| // Copyright Paul Bristow 2006, 2007. |
| // Copyright John Maddock 2006, 2007. |
| |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. |
| // (See accompanying file LICENSE_1_0.txt |
| // or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| // test_triangular.cpp |
| |
| #include <pch.hpp> |
| |
| #ifdef _MSC_VER |
| # pragma warning(disable: 4127) // conditional expression is constant. |
| # pragma warning(disable: 4305) // truncation from 'long double' to 'float' |
| #endif |
| |
| #include <boost/math/concepts/real_concept.hpp> // for real_concept |
| #include <boost/test/test_exec_monitor.hpp> // Boost.Test |
| #include <boost/test/floating_point_comparison.hpp> |
| |
| #include <boost/math/distributions/triangular.hpp> |
| using boost::math::triangular_distribution; |
| #include <boost/math/tools/test.hpp> |
| #include <boost/math/special_functions/fpclassify.hpp> |
| |
| #include <iostream> |
| using std::cout; |
| using std::endl; |
| using std::scientific; |
| using std::fixed; |
| using std::left; |
| using std::right; |
| using std::setw; |
| using std::setprecision; |
| using std::showpos; |
| #include <limits> |
| using std::numeric_limits; |
| |
| template <class RealType> |
| void check_triangular(RealType lower, RealType mode, RealType upper, RealType x, RealType p, RealType q, RealType tol) |
| { |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::cdf( |
| triangular_distribution<RealType>(lower, mode, upper), // distribution. |
| x), // random variable. |
| p, // probability. |
| tol); // tolerance. |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::cdf( |
| complement( |
| triangular_distribution<RealType>(lower, mode, upper), // distribution. |
| x)), // random variable. |
| q, // probability complement. |
| tol); // tolerance. |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::quantile( |
| triangular_distribution<RealType>(lower,mode, upper), // distribution. |
| p), // probability. |
| x, // random variable. |
| tol); // tolerance. |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::quantile( |
| complement( |
| triangular_distribution<RealType>(lower, mode, upper), // distribution. |
| q)), // probability complement. |
| x, // random variable. |
| tol); // tolerance. |
| } // void check_triangular |
| |
| template <class RealType> |
| void test_spots(RealType) |
| { |
| // Basic sanity checks: |
| // |
| // Some test values were generated for the triangular distribution |
| // using the online calculator at |
| // http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm |
| // |
| // Tolerance is just over 5 epsilon expressed as a fraction: |
| RealType tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction. |
| RealType tol5eps = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction. |
| |
| cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << "." << endl; |
| |
| using namespace std; // for ADL of std::exp; |
| |
| // Tests on construction |
| // Default should be 0, 0, 1 |
| BOOST_CHECK_EQUAL(triangular_distribution<RealType>().lower(), -1); |
| BOOST_CHECK_EQUAL(triangular_distribution<RealType>().mode(), 0); |
| BOOST_CHECK_EQUAL(triangular_distribution<RealType>().upper(), 1); |
| BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).first, triangular_distribution<RealType>().lower()); |
| BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).second, triangular_distribution<RealType>().upper()); |
| |
| if (std::numeric_limits<RealType>::has_quiet_NaN == true) |
| { |
| BOOST_CHECK_THROW( // duff parameter lower. |
| triangular_distribution<RealType>(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0, 0), |
| std::domain_error); |
| |
| BOOST_CHECK_THROW( // duff parameter mode. |
| triangular_distribution<RealType>(0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0), |
| std::domain_error); |
| |
| BOOST_CHECK_THROW( // duff parameter upper. |
| triangular_distribution<RealType>(0, 0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())), |
| std::domain_error); |
| } // quiet_NaN tests. |
| |
| BOOST_CHECK_THROW( // duff parameters upper < lower. |
| triangular_distribution<RealType>(1, 0, -1), |
| std::domain_error); |
| |
| BOOST_CHECK_THROW( // duff parameters upper == lower. |
| triangular_distribution<RealType>(0, 0, 0), |
| std::domain_error); |
| BOOST_CHECK_THROW( // duff parameters mode < lower. |
| triangular_distribution<RealType>(0, -1, 1), |
| std::domain_error); |
| |
| BOOST_CHECK_THROW( // duff parameters mode > upper. |
| triangular_distribution<RealType>(0, 2, 1), |
| std::domain_error); |
| |
| // Tests for PDF |
| // // triangular_distribution<RealType>() default is (0, 0, 1), mode == lower. |
| BOOST_CHECK_CLOSE_FRACTION( // x == lower == mode |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0)), |
| static_cast<RealType>(2), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x == upper |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x > upper |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1)), |
| static_cast<RealType>(0), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( // x < lower |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x < lower |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| // triangular_distribution<RealType>() (0, 1, 1) mode == upper |
| BOOST_CHECK_CLOSE_FRACTION( // x == lower |
| pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x == upper |
| pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)), |
| static_cast<RealType>(2), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x > upper |
| pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)), |
| static_cast<RealType>(0), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( // x < lower |
| pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case pdf = 2 * x |
| pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)), |
| static_cast<RealType>(0.5), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case cdf = x * x |
| cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)), |
| static_cast<RealType>(0.25 * 0.25), |
| tolerance); |
| |
| // triangular_distribution<RealType>() (0, 0.5, 1) mode == middle. |
| BOOST_CHECK_CLOSE_FRACTION( // x == lower |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x == upper |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(1)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x > upper |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(-1)), |
| static_cast<RealType>(0), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( // x < lower |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(2)), |
| static_cast<RealType>(0), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x == mode |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.5)), |
| static_cast<RealType>(2), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x == half mode |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.25)), |
| static_cast<RealType>(1), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( // x == half mode |
| pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.75)), |
| static_cast<RealType>(1), |
| tolerance); |
| |
| 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_CHECK_THROW tests. |
| |
| BOOST_CHECK_THROW( // x == infinity NOT OK. |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(std::numeric_limits<RealType>::infinity())), |
| std::domain_error); |
| |
| BOOST_CHECK_THROW( // x == minus infinity not OK too. |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::infinity())), |
| std::domain_error); |
| } |
| if(std::numeric_limits<RealType>::has_quiet_NaN) |
| { // BOOST_CHECK tests for NaN using std::numeric_limits<>::has_quiet_NaN() - should throw. |
| BOOST_CHECK_THROW( |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())), |
| std::domain_error); |
| BOOST_CHECK_THROW( |
| pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::quiet_NaN())), |
| std::domain_error); |
| } // test for x = NaN using std::numeric_limits<>::quiet_NaN() |
| |
| // cdf |
| BOOST_CHECK_EQUAL( // x < lower |
| cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)), |
| static_cast<RealType>(0) ); |
| BOOST_CHECK_CLOSE_FRACTION( // x == lower |
| cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0)), |
| static_cast<RealType>(0), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( // x == upper |
| cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)), |
| static_cast<RealType>(1), |
| tolerance); |
| BOOST_CHECK_EQUAL( // x > upper |
| cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)), |
| static_cast<RealType>(1)); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x == mode |
| cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)), |
| //static_cast<RealType>((mode - lower) / (upper - lower)), |
| static_cast<RealType>(0.5), // (0 --1) / (1 -- 1) = 0.5 |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.9L)), |
| static_cast<RealType>(0.81L), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-1)), |
| static_cast<RealType>(0), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5L)), |
| static_cast<RealType>(0.125L), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)), |
| static_cast<RealType>(0.5), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(+0.5L)), |
| static_cast<RealType>(0.875L), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(1)), |
| static_cast<RealType>(1), |
| tolerance); |
| |
| // cdf complement |
| BOOST_CHECK_EQUAL( // x < lower |
| cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1))), |
| static_cast<RealType>(1)); |
| BOOST_CHECK_EQUAL( // x == lower |
| cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))), |
| static_cast<RealType>(1)); |
| |
| BOOST_CHECK_EQUAL( // x == mode |
| cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0))), |
| static_cast<RealType>(0.5)); |
| |
| BOOST_CHECK_EQUAL( // x == mode |
| cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))), |
| static_cast<RealType>(1)); |
| BOOST_CHECK_EQUAL( // x == mode |
| cdf(complement(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1))), |
| static_cast<RealType>(0)); |
| |
| BOOST_CHECK_EQUAL( // x > upper |
| cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2))), |
| static_cast<RealType>(0)); |
| BOOST_CHECK_EQUAL( // x == upper |
| cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1))), |
| static_cast<RealType>(0)); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x = -0.5 |
| cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5))), |
| static_cast<RealType>(0.875L), |
| tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION( // x = +0.5 |
| cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0.5))), |
| static_cast<RealType>(0.125), |
| tolerance); |
| |
| triangular_distribution<RealType> triang; // Using typedef == triangular_distribution<double> tristd; |
| triangular_distribution<RealType> tristd(0, 0.5, 1); // 'Standard' triangular distribution. |
| |
| BOOST_CHECK_CLOSE_FRACTION( // median of Standard triangular is sqrt(mode/2) if c > 1/2 else 1 - sqrt((1-c)/2) |
| median(tristd), |
| static_cast<RealType>(0.5), |
| tolerance); |
| triangular_distribution<RealType> tri011(0, 1, 1); // Using default RealType double. |
| triangular_distribution<RealType> tri0q1(0, 0.25, 1); // mode is near bottom. |
| triangular_distribution<RealType> tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle. |
| triangular_distribution<RealType> trim12(-1, -0.5, 2); // mode is negative. |
| |
| BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02L), static_cast<RealType>(0.0016L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5L), static_cast<RealType>(0.66666666666666666666666666666666666666666666667L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98L), static_cast<RealType>(0.9994666666666666666666666666666666666666666666L), tolerance); |
| |
| // quantile |
| BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.0016L)), static_cast<RealType>(0.02L), tol5eps); |
| BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.66666666666666666666666666666666666666666666667L)), static_cast<RealType>(0.5), tol5eps); |
| BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(0.3333333333333333333333333333333333333333333333333L))), static_cast<RealType>(0.5), tol5eps); |
| BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.999466666666666666666666666666666666666666666666666L)), static_cast<RealType>(98) / 100, 10 * tol5eps); |
| |
| BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), static_cast<RealType>(0.533333333333333333333333333333333333333333333L), tol5eps); |
| BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), static_cast<RealType>(0.466666666666666666666666666666666666666666667L), tol5eps); |
| BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), static_cast<RealType>(1 - 0.466666666666666666666666666666666666666666667L), tol5eps); |
| |
| BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(1 - 0.999466666666666666666666666666666666666666666666L))), static_cast<RealType>(0.98L), 10 * tol5eps); |
| BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1))), static_cast<RealType>(0), tol5eps); |
| 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 |
| 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: |
| BOOST_CHECK_CLOSE_FRACTION( |
| median(trim12), static_cast<RealType>(-0.13397459621556151), tolerance); |
| 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); // for all distributions. |
| |
| 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_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_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::infinity()), std::domain_error); |
| //BOOST_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); |
| // BOOST_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_CHECK_THROW(triangular_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); |
| BOOST_CHECK_THROW(triangular_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); |
| } |
| BOOST_CHECK_THROW(triangular_distribution<RealType>(1, 0), std::domain_error); // lower > upper! |
| |
| } // template <class RealType>void test_spots(RealType) |
| |
| int test_main(int, char* []) |
| { |
| // 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); |
| |
| for (int i = 0; i < 5; i++) |
| { |
| const triangular_distribution<double>* const dist = dists[i]; |
| cout << "Distribution " << i << endl; |
| BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.)); |
| BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5), quantile(complement(*dist, 0.5)), tol5eps); // OK |
| BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98), quantile(complement(*dist, 1. - 0.98)),tol5eps); |
| // cout << setprecision(17) << median(*dist) << endl; |
| } |
| |
| cout << showpos << setprecision(2) << endl; |
| |
| //triangular_distribution<double>& dist = trim12; |
| for (unsigned i = 0; i < sizeof(xs) /sizeof(double); i++) |
| { |
| double x = xs[i] * (trim12.upper() - trim12.lower()) + trim12.lower(); |
| double dx = cdf(trim12, x); |
| double cx = cdf(complement(trim12, x)); |
| //cout << fixed << showpos << setprecision(3) |
| // << xs[i] << ", " << x << ", " << pdf(trim12, x) << ", " << dx << ", " << cx << ",, " ; |
| |
| BOOST_CHECK_CLOSE_FRACTION(cx, 1 - dx, tol500eps); // cx == 1 - dx |
| |
| // << setprecision(2) << scientific << cr - x << ", " // difference x - quan(cdf) |
| // << setprecision(3) << fixed |
| // << quantile(trim12, dx) << ", " |
| // << quantile(complement(trim12, 1 - dx)) << ", " |
| // << quantile(complement(trim12, cx)) << ", " |
| // << endl; |
| BOOST_CHECK_CLOSE_FRACTION(quantile(trim12, dx), quantile(complement(trim12, 1 - dx)), tol500eps); |
| } |
| cout << endl; |
| // Basic sanity-check spot values. |
| // (Parameter value, arbitrarily zero, only communicates the floating point type). |
| test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 % |
| test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 % |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_spots(0.0L); // Test long double. |
| #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582)) |
| test_spots(boost::math::concepts::real_concept(0.)); // Test real concept. |
| #endif |
| #else |
| std::cout << "<note>The long double tests have been disabled on this platform " |
| "either because the long double overloads of the usual math functions are " |
| "not available at all, or because they are too inaccurate for these tests " |
| "to pass.</note>" << std::cout; |
| #endif |
| |
| return 0; |
| } // int test_main(int, char* []) |
| |
| /* |
| |
| Output: |
| |
| Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_triangular.exe" |
| Running 1 test case... |
| Distribution 0 |
| Distribution 1 |
| Distribution 2 |
| Distribution 3 |
| Distribution 4 |
| Tolerance for type float is 5.96046e-007. |
| Tolerance for type double is 1.11022e-015. |
| Tolerance for type long double is 1.11022e-015. |
| Tolerance for type class boost::math::concepts::real_concept is 1.11022e-015. |
| *** No errors detected |
| |
| |
| |
| */ |
| |
| |
| |
| |
