name, const char* test) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| std::cout << "Testing: " << test << std::endl; |
| |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| value_type (*fp)(value_type, value_type) = boost::math::ellint_rc<value_type, value_type>; |
| #else |
| value_type (*fp)(value_type, value_type) = boost::math::ellint_rc; |
| #endif |
| boost::math::tools::test_result<value_type> result; |
| |
| result = boost::math::tools::test( |
| data, |
| bind_func(fp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), |
| type_name, "boost::math::ellint_rc", test); |
| |
| std::cout << std::endl; |
| |
| } |
| |
| template <typename T> |
| void do_test_ellint_rj(T& data, const char* type_name, const char* test) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| std::cout << "Testing: " << test << std::endl; |
| |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj<value_type, value_type, value_type, value_type>; |
| #else |
| value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj; |
| #endif |
| boost::math::tools::test_result<value_type> result; |
| |
| result = boost::math::tools::test( |
| data, |
| bind_func(fp, 0, 1, 2, 3), |
| extract_result(4)); |
| handle_test_result(result, data[result.worst()], result.worst(), |
| type_name, "boost::math::ellint_rf", test); |
| |
| std::cout << std::endl; |
| |
| } |
| |
| template <typename T> |
| void do_test_ellint_rd(T& data, const char* type_name, const char* test) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| std::cout << "Testing: " << test << std::endl; |
| |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd<value_type, value_type, value_type>; |
| #else |
| value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd; |
| #endif |
| boost::math::tools::test_result<value_type> result; |
| |
| result = boost::math::tools::test( |
| data, |
| bind_func(fp, 0, 1, 2), |
| extract_result(3)); |
| handle_test_result(result, data[result.worst()], result.worst(), |
| type_name, "boost::math::ellint_rd", test); |
| |
| std::cout << std::endl; |
| |
| } |
| |
| template <typename T> |
| void test_spots(T, const char* type_name) |
| { |
| using namespace boost::math; |
| using namespace std; |
| // Spot values from Numerical Computation of Real or Complex |
| // Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227 |
| // RF: |
| T tolerance = (std::max)(T(1e-13f), tools::epsilon<T>() * 5) * 100; // Note 5eps expressed as a persentage!!! |
| T eps2 = 2 * tools::epsilon<T>(); |
| BOOST_CHECK_CLOSE(ellint_rf(T(1), T(2), T(0)), T(1.3110287771461), tolerance); |
| BOOST_CHECK_CLOSE(ellint_rf(T(0.5), T(1), T(0)), T(1.8540746773014), tolerance); |
| BOOST_CHECK_CLOSE(ellint_rf(T(2), T(3), T(4)), T(0.58408284167715), tolerance); |
| // RC: |
| BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(0), T(1)/4), boost::math::constants::pi<T>(), eps2); |
| BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(9)/4, T(2)), log(T(2)), eps2); |
| BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(1)/4, T(-2)), log(T(2))/3, eps2); |
| // RJ: |
| BOOST_CHECK_CLOSE(ellint_rj(T(0), T(1), T(2), T(3)), T(0.77688623778582), tolerance); |
| BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(5)), T(0.14297579667157), tolerance); |
| BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-0.5)), T(0.24723819703052), tolerance); |
| BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-5)), T(-0.12711230042964), tolerance); |
| // RD: |
| BOOST_CHECK_CLOSE(ellint_rd(T(0), T(2), T(1)), T(1.7972103521034), tolerance); |
| BOOST_CHECK_CLOSE(ellint_rd(T(2), T(3), T(4)), T(0.16510527294261), tolerance); |
| |
| // Sanity/consistency checks from Numerical Computation of Real or Complex |
| // Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227 |
| std::tr1::mt19937 ran; |
| std::tr1::uniform_real<float> ur(0, 1000); |
| T eps40 = 40 * tools::epsilon<T>(); |
| |
| for(unsigned i = 0; i < 1000; ++i) |
| { |
| T x = ur(ran); |
| T y = ur(ran); |
| T z = ur(ran); |
| T lambda = ur(ran); |
| T mu = x * y / lambda; |
| // RF, eq 49: |
| T s1 = ellint_rf(x+lambda, y+lambda, lambda) + |
| ellint_rf(x + mu, y + mu, mu); |
| T s2 = ellint_rf(x, y, T(0)); |
| BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40); |
| // RC is degenerate case of RF: |
| s1 = ellint_rc(x, y); |
| s2 = ellint_rf(x, y, y); |
| BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40); |
| // RC, eq 50 (Note have to assume y = x): |
| T mu2 = x * x / lambda; |
| s1 = ellint_rc(lambda, x+lambda) |
| + ellint_rc(mu2, x + mu2); |
| s2 = ellint_rc(T(0), x); |
| BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40); |
| /* |
| T p = ????; // no closed form for a, b and p??? |
| s1 = ellint_rj(x+lambda, y+lambda, lambda, p+lambda) |
| + ellint_rj(x+mu, y+mu, mu, p+mu); |
| s2 = ellint_rj(x, y, T(0), p) |
| - 3 * ellint_rc(a, b); |
| */ |
| // RD, eq 53: |
| s1 = ellint_rd(lambda, x+lambda, y+lambda) |
| + ellint_rd(mu, x+mu, y+mu); |
| s2 = ellint_rd(T(0), x, y) |
| - 3 / (y * sqrt(x+y+lambda+mu)); |
| BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40); |
| // RD is degenerate case of RJ: |
| s1 = ellint_rd(x, y, z); |
| s2 = ellint_rj(x, y, z, z); |
| BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40); |
| } |
| |
| // |
| // Now random spot values: |
| // |
| #include "ellint_rf_data.ipp" |
| |
| do_test_ellint_rf(ellint_rf_data, type_name, "RF: Random data"); |
| |
| #include "ellint_rc_data.ipp" |
| |
| do_test_ellint_rc(ellint_rc_data, type_name, "RC: Random data"); |
| |
| #include "ellint_rj_data.ipp" |
| |
| do_test_ellint_rj(ellint_rj_data, type_name, "RJ: Random data"); |
| |
| #include "ellint_rd_data.ipp" |
| |
| do_test_ellint_rd(ellint_rd_data, type_name, "RD: Random data"); |
| } |
| |
| int test_main(int, char* []) |
| { |
| expected_results(); |
| BOOST_MATH_CONTROL_FP; |
| |
| boost::math::ellint_rj(1.778e-31, 1.407e+18, 10.05, -4.83e-10); |
| |
| test_spots(0.0F, "float"); |
| test_spots(0.0, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_spots(0.0L, "long double"); |
| #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS |
| test_spots(boost::math::concepts::real_concept(0), "real_concept"); |
| #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; |
| } |
| |
| /* |
| |
| test_carlson.cpp |
| Linking... |
| Embedding manifest... |
| Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_carlson.exe" |
| Running 1 test case... |
| Tests run with Microsoft Visual C++ version 8.0, Dinkumware standard library version 405, Win32 |
| Testing: RF: Random data |
| boost::math::ellint_rf<float> Max = 0 RMS Mean=0 |
| Testing: RC: Random data |
| boost::math::ellint_rc<float> Max = 0 RMS Mean=0 |
| Testing: RJ: Random data |
| boost::math::ellint_rf<float> Max = 0 RMS Mean=0 |
| Testing: RD: Random data |
| boost::math::ellint_rd<float> Max = 0 RMS Mean=0 |
| Testing: RF: Random data |
| boost::math::ellint_rf<double> Max = 2.949 RMS Mean=0.7498 |
| worst case at row: 377 |
| { 3.418e+025, 2.594e-005, 3.264e-012, 6.169e-012 } |
| Testing: RC: Random data |
| boost::math::ellint_rc<double> Max = 2.396 RMS Mean=0.6283 |
| worst case at row: 10 |
| { 1.97e-029, 3.224e-025, 2.753e+012 } |
| Testing: RJ: Random data |
| boost::math::ellint_rf<double> Max = 152.9 RMS Mean=11.15 |
| worst case at row: 633 |
| { 1.876e+016, 0.000278, 3.796e-006, -4.412e-005, -1.656e-005 } |
| Testing: RD: Random data |
| boost::math::ellint_rd<double> Max = 2.586 RMS Mean=0.8614 |
| worst case at row: 45 |
| { 2.111e-020, 8.757e-026, 1.923e-023, 1.004e+033 } |
| Testing: RF: Random data |
| boost::math::ellint_rf<long double> Max = 2.949 RMS Mean=0.7498 |
| worst case at row: 377 |
| { 3.418e+025, 2.594e-005, 3.264e-012, 6.169e-012 } |
| Testing: RC: Random data |
| boost::math::ellint_rc<long double> Max = 2.396 RMS Mean=0.6283 |
| worst case at row: 10 |
| { 1.97e-029, 3.224e-025, 2.753e+012 } |
| Testing: RJ: Random data |
| boost::math::ellint_rf<long double> Max = 152.9 RMS Mean=11.15 |
| worst case at row: 633 |
| { 1.876e+016, 0.000278, 3.796e-006, -4.412e-005, -1.656e-005 } |
| Testing: RD: Random data |
| boost::math::ellint_rd<long double> Max = 2.586 RMS Mean=0.8614 |
| worst case at row: 45 |
| { 2.111e-020, 8.757e-026, 1.923e-023, 1.004e+033 } |
| Testing: RF: Random data |
| boost::math::ellint_rf<real_concept> Max = 2.949 RMS Mean=0.7498 |
| worst case at row: 377 |
| { 3.418e+025, 2.594e-005, 3.264e-012, 6.169e-012 } |
| Testing: RC: Random data |
| boost::math::ellint_rc<real_concept> Max = 2.396 RMS Mean=0.6283 |
| worst case at row: 10 |
| { 1.97e-029, 3.224e-025, 2.753e+012 } |
| Testing: RJ: Random data |
| boost::math::ellint_rf<real_concept> Max = 152.9 RMS Mean=11.15 |
| worst case at row: 633 |
| { 1.876e+016, 0.000278, 3.796e-006, -4.412e-005, -1.656e-005 } |
| Testing: RD: Random data |
| boost::math::ellint_rd<real_concept> Max = 2.586 RMS Mean=0.8614 |
| worst case at row: 45 |
| { 2.111e-020, 8.757e-026, 1.923e-023, 1.004e+033 } |
| *** No errors detected |
| |
| */ |