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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
775 lines
34 KiB
C++
775 lines
34 KiB
C++
// Copyright Paul Bristow 2006, 2007.
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// Copyright John Maddock 2006, 2007.
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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_triangular.cpp
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#ifndef SYCL_LANGUAGE_VERSION
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#include <pch.hpp>
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#endif
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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: 4305) // truncation from 'long double' to 'float'
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#endif
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#include <boost/math/tools/config.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/triangular.hpp>
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using boost::math::triangular_distribution;
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#include "../include_private/boost/math/tools/test.hpp"
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#include <boost/math/special_functions/fpclassify.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::scientific;
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using std::fixed;
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using std::left;
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using std::right;
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using std::setw;
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using std::setprecision;
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using std::showpos;
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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_triangular(RealType lower, RealType mode, 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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triangular_distribution<RealType>(lower, mode, 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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triangular_distribution<RealType>(lower, mode, 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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triangular_distribution<RealType>(lower,mode, 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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triangular_distribution<RealType>(lower, mode, 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_triangular
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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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// Some test values were generated for the triangular 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 epsilon expressed as a fraction:
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RealType tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction.
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RealType tol5eps = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction.
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
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using namespace std; // for ADL of std::exp;
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// Tests on construction
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// Default should be 0, 0, 1
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BOOST_CHECK_EQUAL(triangular_distribution<RealType>().lower(), -1);
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BOOST_CHECK_EQUAL(triangular_distribution<RealType>().mode(), 0);
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BOOST_CHECK_EQUAL(triangular_distribution<RealType>().upper(), 1);
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BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).first, triangular_distribution<RealType>().lower());
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BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).second, triangular_distribution<RealType>().upper());
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if (std::numeric_limits<RealType>::has_quiet_NaN == true)
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{
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BOOST_MATH_CHECK_THROW( // duff parameter lower.
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triangular_distribution<RealType>(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0, 0),
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std::domain_error);
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BOOST_MATH_CHECK_THROW( // duff parameter mode.
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triangular_distribution<RealType>(0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0),
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std::domain_error);
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BOOST_MATH_CHECK_THROW( // duff parameter upper.
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triangular_distribution<RealType>(0, 0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
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std::domain_error);
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} // quiet_NaN tests.
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BOOST_MATH_CHECK_THROW( // duff parameters upper < lower.
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triangular_distribution<RealType>(1, 0, -1),
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std::domain_error);
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BOOST_MATH_CHECK_THROW( // duff parameters upper == lower.
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triangular_distribution<RealType>(0, 0, 0),
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std::domain_error);
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BOOST_MATH_CHECK_THROW( // duff parameters mode < lower.
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triangular_distribution<RealType>(0, -1, 1),
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std::domain_error);
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BOOST_MATH_CHECK_THROW( // duff parameters mode > upper.
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triangular_distribution<RealType>(0, 2, 1),
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std::domain_error);
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// Tests for PDF
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// // triangular_distribution<RealType>() default is (0, 0, 1), mode == lower.
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BOOST_CHECK_CLOSE_FRACTION( // x == lower == mode
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pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0)),
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static_cast<RealType>(2),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == upper
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pdf(triangular_distribution<RealType>(0, 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 > upper
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pdf(triangular_distribution<RealType>(0, 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(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)),
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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(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)),
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static_cast<RealType>(0),
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tolerance);
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// triangular_distribution<RealType>() (0, 1, 1) mode == upper
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BOOST_CHECK_CLOSE_FRACTION( // x == lower
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pdf(triangular_distribution<RealType>(0, 1, 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( // x == upper
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pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)),
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static_cast<RealType>(2),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x > upper
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pdf(triangular_distribution<RealType>(0, 1, 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(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)),
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static_cast<RealType>(0),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case pdf = 2 * x
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pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)),
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static_cast<RealType>(0.5),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case cdf = x * x
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cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)),
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static_cast<RealType>(0.25 * 0.25),
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tolerance);
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// triangular_distribution<RealType>() (0, 0.5, 1) mode == middle.
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BOOST_CHECK_CLOSE_FRACTION( // x == lower
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pdf(triangular_distribution<RealType>(0, 0.5, 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( // x == upper
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pdf(triangular_distribution<RealType>(0, 0.5, 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 > upper
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pdf(triangular_distribution<RealType>(0, 0.5, 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(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(2)),
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static_cast<RealType>(0),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == mode
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pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.5)),
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static_cast<RealType>(2),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == half mode
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pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.25)),
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static_cast<RealType>(1),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x == half mode
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pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.75)),
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static_cast<RealType>(1),
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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 NOT OK.
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pdf(triangular_distribution<RealType>(0, 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 not OK too.
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pdf(triangular_distribution<RealType>(0, 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(triangular_distribution<RealType>(0, 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(triangular_distribution<RealType>(0, 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(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)),
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static_cast<RealType>(0) );
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BOOST_CHECK_CLOSE_FRACTION( // x == lower
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cdf(triangular_distribution<RealType>(0, 1, 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( // x == upper
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cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)),
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static_cast<RealType>(1),
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tolerance);
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BOOST_CHECK_EQUAL( // x > upper
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cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)),
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static_cast<RealType>(1));
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BOOST_CHECK_CLOSE_FRACTION( // x == mode
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cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)),
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//static_cast<RealType>((mode - lower) / (upper - lower)),
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static_cast<RealType>(0.5), // (0 --1) / (1 -- 1) = 0.5
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.9L)),
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static_cast<RealType>(0.81L),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(triangular_distribution<RealType>(-1, 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(
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cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5L)),
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static_cast<RealType>(0.125L),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)),
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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(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(+0.5L)),
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static_cast<RealType>(0.875L),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(1)),
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static_cast<RealType>(1),
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tolerance);
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// cdf complement
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BOOST_CHECK_EQUAL( // x < lower
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cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1))),
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static_cast<RealType>(1));
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BOOST_CHECK_EQUAL( // x == lower
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cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))),
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static_cast<RealType>(1));
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BOOST_CHECK_EQUAL( // x == mode
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cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0))),
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static_cast<RealType>(0.5));
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BOOST_CHECK_EQUAL( // x == mode
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cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))),
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static_cast<RealType>(1));
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BOOST_CHECK_EQUAL( // x == mode
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cdf(complement(triangular_distribution<RealType>(0, 1, 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(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2))),
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static_cast<RealType>(0));
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BOOST_CHECK_EQUAL( // x == upper
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cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1))),
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static_cast<RealType>(0));
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BOOST_CHECK_CLOSE_FRACTION( // x = -0.5
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cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5))),
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static_cast<RealType>(0.875L),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION( // x = +0.5
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cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0.5))),
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static_cast<RealType>(0.125),
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tolerance);
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triangular_distribution<RealType> triang; // Using typedef == triangular_distribution<double> tristd;
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triangular_distribution<RealType> tristd(0, 0.5, 1); // 'Standard' triangular distribution.
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BOOST_CHECK_CLOSE_FRACTION( // median of Standard triangular is sqrt(mode/2) if c > 1/2 else 1 - sqrt((1-c)/2)
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median(tristd),
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static_cast<RealType>(0.5),
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tolerance);
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triangular_distribution<RealType> tri011(0, 1, 1); // Using default RealType double.
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triangular_distribution<RealType> tri0q1(0, 0.25, 1); // mode is near bottom.
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triangular_distribution<RealType> tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle.
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triangular_distribution<RealType> trim12(-1, -0.5, 2); // mode is negative.
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BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02L), static_cast<RealType>(0.0016L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5L), static_cast<RealType>(0.66666666666666666666666666666666666666666666667L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98L), static_cast<RealType>(0.9994666666666666666666666666666666666666666666L), tolerance);
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// quantile
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BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.0016L)), static_cast<RealType>(0.02L), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.66666666666666666666666666666666666666666666667L)), static_cast<RealType>(0.5), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(0.3333333333333333333333333333333333333333333333333L))), static_cast<RealType>(0.5), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.999466666666666666666666666666666666666666666666666L)), static_cast<RealType>(98) / 100, 10 * tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), static_cast<RealType>(0.533333333333333333333333333333333333333333333L), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), static_cast<RealType>(0.466666666666666666666666666666666666666666667L), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), static_cast<RealType>(1 - 0.466666666666666666666666666666666666666666667L), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(1 - 0.999466666666666666666666666666666666666666666666L))), static_cast<RealType>(0.98L), 10 * tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1))), static_cast<RealType>(0), tol5eps);
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BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(0.5))), static_cast<RealType>(0.5), tol5eps); // OK
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1 - 0.02L))), static_cast<RealType>(0.1L), tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1 - 0.98L))), static_cast<RealType>(0.9L), tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0)), static_cast<RealType>(1), tol5eps);
|
|
|
|
RealType xs [] = {0, 0.01L, 0.02L, 0.05L, 0.1L, 0.2L, 0.3L, 0.4L, 0.5L, 0.6L, 0.7L, 0.8L, 0.9L, 0.95L, 0.98L, 0.99L, 1};
|
|
|
|
const triangular_distribution<RealType>& distr = triang;
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(distr, 1.)), static_cast<RealType>(-1), tol5eps);
|
|
const triangular_distribution<RealType>* distp = &triang;
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*distp, 1.)), static_cast<RealType>(-1), tol5eps);
|
|
|
|
const triangular_distribution<RealType>* dists [] = {&tristd, &tri011, &tri0q1, &tri0h1, &trim12};
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*dists[1], 1.)), static_cast<RealType>(0), tol5eps);
|
|
|
|
for (int i = 0; i < 5; i++)
|
|
{
|
|
const triangular_distribution<RealType>* const dist = dists[i];
|
|
// cout << "Distribution " << i << endl;
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5L), quantile(complement(*dist, 0.5L)), tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98L), quantile(complement(*dist, 1.L - 0.98L)),tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98L), quantile(complement(*dist, 1.L - 0.98L)),tol5eps);
|
|
} // for i
|
|
|
|
// quantile complement
|
|
for (int i = 0; i < 5; i++)
|
|
{
|
|
const triangular_distribution<RealType>* const dist = dists[i];
|
|
//cout << "Distribution " << i << endl;
|
|
BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
|
|
for (unsigned j = 0; j < sizeof(xs) /sizeof(RealType); j++)
|
|
{
|
|
RealType x = xs[j];
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], x), quantile(complement(*dist, 1 - x)), tol5eps);
|
|
} // for j
|
|
} // for i
|
|
|
|
|
|
check_triangular(
|
|
static_cast<RealType>(0), // lower
|
|
static_cast<RealType>(0.5), // mode
|
|
static_cast<RealType>(1), // upper
|
|
static_cast<RealType>(0.5), // x
|
|
static_cast<RealType>(0.5), // p
|
|
static_cast<RealType>(1 - 0.5), // q
|
|
tolerance);
|
|
|
|
// Some Not-standard triangular tests.
|
|
check_triangular(
|
|
static_cast<RealType>(-1), // lower
|
|
static_cast<RealType>(0), // mode
|
|
static_cast<RealType>(1), // upper
|
|
static_cast<RealType>(0), // x
|
|
static_cast<RealType>(0.5), // p
|
|
static_cast<RealType>(1 - 0.5), // q = 1 - p
|
|
tolerance);
|
|
|
|
check_triangular(
|
|
static_cast<RealType>(1), // lower
|
|
static_cast<RealType>(1), // mode
|
|
static_cast<RealType>(3), // upper
|
|
static_cast<RealType>(2), // x
|
|
static_cast<RealType>(0.75), // p
|
|
static_cast<RealType>(1 - 0.75), // q = 1 - p
|
|
tolerance);
|
|
|
|
check_triangular(
|
|
static_cast<RealType>(-1), // lower
|
|
static_cast<RealType>(1), // mode
|
|
static_cast<RealType>(2), // upper
|
|
static_cast<RealType>(1), // x
|
|
static_cast<RealType>(0.66666666666666666666666666666666666666666667L), // p
|
|
static_cast<RealType>(0.33333333333333333333333333333333333333333333L), // q = 1 - p
|
|
tolerance);
|
|
tolerance = (std::max)(
|
|
boost::math::tools::epsilon<RealType>(),
|
|
static_cast<RealType>(boost::math::tools::epsilon<double>())) * 10; // 10 eps as a fraction.
|
|
cout << "Tolerance (as fraction) for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
|
|
|
|
triangular_distribution<RealType> tridef; // (-1, 0, 1) // Default distribution.
|
|
RealType x = static_cast<RealType>(0.5);
|
|
using namespace std; // ADL of std names.
|
|
// mean:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
mean(tridef), static_cast<RealType>(0), tolerance);
|
|
// variance:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
variance(tridef), static_cast<RealType>(0.16666666666666666666666666666666666666666667L), tolerance);
|
|
// was 0.0833333333333333333333333333333333333333333L
|
|
|
|
// std deviation:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
standard_deviation(tridef), sqrt(variance(tridef)), tolerance);
|
|
// hazard:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
hazard(tridef, x), pdf(tridef, x) / cdf(complement(tridef, x)), tolerance);
|
|
// cumulative hazard:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
chf(tridef, x), -log(cdf(complement(tridef, x))), tolerance);
|
|
// coefficient_of_variation:
|
|
if (mean(tridef) != 0)
|
|
{
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
coefficient_of_variation(tridef), standard_deviation(tridef) / mean(tridef), tolerance);
|
|
}
|
|
// mode:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
mode(tridef), static_cast<RealType>(0), tolerance);
|
|
// skewness:
|
|
// On device the result does not get flushed exactly to zero so the eps difference is by default huge
|
|
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
median(tridef), static_cast<RealType>(0), tolerance);
|
|
#endif
|
|
// https://reference.wolfram.com/language/ref/Skewness.html skewness{-1, 0, +1} = 0
|
|
// skewness[triangulardistribution{-1, 0, +1}] does not compute a result.
|
|
// skewness[triangulardistribution{0, +1}] result == 0
|
|
// skewness[normaldistribution{0,1}] result == 0
|
|
|
|
BOOST_CHECK_EQUAL(
|
|
skewness(tridef), static_cast<RealType>(0));
|
|
// kurtosis:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
kurtosis_excess(tridef), kurtosis(tridef) - static_cast<RealType>(3L), tolerance);
|
|
// kurtosis excess = kurtosis - 3;
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
kurtosis_excess(tridef), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
entropy(tridef), static_cast<RealType>(1)/2, tolerance);
|
|
|
|
{
|
|
triangular_distribution<RealType> tri01(0, 1, 1); // Asymmetric 0, 1, 1 distribution.
|
|
RealType x = static_cast<RealType>(0.5);
|
|
using namespace std; // ADL of std names.
|
|
// mean:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
mean(tri01), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), tolerance);
|
|
// variance: N[variance[triangulardistribution{0, 1}, 1], 50]
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
variance(tri01), static_cast<RealType>(0.055555555555555555555555555555555555555555555555556L), tolerance);
|
|
// std deviation:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
standard_deviation(tri01), sqrt(variance(tri01)), tolerance);
|
|
// hazard:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
hazard(tri01, x), pdf(tri01, x) / cdf(complement(tri01, x)), tolerance);
|
|
// cumulative hazard:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
chf(tri01, x), -log(cdf(complement(tri01, x))), tolerance);
|
|
// coefficient_of_variation:
|
|
if (mean(tri01) != 0)
|
|
{
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
coefficient_of_variation(tri01), standard_deviation(tri01) / mean(tri01), tolerance);
|
|
}
|
|
// mode:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
mode(tri01), static_cast<RealType>(1), tolerance);
|
|
// skewness:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
median(tri01), static_cast<RealType>(0.70710678118654752440084436210484903928483593768847L), tolerance);
|
|
|
|
// https://reference.wolfram.com/language/ref/Skewness.html
|
|
// N[skewness[triangulardistribution{0, 1}, 1], 50]
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
skewness(tri01), static_cast<RealType>(-0.56568542494923801952067548968387923142786875015078L), tolerance);
|
|
// kurtosis:
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
kurtosis_excess(tri01), kurtosis(tri01) - static_cast<RealType>(3L), tolerance);
|
|
// kurtosis excess = kurtosis - 3;
|
|
BOOST_CHECK_CLOSE_FRACTION(
|
|
kurtosis_excess(tri01), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
|
|
} // tri01 tests
|
|
|
|
if(std::numeric_limits<RealType>::has_infinity)
|
|
{ // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
|
|
// Note that infinity is not implemented for real_concept, so these tests
|
|
// are only done for types, like built-in float, double.. that have infinity.
|
|
// Note that these assume that BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
|
|
// #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
|
|
// #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
|
|
// of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
|
|
|
|
using boost::math::policies::policy;
|
|
using boost::math::policies::domain_error;
|
|
using boost::math::policies::ignore_error;
|
|
|
|
// Define a (bad?) policy to ignore domain errors ('bad' arguments):
|
|
typedef policy<domain_error<ignore_error> > inf_policy; // domain error returns infinity.
|
|
triangular_distribution<RealType, inf_policy> tridef_inf(-1, 0., 1);
|
|
// But can't use BOOST_CHECK_EQUAL(?, quiet_NaN)
|
|
using boost::math::isnan;
|
|
BOOST_CHECK((isnan)(pdf(tridef_inf, std::numeric_limits<RealType>::infinity())));
|
|
} // test for infinity using std::numeric_limits<>::infinity()
|
|
else
|
|
{ // real_concept case, does has_infinfity == false, so can't check it throws.
|
|
// cout << std::numeric_limits<RealType>::infinity() << ' '
|
|
// << (boost::math::fpclassify)(std::numeric_limits<RealType>::infinity()) << endl;
|
|
// value of std::numeric_limits<RealType>::infinity() is zero, so FPclassify is zero,
|
|
// so (boost::math::isfinite)(std::numeric_limits<RealType>::infinity()) does not detect infinity.
|
|
// so these tests would never throw.
|
|
//BOOST_MATH_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::infinity()), std::domain_error);
|
|
//BOOST_MATH_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
|
|
// BOOST_MATH_CHECK_THROW(pdf(tridef, boost::math::tools::max_value<RealType>() * 2), std::domain_error); // Doesn't throw.
|
|
BOOST_CHECK_EQUAL(pdf(tridef, boost::math::tools::max_value<RealType>()), 0);
|
|
}
|
|
// Special cases:
|
|
BOOST_CHECK(pdf(tridef, -1) == 0);
|
|
BOOST_CHECK(pdf(tridef, 1) == 0);
|
|
BOOST_CHECK(cdf(tridef, 0) == 0.5);
|
|
BOOST_CHECK(pdf(tridef, 1) == 0);
|
|
BOOST_CHECK(cdf(tridef, 1) == 1);
|
|
BOOST_CHECK(cdf(complement(tridef, -1)) == 1);
|
|
BOOST_CHECK(cdf(complement(tridef, 1)) == 0);
|
|
BOOST_CHECK(quantile(tridef, 1) == 1);
|
|
BOOST_CHECK(quantile(complement(tridef, 1)) == -1);
|
|
|
|
BOOST_CHECK_EQUAL(support(trim12).first, trim12.lower());
|
|
BOOST_CHECK_EQUAL(support(trim12).second, trim12.upper());
|
|
|
|
// Error checks:
|
|
if(std::numeric_limits<RealType>::has_quiet_NaN)
|
|
{ // BOOST_CHECK tests for quiet_NaN (not for real_concept, for example - see notes above).
|
|
BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
|
|
}
|
|
BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(1, 0), std::domain_error); // lower > upper!
|
|
|
|
check_out_of_range<triangular_distribution<RealType> >(-1, 0, 1);
|
|
} // template <class RealType>void test_spots(RealType)
|
|
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
|
{
|
|
// double toleps = std::numeric_limits<double>::epsilon(); // 5 eps as a fraction.
|
|
double tol5eps = std::numeric_limits<double>::epsilon() * 5; // 5 eps as a fraction.
|
|
// double tol50eps = std::numeric_limits<double>::epsilon() * 50; // 50 eps as a fraction.
|
|
double tol500eps = std::numeric_limits<double>::epsilon() * 500; // 500 eps as a fraction.
|
|
|
|
// Check that can construct triangular distribution using the two convenience methods:
|
|
using namespace boost::math;
|
|
triangular triang; // Using typedef
|
|
// == triangular_distribution<double> triang;
|
|
|
|
BOOST_CHECK_EQUAL(triang.lower(), -1); // Check default.
|
|
BOOST_CHECK_EQUAL(triang.mode(), 0);
|
|
BOOST_CHECK_EQUAL(triang.upper(), 1);
|
|
|
|
triangular tristd (0, 0.5, 1); // Using typedef
|
|
|
|
BOOST_CHECK_EQUAL(tristd.lower(), 0);
|
|
BOOST_CHECK_EQUAL(tristd.mode(), 0.5);
|
|
BOOST_CHECK_EQUAL(tristd.upper(), 1);
|
|
|
|
//cout << "X range from " << range(tristd).first << " to " << range(tristd).second << endl;
|
|
//cout << "Supported from "<< support(tristd).first << ' ' << support(tristd).second << endl;
|
|
|
|
BOOST_CHECK_EQUAL(support(tristd).first, tristd.lower());
|
|
BOOST_CHECK_EQUAL(support(tristd).second, tristd.upper());
|
|
|
|
triangular_distribution<> tri011(0, 1, 1); // Using default RealType double.
|
|
// mode is upper
|
|
BOOST_CHECK_EQUAL(tri011.lower(), 0); // Check defaults again.
|
|
BOOST_CHECK_EQUAL(tri011.mode(), 1); // Check defaults again.
|
|
BOOST_CHECK_EQUAL(tri011.upper(), 1);
|
|
BOOST_CHECK_EQUAL(mode(tri011), 1);
|
|
|
|
BOOST_CHECK_EQUAL(pdf(tri011, 0), 0);
|
|
BOOST_CHECK_EQUAL(pdf(tri011, 0.1), 0.2);
|
|
BOOST_CHECK_EQUAL(pdf(tri011, 0.5), 1);
|
|
BOOST_CHECK_EQUAL(pdf(tri011, 0.9), 1.8);
|
|
BOOST_CHECK_EQUAL(pdf(tri011, 1), 2);
|
|
|
|
BOOST_CHECK_EQUAL(cdf(tri011, 0), 0);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(tri011, 0.1), 0.01, tol5eps);
|
|
BOOST_CHECK_EQUAL(cdf(tri011, 0.5), 0.25);
|
|
BOOST_CHECK_EQUAL(cdf(tri011, 0.9), 0.81);
|
|
BOOST_CHECK_EQUAL(cdf(tri011, 1), 1);
|
|
BOOST_CHECK_EQUAL(cdf(tri011, 9), 1);
|
|
BOOST_CHECK_EQUAL(mean(tri011), 0.666666666666666666666666666666666666666666666666667);
|
|
BOOST_CHECK_EQUAL(variance(tri011), 1./18.);
|
|
|
|
triangular tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle.
|
|
BOOST_CHECK_EQUAL(tri0h1.lower(), 0);
|
|
BOOST_CHECK_EQUAL(tri0h1.mode(), 0.5);
|
|
BOOST_CHECK_EQUAL(tri0h1.upper(), 1);
|
|
BOOST_CHECK_EQUAL(mean(tri0h1), 0.5);
|
|
BOOST_CHECK_EQUAL(mode(tri0h1), 0.5);
|
|
BOOST_CHECK_EQUAL(pdf(tri0h1, -1), 0);
|
|
BOOST_CHECK_EQUAL(cdf(tri0h1, -1), 0);
|
|
BOOST_CHECK_EQUAL(pdf(tri0h1, 1), 0);
|
|
BOOST_CHECK_EQUAL(pdf(tri0h1, 999), 0);
|
|
BOOST_CHECK_EQUAL(cdf(tri0h1, 999), 1);
|
|
BOOST_CHECK_EQUAL(cdf(tri0h1, 1), 1);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(tri0h1, 0.1), 0.02, tol5eps);
|
|
BOOST_CHECK_EQUAL(cdf(tri0h1, 0.5), 0.5);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(tri0h1, 0.9), 0.98, tol5eps);
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.), 0., tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.02), 0.1, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.5), 0.5, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.98), 0.9, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 1.), 1., tol5eps);
|
|
|
|
triangular tri0q1(0, 0.25, 1); // mode is near bottom.
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02), 0.0016, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5), 0.66666666666666666666666666666666666666666666667, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98), 0.99946666666666661, tol5eps);
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.0016), 0.02, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.66666666666666666666666666666666666666666666667), 0.5, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, 0.3333333333333333333333333333333333333333333333333)), 0.5, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.99946666666666661), 0.98, 10 * tol5eps);
|
|
|
|
triangular trim12(-1, -0.5, 2); // mode is negative.
|
|
BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), 0.533333333333333333333333333333333333333333333, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), 0.466666666666666666666666666666666666666666667, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), 1 - 0.466666666666666666666666666666666666666666667, tol5eps);
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, 1 - 0.99946666666666661)), 0.98, 10 * tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1.)), 0., tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0.5)), 0.5, tol5eps); // OK
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1. - 0.02)), 0.1, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1. - 0.98)), 0.9, tol5eps);
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0)), 1., tol5eps);
|
|
|
|
double xs [] = {0., 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.98, 0.99, 1.};
|
|
|
|
const triangular_distribution<double>& distr = tristd;
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(distr, 1.)), 0., tol5eps);
|
|
const triangular_distribution<double>* distp = &tristd;
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*distp, 1.)), 0., tol5eps);
|
|
|
|
const triangular_distribution<double>* dists [] = {&tristd, &tri011, &tri0q1, &tri0h1, &trim12};
|
|
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*dists[1], 1.)), 0., tol5eps);
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for (int i = 0; i < 5; i++)
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{
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const triangular_distribution<double>* const dist = dists[i];
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cout << "Distribution " << i << endl;
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BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
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BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5), quantile(complement(*dist, 0.5)), tol5eps); // OK
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BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98), quantile(complement(*dist, 1. - 0.98)),tol5eps);
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// cout << setprecision(17) << median(*dist) << endl;
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}
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cout << showpos << setprecision(2) << endl;
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//triangular_distribution<double>& dist = trim12;
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for (unsigned i = 0; i < sizeof(xs) /sizeof(double); i++)
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{
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double x = xs[i] * (trim12.upper() - trim12.lower()) + trim12.lower();
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double dx = cdf(trim12, x);
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double cx = cdf(complement(trim12, x));
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//cout << fixed << showpos << setprecision(3)
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// << xs[i] << ", " << x << ", " << pdf(trim12, x) << ", " << dx << ", " << cx << ",, " ;
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BOOST_CHECK_CLOSE_FRACTION(cx, 1 - dx, tol500eps); // cx == 1 - dx
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// << setprecision(2) << scientific << cr - x << ", " // difference x - quan(cdf)
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// << setprecision(3) << fixed
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// << quantile(trim12, dx) << ", "
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// << quantile(complement(trim12, 1 - dx)) << ", "
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// << quantile(complement(trim12, cx)) << ", "
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// << endl;
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BOOST_CHECK_CLOSE_FRACTION(quantile(trim12, dx), quantile(complement(trim12, 1 - dx)), tol500eps);
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}
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cout << endl;
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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(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 "
|
|
"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 "
|
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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_triangular.exe"
|
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Running 1 test case...
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Distribution 0
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Distribution 1
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Distribution 2
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Distribution 3
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Distribution 4
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Tolerance for type float is 5.96046e-007.
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|
Tolerance for type double is 1.11022e-015.
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|
Tolerance for type long double is 1.11022e-015.
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|
Tolerance 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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