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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
#ifndef SYCL_LANGUAGE_VERSION
#include <pch.hpp>
#endif
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
# pragma warning(disable: 4100) // unreferenced formal parameter.
#endif
#include <boost/math/tools/config.hpp>
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#endif
#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 "../include_private/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));
// kurtosis:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis(distu01), kurtosis_excess(distu01) + static_cast<RealType>(3), tolerance);
// kurtosis excess:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(distu01), static_cast<RealType>(-1.2), tolerance);
BOOST_CHECK_SMALL(
entropy(distu01), 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(BOOST_BORLANDC, BOOST_TESTED_AT(0x0582)) && !defined(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_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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