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333 lines
11 KiB
C++
333 lines
11 KiB
C++
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// 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.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// test_rayleigh.cpp
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#ifdef _MSC_VER
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# pragma warning(disable: 4127) // conditional expression is constant.
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# pragma warning(disable: 4100) // unreferenced formal parameter.
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#endif
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#include <boost/math/distributions/rayleigh.hpp>
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using boost::math::rayleigh_distribution;
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#include <boost/math/tools/test.hpp>
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include "test_out_of_range.hpp"
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#include <iostream>
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using std::cout;
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using std::endl;
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using std::setprecision;
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template <class RealType>
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void test_spot(RealType s, RealType x, RealType p, RealType q, RealType tolerance)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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rayleigh_distribution<RealType>(s),
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x),
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p,
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(rayleigh_distribution<RealType>(s),
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x)),
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q,
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tolerance); // %
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// Special extra tests for p and q near to unity.
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if(p < 0.999)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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rayleigh_distribution<RealType>(s),
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p),
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x,
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tolerance); // %
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}
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if(q < 0.999)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(rayleigh_distribution<RealType>(s),
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q)),
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x,
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tolerance); // %
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}
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if(std::numeric_limits<RealType>::has_infinity)
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{
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RealType inf = std::numeric_limits<RealType>::infinity();
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BOOST_CHECK_EQUAL(pdf(rayleigh_distribution<RealType>(s), inf), 0);
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BOOST_CHECK_EQUAL(cdf(rayleigh_distribution<RealType>(s), inf), 1);
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BOOST_CHECK_EQUAL(cdf(complement(rayleigh_distribution<RealType>(s), inf)), 0);
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}
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} // void test_spot
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template <class RealType>
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void test_spots(RealType T)
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{
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using namespace std; // ADL of std names.
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// Basic sanity checks.
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// 50 eps as a percentage, up to a maximum of double precision
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// (that's the limit of our test data: obtained by punching
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// numbers into a calculator).
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RealType tolerance = (std::max)(
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static_cast<RealType>(boost::math::tools::epsilon<double>()),
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boost::math::tools::epsilon<RealType>());
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tolerance *= 10 * 100; // 10 eps as a percent
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cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl;
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using namespace boost::math::constants;
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// Things that are errors:
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rayleigh_distribution<RealType> dist(0.5);
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check_out_of_range<rayleigh_distribution<RealType> >(1);
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BOOST_MATH_CHECK_THROW(
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quantile(dist,
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RealType(1.)), // quantile unity should overflow.
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std::overflow_error);
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BOOST_MATH_CHECK_THROW(
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quantile(complement(dist,
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RealType(0.))), // quantile complement zero should overflow.
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std::overflow_error);
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BOOST_MATH_CHECK_THROW(
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pdf(dist, RealType(-1)), // Bad negative x.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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cdf(dist, RealType(-1)), // Bad negative x.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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cdf(rayleigh_distribution<RealType>(-1), // bad sigma < 0
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RealType(1)),
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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cdf(rayleigh_distribution<RealType>(0), // bad sigma == 0
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RealType(1)),
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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quantile(dist, RealType(-1)), // negative quantile probability.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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quantile(dist, RealType(2)), // > unity quantile probability.
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std::domain_error);
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test_spot(
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static_cast<RealType>(1.L), // sigma
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static_cast<RealType>(1.L), // x
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static_cast<RealType>(1 - exp_minus_half<RealType>()), // p
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static_cast<RealType>(exp_minus_half<RealType>()), // q
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tolerance);
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test_spot(
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static_cast<RealType>(0.5L), // sigma
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static_cast<RealType>(0.5L), // x
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static_cast<RealType>(1 - exp_minus_half<RealType>()), // p
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static_cast<RealType>(exp_minus_half<RealType>()), //q
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tolerance);
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test_spot(
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static_cast<RealType>(3.L), // sigma
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static_cast<RealType>(3.L), // x
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static_cast<RealType>(1 - exp_minus_half<RealType>()), // p
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static_cast<RealType>(exp_minus_half<RealType>()), //q
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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rayleigh_distribution<RealType>(1.L),
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static_cast<RealType>(1.L)), // x
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static_cast<RealType>(exp_minus_half<RealType>()), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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rayleigh_distribution<RealType>(0.5L),
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static_cast<RealType>(0.5L)), // x
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static_cast<RealType>(2 * exp_minus_half<RealType>()), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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rayleigh_distribution<RealType>(2.L),
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static_cast<RealType>(2.L)), // x
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static_cast<RealType>(exp_minus_half<RealType>() /2), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::mean(
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rayleigh_distribution<RealType>(1.L)),
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static_cast<RealType>(root_half_pi<RealType>()),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::variance(
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rayleigh_distribution<RealType>(root_two<RealType>())),
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static_cast<RealType>(four_minus_pi<RealType>()),
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tolerance * 100); // %
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BOOST_CHECK_CLOSE(
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::boost::math::mode(
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rayleigh_distribution<RealType>(1.L)),
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static_cast<RealType>(1.L),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::median(
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rayleigh_distribution<RealType>(1.L)),
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static_cast<RealType>(sqrt(log(4.L))), // sigma * sqrt(log_four)
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::skewness(
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rayleigh_distribution<RealType>(1.L)),
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static_cast<RealType>(2.L * root_pi<RealType>()) * (pi<RealType>() - 3) / (pow((4 - pi<RealType>()), static_cast<RealType>(1.5L))),
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tolerance * 100); // %
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BOOST_CHECK_CLOSE(
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::boost::math::skewness(
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rayleigh_distribution<RealType>(1.L)),
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static_cast<RealType>(0.63111065781893713819189935154422777984404221106391L),
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tolerance * 100); // %
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BOOST_CHECK_CLOSE(
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::boost::math::kurtosis_excess(
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rayleigh_distribution<RealType>(1.L)),
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-static_cast<RealType>(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
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((4 - pi<RealType>()) * (4 - pi<RealType>())),
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// static_cast<RealType>(0.2450893006876380628486604106197544154170667057995L),
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tolerance * 1000); // %
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BOOST_CHECK_CLOSE(
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::boost::math::kurtosis(
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rayleigh_distribution<RealType>(1.L)),
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static_cast<RealType>(3.2450893006876380628486604106197544154170667057995L),
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tolerance * 100); // %
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BOOST_CHECK_CLOSE(
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::boost::math::kurtosis_excess(rayleigh_distribution<RealType>(2)),
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::boost::math::kurtosis(rayleigh_distribution<RealType>(2)) -3,
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tolerance* 100); // %
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return;
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} // template <class RealType>void test_spots(RealType)
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BOOST_AUTO_TEST_CASE( test_main )
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{
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// Check that can generate rayleigh distribution using the two convenience methods:
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boost::math::rayleigh ray1(1.); // Using typedef
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rayleigh_distribution<> ray2(1.); // Using default RealType double.
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using namespace boost::math::constants;
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// Basic sanity-check spot values.
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// Double only tests.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::pdf(
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rayleigh_distribution<double>(1.),
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static_cast<double>(1)), // x
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static_cast<double>(exp_minus_half<double>()), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::pdf(
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rayleigh_distribution<double>(0.5),
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static_cast<double>(0.5)), // x
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static_cast<double>(2 * exp_minus_half<double>()), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::pdf(
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rayleigh_distribution<double>(2.),
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static_cast<double>(2)), // x
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static_cast<double>(exp_minus_half<double>() /2 ), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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rayleigh_distribution<double>(1.),
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static_cast<double>(1)), // x
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static_cast<double>(1- exp_minus_half<double>()), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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rayleigh_distribution<double>(2.),
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static_cast<double>(2)), // x
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static_cast<double>(1- exp_minus_half<double>()), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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rayleigh_distribution<double>(3.),
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static_cast<double>(3)), // x
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static_cast<double>(1- exp_minus_half<double>()), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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rayleigh_distribution<double>(4.),
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static_cast<double>(4)), // x
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static_cast<double>(1- exp_minus_half<double>()), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(complement(
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rayleigh_distribution<double>(4.),
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static_cast<double>(4))), // x
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static_cast<double>(exp_minus_half<double>()), // q = 1 - p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile(
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rayleigh_distribution<double>(4.),
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static_cast<double>(1- exp_minus_half<double>())), // x
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static_cast<double>(4), // p
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1e-15); // %
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile(complement(
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rayleigh_distribution<double>(4.),
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static_cast<double>(exp_minus_half<double>()))), // x
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static_cast<double>(4), // p
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1e-15); // %
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// (Parameter value, arbitrarily zero, only communicates the floating point type).
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test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
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test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L); // Test long double.
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
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#endif
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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::endl;
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#endif
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} // BOOST_AUTO_TEST_CASE( test_main )
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/*
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Output is:
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_rayleigh.exe"
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Running 1 test case...
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Tolerance for type float is 0.000119209 %
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Tolerance for type double is 2.22045e-013 %
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Tolerance for type long double is 2.22045e-013 %
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Tolerance for type class boost::math::concepts::real_concept is 2.22045e-013 %
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*** No errors detected
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*/
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