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
802 lines
38 KiB
C++
802 lines
38 KiB
C++
// Copyright Paul A. Bristow 2006, 2017.
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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_students_t.cpp
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// http://en.wikipedia.org/wiki/Student%27s_t_distribution
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3664.htm
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// Basic sanity test for Student's t probability (quantile) (0. < p < 1).
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// and Student's t probability Quantile (0. < p < 1).
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#ifdef _MSC_VER
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# pragma warning (disable :4127) // conditional expression is constant.
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#endif
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#include <boost/math/tools/config.hpp>
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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/special_functions/next.hpp> // for has_denorm_now
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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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#include "test_out_of_range.hpp"
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#include <boost/math/distributions/students_t.hpp>
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using boost::math::students_t_distribution;
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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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RealType naive_pdf(RealType v, RealType t)
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{
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// Calculate the pdf of the students t in a deliberately
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// naive way, using equation (5) from
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// http://mathworld.wolfram.com/Studentst-Distribution.html
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// This is equivalent to, but a different method
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// to the one in the actual implementation, so can be used as
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// a very basic sanity check. However some published values
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// would be nice....
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using namespace std; // for ADL
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using boost::math::beta;
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//return pow(v / (v + t*t), (1+v) / 2) / (sqrt(v) * beta(v/2, RealType(0.5f)));
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RealType result = boost::math::tgamma_ratio((v+1)/2, v/2);
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result /= sqrt(v * boost::math::constants::pi<RealType>());
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result /= pow(1 + t*t/v, (v+1)/2);
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return result;
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}
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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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RealType tolerance = static_cast<RealType>(1e-4); // 1e-6 (as %)
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// Some tests only pass at 1e-5 because probability value is less accurate,
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// a digit in 6th decimal place, although calculated using
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// a t-distribution generator (claimed 6 decimal digits) at
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// http://faculty.vassar.edu/lowry/VassarStats.html
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// http://faculty.vassar.edu/lowry/tsamp.html
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// df = 5, +/-t = 2.0, 1-tailed = 0.050970, 2-tailed = 0.101939
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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// http://en.wikipedia.org/wiki/Student%27s_t_distribution#Table_of_selected_values
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// Using tabulated value of t = 3.182 for 0.975, 3 df, one-sided.
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// http://www.mth.kcl.ac.uk/~shaww/web_page/papers/Tdistribution06.pdf refers to:
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// A lookup table of quantiles of the RealType distribution
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// for 1 to 25 in steps of 0.1 is provided in CSV form at:
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// www.mth.kcl.ac.uk/~shaww/web_page/papers/Tsupp/tquantiles.csv
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// gives accurate t of -3.1824463052837 and 3 degrees of freedom.
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// Values below are from this source, saved as tquantiles.xls.
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// DF are across the columns, probabilities down the rows
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// and the t- values (quantiles) are shown.
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// These values are probably accurate to nearly 64-bit double
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// (perhaps 14 decimal digits).
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(2), // degrees_of_freedom
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static_cast<RealType>(-6.96455673428326)), // t
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static_cast<RealType>(0.01), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(5), // degrees_of_freedom
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static_cast<RealType>(-3.36492999890721)), // t
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static_cast<RealType>(0.01), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(1), // degrees_of_freedom
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static_cast<RealType>(-31830.988607907)), // t
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static_cast<RealType>(0.00001), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(25.), // degrees_of_freedom
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static_cast<RealType>(-5.2410429995425)), // t
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static_cast<RealType>(0.00001), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(1), // degrees_of_freedom
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static_cast<RealType>(-63661.97723)), // t
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static_cast<RealType>(0.000005), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(-17.89686614)), // t
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static_cast<RealType>(0.000005), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(25.), // degrees_of_freedom
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static_cast<RealType>(-5.510848412)), // t
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static_cast<RealType>(0.000005), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(10.), // degrees_of_freedom
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static_cast<RealType>(-1.812461123)), // t
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static_cast<RealType>(0.05), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(10), // degrees_of_freedom
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static_cast<RealType>(1.812461123)), // t
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static_cast<RealType>(0.95), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(
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students_t_distribution<RealType>(10), // degrees_of_freedom
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static_cast<RealType>(1.812461123))), // t
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static_cast<RealType>(0.05), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(10), // degrees_of_freedom
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static_cast<RealType>(9.751995491)), // t
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static_cast<RealType>(0.999999), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(10.), // degrees_of_freedom - for ALL degrees_of_freedom!
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static_cast<RealType>(0.)), // t
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static_cast<RealType>(0.5), // probability.
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tolerance);
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// Student's t Inverse function tests.
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// Special cases
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BOOST_MATH_CHECK_THROW(boost::math::quantile(
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students_t_distribution<RealType>(1.), // degrees_of_freedom (ignored).
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static_cast<RealType>(0)), std::overflow_error); // t == -infinity.
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BOOST_MATH_CHECK_THROW(boost::math::quantile(
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students_t_distribution<RealType>(1.), // degrees_of_freedom (ignored).
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static_cast<RealType>(1)), std::overflow_error); // t == +infinity.
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BOOST_CHECK_EQUAL(boost::math::quantile(
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students_t_distribution<RealType>(1.), // degrees_of_freedom (ignored).
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static_cast<RealType>(0.5)), // probability == half - special case.
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static_cast<RealType>(0)); // t == zero.
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BOOST_CHECK_EQUAL(boost::math::quantile(
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complement(
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students_t_distribution<RealType>(1.), // degrees_of_freedom (ignored).
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static_cast<RealType>(0.5))), // probability == half - special case.
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static_cast<RealType>(0)); // t == zero.
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(1.), // degrees_of_freedom (ignored).
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static_cast<RealType>(0.5)), // probability == half - special case.
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static_cast<RealType>(0), // t == zero.
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tolerance);
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BOOST_CHECK_CLOSE( // Tests of p middling.
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::boost::math::cdf(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(-0.559429644)), // t
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static_cast<RealType>(0.3), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(0.3)), // probability.
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static_cast<RealType>(-0.559429644), // t
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(0.7))), // probability.
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static_cast<RealType>(-0.559429644), // t
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tolerance);
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BOOST_CHECK_CLOSE( // Tests of p high.
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::boost::math::cdf(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(1.475884049)), // t
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static_cast<RealType>(0.9), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(0.9)), // probability.
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static_cast<RealType>(1.475884049), // t
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tolerance);
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BOOST_CHECK_CLOSE( // Tests of p low.
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::boost::math::cdf(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(-1.475884049)), // t
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static_cast<RealType>(0.1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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students_t_distribution<RealType>(5.), // degrees_of_freedom
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static_cast<RealType>(0.1)), // probability.
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static_cast<RealType>(-1.475884049), // t
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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students_t_distribution<RealType>(2.), // degrees_of_freedom
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static_cast<RealType>(-6.96455673428326)), // t
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static_cast<RealType>(0.01), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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students_t_distribution<RealType>(2.), // degrees_of_freedom
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static_cast<RealType>(0.01)), // probability.
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static_cast<RealType>(-6.96455673428326), // t
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tolerance);
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//
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// Some special tests to exercise the double-precision approximations
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// to the quantile:
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//
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// tolerance is 50 eps expressed as a percent:
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//
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tolerance = boost::math::tools::epsilon<RealType>() * 5000;
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//
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// But higher error rates at 128 bit precision?
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//
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if (boost::math::tools::digits<RealType>() > 100)
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tolerance *= 500;
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(2.00390625L), // degrees_of_freedom.
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static_cast<RealType>(0.5625L)), // probability.
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static_cast<RealType>(0.178133131573788108465134803511798566L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(1L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-10.1531703876088604621071476634194722L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(1L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(2.41421356237309504880168872421390942L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(2L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-3.81000381000571500952501666878143315L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(2L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.60356745147454630810732088527854144L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(4L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-2.56208431914409044861223047927635034L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(4L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.34439755550909142430681981315923574L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(6L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-2.28348667906973065861212495010082952L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(6L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.27334930914664286821103236660071906L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(8L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-2.16296475406014719458642055768894376L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(8L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.24031826078267310637634677726479038L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(10L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-2.09596136475109350926340169211429572L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(10L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.2212553950039221407185188573696834L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(2.125L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-3.62246031671091980110493455859296532L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(2.125L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.56905270993307293450392958697861969L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(3L), // degrees_of_freedom.
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static_cast<RealType>(0.03125L)), // probability.
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static_cast<RealType>(-2.90004411882995814036141778367917946L), // t.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile(
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students_t_distribution<RealType>(3L), // degrees_of_freedom.
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static_cast<RealType>(0.875L)), // probability.
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static_cast<RealType>(1.42262528146180931868169289781115099L), // t.
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tolerance);
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if(boost::is_floating_point<RealType>::value)
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{
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BOOST_CHECK_CLOSE(boost::math::cdf(
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students_t_distribution<RealType>(1e30f),
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boost::math::quantile(
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students_t_distribution<RealType>(1e30f), static_cast<RealType>(0.25f))),
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static_cast<RealType>(0.25f), tolerance);
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BOOST_CHECK_CLOSE(boost::math::cdf(
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students_t_distribution<RealType>(1e20f),
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boost::math::quantile(
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students_t_distribution<RealType>(1e20f), static_cast<RealType>(0.25f))),
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static_cast<RealType>(0.25f), tolerance);
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BOOST_CHECK_CLOSE(boost::math::cdf(
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students_t_distribution<RealType>(static_cast<RealType>(0x7FFFFFFF)),
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boost::math::quantile(
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students_t_distribution<RealType>(static_cast<RealType>(0x7FFFFFFF)), static_cast<RealType>(0.25f))),
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static_cast<RealType>(0.25f), tolerance);
|
|
BOOST_CHECK_CLOSE(boost::math::cdf(
|
|
students_t_distribution<RealType>(static_cast<RealType>(0x10000000)),
|
|
boost::math::quantile(
|
|
students_t_distribution<RealType>(static_cast<RealType>(0x10000000)), static_cast<RealType>(0.25f))),
|
|
static_cast<RealType>(0.25f), tolerance);
|
|
BOOST_CHECK_CLOSE(boost::math::cdf(
|
|
students_t_distribution<RealType>(static_cast<RealType>(0x0fffffff)),
|
|
boost::math::quantile(
|
|
students_t_distribution<RealType>(static_cast<RealType>(0x0fffffff)), static_cast<RealType>(0.25f))),
|
|
static_cast<RealType>(0.25f), tolerance);
|
|
//
|
|
// Bug cases:
|
|
//
|
|
if (std::numeric_limits<RealType>::is_specialized && boost::math::detail::has_denorm_now<RealType>())
|
|
{
|
|
BOOST_CHECK_THROW(boost::math::quantile(students_t_distribution<RealType>((std::numeric_limits<RealType>::min)() / 2), static_cast<RealType>(0.0025f)), std::overflow_error);
|
|
}
|
|
}
|
|
|
|
// Student's t pdf tests.
|
|
// for PDF checks, use 100 eps tolerance expressed as a percent:
|
|
tolerance = boost::math::tools::epsilon<RealType>() * 10000;
|
|
|
|
for(unsigned i = 1; i < 20; i += 3)
|
|
{
|
|
for(RealType r = -10; r < 10; r += 0.125)
|
|
{
|
|
//std::cout << "df=" << i << " t=" << r << std::endl;
|
|
BOOST_CHECK_CLOSE(
|
|
boost::math::pdf(
|
|
students_t_distribution<RealType>(static_cast<RealType>(i)),
|
|
r),
|
|
naive_pdf<RealType>(static_cast<RealType>(i), r),
|
|
tolerance);
|
|
}
|
|
}
|
|
|
|
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
|
|
students_t_distribution<RealType> dist(8);
|
|
RealType x = static_cast<RealType>(0.125);
|
|
using namespace std; // ADL of std names.
|
|
// mean:
|
|
BOOST_CHECK_CLOSE(
|
|
mean(dist)
|
|
, static_cast<RealType>(0), tol2);
|
|
// variance:
|
|
// BOOST_CHECK_CLOSE(
|
|
// variance(dist)
|
|
// , static_cast<RealType>(13.0L / 6.0L), tol2);
|
|
//// was , static_cast<RealType>(8.0L / 6.0L), tol2);
|
|
// std deviation:
|
|
BOOST_CHECK_CLOSE(
|
|
standard_deviation(dist)
|
|
, static_cast<RealType>(sqrt(8.0L / 6.0L)), tol2);
|
|
// hazard:
|
|
BOOST_CHECK_CLOSE(
|
|
hazard(dist, x)
|
|
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
|
|
// cumulative hazard:
|
|
BOOST_CHECK_CLOSE(
|
|
chf(dist, x)
|
|
, -log(cdf(complement(dist, x))), tol2);
|
|
// coefficient_of_variation:
|
|
BOOST_MATH_CHECK_THROW(
|
|
coefficient_of_variation(dist),
|
|
std::overflow_error);
|
|
// mode:
|
|
BOOST_CHECK_CLOSE(
|
|
mean(dist)
|
|
, static_cast<RealType>(0), tol2);
|
|
// median:
|
|
BOOST_CHECK_CLOSE(
|
|
median(dist)
|
|
, static_cast<RealType>(0), tol2);
|
|
// skewness:
|
|
BOOST_CHECK_CLOSE(
|
|
skewness(dist)
|
|
, static_cast<RealType>(0), tol2);
|
|
// kurtosis:
|
|
BOOST_CHECK_CLOSE(
|
|
kurtosis(dist)
|
|
, static_cast<RealType>(4.5), tol2);
|
|
// kurtosis excess:
|
|
BOOST_CHECK_CLOSE(
|
|
kurtosis_excess(dist)
|
|
, static_cast<RealType>(1.5), tol2);
|
|
|
|
using std::log;
|
|
using std::sqrt;
|
|
RealType expected_entropy = (RealType(9)/2)*(boost::math::digamma(RealType(9)/2) - boost::math::digamma(RealType(4))) + log(sqrt(RealType(8))*boost::math::beta(RealType(4), RealType(1)/2));
|
|
BOOST_CHECK_CLOSE(
|
|
entropy(dist)
|
|
, expected_entropy, 300*tol2);
|
|
|
|
// Parameter estimation. These results are close to but
|
|
// not identical to those reported on the NIST website at
|
|
// http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm
|
|
// the NIST results appear to be calculated using a normal
|
|
// approximation, which slightly under-estimates the degrees of
|
|
// freedom required, particularly when the result is small.
|
|
//
|
|
BOOST_CHECK_EQUAL(
|
|
ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(0.005),
|
|
static_cast<RealType>(0.01),
|
|
static_cast<RealType>(1.0))),
|
|
99);
|
|
BOOST_CHECK_EQUAL(
|
|
ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
|
|
static_cast<RealType>(1.5),
|
|
static_cast<RealType>(0.005),
|
|
static_cast<RealType>(0.01),
|
|
static_cast<RealType>(1.0))),
|
|
14);
|
|
BOOST_CHECK_EQUAL(
|
|
ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(0.025),
|
|
static_cast<RealType>(0.01),
|
|
static_cast<RealType>(1.0))),
|
|
76);
|
|
BOOST_CHECK_EQUAL(
|
|
ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
|
|
static_cast<RealType>(1.5),
|
|
static_cast<RealType>(0.025),
|
|
static_cast<RealType>(0.01),
|
|
static_cast<RealType>(1.0))),
|
|
11);
|
|
BOOST_CHECK_EQUAL(
|
|
ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(0.05),
|
|
static_cast<RealType>(0.01),
|
|
static_cast<RealType>(1.0))),
|
|
65);
|
|
BOOST_CHECK_EQUAL(
|
|
ceil(students_t_distribution<RealType>::find_degrees_of_freedom(
|
|
static_cast<RealType>(1.5),
|
|
static_cast<RealType>(0.05),
|
|
static_cast<RealType>(0.01),
|
|
static_cast<RealType>(1.0))),
|
|
9);
|
|
|
|
// Test for large degrees of freedom when should be same as normal.
|
|
RealType inf = std::numeric_limits<RealType>::infinity();
|
|
RealType nan = std::numeric_limits<RealType>::quiet_NaN();
|
|
|
|
std::string type = typeid(RealType).name();
|
|
// if (type != "class boost::math::concepts::real_concept") fails for gcc
|
|
|
|
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
|
|
BOOST_MATH_IF_CONSTEXPR(!std::is_same<RealType, boost::math::concepts::real_concept>::value)
|
|
#endif
|
|
{ // Ordinary floats only.
|
|
RealType limit = 1/ boost::math::tools::epsilon<RealType>();
|
|
// Default policy to get full accuracy.
|
|
// std::cout << "Switch over to normal if df > " << limit << std::endl;
|
|
// float Switch over to normal if df > 8.38861e+006
|
|
// double Switch over to normal if df > 4.5036e+015
|
|
// Can't test real_concept - doesn't converge.
|
|
|
|
boost::math::normal_distribution<RealType> n(0, 1); //
|
|
students_t_distribution<RealType> st(boost::math::tools::max_value<RealType>()); // Well over the switchover point,
|
|
// PDF
|
|
BOOST_CHECK_EQUAL(pdf(st, 0), pdf(n, 0.)); // Should be exactly equal.
|
|
|
|
students_t_distribution<RealType> st2(limit /5 ); // Just below the switchover point,
|
|
BOOST_CHECK_CLOSE_FRACTION(pdf(st2, 0), pdf(n, 0.), tolerance); // Should be very close to normal.
|
|
// CDF
|
|
BOOST_CHECK_EQUAL(cdf(st, 0), cdf(n, 0.)); // Should be exactly equal.
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(st2, 0), cdf(n, 0.), tolerance); // Should be very close to normal.
|
|
|
|
// Tests for df = infinity.
|
|
students_t_distribution<RealType> infdf(inf);
|
|
BOOST_CHECK_EQUAL(infdf.degrees_of_freedom(), inf);
|
|
BOOST_CHECK_EQUAL(mean(infdf), 0); // OK.
|
|
#ifndef BOOST_NO_EXCEPTIONS
|
|
BOOST_MATH_CHECK_THROW(students_t_distribution<RealType> minfdf(-inf), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(students_t_distribution<RealType> minfdf(nan), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(students_t_distribution<RealType> minfdf(-nan), std::domain_error);
|
|
#endif
|
|
BOOST_CHECK_EQUAL(pdf(infdf, -inf), 0);
|
|
BOOST_CHECK_EQUAL(pdf(infdf, +inf), 0);
|
|
BOOST_CHECK_EQUAL(cdf(infdf, -inf), 0);
|
|
BOOST_CHECK_EQUAL(cdf(infdf, +inf), 1);
|
|
|
|
// BOOST_CHECK_CLOSE_FRACTION(pdf(infdf, 0), static_cast<RealType>(0.3989422804014326779399460599343818684759L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(pdf(infdf, 0),boost::math::constants::one_div_root_two_pi<RealType>() , tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(cdf(infdf, 0),boost::math::constants::half<RealType>() , tolerance);
|
|
|
|
// Checks added for Trac #7717 report by Thomas Mang.
|
|
|
|
BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(quantile(dist, 2), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(pdf(students_t_distribution<RealType>(0), 0), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(pdf(students_t_distribution<RealType>(-1), 0), std::domain_error);
|
|
|
|
// Check on df for mean (moment k = 1)
|
|
BOOST_MATH_CHECK_THROW(mean(students_t_distribution<RealType>(nan)), std::domain_error);
|
|
// BOOST_MATH_CHECK_THROW(mean(students_t_distribution<RealType>(inf)), std::domain_error); inf is now OK
|
|
BOOST_MATH_CHECK_THROW(mean(students_t_distribution<RealType>(-1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(mean(students_t_distribution<RealType>(0)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(mean(students_t_distribution<RealType>(1)), std::domain_error); // df == k
|
|
BOOST_CHECK_EQUAL(mean(students_t_distribution<RealType>(2)), 0); // OK.
|
|
BOOST_CHECK_EQUAL(mean(students_t_distribution<RealType>(inf)), 0); // OK.
|
|
|
|
// Check on df for variance (moment 2)
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(nan)), std::domain_error);
|
|
// BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(inf)), std::domain_error); // inf is now OK.
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(-1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(0)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(static_cast<RealType>(1.99999L))), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(static_cast<RealType>(1.99999L))), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(variance(students_t_distribution<RealType>(2)), std::domain_error); // df ==
|
|
BOOST_CHECK_EQUAL(variance(students_t_distribution<RealType>(2.5)), 5); // OK.
|
|
BOOST_CHECK_EQUAL(variance(students_t_distribution<RealType>(3)), 3); // OK.
|
|
BOOST_CHECK_EQUAL(variance(students_t_distribution<RealType>(inf)), 1); // OK.
|
|
|
|
// Check on df for skewness (moment 3)
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(nan)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(-1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(0)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(1.5L)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(2)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(skewness(students_t_distribution<RealType>(3)), std::domain_error); // df == k
|
|
BOOST_CHECK_EQUAL(skewness(students_t_distribution<RealType>(3.5)), 0); // OK.
|
|
BOOST_CHECK_EQUAL(skewness(students_t_distribution<RealType>(4)), 0); // OK.
|
|
BOOST_CHECK_EQUAL(skewness(students_t_distribution<RealType>(inf)), 0); // OK.
|
|
|
|
// Check on df for kurtosis_excess (moment 4)
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(nan)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(-1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(0)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(1.5L)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(2)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(static_cast<RealType>(2.1))), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(3)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis_excess(students_t_distribution<RealType>(4)), std::domain_error); // df == k
|
|
BOOST_CHECK_EQUAL(kurtosis_excess(students_t_distribution<RealType>(5)), 6); // OK.
|
|
BOOST_CHECK_EQUAL(kurtosis_excess(students_t_distribution<RealType>(inf)), 0); // OK.
|
|
|
|
// Check on df for kurtosis (moment 4)
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(nan)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(-1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(0)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(1)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(2)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(static_cast<RealType>(2.0001L))), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(3)), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(kurtosis(students_t_distribution<RealType>(4)), std::domain_error); // df == k
|
|
BOOST_CHECK_EQUAL(kurtosis(students_t_distribution<RealType>(5)), 9); // OK.
|
|
BOOST_CHECK_EQUAL(kurtosis(students_t_distribution<RealType>(inf)), 3); // OK.
|
|
|
|
}
|
|
|
|
|
|
// Use a new distribution ignore_error_students_t with a custom policy to ignore all errors,
|
|
// and check returned values are as expected.
|
|
|
|
/*
|
|
Sandia-darwin-intel-12.0 - math - test_students_t / intel-darwin-12.0
|
|
../libs/math/test/test_students_t.cpp(544): error: "domain_error" has already been declared in the current scope
|
|
using boost::math::policies::domain_error;
|
|
|
|
../libs/math/test/test_students_t.cpp(552): error: "pole_error" has already been declared in the current scope
|
|
using boost::math::policies::pole_error;
|
|
|
|
Unclear where previous declaration is.
|
|
Does not seem to be in student_t.hpp or any included files???
|
|
|
|
So to avoid this perceived problem by this compiler,
|
|
the ignore policy below uses fully specified names.
|
|
*/
|
|
|
|
using boost::math::policies::policy;
|
|
// Types of error whose action can be altered by policies:.
|
|
//using boost::math::policies::evaluation_error;
|
|
//using boost::math::policies::domain_error;
|
|
//using boost::math::policies::overflow_error;
|
|
//using boost::math::policies::underflow_error;
|
|
//using boost::math::policies::domain_error;
|
|
//using boost::math::policies::pole_error;
|
|
|
|
//// Actions on error (in enum error_policy_type):
|
|
//using boost::math::policies::errno_on_error;
|
|
//using boost::math::policies::ignore_error;
|
|
//using boost::math::policies::throw_on_error;
|
|
//using boost::math::policies::denorm_error;
|
|
//using boost::math::policies::pole_error;
|
|
//using boost::math::policies::user_error;
|
|
|
|
typedef policy<
|
|
boost::math::policies::domain_error<boost::math::policies::ignore_error>,
|
|
boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
|
|
boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
|
|
boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
|
|
boost::math::policies::pole_error<boost::math::policies::ignore_error>,
|
|
boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
|
|
> my_ignore_policy;
|
|
|
|
typedef students_t_distribution<RealType, my_ignore_policy> ignore_error_students_t;
|
|
|
|
|
|
|
|
// Only test NaN and infinity if type has these features (realconcept returns zero).
|
|
// Integers are always converted to RealType,
|
|
// others requires static cast to RealType from long double.
|
|
|
|
if(std::numeric_limits<RealType>::has_quiet_NaN)
|
|
{
|
|
// Mean
|
|
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_students_t(-1))));
|
|
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_students_t(0))));
|
|
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_students_t(1))));
|
|
|
|
// Variance
|
|
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_students_t(std::numeric_limits<RealType>::quiet_NaN()))));
|
|
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_students_t(-1))));
|
|
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_students_t(0))));
|
|
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_students_t(1))));
|
|
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_students_t(static_cast<RealType>(1.7L)))));
|
|
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_students_t(2))));
|
|
|
|
// Skewness
|
|
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_students_t(std::numeric_limits<RealType>::quiet_NaN()))));
|
|
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_students_t(-1))));
|
|
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_students_t(0))));
|
|
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_students_t(1))));
|
|
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_students_t(2))));
|
|
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_students_t(3))));
|
|
|
|
// Kurtosis
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(std::numeric_limits<RealType>::quiet_NaN()))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(-1))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(0))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(1))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(2))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(static_cast<RealType>(2.0001L)))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(3))));
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_students_t(4))));
|
|
|
|
// Kurtosis excess
|
|
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(std::numeric_limits<RealType>::quiet_NaN()))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(-1))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(0))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(1))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(2))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(static_cast<RealType>(2.0001L)))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(3))));
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BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_students_t(4))));
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} // has_quiet_NaN
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BOOST_CHECK(boost::math::isfinite(mean(ignore_error_students_t(1 + std::numeric_limits<RealType>::epsilon()))));
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BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits<RealType>::epsilon()))));
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BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(static_cast<RealType>(2.0001L)))));
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BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits<RealType>::epsilon()))));
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BOOST_CHECK(boost::math::isfinite(skewness(ignore_error_students_t(3 + 3 * std::numeric_limits<RealType>::epsilon()))));
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BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(4 + 4 * std::numeric_limits<RealType>::epsilon()))));
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BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(static_cast<RealType>(4.0001L)))));
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// check_out_of_range<students_t_distribution<RealType> >(1);
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// Cannot be used because fails "exception std::domain_error is expected but not raised"
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// if df = +infinity is allowed, must use new version that allows skipping infinity tests.
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// Infinite == true
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check_support<students_t_distribution<RealType> >(students_t_distribution<RealType>(1), true);
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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 students_t distribution using the two convenience methods:
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using namespace boost::math;
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students_t myst1(2); // Using typedef
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students_t_distribution<> myst2(2); // Using default RealType double.
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//students_t_distribution<double> myst3(2); // Using explicit RealType double.
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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(0x582)) && !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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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_students_t.exe"
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Running 1 test case...
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Tolerance for type float is 0.0001 %
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Tolerance for type double is 0.0001 %
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Tolerance for type long double is 0.0001 %
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Tolerance for type class boost::math::concepts::real_concept is 0.0001 %
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*** No errors detected
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*/
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