| // 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/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/normal.hpp> |
| using boost::math::normal_distribution; |
| #include <boost/math/tools/test.hpp> |
| |
| #include <iostream> |
| 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, |
| BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd |
| BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd |
| |
| // Tests on extreme values of random variate x, if has numeric_limit 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 |
| BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean |
| BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean |
| BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd |
| } |
| |
| if (std::numeric_limits<RealType>::has_quiet_NaN) |
| { |
| // No longer allow x to be NaN, then these tests should throw. |
| BOOST_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN |
| BOOST_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN |
| BOOST_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity |
| BOOST_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity |
| BOOST_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); |
| using namespace std; // ADL of std 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 |
| |
| |
| } // template <class RealType>void test_spots(RealType) |
| |
| int test_main(int, char* []) |
| { |
| // 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::cout; |
| #endif |
| |
| return 0; |
| } // int test_main(int, char* []) |
| |
| /* |
| |
| 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 ========== |
| |
| |
| */ |
| |
| |
