diff options
Diffstat (limited to 'src/boost/libs/math/test/test_arcsine.cpp')
| -rw-r--r-- | src/boost/libs/math/test/test_arcsine.cpp | 605 |
1 files changed, 605 insertions, 0 deletions
diff --git a/src/boost/libs/math/test/test_arcsine.cpp b/src/boost/libs/math/test/test_arcsine.cpp new file mode 100644 index 00000000..ed7bb709 --- /dev/null +++ b/src/boost/libs/math/test/test_arcsine.cpp @@ -0,0 +1,605 @@ +// test_arcsine_dist.cpp + +// Copyright John Maddock 2014. +// Copyright Paul A. Bristow 2014. + +// 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) + +// Tests for the arcsine Distribution. + +#include <pch.hpp> // Must be 1st include, and include_directory /libs/math/src/tr1/ is needed. + +#ifdef _MSC_VER +# pragma warning(disable: 4127) // Conditional expression is constant. +# pragma warning (disable : 4996) // POSIX name for this item is deprecated. +# pragma warning (disable : 4224) // Nonstandard extension used : formal parameter 'arg' was previously defined as a type. +#endif + +#include <boost/math/concepts/real_concept.hpp> // for real_concept. +using ::boost::math::concepts::real_concept; +#include <boost/math/tools/test.hpp> // for real_concept. + +#include <boost/math/distributions/arcsine.hpp> // for arcsine_distribution. +using boost::math::arcsine_distribution; + +#include <boost/math/constants/constants.hpp> +using boost::math::constants::one_div_root_two; + +#define BOOST_TEST_MAIN +#include <boost/test/unit_test.hpp> // for test_main +#include <boost/test/tools/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION + +#include <cmath> + +#include "test_out_of_range.hpp" + +#include <iostream> +using std::cout; +using std::endl; +#include <limits> +using std::numeric_limits; + + +template <class RealType> +void test_ignore_policy(RealType) +{ + // Check on returns when errors are ignored. + if ((typeid(RealType) != typeid(boost::math::concepts::real_concept)) + && std::numeric_limits<RealType>::has_infinity + && std::numeric_limits<RealType>::has_quiet_NaN + ) + { // Ordinary floats only. + + using namespace boost::math; + // RealType inf = std::numeric_limits<RealType>::infinity(); + RealType nan = std::numeric_limits<RealType>::quiet_NaN(); + + 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> + > ignore_all_policy; + + typedef arcsine_distribution<RealType, ignore_all_policy> ignore_error_arcsine; + + // 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) + { + // Demonstrate output of PDF with infinity, + // but strin goutput from NaN is platform dependent, so can't use BOOST_CHECK. + if (std::numeric_limits<RealType>::has_infinity) + { + //std::cout << "pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) = " << pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) << std::endl; + // Outputs: pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) = 1.#QNAN + } + BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity + BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity + BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(-2)))); // x < xmin + BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(-2)))); // x < xmin + BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(+2)))); // x > x_max + BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(+2)))); // x > x_max + + // Mean + BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-nan, 0)))); + BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(+nan, 0)))); + + if (std::numeric_limits<RealType>::has_infinity) + { + //BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity(), 0)))); + // std::cout << "arcsine(-inf,+1) mean " << mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity())) << std::endl; + //BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(std::numeric_limits<RealType>::infinity(), 0)))); + } + + // NaN constructors. + BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(2, nan)))); + BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, nan)))); + BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, 2)))); + + // Variance + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(nan, 0)))); + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, nan)))); + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, nan)))); + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(0, 0)))); + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, 0)))); + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(static_cast<RealType>(1.7L), 0)))); + BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, 0)))); + + // Skewness + BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(nan, 0)))); + BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(-1, nan)))); + BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(0, 0)))); + BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(1, 0)))); + BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(2, 0)))); + BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(3, 0)))); + + // Kurtosis + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(nan, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(-1, nan)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(0, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(1, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(2, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(3, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(4, 0)))); + + // Kurtosis excess + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(nan, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(-1, nan)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(0, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(1, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(2, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(3, 0)))); + BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(4, 0)))); + } // has_quiet_NaN + + // + BOOST_CHECK(boost::math::isfinite(mean(ignore_error_arcsine(0, std::numeric_limits<RealType>::epsilon())))); + + check_support<arcsine_distribution<RealType> >(arcsine_distribution<RealType>(0, 1)); + } // ordinary floats. +} // template <class RealType> void test_ignore_policy(RealType) + + +template <class RealType> +RealType informax() +{ //! \return Infinity else max_value. + return ((std::numeric_limits<RealType>::has_infinity) ? + std::numeric_limits<RealType>::infinity() : boost::math::tools::max_value<RealType>()); +} + +template <class RealType> +void test_spot( + RealType a, // alpha a or lo or x_min + RealType b, // arcsine b or hi or x_maz + RealType x, // Probability + RealType P, // CDF of arcsine(a, b) + RealType Q, // Complement of CDF of arcsine (a, b) + RealType tol) // Test tolerance. +{ + boost::math::arcsine_distribution<RealType> anarcsine(a, b); + BOOST_CHECK_CLOSE_FRACTION(cdf(anarcsine, x), P, tol); + if ((P < 0.99) && (Q < 0.99)) + { // We can only check this if P is not too close to 1, + // so that we can guarantee that Q is free of error, + // (and similarly for Q). + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(anarcsine, x)), Q, tol); + if (x != 0) + { + BOOST_CHECK_CLOSE_FRACTION( + quantile(anarcsine, P), x, tol); + } + else + { + // Just check quantile is very small: + if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) + && (boost::is_floating_point<RealType>::value)) + { + // Limit where this is checked: if exponent range is very large we may + // run out of iterations in our root finding algorithm. + BOOST_CHECK(quantile(anarcsine, P) < boost::math::tools::epsilon<RealType>() * 10); + } + } // if k + if (x != 0) + { + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(anarcsine, Q)), x, tol * 10); + } + else + { // Just check quantile is very small: + if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value)) + { // Limit where this is checked: if exponent range is very large we may + // run out of iterations in our root finding algorithm. + BOOST_CHECK(quantile(complement(anarcsine, Q)) < boost::math::tools::epsilon<RealType>() * 10); + } + } // if x + } +} // template <class RealType> void test_spot + +template <class RealType> // Any floating-point type RealType. +void test_spots(RealType) +{ + // Basic sanity checks with 'known good' values. + // so set tolerance to a few eps expressed as a fraction, or + // few eps of type double expressed as a fraction, + // whichever is the larger. + + RealType tolerance = (std::max) + (boost::math::tools::epsilon<RealType>(), + static_cast<RealType>(std::numeric_limits<double>::epsilon())); // 0 if real_concept. + + tolerance *= 2; // Note: NO * 100 because tolerance is a fraction, NOT %. + cout << "tolerance = " << tolerance << endl; + + using boost::math::arcsine_distribution; + using ::boost::math::cdf; + using ::boost::math::pdf; + using ::boost::math::complement; + using ::boost::math::quantile; + + // Basic sanity-check spot values. + + // Test values from Wolfram alpha, for example: + // http://www.wolframalpha.com/input/?i=+N%5BPDF%5Barcsinedistribution%5B0%2C+1%5D%2C+0.5%5D%2C+50%5D + // N[PDF[arcsinedistribution[0, 1], 0.5], 50] + // 0.63661977236758134307553505349005744813783858296183 + + arcsine_distribution<RealType> arcsine_01; // (Our) Standard arcsine. + // Member functions. + BOOST_CHECK_EQUAL(arcsine_01.x_min(), 0); + BOOST_CHECK_EQUAL(arcsine_01.x_max(), 1); + + // Derived functions. + BOOST_CHECK_EQUAL(mean(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly. + BOOST_CHECK_EQUAL(median(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly. + BOOST_CHECK_EQUAL(variance(arcsine_01), 0.125); // 1/8 = 0.125 + BOOST_CHECK_CLOSE_FRACTION(standard_deviation(arcsine_01), one_div_root_two<double>() / 2, tolerance); // 1/ sqrt(s) = 0.35355339059327379 + BOOST_CHECK_EQUAL(skewness(arcsine_01), 0); // + BOOST_CHECK_EQUAL(kurtosis_excess(arcsine_01), -1.5); // 3/2 + BOOST_CHECK_EQUAL(support(arcsine_01).first, 0); // + BOOST_CHECK_EQUAL(range(arcsine_01).first, 0); // + BOOST_MATH_CHECK_THROW(mode(arcsine_01), std::domain_error); // Two modes at x_min and x_max, so throw instead. + + // PDF + // pdf of x = 1/4 is same as reflected value at x = 3/4. + // N[PDF[arcsinedistribution[0, 1], 0.25], 50] + // N[PDF[arcsinedistribution[0, 1], 0.75], 50] + // 0.73510519389572273268176866441729258852984864048885 + + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000001), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000005), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.05), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.5), static_cast<RealType>(0.63661977236758134307553505349005744813783858296183L), tolerance); + // Note loss of significance when x is near x_max. + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.95), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 8 * tolerance); // Less accurate. + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.999995), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), 50000 * tolerance); // Much less accurate. + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.999999), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), 100000 * tolerance);// Even less accurate. + + // Extreme x. + if (std::numeric_limits<RealType>::has_infinity) + { // + BOOST_CHECK_EQUAL(pdf(arcsine_01, 0), informax<RealType>()); // + BOOST_CHECK_EQUAL(pdf(arcsine_01, 1), informax<RealType>()); // + } + + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, tolerance), + 1 /(sqrt(tolerance) * boost::math::constants::pi<RealType>()), 2 * tolerance); // + BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, static_cast<RealType>(1) - tolerance), + 1 /(sqrt(tolerance) * boost::math::constants::pi<RealType>()), 2 * tolerance); // + + // CDF + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.000001), static_cast<RealType>(0.00063661987847092448418377367957384866092127786060574L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.000005), static_cast<RealType>(0.0014235262731079289297302426454125318201831474507326L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.05), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.5), static_cast<RealType>(0.5L), tolerance); // Exact. + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.95), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), 2 * tolerance); + // Values near unity should use the cdf complemented for better accuracy, + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.999995), static_cast<RealType>(0.99857647372689207107026975735458746817981685254927L), 100 * tolerance); // Less accurate. + BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.999999), static_cast<RealType>(0.99936338012152907551581622632042615133907872213939L), 1000 * tolerance); // Less accurate. + + // Complement CDF + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.000001)), static_cast<RealType>(1 - 0.00063661987847092448418377367957384866092127786060574L), 2 * tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.000001)), static_cast<RealType>(0.99936338012152907551581622632043L), 2 * tolerance); // + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.05)), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.5)), static_cast<RealType>(0.5L), tolerance); // Exact. + // Some values near unity when complement is expected to be less accurate. + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.95)), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), 8 * tolerance); // 2 for asin + BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.999999)), static_cast<RealType>(1 - 0.99936338012152907551581622632042615133907872213939L), 1000000 * tolerance); // 10000 for asin, 1000000 for acos. + + // Quantile. + + // Check 1st, 2nd and 3rd quartiles. + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.25L)), static_cast<RealType>(0.14644660940672624L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5 + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.75L)), static_cast<RealType>(0.85355339059327373L), tolerance); + + // N[CDF[arcsinedistribution[0, 1], 0.05], 50] == 0.14356629312870627075094188477505571882161519989741 + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), 0.05, tolerance); + + // Quantile of complement. + // N[1-CDF[arcsinedistribution[0, 1], 0.05], 50] == 0.85643370687129372924905811522494428117838480010259 + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L))), 0.05, tolerance * 2); + // N[sin^2[0.75 * pi/2],50] == 0.85355339059327376220042218105242451964241796884424 + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.25L))), static_cast<RealType>(0.85355339059327376220042218105242451964241796884424L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.5L))), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5 + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.75L))), static_cast<RealType>(0.14644660940672623779957781894757548035758203115576L), 2 * tolerance); // Less accurate. + + // N[CDF[arcsinedistribution[0, 1], 0.25], 5 + // 0.33333333333333333333333333333333333333333333333333 + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(1) / 3), static_cast<RealType>(0.25L), 2 * tolerance); + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5 + BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(2) / 3), static_cast<RealType>(0.75L), tolerance); + + // Arcsine(-1, +1) xmin = -1, x_max = +1 symmetric about zero. + arcsine_distribution<RealType> as_m11(-1, +1); + + BOOST_CHECK_EQUAL(as_m11.x_min(), -1); // + BOOST_CHECK_EQUAL(as_m11.x_max(), +1); + BOOST_CHECK_EQUAL(mean(as_m11), 0); // + BOOST_CHECK_EQUAL(median(as_m11), 0); // + BOOST_CHECK_CLOSE_FRACTION(standard_deviation(as_m11), one_div_root_two<RealType>(), tolerance * 2); // + + BOOST_CHECK_EQUAL(variance(as_m11), 0.5); // 1 - (-1) = 2 ^ 2 = 4 /8 = 0.5 + BOOST_CHECK_EQUAL(skewness(as_m11), 0); // + BOOST_CHECK_EQUAL(kurtosis_excess(as_m11), -1.5); // 3/2 + + + BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.05), static_cast<RealType>(0.31870852113797122803869876869296281629727218095644L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.5), static_cast<RealType>(0.36755259694786136634088433220864629426492432024443L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.95), static_cast<RealType>(1.0194074882503562519812229448639426942621591013381L), 2 * tolerance); // Less accurate. + + BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.05), static_cast<RealType>(0.51592213323666034437274347433261364289389772737836L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.5), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), 2 * tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.95), static_cast<RealType>(0.89891737589574013042121018491729701360300248368629L), tolerance); // Not less accurate. + + // Quantile + BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(1) / 3), -static_cast<RealType>(0.5L), 2 * tolerance); // p = 1/3 x = -0.5 + BOOST_CHECK_SMALL(quantile(as_m11, static_cast<RealType>(0.5L)), 2 * tolerance); // p = 0.5, x = 0 + BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(2) / 3), +static_cast<RealType>(0.5L), 4 * tolerance); // p = 2/3, x = +0.5 + + // Loop back tests. + test_spot( + static_cast<RealType>(0), // lo or a + static_cast<RealType>(1), // hi or b + static_cast<RealType>(0.05), // Random variate x + static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Probability of result (CDF of arcsine), P + static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Complement of CDF Q = 1 - P + tolerance); // Test tolerance. + + test_spot( + static_cast<RealType>(0), // lo or a + static_cast<RealType>(1), // hi or b + static_cast<RealType>(0.95), // Random variate x + static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Probability of result (CDF of arcsine), P + static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Complement of CDF Q = 1 - P + tolerance * 4); // Test tolerance (slightly inceased compared to x < 0.5 above). + + test_spot( + static_cast<RealType>(0), // lo or a + static_cast<RealType>(1), // hi or b + static_cast<RealType>(static_cast<RealType>(0.5L)), // Random variate x + static_cast<RealType>(static_cast<RealType>(0.5L)), // Probability of result (CDF of arcsine), P + static_cast<RealType>(static_cast<RealType>(0.5L)), // Complement of CDF Q = 1 - P + tolerance * 4); // Test tolerance. + + // Arcsine(-2, -1) xmin = -2, x_max = -1 - Asymmetric both negative. + arcsine_distribution<RealType> as_m2m1(-2, -1); + + BOOST_CHECK_EQUAL(as_m2m1.x_min(), -2); // + BOOST_CHECK_EQUAL(as_m2m1.x_max(), -1); + BOOST_CHECK_EQUAL(mean(as_m2m1), -1.5); // 1 / (1 + 1) = 1/2 exactly. + BOOST_CHECK_EQUAL(median(as_m2m1), -1.5); // 1 / (1 + 1) = 1/2 exactly. + BOOST_CHECK_EQUAL(variance(as_m2m1), 0.125); + BOOST_CHECK_EQUAL(skewness(as_m2m1), 0); // + BOOST_CHECK_EQUAL(kurtosis_excess(as_m2m1), -1.5); // 3/2 + + BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.95), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 4 * tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.5), static_cast<RealType>(0.63661977236758134307553505349005744813783858296183L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.05), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 4 * tolerance); // Less accurate. + + BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.05), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.5), static_cast<RealType>(0.5L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.95), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), 8 * tolerance); // Not much less accurate. + + // Quantile + BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L)), -static_cast<RealType>(1.05L), 2 * tolerance); // + BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.5L)), -static_cast<RealType>(1.5L), 2 * tolerance); // + BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), -static_cast<RealType>(1.95L), 4 * tolerance); // + + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(as_m2m1, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L))), -static_cast<RealType>(1.05L), 2 * tolerance); // + BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.5L)), -static_cast<RealType>(1.5L), 2 * tolerance); // + BOOST_CHECK_CLOSE_FRACTION(quantile(complement(as_m2m1, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L))), -static_cast<RealType>(1.95L), 4 * tolerance); + + // Tests that should throw: + BOOST_MATH_CHECK_THROW(mode(arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1))), std::domain_error); + // mode is undefined, and must throw domain_error! + + + BOOST_MATH_CHECK_THROW( // For various bad arguments. + pdf( + arcsine_distribution<RealType>(static_cast<RealType>(+1), static_cast<RealType>(-1)), // min_x > max_x + static_cast<RealType>(1)), std::domain_error); + + BOOST_MATH_CHECK_THROW( + pdf( + arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(0)), // bad constructor parameters. + static_cast<RealType>(1)), std::domain_error); + + BOOST_MATH_CHECK_THROW( + pdf( + arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(-1)), // bad constructor parameters. + static_cast<RealType>(1)), std::domain_error); + + BOOST_MATH_CHECK_THROW( + pdf( + arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // equal constructor parameters. + static_cast<RealType>(-1)), std::domain_error); + + BOOST_MATH_CHECK_THROW( + pdf( + arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1)), // bad x > 1. + static_cast<RealType>(999)), std::domain_error); + + // Checks on things that are errors. + + // Construction with 'bad' parameters. + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(+1, -1), std::domain_error); // max < min. + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(+1, 0), std::domain_error); // max < min. + + arcsine_distribution<> dist; + BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error); + BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error); + BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + + // Various combinations of bad contructor and member function parameters. + BOOST_MATH_CHECK_THROW(pdf(boost::math::arcsine_distribution<RealType>(0, 1), -1), std::domain_error); + BOOST_MATH_CHECK_THROW(pdf(boost::math::arcsine_distribution<RealType>(-1, 1), +2), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(boost::math::arcsine_distribution<RealType>(1, 1), -1), std::domain_error); + BOOST_MATH_CHECK_THROW(quantile(boost::math::arcsine_distribution<RealType>(1, 1), 2), std::domain_error); + + // No longer allow any parameter to be NaN or inf, so all these tests should throw. + if (std::numeric_limits<RealType>::has_quiet_NaN) + { + // Attempt to construct from non-finite parameters should throw. + RealType nan = std::numeric_limits<RealType>::quiet_NaN(); +#ifndef BOOST_NO_EXCEPTIONS + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(nan), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, nan), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(nan, 1), std::domain_error); +#else + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(nan), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, nan), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(nan, 1), std::domain_error); +#endif + + arcsine_distribution<RealType> w(RealType(-1), RealType(+1)); + // NaN parameters to member functions should throw. + BOOST_MATH_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN + BOOST_MATH_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN + BOOST_MATH_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan + BOOST_MATH_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan + BOOST_MATH_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan + } // has_quiet_NaN + + if (std::numeric_limits<RealType>::has_infinity) + { + // Attempt to construct from non-finite should throw. + RealType inf = std::numeric_limits<RealType>::infinity(); +#ifndef BOOST_NO_EXCEPTIONS + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(inf), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, inf), std::domain_error); +#else + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(inf), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, inf), std::domain_error); +#endif + // Infinite parameters to member functions should throw. + arcsine_distribution<RealType> w(RealType(0), RealType(1)); +#ifndef BOOST_NO_EXCEPTIONS + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(inf), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, inf), std::domain_error); +#else + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(inf), std::domain_error); + BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, inf), std::domain_error); +#endif + BOOST_MATH_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf + BOOST_MATH_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf + BOOST_MATH_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf + BOOST_MATH_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf + BOOST_MATH_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf + } // has_infinity + + // Error handling checks: + check_out_of_range<boost::math::arcsine_distribution<RealType> >(-1, +1); // (All) valid constructor parameter values. + // and range and non-finite. + + test_ignore_policy(static_cast<RealType>(0)); + + } // template <class RealType>void test_spots(RealType) + + BOOST_AUTO_TEST_CASE(test_main) + { + BOOST_MATH_CONTROL_FP; + + // Check that can generate arcsine distribution using convenience method: + using boost::math::arcsine; + + arcsine_distribution<> arcsine_01; // Using default RealType double. + // Note: NOT arcsine01() - or compiler will assume a function. + + arcsine as; // Using typedef for default standard arcsine. + + // + BOOST_CHECK_EQUAL(as.x_min(), 0); // + BOOST_CHECK_EQUAL(as.x_max(), 1); + BOOST_CHECK_EQUAL(mean(as), 0.5); // 1 / (1 + 1) = 1/2 exactly. + BOOST_CHECK_EQUAL(median(as), 0.5); // 1 / (1 + 1) = 1/2 exactly. + BOOST_CHECK_EQUAL(variance(as), 0.125); //0.125 + BOOST_CHECK_CLOSE_FRACTION(standard_deviation(as), one_div_root_two<double>() / 2, std::numeric_limits<double>::epsilon()); // 0.353553 + BOOST_CHECK_EQUAL(skewness(as), 0); // + BOOST_CHECK_EQUAL(kurtosis_excess(as), -1.5); // 3/2 + BOOST_CHECK_EQUAL(support(as).first, 0); // + BOOST_CHECK_EQUAL(range(as).first, 0); // + BOOST_MATH_CHECK_THROW(mode(as), std::domain_error); // Two modes at x_min and x_max, so throw instead. + + // (Parameter value, arbitrarily zero, only communicates the floating point type). + test_spots(0.0F); // Test float. + test_spots(0.0); // Test double. + #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + test_spots(0.0L); // Test long double. + #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) + test_spots(boost::math::concepts::real_concept(0.)); // Test real concept. + #endif + #endif + /* */ + } // BOOST_AUTO_TEST_CASE( test_main ) + + /* + + +Microsoft Visual Studio Professional 2013 +Version 12.0.30110.00 Update 1 + + 1> Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe" + 1> Running 1 test case... + 1> Platform: Win32 + 1> Compiler: Microsoft Visual C++ version 12.0 ???? MSVC says 2013 + 1> STL : Dinkumware standard library version 610 + 1> Boost : 1.56.0 + + Sample Output is: + + 1> Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe" + 1> Running 1 test case... + 1> Platform: Win32 + 1> Compiler: Microsoft Visual C++ version 12.0 + 1> STL : Dinkumware standard library version 610 + 1> Boost : 1.56.0 + 1> tolerance = 2.38419e-007 + 1> tolerance = 4.44089e-016 + 1> tolerance = 4.44089e-016 + 1> tolerance = 4.44089e-016 + 1> + 1> *** No errors detected + + GCC 4.9.1 + + Running 1 test case... + tolerance = 2.38419e-007 + tolerance = 4.44089e-016 + tolerance = 4.44089e-016 + tolerance = 4.44089e-016 + + *** No errors detected + + RUN SUCCESSFUL (total time: 141ms) + + */ |