462 lines
21 KiB
C++
462 lines
21 KiB
C++
// Copyright Paul Bristow 2007.
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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_uniform.cpp
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#include <pch.hpp>
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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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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include <boost/math/distributions/uniform.hpp>
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using boost::math::uniform_distribution;
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#include <boost/math/tools/test.hpp>
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#include "test_out_of_range.hpp"
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#include <iostream>
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#include <iomanip>
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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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#include <limits>
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using std::numeric_limits;
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template <class RealType>
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void check_uniform(RealType lower, RealType upper, RealType x, RealType p, RealType q, RealType tol)
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{
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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uniform_distribution<RealType>(lower, upper), // distribution.
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x), // random variable.
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p, // probability.
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tol); // tolerance.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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complement(
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uniform_distribution<RealType>(lower, upper), // distribution.
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x)), // random variable.
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q, // probability complement.
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tol); // tolerance.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile(
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uniform_distribution<RealType>(lower, upper), // distribution.
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p), // probability.
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x, // random variable.
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tol); // tolerance.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile(
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complement(
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uniform_distribution<RealType>(lower, upper), // distribution.
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q)), // probability complement.
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x, // random variable.
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tol); // tolerance.
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} // void check_uniform
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template <class RealType>
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void test_spots(RealType)
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{
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// Basic sanity checks
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//
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// These test values were generated for the normal distribution
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// using the online calculator at
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// http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
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//
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// Tolerance is just over 5 decimal digits expressed as a fraction:
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// that's the limit of the test data.
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RealType tolerance = 2e-5f;
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
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using std::exp;
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// Tests for PDF
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//
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BOOST_CHECK_CLOSE_FRACTION( // x == upper
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)),
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static_cast<RealType>(1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == lower
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1)),
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static_cast<RealType>(1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x > upper
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-1)),
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static_cast<RealType>(0),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x < lower
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2)),
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static_cast<RealType>(0),
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tolerance);
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if(std::numeric_limits<RealType>::has_infinity)
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{ // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
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// Note that infinity is not implemented for real_concept, so these tests
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// are only done for types, like built-in float, double.. that have infinity.
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// Note that these assume that BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
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// #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
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// #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
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// of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
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BOOST_MATH_CHECK_THROW( // x == infinity should NOT be OK.
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::infinity())),
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std::domain_error);
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BOOST_MATH_CHECK_THROW( // x == minus infinity should be OK too.
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::infinity())),
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std::domain_error);
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}
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if(std::numeric_limits<RealType>::has_quiet_NaN)
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{ // BOOST_CHECK tests for NaN using std::numeric_limits<>::has_quiet_NaN() - should throw.
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BOOST_MATH_CHECK_THROW(
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::quiet_NaN())),
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std::domain_error);
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} // test for x = NaN using std::numeric_limits<>::quiet_NaN()
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// cdf
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BOOST_CHECK_EQUAL( // x < lower
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cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-1)),
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static_cast<RealType>(0) );
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)),
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static_cast<RealType>(0),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5)),
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static_cast<RealType>(0.5),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1)),
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static_cast<RealType>(0.1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9)),
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static_cast<RealType>(0.9),
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tolerance);
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BOOST_CHECK_EQUAL( // x > upper
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cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2)),
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static_cast<RealType>(1));
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// cdf complement
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BOOST_CHECK_EQUAL( // x < lower
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cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))),
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static_cast<RealType>(1));
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BOOST_CHECK_EQUAL( // x == 0
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cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))),
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static_cast<RealType>(1));
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BOOST_CHECK_CLOSE_FRACTION( // x = 0.1
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cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1))),
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static_cast<RealType>(0.9),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x = 0.5
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cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5))),
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static_cast<RealType>(0.5),
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tolerance);
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BOOST_CHECK_EQUAL( // x == 1
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cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1))),
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static_cast<RealType>(0));
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BOOST_CHECK_EQUAL( // x > upper
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cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2))),
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static_cast<RealType>(0));
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// quantile
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9)),
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static_cast<RealType>(0.9),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1)),
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static_cast<RealType>(0.1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5)),
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static_cast<RealType>(0.5),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)),
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static_cast<RealType>(0),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1)),
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static_cast<RealType>(1),
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tolerance);
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// quantile complement
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1))),
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static_cast<RealType>(0.9),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9))),
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static_cast<RealType>(0.1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5))),
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static_cast<RealType>(0.5),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))),
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static_cast<RealType>(1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1))),
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static_cast<RealType>(0),
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tolerance);
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// Some tests using a different location & scale, neight zero or unity.
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BOOST_CHECK_CLOSE_FRACTION( // x == mid
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pdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(1)),
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static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == upper
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pdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(+2)),
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static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333), // 1 / (2 - -1) = 1/3
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == lower
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cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(-1)),
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static_cast<RealType>(0),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == upper
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cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(0)),
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static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == upper
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cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(1)),
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static_cast<RealType>(0.6666666666666666666666666666666666666666666666666667),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == lower
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cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(2)),
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static_cast<RealType>(1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == upper
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quantile(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(0.6666666666666666666666666666666666666666666666666667)),
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static_cast<RealType>(1),
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tolerance);
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check_uniform(
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static_cast<RealType>(0), // lower
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static_cast<RealType>(1), // upper
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static_cast<RealType>(0.5), // x
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static_cast<RealType>(0.5), // p
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static_cast<RealType>(1 - 0.5), // q
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tolerance);
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// Some Not-standard uniform tests.
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check_uniform(
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static_cast<RealType>(-1), // lower
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static_cast<RealType>(1), // upper
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static_cast<RealType>(0), // x
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static_cast<RealType>(0.5), // p
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static_cast<RealType>(1 - 0.5), // q = 1 - p
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tolerance);
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check_uniform(
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static_cast<RealType>(1), // lower
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static_cast<RealType>(3), // upper
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static_cast<RealType>(2), // x
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static_cast<RealType>(0.5), // p
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static_cast<RealType>(1 - 0.5), // q = 1 - p
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tolerance);
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check_uniform(
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static_cast<RealType>(-1), // lower
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static_cast<RealType>(2), // upper
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static_cast<RealType>(1), // x
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static_cast<RealType>(0.66666666666666666666666666666666666666666667), // p
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static_cast<RealType>(0.33333333333333333333333333333333333333333333), // q = 1 - p
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tolerance);
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tolerance = (std::max)(
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boost::math::tools::epsilon<RealType>(),
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static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5; // 5 eps as a fraction.
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cout << "Tolerance (as fraction) for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
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uniform_distribution<RealType> distu01(0, 1);
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RealType x = static_cast<RealType>(0.5);
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using namespace std; // ADL of std names.
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// mean:
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BOOST_CHECK_CLOSE_FRACTION(
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mean(distu01), static_cast<RealType>(0.5), tolerance);
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// variance:
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BOOST_CHECK_CLOSE_FRACTION(
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variance(distu01), static_cast<RealType>(0.0833333333333333333333333333333333333333333), tolerance);
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// std deviation:
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BOOST_CHECK_CLOSE_FRACTION(
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standard_deviation(distu01), sqrt(variance(distu01)), tolerance);
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// hazard:
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BOOST_CHECK_CLOSE_FRACTION(
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hazard(distu01, x), pdf(distu01, x) / cdf(complement(distu01, x)), tolerance);
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// cumulative hazard:
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BOOST_CHECK_CLOSE_FRACTION(
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chf(distu01, x), -log(cdf(complement(distu01, x))), tolerance);
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// coefficient_of_variation:
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BOOST_CHECK_CLOSE_FRACTION(
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coefficient_of_variation(distu01), standard_deviation(distu01) / mean(distu01), tolerance);
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// mode:
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BOOST_CHECK_CLOSE_FRACTION(
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mode(distu01), static_cast<RealType>(0), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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median(distu01), static_cast<RealType>(0.5), tolerance);
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// skewness:
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BOOST_CHECK_EQUAL(
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skewness(distu01), static_cast<RealType>(0));
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// kertosis:
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BOOST_CHECK_CLOSE_FRACTION(
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kurtosis(distu01), kurtosis_excess(distu01) + static_cast<RealType>(3), tolerance);
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// kertosis excess:
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BOOST_CHECK_CLOSE_FRACTION(
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kurtosis_excess(distu01), static_cast<RealType>(-1.2), tolerance);
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if(std::numeric_limits<RealType>::has_infinity)
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{ // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
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// Note that infinity is not implemented for real_concept, so these tests
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// are only done for types, like built-in float, double, long double, that have infinity.
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// Note that these assume that BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
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// #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
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// #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
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// of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
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BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::infinity()), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(distu01, -std::numeric_limits<RealType>::infinity()), std::domain_error);
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} // test for infinity using std::numeric_limits<>::infinity()
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else
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{ // real_concept case, does has_infinfity == false, so can't check it throws.
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// cout << std::numeric_limits<RealType>::infinity() << ' '
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// << (boost::math::fpclassify)(std::numeric_limits<RealType>::infinity()) << endl;
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// value of std::numeric_limits<RealType>::infinity() is zero, so FPclassify is zero,
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// so (boost::math::isfinite)(std::numeric_limits<RealType>::infinity()) does not detect infinity.
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// so these tests would never throw.
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//BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::infinity()), std::domain_error);
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//BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
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// BOOST_MATH_CHECK_THROW(pdf(distu01, boost::math::tools::max_value<RealType>() * 2), std::domain_error); // Doesn't throw.
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BOOST_CHECK_EQUAL(pdf(distu01, boost::math::tools::max_value<RealType>()), 0);
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}
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// Special cases:
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BOOST_CHECK(pdf(distu01, 0) == 1);
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BOOST_CHECK(cdf(distu01, 0) == 0);
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BOOST_CHECK(pdf(distu01, 1) == 1);
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BOOST_CHECK(cdf(distu01, 1) == 1);
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BOOST_CHECK(cdf(complement(distu01, 0)) == 1);
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BOOST_CHECK(cdf(complement(distu01, 1)) == 0);
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BOOST_CHECK(quantile(distu01, 0) == 0);
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BOOST_CHECK(quantile(complement(distu01, 0)) == 1);
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BOOST_CHECK(quantile(distu01, 1) == 1);
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BOOST_CHECK(quantile(complement(distu01, 1)) == 0);
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// Error checks:
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if(std::numeric_limits<RealType>::has_quiet_NaN)
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{ // BOOST_CHECK tests for constructing with quiet_NaN (not for real_concept, for example - see notes above).
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BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
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BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
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}
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BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(1, 0), std::domain_error); // lower > upper!
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BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(1, 1), std::domain_error); // lower == upper!
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check_out_of_range<uniform_distribution<RealType> >(1, 5);
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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 construct uniform distribution using the two convenience methods:
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using namespace boost::math;
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uniform unistd; // Using typedef
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// == uniform_distribution<double> unistd;
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BOOST_CHECK_EQUAL(unistd.lower(), 0); // Check defaults.
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BOOST_CHECK_EQUAL(unistd.upper(), 1);
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uniform_distribution<> myu01(0, 1); // Using default RealType double.
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BOOST_CHECK_EQUAL(myu01.lower(), 0); // Check defaults again.
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BOOST_CHECK_EQUAL(myu01.upper(), 1);
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// Test on extreme values of random variate x, using just double because it has numeric_limit infinity etc..
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// No longer allow x to be + or - infinity, then these tests should throw.
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BOOST_MATH_CHECK_THROW(pdf(unistd, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
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BOOST_MATH_CHECK_THROW(pdf(unistd, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
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BOOST_MATH_CHECK_THROW(cdf(unistd, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
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BOOST_MATH_CHECK_THROW(cdf(unistd, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
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BOOST_CHECK_EQUAL(pdf(unistd, +(std::numeric_limits<double>::max)()), 0); // x = + max
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BOOST_CHECK_EQUAL(pdf(unistd, -(std::numeric_limits<double>::min)()), 0); // x = - min
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BOOST_CHECK_EQUAL(cdf(unistd, +(std::numeric_limits<double>::max)()), 1); // x = + max
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BOOST_CHECK_EQUAL(cdf(unistd, -(std::numeric_limits<double>::min)()), 0); // x = - min
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#ifndef BOOST_NO_EXCEPTIONS
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BOOST_MATH_CHECK_THROW(uniform_distribution<> zinf(0, +std::numeric_limits<double>::infinity()), std::domain_error); // zero to infinity using default RealType double.
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#else
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BOOST_MATH_CHECK_THROW(uniform_distribution<>(0, +std::numeric_limits<double>::infinity()), std::domain_error); // zero to infinity using default RealType double.
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#endif
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uniform_distribution<> zmax(0, +(std::numeric_limits<double>::max)()); // zero to max using default RealType double.
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BOOST_CHECK_EQUAL(zmax.lower(), 0); // Check defaults again.
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BOOST_CHECK_EQUAL(zmax.upper(), +(std::numeric_limits<double>::max)());
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BOOST_CHECK_EQUAL(pdf(zmax, -1), 0); // pdf is 1/(0 - max) = almost zero for all x
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BOOST_CHECK_EQUAL(pdf(zmax, 0), (std::numeric_limits<double>::min)()/4); // x =
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BOOST_CHECK_EQUAL(pdf(zmax, 1), (std::numeric_limits<double>::min)()/4); // x =
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BOOST_MATH_CHECK_THROW(pdf(zmax, +std::numeric_limits<double>::infinity()), std::domain_error); // pdf is 1/(0 - infinity) = zero for all x
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BOOST_MATH_CHECK_THROW(pdf(zmax, -std::numeric_limits<double>::infinity()), std::domain_error);
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BOOST_CHECK_EQUAL(pdf(zmax, +(std::numeric_limits<double>::max)()), (std::numeric_limits<double>::min)()/4); // x =
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BOOST_CHECK_EQUAL(pdf(zmax, -(std::numeric_limits<double>::max)()), 0); // x =
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#ifndef BOOST_NO_EXCEPTIONS
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// Ensure NaN throws an exception.
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BOOST_MATH_CHECK_THROW(uniform_distribution<> zNaN(0, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(unistd, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
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#else
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BOOST_MATH_CHECK_THROW(uniform_distribution<>(0, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(unistd, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
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#endif
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// Basic sanity-check spot values.
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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(0x0582))
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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:
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_uniform.exe"
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Running 1 test case...
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Tolerance for type float is 2e-005.
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Tolerance (as fraction) for type float is 5.96046e-007.
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Tolerance for type double is 2e-005.
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Tolerance (as fraction) for type double is 1.11022e-015.
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Tolerance for type long double is 2e-005.
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Tolerance (as fraction) for type long double is 1.11022e-015.
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Tolerance for type class boost::math::concepts::real_concept is 2e-005.
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Tolerance (as fraction) for type class boost::math::concepts::real_concept is 1.11022e-015.
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*** No errors detected
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*/
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