// 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) // test_rayleigh.cpp #ifdef _MSC_VER # pragma warning(disable: 4127) // conditional expression is constant. # pragma warning(disable: 4100) // unreferenced formal parameter. #endif #include <boost/math/concepts/real_concept.hpp> // for real_concept #include <boost/math/distributions/rayleigh.hpp> using boost::math::rayleigh_distribution; #include <boost/math/tools/test.hpp> #define BOOST_TEST_MAIN #include <boost/test/unit_test.hpp> // Boost.Test #include <boost/test/floating_point_comparison.hpp> #include "test_out_of_range.hpp" #include <iostream> using std::cout; using std::endl; using std::setprecision; template <class RealType> void test_spot(RealType s, RealType x, RealType p, RealType q, RealType tolerance) { BOOST_CHECK_CLOSE( ::boost::math::cdf( rayleigh_distribution<RealType>(s), x), p, tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::cdf( complement(rayleigh_distribution<RealType>(s), x)), q, tolerance); // % // Special extra tests for p and q near to unity. if(p < 0.999) { BOOST_CHECK_CLOSE( ::boost::math::quantile( rayleigh_distribution<RealType>(s), p), x, tolerance); // % } if(q < 0.999) { BOOST_CHECK_CLOSE( ::boost::math::quantile( complement(rayleigh_distribution<RealType>(s), q)), x, tolerance); // % } if(std::numeric_limits<RealType>::has_infinity) { RealType inf = std::numeric_limits<RealType>::infinity(); BOOST_CHECK_EQUAL(pdf(rayleigh_distribution<RealType>(s), inf), 0); BOOST_CHECK_EQUAL(cdf(rayleigh_distribution<RealType>(s), inf), 1); BOOST_CHECK_EQUAL(cdf(complement(rayleigh_distribution<RealType>(s), inf)), 0); } } // void test_spot template <class RealType> void test_spots(RealType T) { using namespace std; // ADL of std names. // Basic sanity checks. // 50 eps as a percentage, up to a maximum of double precision // (that's the limit of our test data: obtained by punching // numbers into a calculator). RealType tolerance = (std::max)( static_cast<RealType>(boost::math::tools::epsilon<double>()), boost::math::tools::epsilon<RealType>()); tolerance *= 10 * 100; // 10 eps as a percent cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl; using namespace boost::math::constants; // Things that are errors: rayleigh_distribution<RealType> dist(0.5); check_out_of_range<rayleigh_distribution<RealType> >(1); BOOST_MATH_CHECK_THROW( quantile(dist, RealType(1.)), // quantile unity should overflow. std::overflow_error); BOOST_MATH_CHECK_THROW( quantile(complement(dist, RealType(0.))), // quantile complement zero should overflow. std::overflow_error); BOOST_MATH_CHECK_THROW( pdf(dist, RealType(-1)), // Bad negative x. std::domain_error); BOOST_MATH_CHECK_THROW( cdf(dist, RealType(-1)), // Bad negative x. std::domain_error); BOOST_MATH_CHECK_THROW( cdf(rayleigh_distribution<RealType>(-1), // bad sigma < 0 RealType(1)), std::domain_error); BOOST_MATH_CHECK_THROW( cdf(rayleigh_distribution<RealType>(0), // bad sigma == 0 RealType(1)), std::domain_error); BOOST_MATH_CHECK_THROW( quantile(dist, RealType(-1)), // negative quantile probability. std::domain_error); BOOST_MATH_CHECK_THROW( quantile(dist, RealType(2)), // > unity quantile probability. std::domain_error); test_spot( static_cast<RealType>(1.L), // sigma static_cast<RealType>(1.L), // x static_cast<RealType>(1 - exp_minus_half<RealType>()), // p static_cast<RealType>(exp_minus_half<RealType>()), // q tolerance); test_spot( static_cast<RealType>(0.5L), // sigma static_cast<RealType>(0.5L), // x static_cast<RealType>(1 - exp_minus_half<RealType>()), // p static_cast<RealType>(exp_minus_half<RealType>()), //q tolerance); test_spot( static_cast<RealType>(3.L), // sigma static_cast<RealType>(3.L), // x static_cast<RealType>(1 - exp_minus_half<RealType>()), // p static_cast<RealType>(exp_minus_half<RealType>()), //q tolerance); BOOST_CHECK_CLOSE( ::boost::math::pdf( rayleigh_distribution<RealType>(1.L), static_cast<RealType>(1.L)), // x static_cast<RealType>(exp_minus_half<RealType>()), // probability. tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::pdf( rayleigh_distribution<RealType>(0.5L), static_cast<RealType>(0.5L)), // x static_cast<RealType>(2 * exp_minus_half<RealType>()), // probability. tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::pdf( rayleigh_distribution<RealType>(2.L), static_cast<RealType>(2.L)), // x static_cast<RealType>(exp_minus_half<RealType>() /2), // probability. tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::mean( rayleigh_distribution<RealType>(1.L)), static_cast<RealType>(root_half_pi<RealType>()), tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::variance( rayleigh_distribution<RealType>(root_two<RealType>())), static_cast<RealType>(four_minus_pi<RealType>()), tolerance * 100); // % BOOST_CHECK_CLOSE( ::boost::math::mode( rayleigh_distribution<RealType>(1.L)), static_cast<RealType>(1.L), tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::median( rayleigh_distribution<RealType>(1.L)), static_cast<RealType>(sqrt(log(4.L))), // sigma * sqrt(log_four) tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::skewness( rayleigh_distribution<RealType>(1.L)), static_cast<RealType>(2.L * root_pi<RealType>()) * (pi<RealType>() - 3) / (pow((4 - pi<RealType>()), static_cast<RealType>(1.5L))), tolerance * 100); // % BOOST_CHECK_CLOSE( ::boost::math::skewness( rayleigh_distribution<RealType>(1.L)), static_cast<RealType>(0.63111065781893713819189935154422777984404221106391L), tolerance * 100); // % BOOST_CHECK_CLOSE( ::boost::math::kurtosis_excess( rayleigh_distribution<RealType>(1.L)), -static_cast<RealType>(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) / ((4 - pi<RealType>()) * (4 - pi<RealType>())), // static_cast<RealType>(0.2450893006876380628486604106197544154170667057995L), tolerance * 1000); // % BOOST_CHECK_CLOSE( ::boost::math::kurtosis( rayleigh_distribution<RealType>(1.L)), static_cast<RealType>(3.2450893006876380628486604106197544154170667057995L), tolerance * 100); // % BOOST_CHECK_CLOSE( ::boost::math::kurtosis_excess(rayleigh_distribution<RealType>(2)), ::boost::math::kurtosis(rayleigh_distribution<RealType>(2)) -3, tolerance* 100); // % return; } // template <class RealType>void test_spots(RealType) BOOST_AUTO_TEST_CASE( test_main ) { // Check that can generate rayleigh distribution using the two convenience methods: boost::math::rayleigh ray1(1.); // Using typedef rayleigh_distribution<> ray2(1.); // Using default RealType double. using namespace boost::math::constants; // Basic sanity-check spot values. // Double only tests. BOOST_CHECK_CLOSE_FRACTION( ::boost::math::pdf( rayleigh_distribution<double>(1.), static_cast<double>(1)), // x static_cast<double>(exp_minus_half<double>()), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::pdf( rayleigh_distribution<double>(0.5), static_cast<double>(0.5)), // x static_cast<double>(2 * exp_minus_half<double>()), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::pdf( rayleigh_distribution<double>(2.), static_cast<double>(2)), // x static_cast<double>(exp_minus_half<double>() /2 ), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::cdf( rayleigh_distribution<double>(1.), static_cast<double>(1)), // x static_cast<double>(1- exp_minus_half<double>()), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::cdf( rayleigh_distribution<double>(2.), static_cast<double>(2)), // x static_cast<double>(1- exp_minus_half<double>()), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::cdf( rayleigh_distribution<double>(3.), static_cast<double>(3)), // x static_cast<double>(1- exp_minus_half<double>()), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::cdf( rayleigh_distribution<double>(4.), static_cast<double>(4)), // x static_cast<double>(1- exp_minus_half<double>()), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::cdf(complement( rayleigh_distribution<double>(4.), static_cast<double>(4))), // x static_cast<double>(exp_minus_half<double>()), // q = 1 - p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::quantile( rayleigh_distribution<double>(4.), static_cast<double>(1- exp_minus_half<double>())), // x static_cast<double>(4), // p 1e-15); // % BOOST_CHECK_CLOSE_FRACTION( ::boost::math::quantile(complement( rayleigh_distribution<double>(4.), static_cast<double>(exp_minus_half<double>()))), // x static_cast<double>(4), // p 1e-15); // % // (Parameter value, arbitrarily zero, only communicates the floating point type). test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 % test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 % #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS test_spots(0.0L); // Test long double. #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) test_spots(boost::math::concepts::real_concept(0.)); // Test 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::endl; #endif } // BOOST_AUTO_TEST_CASE( test_main ) /* Output is: Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_rayleigh.exe" Running 1 test case... Tolerance for type float is 0.000119209 % Tolerance for type double is 2.22045e-013 % Tolerance for type long double is 2.22045e-013 % Tolerance for type class boost::math::concepts::real_concept is 2.22045e-013 % *** No errors detected */