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Diffstat (limited to 'src/boost/libs/math/test/test_gamma_dist.cpp')
-rw-r--r-- | src/boost/libs/math/test/test_gamma_dist.cpp | 268 |
1 files changed, 268 insertions, 0 deletions
diff --git a/src/boost/libs/math/test/test_gamma_dist.cpp b/src/boost/libs/math/test/test_gamma_dist.cpp new file mode 100644 index 00000000..7ee1ee5d --- /dev/null +++ b/src/boost/libs/math/test/test_gamma_dist.cpp @@ -0,0 +1,268 @@ +// Copyright John Maddock 2006. +// Copyright Paul A. Bristow 2007, 2010. + +// 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_gamma_dist.cpp + +// http://en.wikipedia.org/wiki/Gamma_distribution +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm +// Also: +// Weisstein, Eric W. "Gamma Distribution." +// From MathWorld--A Wolfram Web Resource. +// http://mathworld.wolfram.com/GammaDistribution.html + +#include <pch.hpp> // include directory libs/math/src/tr1/ is needed. + +#include <boost/math/concepts/real_concept.hpp> // for real_concept +#define BOOST_TEST_MAIN +#include <boost/test/unit_test.hpp> // Boost.Test +#include <boost/test/tools/floating_point_comparison.hpp> + +#include <boost/math/distributions/gamma.hpp> + using boost::math::gamma_distribution; +#include <boost/math/tools/test.hpp> +#include "test_out_of_range.hpp" + +#include <iostream> +#include <iomanip> + using std::cout; + using std::endl; + using std::setprecision; +#include <limits> + using std::numeric_limits; + +template <class RealType> +RealType NaivePDF(RealType shape, RealType scale, RealType x) +{ + // Deliberately naive PDF calculator again which + // we'll compare our pdf function. However some + // published values to compare against would be better.... + using namespace std; + RealType result = log(x) * (shape - 1) - x / scale - boost::math::lgamma(shape) - log(scale) * shape; + return exp(result); +} + +template <class RealType> +void check_gamma(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol) +{ + BOOST_CHECK_CLOSE( + ::boost::math::cdf( + gamma_distribution<RealType>(shape, scale), // distribution. + x), // random variable. + p, // probability. + tol); // %tolerance. + BOOST_CHECK_CLOSE( + ::boost::math::cdf( + complement( + gamma_distribution<RealType>(shape, scale), // distribution. + x)), // random variable. + q, // probability complement. + tol); // %tolerance. + if(p < 0.999) + { + BOOST_CHECK_CLOSE( + ::boost::math::quantile( + gamma_distribution<RealType>(shape, scale), // distribution. + p), // probability. + x, // random variable. + tol); // %tolerance. + } + if(q < 0.999) + { + BOOST_CHECK_CLOSE( + ::boost::math::quantile( + complement( + gamma_distribution<RealType>(shape, scale), // distribution. + q)), // probability complement. + x, // random variable. + tol); // %tolerance. + } + // PDF: + BOOST_CHECK_CLOSE( + boost::math::pdf( + gamma_distribution<RealType>(shape, scale), // distribution. + x), // random variable. + NaivePDF(shape, scale, x), // PDF + tol); // %tolerance. +} + +template <class RealType> +void test_spots(RealType) +{ + // Basic sanity checks + // + // 15 decimal places expressed as a persentage. + // The first tests use values generated by MathCAD, + // and should be accurate to around double precision. + // + RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits<RealType>::epsilon() * 20) * 100; + cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; + + check_gamma( + static_cast<RealType>(0.5), + static_cast<RealType>(1), + static_cast<RealType>(0.5), + static_cast<RealType>(0.682689492137085), + static_cast<RealType>(1-0.682689492137085), + tolerance); + check_gamma( + static_cast<RealType>(2), + static_cast<RealType>(1), + static_cast<RealType>(0.5), + static_cast<RealType>(0.090204010431050), + static_cast<RealType>(1-0.090204010431050), + tolerance); + check_gamma( + static_cast<RealType>(40), + static_cast<RealType>(1), + static_cast<RealType>(10), + static_cast<RealType>(7.34163631456064E-13), + static_cast<RealType>(1-7.34163631456064E-13), + tolerance); + + // + // Some more test data generated by the online + // calculator at http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm + // This has the advantage of supporting the scale parameter as well + // as shape, but has only a few digits accuracy, and produces + // some deeply suspect values if the shape parameter is < 1 + // (it doesn't agree with MathCAD or this implementation). + // To be fair the incomplete gamma is tricky to get right in this area... + // + tolerance = 1e-5f * 100; // 5 decimal places as a persentage + cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; + + check_gamma( + static_cast<RealType>(2), + static_cast<RealType>(1)/5, + static_cast<RealType>(0.1), + static_cast<RealType>(0.090204), + static_cast<RealType>(1-0.090204), + tolerance); + check_gamma( + static_cast<RealType>(2), + static_cast<RealType>(1)/5, + static_cast<RealType>(0.5), + static_cast<RealType>(1-0.287298), + static_cast<RealType>(0.287298), + tolerance); + check_gamma( + static_cast<RealType>(3), + static_cast<RealType>(2), + static_cast<RealType>(1), + static_cast<RealType>(0.014388), + static_cast<RealType>(1-0.014388), + tolerance * 10); // one less decimal place in the test value + check_gamma( + static_cast<RealType>(3), + static_cast<RealType>(2), + static_cast<RealType>(5), + static_cast<RealType>(0.456187), + static_cast<RealType>(1-0.456187), + tolerance); + + + RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a persentage + gamma_distribution<RealType> dist(8, 3); + RealType x = static_cast<RealType>(0.125); + using namespace std; // ADL of std names. + // mean: + BOOST_CHECK_CLOSE( + mean(dist) + , static_cast<RealType>(8*3), tol2); + // variance: + BOOST_CHECK_CLOSE( + variance(dist) + , static_cast<RealType>(8*3*3), tol2); + // std deviation: + BOOST_CHECK_CLOSE( + standard_deviation(dist) + , sqrt(static_cast<RealType>(8*3*3)), 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_CHECK_CLOSE( + coefficient_of_variation(dist) + , standard_deviation(dist) / mean(dist), tol2); + // mode: + BOOST_CHECK_CLOSE( + mode(dist) + , static_cast<RealType>(7 * 3), tol2); + // skewness: + BOOST_CHECK_CLOSE( + skewness(dist) + , 2 / sqrt(static_cast<RealType>(8)), tol2); + // kertosis: + BOOST_CHECK_CLOSE( + kurtosis(dist) + , 3 + 6 / static_cast<RealType>(8), tol2); + // kertosis excess: + BOOST_CHECK_CLOSE( + kurtosis_excess(dist) + , 6 / static_cast<RealType>(8), tol2); + + BOOST_CHECK_CLOSE( + median(dist), static_cast<RealType>(23.007748327502412), // double precision test value + (std::max)(tol2, static_cast<RealType>(std::numeric_limits<double>::epsilon() * 2 * 100))); // 2 eps as persent + // Rely on default definition in derived accessors. + + // error tests + check_out_of_range<boost::math::gamma_distribution<RealType> >(1, 1); + BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(0, 1), std::domain_error); + BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(-1, 1), std::domain_error); + BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, 0), std::domain_error); + BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, -1), std::domain_error); + +} // template <class RealType>void test_spots(RealType) + +BOOST_AUTO_TEST_CASE( test_main ) +{ + // 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. +#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS + 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::endl; +#endif + + +} // BOOST_AUTO_TEST_CASE( test_main ) + + +/* + +Output: + +Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_gamma_dist.exe" +Running 1 test case... +Tolerance for type float is 0.000238419 % +Tolerance for type float is 0.001 % +Tolerance for type double is 5e-012 % +Tolerance for type double is 0.001 % +Tolerance for type long double is 5e-012 % +Tolerance for type long double is 0.001 % +Tolerance for type class boost::math::concepts::real_concept is 5e-012 % +Tolerance for type class boost::math::concepts::real_concept is 0.001 % +*** No errors detected + +*/ + + |