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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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