mirror of
https://github.com/boostorg/math.git
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e9cd6c96fd
Add SYCL testing of normal dist Add CUDA testing of normal dist Add NVRTC testing of normal dist NVRTC fixes Move headers for NVRTC support Add GPU support to inverse gaussian dist Add NVRTC testing of inverse Gaussian dist Add CUDA testing of inverse gaussian dist Add SYCL testing of inverse gaussian dist Add GPU support to lognormal dist Add SYCL testing of lognormal dist Add CUDA testing of lognormal dist Add nvrtc testing of lognormal dist Add GPU support to negative binomial dist Avoid float_prior on GPU platform Add NVRTC testing of negative binomial dist Fix ambiguous use of nextafter Add CUDA testing of negative binomial dist Fix float_prior workaround Add SYCL testing of negative binomial dist Add GPU support to non_central_beta dist Add SYCL testing of nc beta dist Add CUDA testing of nc beta dist Enable generic dist handling on GPU Add GPU support to brent_find_minima Add NVRTC testing of nc beta dist Add utility header Replace non-functional macro with new function Add GPU support to non central chi squared dist Add SYCL testing of non central chi squared dist Add missing macro definition Markup generic quantile finder Add CUDA testing of non central chi squared dist Add NVRTC testing of non central chi squared dist Add GPU support to the non-central f dist Add SYCL testing of ncf Add CUDA testing of ncf dist Add NVRTC testing of ncf dist Add GPU support to students_t dist Add SYCL testing of students_t dist Add CUDA testing of students_t Add NVRTC testing of students_t dist Workaround for header cycle Add GPU support to pareto dist Add SYCL testing of pareto dist Add CUDA testing of pareto dist Add NVRTC testing of pareto dist Add missing header Add GPU support to poisson dist Add SYCL testing of poisson dist Add CUDA testing of poisson dist Add NVRTC testing of poisson dist Add forward decl for NVRTC platform Add GPU support to rayleigh dist Add CUDA testing of rayleigh dist Add SYCL testing of rayleigh dist Add NVRTC testing of rayleigh dist Add GPU support to triangular dist Add SYCL testing of triangular dist Add NVRTC testing of triangular dist Add CUDA testing of triangular dist Add GPU support to the uniform dist Add CUDA testing of uniform dist Add SYCL testing of uniform dist Add NVRTC testing of uniform dist Fix missing header Add markers to docs
398 lines
17 KiB
C++
398 lines
17 KiB
C++
// Copyright Paul A. Bristow 2007, 2009.
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// Copyright John Maddock 2006.
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// Copyright Matt Borland 2023.
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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_pareto.cpp
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// http://en.wikipedia.org/wiki/pareto_distribution
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
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// Also:
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// Weisstein, Eric W. "pareto Distribution."
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// From MathWorld--A Wolfram Web Resource.
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// http://mathworld.wolfram.com/paretoDistribution.html
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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 : 4996) // POSIX name for this item is deprecated
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# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'arg' was previously defined as a type
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# pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored
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# pragma warning(disable: 4100) // unreferenced formal parameter.
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#endif
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#include <boost/math/tools/config.hpp>
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#include "../include_private/boost/math/tools/test.hpp"
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#endif
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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/pareto.hpp>
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using boost::math::pareto_distribution;
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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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#include <limits>
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using std::numeric_limits;
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#include <type_traits>
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template <class RealType>
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void check_pareto(RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
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{
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RealType logtol = tol * 10;
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#ifndef BOOST_MATH_HAS_GPU_SUPPORT
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BOOST_IF_CONSTEXPR (std::is_same<RealType, long double>::value ||
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std::is_same<RealType, boost::math::concepts::real_concept>::value)
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{
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logtol *= 100;
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}
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#endif
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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pareto_distribution<RealType>(scale, shape), // distribution.
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x), // random variable.
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p, // probability.
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tol); // tolerance eps.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf(
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complement(
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pareto_distribution<RealType>(scale, shape), // distribution.
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x)), // random variable.
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q, // probability complement.
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tol); // tolerance eps.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::logcdf(
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pareto_distribution<RealType>(scale, shape), // distribution.
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x), // random variable.
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log(p), // probability.
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logtol); // tolerance eps.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::logcdf(
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complement(
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pareto_distribution<RealType>(scale, shape), // distribution.
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x)), // random variable.
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log(q), // probability complement.
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logtol); // tolerance eps.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile(
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pareto_distribution<RealType>(scale, shape), // distribution.
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p), // probability.
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x, // random variable.
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tol); // tolerance eps.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile(
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complement(
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pareto_distribution<RealType>(scale, shape), // distribution.
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q)), // probability complement.
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x, // random variable.
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tol); // tolerance eps.
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} // check_pareto
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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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// Tolerance are based on units of epsilon, but capped at
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// double precision, since that's the limit of our test data:
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//
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RealType tol = (std::max)((RealType)boost::math::tools::epsilon<double>(), boost::math::tools::epsilon<RealType>());
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RealType tol5eps = tol * 5;
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RealType tol10eps = tol * 10;
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RealType tol100eps = tol * 100;
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RealType tol1000eps = tol * 1000;
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check_pareto(
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static_cast<RealType>(1.1L), //
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static_cast<RealType>(5.5L),
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static_cast<RealType>(2.2L),
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static_cast<RealType>(0.97790291308792L),
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static_cast<RealType>(0.0220970869120796L),
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tol10eps * 4);
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check_pareto(
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static_cast<RealType>(0.5L),
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static_cast<RealType>(10.1L),
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static_cast<RealType>(1.5L),
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static_cast<RealType>(0.99998482686481L),
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static_cast<RealType>(1.51731351900608e-005L),
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tol100eps * 1000); // Much less accurate as p close to unity.
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check_pareto(
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static_cast<RealType>(0.1L),
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static_cast<RealType>(2.3L),
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static_cast<RealType>(1.5L),
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static_cast<RealType>(0.99802762220697L),
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static_cast<RealType>(0.00197237779302972L),
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tol1000eps);
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// Example from 23.3 page 259
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check_pareto(
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static_cast<RealType>(2.30444301457005L),
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static_cast<RealType>(4),
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static_cast<RealType>(2.4L),
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static_cast<RealType>(0.15L),
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static_cast<RealType>(0.85L),
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tol100eps);
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check_pareto(
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static_cast<RealType>(2),
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static_cast<RealType>(3),
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static_cast<RealType>(3.4L),
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static_cast<RealType>(0.796458375737838L),
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static_cast<RealType>(0.203541624262162L),
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tol10eps);
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check_pareto( // Probability near 0.5
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static_cast<RealType>(2),
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static_cast<RealType>(2),
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static_cast<RealType>(3),
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static_cast<RealType>(0.5555555555555555555555555555555555555556L),
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static_cast<RealType>(0.4444444444444444444444444444444444444444L),
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tol5eps); // accurate.
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// Tests for:
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// pdf for shapes 1, 2 & 3 (exact)
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BOOST_CHECK_CLOSE_FRACTION(
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pdf(pareto_distribution<RealType>(1, 1), 1),
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static_cast<RealType>(1), //
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tol5eps);
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BOOST_CHECK_CLOSE_FRACTION( pdf(pareto_distribution<RealType>(1, 2), 1),
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static_cast<RealType>(2), //
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tol5eps);
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BOOST_CHECK_CLOSE_FRACTION( pdf(pareto_distribution<RealType>(1, 3), 1),
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static_cast<RealType>(3), //
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tol5eps);
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// cdf
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BOOST_CHECK_EQUAL( // x = scale
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cdf(pareto_distribution<RealType>(1, 1), 1),
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static_cast<RealType>(0) );
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// Compare with values from StatCalc K. Krishnamoorthy, ISBN 1-58488-635-8 eq 23.1.3
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BOOST_CHECK_CLOSE_FRACTION( // small x
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cdf(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4)),
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static_cast<RealType>(0.929570372227626L), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION( // small x
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cdf(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4)),
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static_cast<RealType>(1 - 0.0704296277723743L), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION( // small x
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cdf(complement(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4))),
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static_cast<RealType>(0.0704296277723743L), tol5eps);
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// quantile
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BOOST_CHECK_EQUAL( // x = scale
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quantile(pareto_distribution<RealType>(1, 1), 0),
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static_cast<RealType>(1) );
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BOOST_CHECK_EQUAL( // x = scale
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quantile(complement(pareto_distribution<RealType>(1, 1), 1)),
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static_cast<RealType>(1) );
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BOOST_CHECK_CLOSE_FRACTION( // small x
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cdf(complement(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4))),
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static_cast<RealType>(0.0704296277723743L), tol5eps);
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using namespace std; // ADL of std names.
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pareto_distribution<RealType> pareto15(1, 5);
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// Note: shape must be big enough (5) that all moments up to kurtosis are defined
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// to allow all functions to be tested.
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// mean:
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BOOST_CHECK_CLOSE_FRACTION(
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mean(pareto15), static_cast<RealType>(1.25), tol5eps); // 1.25 == 5/4
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BOOST_CHECK_EQUAL(
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mean(pareto15), static_cast<RealType>(1.25)); // 1.25 == 5/4 (expect exact so check equal)
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pareto_distribution<RealType> p12(1, 2); //
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BOOST_CHECK_EQUAL(
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mean(p12), static_cast<RealType>(2)); // Exactly two.
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// variance:
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BOOST_CHECK_CLOSE_FRACTION(
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variance(pareto15), static_cast<RealType>(0.10416666666666667L), tol5eps);
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// std deviation:
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BOOST_CHECK_CLOSE_FRACTION(
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standard_deviation(pareto15), static_cast<RealType>(0.32274861218395140L), tol5eps);
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// hazard: No independent test values found yet.
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//BOOST_CHECK_CLOSE_FRACTION(
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// hazard(pareto15, x), pdf(pareto15, x) / cdf(complement(pareto15, x)), tol5eps);
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//// cumulative hazard:
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//BOOST_CHECK_CLOSE_FRACTION(
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// chf(pareto15, x), -log(cdf(complement(pareto15, x))), tol5eps);
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//// coefficient_of_variation:
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BOOST_CHECK_CLOSE_FRACTION(
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coefficient_of_variation(pareto15), static_cast<RealType>(0.25819888974716110L), tol5eps);
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// mode:
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BOOST_CHECK_CLOSE_FRACTION(
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mode(pareto15), static_cast<RealType>(1), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(
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median(pareto15), static_cast<RealType>(1.1486983549970351L), tol5eps);
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// skewness:
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BOOST_CHECK_CLOSE_FRACTION(
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skewness(pareto15), static_cast<RealType>(4.6475800154489004L), tol5eps);
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// kurtosis:
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BOOST_CHECK_CLOSE_FRACTION(
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kurtosis(pareto15), static_cast<RealType>(73.8L), tol5eps);
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// kurtosis excess:
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BOOST_CHECK_CLOSE_FRACTION(
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kurtosis_excess(pareto15), static_cast<RealType>(70.8L), tol5eps);
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// Check difference between kurtosis and excess:
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BOOST_CHECK_CLOSE_FRACTION(
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kurtosis_excess(pareto15), kurtosis(pareto15) - static_cast<RealType>(3L), tol5eps);
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// Check kurtosis excess = kurtosis - 3;
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RealType expected_entropy = 1 + RealType(1)/RealType(5) + log(RealType(1)/RealType(5));
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BOOST_CHECK_CLOSE_FRACTION(
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entropy(pareto15), expected_entropy, tol5eps);
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// Error condition checks:
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check_out_of_range<pareto_distribution<RealType> >(1, 1);
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BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(0, 1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(1, 0), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(-1, 1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(1, -1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(1, 1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(cdf(pareto_distribution<RealType>(1, 1), 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(quantile(pareto_distribution<RealType>(1, 1), -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(quantile(pareto_distribution<RealType>(1, 1), 2), std::domain_error);
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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 pareto distribution using the two convenience methods:
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boost::math::pareto myp1(1., 1); // Using typedef
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pareto_distribution<> myp2(1., 1); // Using default RealType double.
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boost::math::pareto pareto11; // Use default values (scale = 1, shape = 1).
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// Note NOT pareto11() as the compiler will interpret as a function!
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// Basic sanity-check spot values.
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BOOST_CHECK_EQUAL(pareto11.scale(), 1); // Check defaults again.
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BOOST_CHECK_EQUAL(pareto11.shape(), 1);
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BOOST_CHECK_EQUAL(myp1.scale(), 1);
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BOOST_CHECK_EQUAL(myp1.shape(), 1);
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BOOST_CHECK_EQUAL(myp2.scale(), 1);
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BOOST_CHECK_EQUAL(myp2.shape(), 1);
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// Test range and support using double only,
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// because it supports numeric_limits max for pseudo-infinity.
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BOOST_CHECK_EQUAL(range(myp2).first, 0); // range 0 to +infinity
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BOOST_CHECK_EQUAL(range(myp2).second, (numeric_limits<double>::max)());
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BOOST_CHECK_EQUAL(support(myp2).first, myp2.scale()); // support scale to + infinity.
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BOOST_CHECK_EQUAL(support(myp2).second, (numeric_limits<double>::max)());
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// Check some bad parameters to the distribution.
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#ifndef BOOST_NO_EXCEPTIONS
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BOOST_MATH_CHECK_THROW(boost::math::pareto mypm1(-1, 1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto myp0(0, 1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto myp1m1(1, -1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto myp10(1, 0), std::domain_error); // Using typedef
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#else
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BOOST_MATH_CHECK_THROW(boost::math::pareto(-1, 1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto(0, 1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto(1, -1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto(1, 0), std::domain_error); // Using typedef
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#endif
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// Check some moments that should fail because shape not big enough.
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BOOST_MATH_CHECK_THROW(variance(myp2), std::domain_error);
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BOOST_MATH_CHECK_THROW(standard_deviation(myp2), std::domain_error);
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BOOST_MATH_CHECK_THROW(skewness(myp2), std::domain_error);
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BOOST_MATH_CHECK_THROW(kurtosis(myp2), std::domain_error);
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BOOST_MATH_CHECK_THROW(kurtosis_excess(myp2), std::domain_error);
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// Test on extreme values of distribution parameters,
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// using just double because it has numeric_limit infinity etc.
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#ifndef BOOST_NO_EXCEPTIONS
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BOOST_MATH_CHECK_THROW(boost::math::pareto mypinf1(+std::numeric_limits<double>::infinity(), 1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto myp1inf(1, +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto mypinf1(+std::numeric_limits<double>::infinity(), +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
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#else
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BOOST_MATH_CHECK_THROW(boost::math::pareto(+std::numeric_limits<double>::infinity(), 1), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto(1, +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
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BOOST_MATH_CHECK_THROW(boost::math::pareto(+std::numeric_limits<double>::infinity(), +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
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#endif
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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(pareto11, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
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BOOST_MATH_CHECK_THROW(pdf(pareto11, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
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BOOST_MATH_CHECK_THROW(cdf(pareto11, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
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BOOST_MATH_CHECK_THROW(cdf(pareto11, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
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BOOST_CHECK_EQUAL(pdf(pareto11, 0.5), 0); // x < scale but > 0
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BOOST_CHECK_EQUAL(pdf(pareto11, (std::numeric_limits<double>::min)()), 0); // x almost zero but > 0
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BOOST_CHECK_EQUAL(pdf(pareto11, 1), 1); // x == scale, result == shape == 1
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BOOST_CHECK_EQUAL(pdf(pareto11, +(std::numeric_limits<double>::max)()), 0); // x = +max, pdf has fallen to zero.
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BOOST_MATH_CHECK_THROW(pdf(pareto11, 0), std::domain_error); // x == 0
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BOOST_MATH_CHECK_THROW(pdf(pareto11, -1), std::domain_error); // x = -1
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BOOST_MATH_CHECK_THROW(pdf(pareto11, -(std::numeric_limits<double>::max)()), std::domain_error); // x = - max
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BOOST_MATH_CHECK_THROW(pdf(pareto11, -(std::numeric_limits<double>::min)()), std::domain_error); // x = - min
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BOOST_CHECK_EQUAL(cdf(pareto11, 1), 0); // x == scale, cdf = zero.
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BOOST_CHECK_EQUAL(cdf(pareto11, +(std::numeric_limits<double>::max)()), 1); // x = + max, cdf = unity.
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BOOST_MATH_CHECK_THROW(cdf(pareto11, 0), std::domain_error); // x == 0
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BOOST_MATH_CHECK_THROW(cdf(pareto11, -(std::numeric_limits<double>::min)()), std::domain_error); // x = - min,
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BOOST_MATH_CHECK_THROW(cdf(pareto11, -(std::numeric_limits<double>::max)()), std::domain_error); // x = - max,
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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 tol5eps = 0.0001 %
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test_spots(0.0); // Test double. OK at decdigits 7, tol5eps = 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(BOOST_BORLANDC, BOOST_TESTED_AT(0x0582)) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
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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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Compiling...
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test_pareto.cpp
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Linking...
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Embedding manifest...
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_pareto.exe"
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Running 1 test case...
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*** No errors detected
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*/
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