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- // Copyright Paul Bristow 2007.
- // Copyright John Maddock 2006.
- // 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_uniform.cpp
- #include <pch.hpp>
- #ifdef _MSC_VER
- # pragma warning(disable: 4127) // conditional expression is constant.
- # pragma warning(disable: 4100) // unreferenced formal parameter.
- #endif
- #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/uniform.hpp>
- using boost::math::uniform_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>
- void check_uniform(RealType lower, RealType upper, RealType x, RealType p, RealType q, RealType tol)
- {
- BOOST_CHECK_CLOSE_FRACTION(
- ::boost::math::cdf(
- uniform_distribution<RealType>(lower, upper), // distribution.
- x), // random variable.
- p, // probability.
- tol); // tolerance.
- BOOST_CHECK_CLOSE_FRACTION(
- ::boost::math::cdf(
- complement(
- uniform_distribution<RealType>(lower, upper), // distribution.
- x)), // random variable.
- q, // probability complement.
- tol); // tolerance.
- BOOST_CHECK_CLOSE_FRACTION(
- ::boost::math::quantile(
- uniform_distribution<RealType>(lower, upper), // distribution.
- p), // probability.
- x, // random variable.
- tol); // tolerance.
- BOOST_CHECK_CLOSE_FRACTION(
- ::boost::math::quantile(
- complement(
- uniform_distribution<RealType>(lower, upper), // distribution.
- q)), // probability complement.
- x, // random variable.
- tol); // tolerance.
- } // void check_uniform
- template <class RealType>
- void test_spots(RealType)
- {
- // Basic sanity checks
- //
- // These test values were generated for the normal 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 decimal digits expressed as a fraction:
- // that's the limit of the test data.
- RealType tolerance = 2e-5f;
- cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
- using std::exp;
- // Tests for PDF
- //
- BOOST_CHECK_CLOSE_FRACTION( // x == upper
- pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)),
- static_cast<RealType>(1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == lower
- pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1)),
- static_cast<RealType>(1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x > upper
- pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-1)),
- static_cast<RealType>(0),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x < lower
- pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2)),
- static_cast<RealType>(0),
- 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_MATH_CHECK_THROW tests.
- BOOST_MATH_CHECK_THROW( // x == infinity should NOT be OK.
- pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::infinity())),
- std::domain_error);
- BOOST_MATH_CHECK_THROW( // x == minus infinity should be OK too.
- pdf(uniform_distribution<RealType>(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_MATH_CHECK_THROW(
- pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
- std::domain_error);
- BOOST_MATH_CHECK_THROW(
- pdf(uniform_distribution<RealType>(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(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-1)),
- static_cast<RealType>(0) );
- BOOST_CHECK_CLOSE_FRACTION(
- cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)),
- static_cast<RealType>(0),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5)),
- static_cast<RealType>(0.5),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1)),
- static_cast<RealType>(0.1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9)),
- static_cast<RealType>(0.9),
- tolerance);
- BOOST_CHECK_EQUAL( // x > upper
- cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2)),
- static_cast<RealType>(1));
- // cdf complement
- BOOST_CHECK_EQUAL( // x < lower
- cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))),
- static_cast<RealType>(1));
- BOOST_CHECK_EQUAL( // x == 0
- cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))),
- static_cast<RealType>(1));
- BOOST_CHECK_CLOSE_FRACTION( // x = 0.1
- cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1))),
- static_cast<RealType>(0.9),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x = 0.5
- cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5))),
- static_cast<RealType>(0.5),
- tolerance);
- BOOST_CHECK_EQUAL( // x == 1
- cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1))),
- static_cast<RealType>(0));
- BOOST_CHECK_EQUAL( // x > upper
- cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2))),
- static_cast<RealType>(0));
- // quantile
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9)),
- static_cast<RealType>(0.9),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1)),
- static_cast<RealType>(0.1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5)),
- static_cast<RealType>(0.5),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)),
- static_cast<RealType>(0),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1)),
- static_cast<RealType>(1),
- tolerance);
- // quantile complement
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1))),
- static_cast<RealType>(0.9),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9))),
- static_cast<RealType>(0.1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5))),
- static_cast<RealType>(0.5),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))),
- static_cast<RealType>(1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1))),
- static_cast<RealType>(0),
- tolerance);
- // Some tests using a different location & scale, neight zero or unity.
- BOOST_CHECK_CLOSE_FRACTION( // x == mid
- pdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(1)),
- static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == upper
- pdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(+2)),
- static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333), // 1 / (2 - -1) = 1/3
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == lower
- cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(-1)),
- static_cast<RealType>(0),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == upper
- cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(0)),
- static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == upper
- cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(1)),
- static_cast<RealType>(0.6666666666666666666666666666666666666666666666666667),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == lower
- cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(2)),
- static_cast<RealType>(1),
- tolerance);
- BOOST_CHECK_CLOSE_FRACTION( // x == upper
- quantile(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(0.6666666666666666666666666666666666666666666666666667)),
- static_cast<RealType>(1),
- tolerance);
- check_uniform(
- static_cast<RealType>(0), // lower
- 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 uniform tests.
- check_uniform(
- static_cast<RealType>(-1), // lower
- 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_uniform(
- static_cast<RealType>(1), // lower
- static_cast<RealType>(3), // upper
- static_cast<RealType>(2), // x
- static_cast<RealType>(0.5), // p
- static_cast<RealType>(1 - 0.5), // q = 1 - p
- tolerance);
- check_uniform(
- static_cast<RealType>(-1), // lower
- static_cast<RealType>(2), // upper
- static_cast<RealType>(1), // x
- static_cast<RealType>(0.66666666666666666666666666666666666666666667), // p
- static_cast<RealType>(0.33333333333333333333333333333333333333333333), // q = 1 - p
- tolerance);
- tolerance = (std::max)(
- boost::math::tools::epsilon<RealType>(),
- static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5; // 5 eps as a fraction.
- cout << "Tolerance (as fraction) for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
- uniform_distribution<RealType> distu01(0, 1);
- RealType x = static_cast<RealType>(0.5);
- using namespace std; // ADL of std names.
- // mean:
- BOOST_CHECK_CLOSE_FRACTION(
- mean(distu01), static_cast<RealType>(0.5), tolerance);
- // variance:
- BOOST_CHECK_CLOSE_FRACTION(
- variance(distu01), static_cast<RealType>(0.0833333333333333333333333333333333333333333), tolerance);
- // std deviation:
- BOOST_CHECK_CLOSE_FRACTION(
- standard_deviation(distu01), sqrt(variance(distu01)), tolerance);
- // hazard:
- BOOST_CHECK_CLOSE_FRACTION(
- hazard(distu01, x), pdf(distu01, x) / cdf(complement(distu01, x)), tolerance);
- // cumulative hazard:
- BOOST_CHECK_CLOSE_FRACTION(
- chf(distu01, x), -log(cdf(complement(distu01, x))), tolerance);
- // coefficient_of_variation:
- BOOST_CHECK_CLOSE_FRACTION(
- coefficient_of_variation(distu01), standard_deviation(distu01) / mean(distu01), tolerance);
- // mode:
- BOOST_CHECK_CLOSE_FRACTION(
- mode(distu01), static_cast<RealType>(0), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(
- median(distu01), static_cast<RealType>(0.5), tolerance);
- // skewness:
- BOOST_CHECK_EQUAL(
- skewness(distu01), static_cast<RealType>(0));
- // kertosis:
- BOOST_CHECK_CLOSE_FRACTION(
- kurtosis(distu01), kurtosis_excess(distu01) + static_cast<RealType>(3), tolerance);
- // kertosis excess:
- BOOST_CHECK_CLOSE_FRACTION(
- kurtosis_excess(distu01), static_cast<RealType>(-1.2), 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, long 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_MATH_CHECK_THROW tests.
- BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::infinity()), std::domain_error);
- BOOST_MATH_CHECK_THROW(pdf(distu01, -std::numeric_limits<RealType>::infinity()), std::domain_error);
- } // 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_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::infinity()), std::domain_error);
- //BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
- // BOOST_MATH_CHECK_THROW(pdf(distu01, boost::math::tools::max_value<RealType>() * 2), std::domain_error); // Doesn't throw.
- BOOST_CHECK_EQUAL(pdf(distu01, boost::math::tools::max_value<RealType>()), 0);
- }
- // Special cases:
- BOOST_CHECK(pdf(distu01, 0) == 1);
- BOOST_CHECK(cdf(distu01, 0) == 0);
- BOOST_CHECK(pdf(distu01, 1) == 1);
- BOOST_CHECK(cdf(distu01, 1) == 1);
- BOOST_CHECK(cdf(complement(distu01, 0)) == 1);
- BOOST_CHECK(cdf(complement(distu01, 1)) == 0);
- BOOST_CHECK(quantile(distu01, 0) == 0);
- BOOST_CHECK(quantile(complement(distu01, 0)) == 1);
- BOOST_CHECK(quantile(distu01, 1) == 1);
- BOOST_CHECK(quantile(complement(distu01, 1)) == 0);
- // Error checks:
- if(std::numeric_limits<RealType>::has_quiet_NaN)
- { // BOOST_CHECK tests for constructing with quiet_NaN (not for real_concept, for example - see notes above).
- BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
- BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
- }
- BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(1, 0), std::domain_error); // lower > upper!
- BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(1, 1), std::domain_error); // lower == upper!
- check_out_of_range<uniform_distribution<RealType> >(1, 5);
- } // template <class RealType>void test_spots(RealType)
- BOOST_AUTO_TEST_CASE( test_main )
- {
- // Check that can construct uniform distribution using the two convenience methods:
- using namespace boost::math;
- uniform unistd; // Using typedef
- // == uniform_distribution<double> unistd;
- BOOST_CHECK_EQUAL(unistd.lower(), 0); // Check defaults.
- BOOST_CHECK_EQUAL(unistd.upper(), 1);
- uniform_distribution<> myu01(0, 1); // Using default RealType double.
- BOOST_CHECK_EQUAL(myu01.lower(), 0); // Check defaults again.
- BOOST_CHECK_EQUAL(myu01.upper(), 1);
- // Test on extreme values of random variate x, using just double because it has numeric_limit infinity etc..
- // No longer allow x to be + or - infinity, then these tests should throw.
- BOOST_MATH_CHECK_THROW(pdf(unistd, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
- BOOST_MATH_CHECK_THROW(pdf(unistd, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
- BOOST_MATH_CHECK_THROW(cdf(unistd, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
- BOOST_MATH_CHECK_THROW(cdf(unistd, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
- BOOST_CHECK_EQUAL(pdf(unistd, +(std::numeric_limits<double>::max)()), 0); // x = + max
- BOOST_CHECK_EQUAL(pdf(unistd, -(std::numeric_limits<double>::min)()), 0); // x = - min
- BOOST_CHECK_EQUAL(cdf(unistd, +(std::numeric_limits<double>::max)()), 1); // x = + max
- BOOST_CHECK_EQUAL(cdf(unistd, -(std::numeric_limits<double>::min)()), 0); // x = - min
- #ifndef BOOST_NO_EXCEPTIONS
- BOOST_MATH_CHECK_THROW(uniform_distribution<> zinf(0, +std::numeric_limits<double>::infinity()), std::domain_error); // zero to infinity using default RealType double.
- #else
- BOOST_MATH_CHECK_THROW(uniform_distribution<>(0, +std::numeric_limits<double>::infinity()), std::domain_error); // zero to infinity using default RealType double.
- #endif
- uniform_distribution<> zmax(0, +(std::numeric_limits<double>::max)()); // zero to max using default RealType double.
- BOOST_CHECK_EQUAL(zmax.lower(), 0); // Check defaults again.
- BOOST_CHECK_EQUAL(zmax.upper(), +(std::numeric_limits<double>::max)());
- BOOST_CHECK_EQUAL(pdf(zmax, -1), 0); // pdf is 1/(0 - max) = almost zero for all x
- BOOST_CHECK_EQUAL(pdf(zmax, 0), (std::numeric_limits<double>::min)()/4); // x =
- BOOST_CHECK_EQUAL(pdf(zmax, 1), (std::numeric_limits<double>::min)()/4); // x =
- BOOST_MATH_CHECK_THROW(pdf(zmax, +std::numeric_limits<double>::infinity()), std::domain_error); // pdf is 1/(0 - infinity) = zero for all x
- BOOST_MATH_CHECK_THROW(pdf(zmax, -std::numeric_limits<double>::infinity()), std::domain_error);
- BOOST_CHECK_EQUAL(pdf(zmax, +(std::numeric_limits<double>::max)()), (std::numeric_limits<double>::min)()/4); // x =
- BOOST_CHECK_EQUAL(pdf(zmax, -(std::numeric_limits<double>::max)()), 0); // x =
- #ifndef BOOST_NO_EXCEPTIONS
- // Ensure NaN throws an exception.
- BOOST_MATH_CHECK_THROW(uniform_distribution<> zNaN(0, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
- BOOST_MATH_CHECK_THROW(pdf(unistd, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
- #else
- BOOST_MATH_CHECK_THROW(uniform_distribution<>(0, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
- BOOST_MATH_CHECK_THROW(pdf(unistd, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
- #endif
- // 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_uniform.exe"
- Running 1 test case...
- Tolerance for type float is 2e-005.
- Tolerance (as fraction) for type float is 5.96046e-007.
- Tolerance for type double is 2e-005.
- Tolerance (as fraction) for type double is 1.11022e-015.
- Tolerance for type long double is 2e-005.
- Tolerance (as fraction) for type long double is 1.11022e-015.
- Tolerance for type class boost::math::concepts::real_concept is 2e-005.
- Tolerance (as fraction) for type class boost::math::concepts::real_concept is 1.11022e-015.
- *** No errors detected
- */
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