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Diffstat (limited to 'src/boost/libs/math/test/test_normal.cpp')
| -rw-r--r-- | src/boost/libs/math/test/test_normal.cpp | 391 |
1 files changed, 391 insertions, 0 deletions
diff --git a/src/boost/libs/math/test/test_normal.cpp b/src/boost/libs/math/test/test_normal.cpp new file mode 100644 index 00000000..757e942c --- /dev/null +++ b/src/boost/libs/math/test/test_normal.cpp @@ -0,0 +1,391 @@ +// Copyright Paul A. Bristow 2010. +// Copyright John Maddock 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_normal.cpp + +// http://en.wikipedia.org/wiki/Normal_distribution +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm +// Also: +// Weisstein, Eric W. "Normal Distribution." +// From MathWorld--A Wolfram Web Resource. +// http://mathworld.wolfram.com/NormalDistribution.html + +#include <pch.hpp> // include directory /libs/math/src/tr1/ is needed. + +#ifdef _MSC_VER +# pragma warning (disable: 4127) // conditional expression is constant +// caused by using if(std::numeric_limits<RealType>::has_infinity) +// and if (std::numeric_limits<RealType>::has_quiet_NaN) +#endif + +#include <boost/math/tools/test.hpp> +#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/normal.hpp> + using boost::math::normal_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 mean, RealType sd, 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; + return exp(-(x-mean)*(x-mean)/(2*sd*sd))/(sd * sqrt(2*boost::math::constants::pi<RealType>())); +} + +template <class RealType> +void check_normal(RealType mean, RealType sd, RealType x, RealType p, RealType q, RealType tol) +{ + BOOST_CHECK_CLOSE( + ::boost::math::cdf( + normal_distribution<RealType>(mean, sd), // distribution. + x), // random variable. + p, // probability. + tol); // %tolerance. + BOOST_CHECK_CLOSE( + ::boost::math::cdf( + complement( + normal_distribution<RealType>(mean, sd), // distribution. + x)), // random variable. + q, // probability complement. + tol); // %tolerance. + BOOST_CHECK_CLOSE( + ::boost::math::quantile( + normal_distribution<RealType>(mean, sd), // distribution. + p), // probability. + x, // random variable. + tol); // %tolerance. + BOOST_CHECK_CLOSE( + ::boost::math::quantile( + complement( + normal_distribution<RealType>(mean, sd), // distribution. + q)), // probability complement. + x, // random variable. + tol); // %tolerance. +} + +template <class RealType> +void test_spots(RealType) +{ + // Basic sanity checks + RealType tolerance = 1e-2f; // 1e-4 (as %) + // Some tests only pass at 1e-4 because values generated by + // http://faculty.vassar.edu/lowry/VassarStats.html + // give only 5 or 6 *fixed* places, so small values have fewer digits. + + // Check some bad parameters to the distribution, +#ifndef BOOST_NO_EXCEPTIONS + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd +#else + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, 0), std::domain_error); // zero sd + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, -1), std::domain_error); // negative sd +#endif + + // Tests on extreme values of random variate x, if has std::numeric_limits infinity etc. + normal_distribution<RealType> N01; + if(std::numeric_limits<RealType>::has_infinity) + { + BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0 + BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0 + BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1 + BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0 + BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0 + BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1 +#ifndef BOOST_NO_EXCEPTIONS + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd +#else + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean + BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd +#endif + } + + if (std::numeric_limits<RealType>::has_quiet_NaN) + { + // No longer allow x to be NaN, then these tests should throw. + BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN + BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN + BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity + BOOST_MATH_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity + BOOST_MATH_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity + } + + cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; + + check_normal( + static_cast<RealType>(5), + static_cast<RealType>(2), + static_cast<RealType>(4.8), + static_cast<RealType>(0.46017), + static_cast<RealType>(1 - 0.46017), + tolerance); + + check_normal( + static_cast<RealType>(5), + static_cast<RealType>(2), + static_cast<RealType>(5.2), + static_cast<RealType>(1 - 0.46017), + static_cast<RealType>(0.46017), + tolerance); + + check_normal( + static_cast<RealType>(5), + static_cast<RealType>(2), + static_cast<RealType>(2.2), + static_cast<RealType>(0.08076), + static_cast<RealType>(1 - 0.08076), + tolerance); + + check_normal( + static_cast<RealType>(5), + static_cast<RealType>(2), + static_cast<RealType>(7.8), + static_cast<RealType>(1 - 0.08076), + static_cast<RealType>(0.08076), + tolerance); + + check_normal( + static_cast<RealType>(-3), + static_cast<RealType>(5), + static_cast<RealType>(-4.5), + static_cast<RealType>(0.38209), + static_cast<RealType>(1 - 0.38209), + tolerance); + + check_normal( + static_cast<RealType>(-3), + static_cast<RealType>(5), + static_cast<RealType>(-1.5), + static_cast<RealType>(1 - 0.38209), + static_cast<RealType>(0.38209), + tolerance); + + check_normal( + static_cast<RealType>(-3), + static_cast<RealType>(5), + static_cast<RealType>(-8.5), + static_cast<RealType>(0.13567), + static_cast<RealType>(1 - 0.13567), + tolerance); + + check_normal( + static_cast<RealType>(-3), + static_cast<RealType>(5), + static_cast<RealType>(2.5), + static_cast<RealType>(1 - 0.13567), + static_cast<RealType>(0.13567), + tolerance); + + // + // Tests for PDF: we know that the peak value is at 1/sqrt(2*pi) + // + tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage + BOOST_CHECK_CLOSE( + pdf(normal_distribution<RealType>(), static_cast<RealType>(0)), + static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi) + tolerance); + BOOST_CHECK_CLOSE( + pdf(normal_distribution<RealType>(3), static_cast<RealType>(3)), + static_cast<RealType>(0.3989422804014326779399460599343818684759L), + tolerance); + BOOST_CHECK_CLOSE( + pdf(normal_distribution<RealType>(3, 5), static_cast<RealType>(3)), + static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5), + tolerance); + + // + // Spot checks for mean = -5, sd = 6: + // + for(RealType x = -15; x < 5; x += 0.125) + { + BOOST_CHECK_CLOSE( + pdf(normal_distribution<RealType>(-5, 6), x), + NaivePDF(RealType(-5), RealType(6), x), + tolerance); + } + + RealType tol2 = boost::math::tools::epsilon<RealType>() * 5; + normal_distribution<RealType> dist(8, 3); + RealType x = static_cast<RealType>(0.125); + + BOOST_MATH_STD_USING // ADL of std math lib names + + // mean: + BOOST_CHECK_CLOSE( + mean(dist) + , static_cast<RealType>(8), tol2); + // variance: + BOOST_CHECK_CLOSE( + variance(dist) + , static_cast<RealType>(9), tol2); + // std deviation: + BOOST_CHECK_CLOSE( + standard_deviation(dist) + , static_cast<RealType>(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>(8), tol2); + + BOOST_CHECK_CLOSE( + median(dist) + , static_cast<RealType>(8), tol2); + + // skewness: + BOOST_CHECK_CLOSE( + skewness(dist) + , static_cast<RealType>(0), tol2); + // kertosis: + BOOST_CHECK_CLOSE( + kurtosis(dist) + , static_cast<RealType>(3), tol2); + // kertosis excess: + BOOST_CHECK_CLOSE( + kurtosis_excess(dist) + , static_cast<RealType>(0), tol2); + + normal_distribution<RealType> norm01(0, 1); // Test default (0, 1) + BOOST_CHECK_CLOSE( + mean(norm01), + static_cast<RealType>(0), 0); // Mean == zero + + normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1) + BOOST_CHECK_CLOSE( + mean(defsd_norm01), + static_cast<RealType>(0), 0); // Mean == zero + + normal_distribution<RealType> def_norm01; // Test default (0, sd = 1) + BOOST_CHECK_CLOSE( + mean(def_norm01), + static_cast<RealType>(0), 0); // Mean == zero + + BOOST_CHECK_CLOSE( + standard_deviation(def_norm01), + static_cast<RealType>(1), 0); // Mean == zero + + // Error tests: + check_out_of_range<boost::math::normal_distribution<RealType> >(0, 1); // (All) valid constructor parameter values. + + BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, 0), 0), std::domain_error); + BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, -1), 0), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), -1), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), 2), std::domain_error); +} // template <class RealType>void test_spots(RealType) + +BOOST_AUTO_TEST_CASE( test_main ) +{ + // Check that can generate normal distribution using the two convenience methods: + boost::math::normal myf1(1., 2); // Using typedef + normal_distribution<> myf2(1., 2); // Using default RealType double. + boost::math::normal myn01; // Use default values. + // Note NOT myn01() as the compiler will interpret as a function! + + // Check the synonyms, provided to allow generic use of find_location and find_scale. + BOOST_CHECK_EQUAL(myn01.mean(), myn01.location()); + BOOST_CHECK_EQUAL(myn01.standard_deviation(), myn01.scale()); + + // 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::endl; +#endif + + +} // BOOST_AUTO_TEST_CASE( test_main ) + +/* + +Output: + +Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe" +Running 1 test case... +Tolerance for type float is 0.01 % +Tolerance for type double is 0.01 % +Tolerance for type long double is 0.01 % +Tolerance for type class boost::math::concepts::real_concept is 0.01 % +*** No errors detected + + + + +------ Build started: Project: test_normal, Configuration: Release Win32 ------ + test_normal.cpp + Generating code + Finished generating code + test_normal.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_normal.exe + Running 1 test case... + Tolerance for type float is 0.01 % + Tolerance for type double is 0.01 % + Tolerance for type long double is 0.01 % + Tolerance for type class boost::math::concepts::real_concept is 0.01 % + + *** No errors detected + Detected memory leaks! + Dumping objects -> + {2413} normal block at 0x00321190, 42 bytes long. + Data: <class boost::mat> 63 6C 61 73 73 20 62 6F 6F 73 74 3A 3A 6D 61 74 + {2412} normal block at 0x003231F0, 8 bytes long. + Data: < 2 22 > 90 11 32 00 98 32 32 00 + {1824} normal block at 0x00323180, 12 bytes long. + Data: <long double > 6C 6F 6E 67 20 64 6F 75 62 6C 65 00 + {1823} normal block at 0x00323298, 8 bytes long. + Data: < 12 `22 > 80 31 32 00 60 32 32 00 + {1227} normal block at 0x00323148, 7 bytes long. + Data: <double > 64 6F 75 62 6C 65 00 + {1226} normal block at 0x00323260, 8 bytes long. + Data: <H12 02 > 48 31 32 00 A0 30 32 00 + {633} normal block at 0x003230D8, 6 bytes long. + Data: <float > 66 6C 6F 61 74 00 + {632} normal block at 0x003230A0, 8 bytes long. + Data: < 02 > D8 30 32 00 00 00 00 00 + Object dump complete. +========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ========== + + +*/ + + |