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- // 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/tools/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
- */
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