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WSJT-X/boost/libs/math/test/test_geometric.cpp

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// test_geometric.cpp
// Copyright Paul A. Bristow 2010.
// Copyright John Maddock 2010.
// 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 Geometric Distribution.
// Note that these defines must be placed BEFORE #includes.
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
// because several tests overflow & underflow by design.
#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
#endif
#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
# define TEST_FLOAT
# define TEST_DOUBLE
# define TEST_LDOUBLE
# define TEST_REAL_CONCEPT
#endif
#include <boost/math/tools/test.hpp>
#include <boost/math/concepts/real_concept.hpp> // for real_concept
using ::boost::math::concepts::real_concept;
#include <boost/math/distributions/geometric.hpp> // for geometric_distribution
using boost::math::geometric_distribution;
using boost::math::geometric; // using typedef for geometric_distribution<double>
#include <boost/math/distributions/negative_binomial.hpp> // for some comparisons.
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // for test_main
#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION
#include "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
using std::setprecision;
using std::showpoint;
#include <limits>
using std::numeric_limits;
template <class RealType>
void test_spot( // Test a single spot value against 'known good' values.
RealType k, // Number of failures.
RealType p, // Probability of success_fraction.
RealType P, // CDF probability.
RealType Q, // Complement of CDF.
RealType tol) // Test tolerance.
{
boost::math::geometric_distribution<RealType> g(p);
BOOST_CHECK_EQUAL(p, g.success_fraction());
BOOST_CHECK_CLOSE_FRACTION(cdf(g, k), 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:
//
BOOST_CHECK_CLOSE_FRACTION(
cdf(complement(g, k)), Q, tol);
if(k != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
quantile(g, P), k, 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(g, P) < boost::math::tools::epsilon<RealType>() * 10);
}
}
if(k != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
quantile(complement(g, Q)), k, 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(complement(g, Q)) < boost::math::tools::epsilon<RealType>() * 10);
}
}
} // if((P < 0.99) && (Q < 0.99))
// Parameter estimation test: estimate success ratio:
BOOST_CHECK_CLOSE_FRACTION(
geometric_distribution<RealType>::find_lower_bound_on_p(
1+k, P),
p, 0.02); // Wide tolerance needed for some tests.
// Note we bump up the sample size here, purely for the sake of the test,
// internally the function has to adjust the sample size so that we get
// the right upper bound, our test undoes this, so we can verify the result.
BOOST_CHECK_CLOSE_FRACTION(
geometric_distribution<RealType>::find_upper_bound_on_p(
1+k+1, Q),
p, 0.02);
if(Q < P)
{
//
// We check two things here, that the upper and lower bounds
// are the right way around, and that they do actually bracket
// the naive estimate of p = successes / (sample size)
//
BOOST_CHECK(
geometric_distribution<RealType>::find_lower_bound_on_p(
1+k, Q)
<=
geometric_distribution<RealType>::find_upper_bound_on_p(
1+k, Q)
);
BOOST_CHECK(
geometric_distribution<RealType>::find_lower_bound_on_p(
1+k, Q)
<=
1 / (1+k)
);
BOOST_CHECK(
1 / (1+k)
<=
geometric_distribution<RealType>::find_upper_bound_on_p(
1+k, Q)
);
}
else
{
// As above but when P is small.
BOOST_CHECK(
geometric_distribution<RealType>::find_lower_bound_on_p(
1+k, P)
<=
geometric_distribution<RealType>::find_upper_bound_on_p(
1+k, P)
);
BOOST_CHECK(
geometric_distribution<RealType>::find_lower_bound_on_p(
1+k, P)
<=
1 / (1+k)
);
BOOST_CHECK(
1 / (1+k)
<=
geometric_distribution<RealType>::find_upper_bound_on_p(
1+k, P)
);
}
// Estimate sample size:
BOOST_CHECK_CLOSE_FRACTION(
geometric_distribution<RealType>::find_minimum_number_of_trials(
k, p, P),
1+k, 0.02); // Can differ 50 to 51 for small p
BOOST_CHECK_CLOSE_FRACTION(
geometric_distribution<RealType>::find_maximum_number_of_trials(
k, p, Q),
1+k, 0.02);
} // test_spot
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
// Basic sanity checks.
// Most test data is to double precision (17 decimal digits) only,
cout << "Floating point Type is " << typeid(RealType).name() << endl;
// so set tolerance to 1000 eps expressed as a fraction,
// or 1000 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()));
tolerance *= 10; // 10 eps
cout << "Tolerance = " << tolerance << "." << endl;
RealType tol1eps = boost::math::tools::epsilon<RealType>(); // Very tight, suit exact values.
//RealType tol2eps = boost::math::tools::epsilon<RealType>() * 2; // Tight, values.
RealType tol5eps = boost::math::tools::epsilon<RealType>() * 5; // Wider 5 epsilon.
cout << "Tolerance 5 eps = " << tol5eps << "." << endl;
// Sources of spot test values are mainly R.
using boost::math::geometric_distribution;
using boost::math::geometric;
using boost::math::cdf;
using boost::math::pdf;
using boost::math::quantile;
using boost::math::complement;
BOOST_MATH_STD_USING // for std math functions
// Test geometric using cdf spot values R
// These test quantiles and complements as well.
test_spot( //
static_cast<RealType>(2), // Number of failures, k
static_cast<RealType>(0.5), // Probability of success as fraction, p
static_cast<RealType>(0.875L), // Probability of result (CDF), P
static_cast<RealType>(0.125L), // complement CCDF Q = 1 - P
tolerance);
test_spot( //
static_cast<RealType>(0), // Number of failures, k
static_cast<RealType>(0.25), // Probability of success as fraction, p
static_cast<RealType>(0.25), // Probability of result (CDF), P
static_cast<RealType>(0.75), // Q = 1 - P
tolerance);
test_spot(
// R formatC(pgeom(10,0.25), digits=17) [1] "0.95776486396789551"
// formatC(pgeom(10,0.25, FALSE), digits=17) [1] "0.042235136032104499"
static_cast<RealType>(10), // Number of failures, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.95776486396789551L), // Probability of result (CDF), P
static_cast<RealType>(0.042235136032104499L), // Q = 1 - P
tolerance);
test_spot( //
// > R formatC(pgeom(50,0.25, TRUE), digits=17) [1] "0.99999957525875771"
// > R formatC(pgeom(50,0.25, FALSE), digits=17) [1] "4.2474124232020353e-07"
static_cast<RealType>(50), // Number of failures, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.99999957525875771), // Probability of result (CDF), P
static_cast<RealType>(4.2474124232020353e-07), // Q = 1 - P
tolerance);
/*
// This causes failures in find_upper_bound_on_p p is small branch.
test_spot( // formatC(pgeom(50,0.01, TRUE), digits=17)[1] "0.40104399353383874"
// > formatC(pgeom(50,0.01, FALSE), digits=17) [1] "0.59895600646616121"
static_cast<RealType>(50), // Number of failures, k
static_cast<RealType>(0.01), // Probability of success, p
static_cast<RealType>(0.40104399353383874), // Probability of result (CDF), P
static_cast<RealType>(0.59895600646616121), // Q = 1 - P
tolerance);
*/
test_spot( // > formatC(pgeom(50,0.99, TRUE), digits=17) [1] " 1"
// formatC(pgeom(50,0.99, FALSE), digits=17) [1] "1.0000000000000364e-102"
static_cast<RealType>(50), // Number of failures, k
static_cast<RealType>(0.99), // Probability of success, p
static_cast<RealType>(1), // Probability of result (CDF), P
static_cast<RealType>(1.0000000000000364e-102), // Q = 1 - P
tolerance);
test_spot( // > formatC(pgeom(1,0.99, TRUE), digits=17) [1] "0.99990000000000001"
// > formatC(pgeom(1,0.99, FALSE), digits=17) [1] "0.00010000000000000009"
static_cast<RealType>(1), // Number of failures, k
static_cast<RealType>(0.99), // Probability of success, p
static_cast<RealType>(0.9999), // Probability of result (CDF), P
static_cast<RealType>(0.0001), // Q = 1 - P
tolerance);
if(std::numeric_limits<RealType>::is_specialized)
{ // An extreme value test that is more accurate than using negative binomial.
// Since geometric only uses exp and log functions.
test_spot( // > formatC(pgeom(10000, 0.001, TRUE), digits=17) [1] "0.99995487182736897"
// > formatC(pgeom(10000,0.001, FALSE), digits=17) [1] "4.5128172631071587e-05"
static_cast<RealType>(10000L), // Number of failures, k
static_cast<RealType>(0.001L), // Probability of success, p
static_cast<RealType>(0.99995487182736897L), // Probability of result (CDF), P
static_cast<RealType>(4.5128172631071587e-05L), // Q = 1 - P
tolerance); //
} // numeric_limit is specialized
// End of single spot tests using RealType
// Tests on PDF:
BOOST_CHECK_CLOSE_FRACTION( //> formatC(dgeom(0,0.5), digits=17)[1] " 0.5"
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(0.0) ), // Number of failures, k is very small but not integral,
static_cast<RealType>(0.5), // nearly success probability.
tolerance);
BOOST_CHECK_CLOSE_FRACTION( //> formatC(dgeom(0,0.5), digits=17)[1] " 0.5"
// R treates geom as a discrete distribution.
// > formatC(dgeom(1.999999,0.5, FALSE), digits=17) [1] " 0"
// Warning message:
// In dgeom(1.999999, 0.5, FALSE) : non-integer x = 1.999999
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(0.0001L) ), // Number of failures, k is very small but not integral,
static_cast<RealType>(0.4999653438420768L), // nearly success probability.
tolerance);
BOOST_CHECK_CLOSE_FRACTION( // > formatC(pgeom(0.0001,0.5, TRUE), digits=17)[1] " 0.5"
// > formatC(pgeom(0.0001,0.5, FALSE), digits=17) [1] " 0.5"
// R treates geom as a discrete distribution.
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(0.0001L) ), // Number of failures, k is very small but not integral,
static_cast<RealType>(0.4999653438420768L), // nearly success probability.
tolerance);
BOOST_CHECK_CLOSE_FRACTION( // formatC(dgeom(1,0.01), digits=17)[1] "0.0099000000000000008"
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.01L)),
static_cast<RealType>(1) ), // Number of failures, k
static_cast<RealType>(0.0099000000000000008), //
tolerance);
BOOST_CHECK_CLOSE_FRACTION( //> formatC(dgeom(1,0.99), digits=17)[1] "0.0099000000000000043"
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.99L)),
static_cast<RealType>(1) ), // Number of failures, k
static_cast<RealType>(0.00990000000000000043L), //
tolerance);
BOOST_CHECK_CLOSE_FRACTION( //> > formatC(dgeom(0,0.99), digits=17)[1] "0.98999999999999999"
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.99L)),
static_cast<RealType>(0) ), // Number of failures, k
static_cast<RealType>(0.98999999999999999L), //
tolerance);
// p near unity.
BOOST_CHECK_CLOSE_FRACTION( // > formatC(dgeom(100,0.99), digits=17)[1] "9.9000000000003448e-201"
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.99L)),
static_cast<RealType>(100) ), // Number of failures, k
static_cast<RealType>(9.9000000000003448e-201L), //
100 * tolerance); // Note difference
// p nearer unity.
BOOST_CHECK_CLOSE_FRACTION( //
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.9999)),
static_cast<RealType>(10) ), // Number of failures, k
// static_cast<double>(9.9989999999889024e-41), // Boost.Math
// static_cast<float>(1.00156406e-040)
static_cast<RealType>(9.999e-41), // exact from 100 digit calculator.
2e3 * tolerance); // Note bigger tolerance needed.
// Moshier Cephes 100 digits calculator says 9.999e-41
//0.9999*pow(1-0.9999,10)
// 9.9990000000000000000000000000000000000000000000000000000000000000000000E-41
// 9.998999999988988e-041
// > formatC(dgeom(10, 0.9999), digits=17) [1] "9.9989999999889024e-41"
// p * pow(q, k) 9.9989999999889880e-041
// exp(p * k * log1p(-p)) 9.9989999999889024e-041
// 0.9999999999 * pow(1-0.9999999999,10)= 9.9999999990E-101
// > formatC(dgeom(10,0.9999999999), digits=17) [1] "1.0000008273040127e-100"
BOOST_CHECK_CLOSE_FRACTION( //
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.9999999999L)),
static_cast<RealType>(10) ), //
static_cast<RealType>(9.9999999990E-101L), // 1.0000008273040179e-100
1e9 * tolerance); // Note big tolerance needed.
// 1.0000008273040179e-100 Boost.Math
// 1.0000008273040127e-100 R
// 0.9999999990000004e-100 100 digit calculator 'exact'
BOOST_CHECK_CLOSE_FRACTION( //
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.00000000001L)),
static_cast<RealType>(10) ), //
static_cast<RealType>(9.999999999e-12L), // get 9.9999999989999994e-012
1 * tolerance); // Note small tolerance needed.
BOOST_CHECK_CLOSE_FRACTION( //
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.00000000001L)),
static_cast<RealType>(1000) ), //
static_cast<RealType>(9.9999999e-12L), // get 9.9999998999999913e-012
tolerance); // Note small tolerance needed.
///////////////////////////////////////////////////
BOOST_CHECK_CLOSE_FRACTION( //
// > formatC(dgeom(0.0001,0.5, FALSE), digits=17) [1] " 0.5"
// R treates geom as a discrete distribution.
// But Boost.Math is continuous, so if you want R behaviour,
// make number of failures, k into an integer with the floor function.
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(floor(0.0001L)) ), // Number of failures, k is very small but MADE integral,
static_cast<RealType>(0.5), // nearly success probability.
tolerance);
// R switches over at about 1e7 from k = 0, returning 0.5, to k = 1, returning 0.25.
// Boost.Math does not do this, even for 0.9999999999999999
// > formatC(pgeom(0.999999,0.5, FALSE), digits=17) [1] " 0.5"
// > formatC(pgeom(0.9999999,0.5, FALSE), digits=17) [1] " 0.25"
BOOST_CHECK_CLOSE_FRACTION( // > formatC(pgeom(0.0001,0.5, TRUE), digits=17)[1] " 0.5"
// > formatC(pgeom(0.0001,0.5, FALSE), digits=17) [1] " 0.5"
// R treates geom as a discrete distribution.
// But Boost.Math is continuous, so if you want R behaviour,
// make number of failures, k into an integer with the floor function.
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(floor(0.9999999999999999L)) ), // Number of failures, k is very small but MADE integral,
static_cast<RealType>(0.5), // nearly success probability.
tolerance);
BOOST_CHECK_CLOSE_FRACTION( // > formatC(pgeom(0.0001,0.5, TRUE), digits=17)[1] " 0.5"
// > formatC(pgeom(0.0001,0.5, FALSE), digits=17) [1] " 0.5"
// R treates geom as a discrete distribution.
// But Boost.Math is continuous, so if you want R behaviour,
// make number of failures, k into an integer with the floor function.
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(floor(1. - tolerance)) ),
// Number of failures, k is very small but MADE integral,
// Need to use tolerance here,
// as epsilon is ill-defined for Real concept:
// numeric_limits<RealType>::epsilon() 0
static_cast<RealType>(0.5), // nearly success probability.
tolerance * 10);
BOOST_CHECK_CLOSE_FRACTION(
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.0001L)),
static_cast<RealType>(2)), // k = 2.
static_cast<RealType>(9.99800010e-5L), // 'exact '
tolerance);
//> formatC(dgeom(2, 0.9999), digits=17) [1] "9.9989999999977806e-09"
BOOST_CHECK_CLOSE_FRACTION(
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.9999L)),
static_cast<RealType>(2)), // k = 0
static_cast<RealType>(9.999e-9L), // 'exact'
1000*tolerance);
BOOST_CHECK_CLOSE_FRACTION(
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.9999L)),
static_cast<RealType>(3)), // k = 3
static_cast<RealType>(9.999e-13L), // get
1000*tolerance);
BOOST_CHECK_CLOSE_FRACTION(
pdf(geometric_distribution<RealType>(static_cast<RealType>(0.9999L)),
static_cast<RealType>(5)), // k = 5
static_cast<RealType>(9.999e-21L), // 9.9989999999944947e-021
1000*tolerance);
BOOST_CHECK_CLOSE_FRACTION(
pdf(geometric_distribution<RealType>( static_cast<RealType>(0.0001L)),
static_cast<RealType>(3)), // k = 0.
static_cast<RealType>(9.99700029999e-5L), //
tolerance);
// Tests on cdf:
// MathCAD pgeom k, r, p) == failures, successes, probability.
BOOST_CHECK_CLOSE_FRACTION(cdf(
geometric_distribution<RealType>(static_cast<RealType>(0.5)), // prob 0.5
static_cast<RealType>(0) ), // k = 0
static_cast<RealType>(0.5), // probability =p
tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(
geometric_distribution<RealType>(static_cast<RealType>(0.5)), //
static_cast<RealType>(0) )), // k = 0
static_cast<RealType>(0.5), // probability =
tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(
geometric_distribution<RealType>(static_cast<RealType>(0.25)), // prob 0.5
static_cast<RealType>(1) ), // k = 0
static_cast<RealType>(0.4375L), // probability =p
tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(
geometric_distribution<RealType>(static_cast<RealType>(0.25)), //
static_cast<RealType>(1) )), // k = 0
static_cast<RealType>(1-0.4375L), // probability =
tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(
geometric_distribution<RealType>(static_cast<RealType>(0.5)), //
static_cast<RealType>(1) )), // k = 0
static_cast<RealType>(0.25), // probability = exact 0.25
tolerance);
BOOST_CHECK_CLOSE_FRACTION( //
cdf(geometric_distribution<RealType>(static_cast<RealType>(0.5)),
static_cast<RealType>(4)), // k =4.
static_cast<RealType>(0.96875L), // exact
tolerance);
// Tests of other functions, mean and other moments ...
geometric_distribution<RealType> dist(static_cast<RealType>(0.25));
// mean:
BOOST_CHECK_CLOSE_FRACTION(
mean(dist), static_cast<RealType>((1 - 0.25) /0.25), tol5eps);
BOOST_CHECK_CLOSE_FRACTION(
mode(dist), static_cast<RealType>(0), tol1eps);
// variance:
BOOST_CHECK_CLOSE_FRACTION(
variance(dist), static_cast<RealType>((1 - 0.25) / (0.25 * 0.25)), tol5eps);
// std deviation:
// sqrt(0.75/0.125)
BOOST_CHECK_CLOSE_FRACTION(
standard_deviation(dist), //
static_cast<RealType>(sqrt((1.0L - 0.25L) / (0.25L * 0.25L))), // using 100 digit calc
tol5eps);
BOOST_CHECK_CLOSE_FRACTION(
skewness(dist), //
static_cast<RealType>((2-0.25L) /sqrt(0.75L)),
// using calculator
tol5eps);
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(dist), //
static_cast<RealType>(6 + 0.0625L/0.75L), //
tol5eps);
// 6.083333333333333 6.166666666666667
BOOST_CHECK_CLOSE_FRACTION(
kurtosis(dist), // true
static_cast<RealType>(9 + 0.0625L/0.75L), //
tol5eps);
// hazard:
RealType x = static_cast<RealType>(0.125);
BOOST_CHECK_CLOSE_FRACTION(
hazard(dist, x)
, pdf(dist, x) / cdf(complement(dist, x)), tol5eps);
// cumulative hazard:
BOOST_CHECK_CLOSE_FRACTION(
chf(dist, x), -log(cdf(complement(dist, x))), tol5eps);
// coefficient_of_variation:
BOOST_CHECK_CLOSE_FRACTION(
coefficient_of_variation(dist)
, standard_deviation(dist) / mean(dist), tol5eps);
// Special cases for PDF:
BOOST_CHECK_EQUAL(
pdf(
geometric_distribution<RealType>(static_cast<RealType>(0)), //
static_cast<RealType>(0)),
static_cast<RealType>(0) );
BOOST_CHECK_EQUAL(
pdf(
geometric_distribution<RealType>(static_cast<RealType>(0)),
static_cast<RealType>(0.0001)),
static_cast<RealType>(0) );
BOOST_CHECK_EQUAL(
pdf(
geometric_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(0.001)),
static_cast<RealType>(0) );
BOOST_CHECK_EQUAL(
pdf(
geometric_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(8)),
static_cast<RealType>(0) );
BOOST_CHECK_SMALL(
pdf(
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(0))-
static_cast<RealType>(0.25),
2 * boost::math::tools::epsilon<RealType>() ); // Expect exact, but not quite.
// numeric_limits<RealType>::epsilon()); // Not suitable for real concept!
// Quantile boundary cases checks:
BOOST_CHECK_EQUAL(
quantile( // zero P < cdf(0) so should be exactly zero.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(0)),
static_cast<RealType>(0));
BOOST_CHECK_EQUAL(
quantile( // min P < cdf(0) so should be exactly zero.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(boost::math::tools::min_value<RealType>())),
static_cast<RealType>(0));
BOOST_CHECK_CLOSE_FRACTION(
quantile( // Small P < cdf(0) so should be near zero.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(boost::math::tools::epsilon<RealType>())), //
static_cast<RealType>(0),
tol5eps);
BOOST_CHECK_CLOSE_FRACTION(
quantile( // Small P < cdf(0) so should be exactly zero.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(0.0001)),
static_cast<RealType>(0),
tolerance);
//BOOST_CHECK( // Fails with overflow for real_concept
//quantile( // Small P near 1 so k failures should be big.
//geometric_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
//static_cast<RealType>(1 - boost::math::tools::epsilon<RealType>())) <=
//static_cast<RealType>(189.56999032670058) // 106.462769 for float
//);
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_THROW_ON_OVERFLOW_POLICY == throw_on_error would throw here.
// #define BOOST_MAT_DOMAIN_ERROR_POLICY IS defined throw_on_error,
// so the throw path of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
BOOST_CHECK(
quantile( // At P == 1 so k failures should be infinite.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(1)) ==
//static_cast<RealType>(boost::math::tools::infinity<RealType>())
static_cast<RealType>(std::numeric_limits<RealType>::infinity()) );
BOOST_CHECK_EQUAL(
quantile( // At 1 == P so should be infinite.
geometric_distribution<RealType>( static_cast<RealType>(0.25)),
static_cast<RealType>(1)), //
std::numeric_limits<RealType>::infinity() );
BOOST_CHECK_EQUAL(
quantile(complement( // Q zero 1 so P == 1 < cdf(0) so should be exactly infinity.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(0))),
std::numeric_limits<RealType>::infinity() );
} // test for infinity using std::numeric_limits<>::infinity()
else
{ // real_concept case, so check it throws rather than returning infinity.
BOOST_CHECK_EQUAL(
quantile( // At P == 1 so k failures should be infinite.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(1)),
boost::math::tools::max_value<RealType>() );
BOOST_CHECK_EQUAL(
quantile(complement( // Q zero 1 so P == 1 < cdf(0) so should be exactly infinity.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(0))),
boost::math::tools::max_value<RealType>());
} // has infinity
BOOST_CHECK( // Should work for built-in and real_concept.
quantile(complement( // Q near to 1 so P nearly 1, so should be large > 300.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(boost::math::tools::min_value<RealType>())))
>= static_cast<RealType>(300) );
BOOST_CHECK_EQUAL(
quantile( // P == 0 < cdf(0) so should be zero.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(0)),
static_cast<RealType>(0));
// Quantile Complement boundary cases:
BOOST_CHECK_EQUAL(
quantile(complement( // Q = 1 so P = 0 < cdf(0) so should be exactly zero.
geometric_distribution<RealType>( static_cast<RealType>(0.25)),
static_cast<RealType>(1))),
static_cast<RealType>(0)
);
BOOST_CHECK_EQUAL(
quantile(complement( // Q very near 1 so P == epsilon < cdf(0) so should be exactly zero.
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(1 - boost::math::tools::epsilon<RealType>()))),
static_cast<RealType>(0)
);
// Check that duff arguments throw domain_error:
BOOST_MATH_CHECK_THROW(
pdf( // Negative success_fraction!
geometric_distribution<RealType>(static_cast<RealType>(-0.25)),
static_cast<RealType>(0)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf( // Success_fraction > 1!
geometric_distribution<RealType>(static_cast<RealType>(1.25)),
static_cast<RealType>(0)),
std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf( // Negative k argument !
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(-1)),
std::domain_error);
//BOOST_MATH_CHECK_THROW(
//pdf( // check limit on k (failures)
//geometric_distribution<RealType>(static_cast<RealType>(0.25)),
//std::numeric_limits<RealType>infinity()),
//std::domain_error);
BOOST_MATH_CHECK_THROW(
cdf( // Negative k argument !
geometric_distribution<RealType>(static_cast<RealType>(0.25)),
static_cast<RealType>(-1)),
std::domain_error);
BOOST_MATH_CHECK_THROW(
cdf( // Negative success_fraction!
geometric_distribution<RealType>(static_cast<RealType>(-0.25)),
static_cast<RealType>(0)), std::domain_error);
BOOST_MATH_CHECK_THROW(
cdf( // Success_fraction > 1!
geometric_distribution<RealType>(static_cast<RealType>(1.25)),
static_cast<RealType>(0)), std::domain_error);
BOOST_MATH_CHECK_THROW(
quantile( // Negative success_fraction!
geometric_distribution<RealType>(static_cast<RealType>(-0.25)),
static_cast<RealType>(0)), std::domain_error);
BOOST_MATH_CHECK_THROW(
quantile( // Success_fraction > 1!
geometric_distribution<RealType>(static_cast<RealType>(1.25)),
static_cast<RealType>(0)), std::domain_error);
check_out_of_range<geometric_distribution<RealType> >(0.5);
// End of check throwing 'duff' out-of-domain values.
{ // Compare geometric and negative binomial functions.
using boost::math::negative_binomial_distribution;
using boost::math::geometric_distribution;
RealType k = static_cast<RealType>(2.L);
RealType alpha = static_cast<RealType>(0.05L);
RealType p = static_cast<RealType>(0.5L);
BOOST_CHECK_CLOSE_FRACTION( // Successes parameter in negative binomial is 1 for geometric.
geometric_distribution<RealType>::find_lower_bound_on_p(k, alpha),
negative_binomial_distribution<RealType>::find_lower_bound_on_p(k, static_cast<RealType>(1), alpha),
tolerance);
BOOST_CHECK_CLOSE_FRACTION( // Successes parameter in negative binomial is 1 for geometric.
geometric_distribution<RealType>::find_upper_bound_on_p(k, alpha),
negative_binomial_distribution<RealType>::find_upper_bound_on_p(k, static_cast<RealType>(1), alpha),
tolerance);
BOOST_CHECK_CLOSE_FRACTION( // Should be identical - successes parameter is not used.
geometric_distribution<RealType>::find_maximum_number_of_trials(k, p, alpha),
negative_binomial_distribution<RealType>::find_maximum_number_of_trials(k, p, alpha),
tolerance);
}
//geometric::find_upper_bound_on_p(k, alpha);
return;
} // template <class RealType> void test_spots(RealType) // Any floating-point type RealType.
BOOST_AUTO_TEST_CASE( test_main )
{
// Check that can generate geometric distribution using the two convenience methods:
using namespace boost::math;
geometric g05d(0.5); // Using typedef - default type is double.
geometric_distribution<> g05dd(0.5); // Using default RealType double.
// Basic sanity-check spot values.
// Test some simple double only examples.
geometric_distribution<double> mydist(0.25);
// success fraction == 0.25 == 25% or 1 in 4 successes.
// Note: double values (matching the distribution definition) avoid the need for any casting.
// Check accessor functions return exact values for double at least.
BOOST_CHECK_EQUAL(mydist.success_fraction(), static_cast<double>(1./4.));
//cout << numeric_limits<RealType>::epsilon() << endl;
// (Parameter value, arbitrarily zero, only communicates the floating point type).
#ifdef TEST_FLOAT
test_spots(0.0F); // Test float.
#endif
#ifdef TEST_DOUBLE
test_spots(0.0); // Test double.
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
test_spots(0.0L); // Test long double.
#endif
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
#ifdef TEST_REAL_CONCEPT
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
#endif
#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 )
/*
*/
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