// (C) Copyright John Maddock 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/distributions/non_central_chi_squared.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
#include <iostream>
#include <iomanip>
#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
{\
unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
BOOST_CHECK_CLOSE(a, b, prec); \
if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
{\
std::cerr << "Failure was at row " << i << std::endl;\
std::cerr << std::setprecision(35); \
std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
}\
}
#define BOOST_CHECK_EX(a, i) \
{\
unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
BOOST_CHECK(a); \
if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
{\
std::cerr << "Failure was at row " << i << std::endl;\
std::cerr << std::setprecision(35); \
std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
}\
}
template <class RealType>
RealType naive_pdf(RealType v, RealType lam, RealType x)
{
// Formula direct from
// http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html
// with no simplification:
RealType sum, term, prefix(1);
RealType eps = boost::math::tools::epsilon<RealType>();
term = sum = pdf(boost::math::chi_squared_distribution<RealType>(v), x);
for(int i = 1;; ++i)
{
prefix *= lam / (2 * i);
term = prefix * pdf(boost::math::chi_squared_distribution<RealType>(v + 2 * i), x);
sum += term;
if(term / sum < eps)
break;
}
return sum * exp(-lam / 2);
}
template <class RealType>
void test_spot(
RealType df, // Degrees of freedom
RealType ncp, // non-centrality param
RealType cs, // Chi Square statistic
RealType P, // CDF
RealType Q, // Complement of CDF
RealType tol) // Test tolerance
{
boost::math::non_central_chi_squared_distribution<RealType> dist(df, ncp);
BOOST_CHECK_CLOSE(
cdf(dist, cs), P, tol);
#ifndef BOOST_NO_EXCEPTIONS
try{
BOOST_CHECK_CLOSE(
pdf(dist, cs), naive_pdf(dist.degrees_of_freedom(), ncp, cs), tol * 150);
}
catch(const std::overflow_error&)
{
}
#endif
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 Q is reasonably free of error:
//
BOOST_CHECK_CLOSE(
cdf(complement(dist, cs)), Q, tol);
BOOST_CHECK_CLOSE(
quantile(dist, P), cs, tol * 10);
BOOST_CHECK_CLOSE(
quantile(complement(dist, Q)), cs, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_degrees_of_freedom(ncp, cs, P), df, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_degrees_of_freedom(boost::math::complement(ncp, cs, Q)), df, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_non_centrality(df, cs, P), ncp, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_non_centrality(boost::math::complement(df, cs, Q)), ncp, tol * 10);
}
}
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
#ifndef ERROR_REPORTING_MODE
RealType tolerance = (std::max)(
boost::math::tools::epsilon<RealType>(),
(RealType)boost::math::tools::epsilon<double>() * 5) * 150;
//
// At float precision we need to up the tolerance, since
// the input values are rounded off to inexact quantities
// the results get thrown off by a noticeable amount.
//
if(boost::math::tools::digits<RealType>() < 50)
tolerance *= 50;
if(boost::is_floating_point<RealType>::value != 1)
tolerance *= 20; // real_concept special functions are less accurate
std::cout << "Tolerance = " << tolerance << "%." << std::endl;
using boost::math::chi_squared_distribution;
using ::boost::math::chi_squared;
using ::boost::math::cdf;
using ::boost::math::pdf;
//
// Test against the data from Table 6 of:
//
// "Self-Validating Computations of Probabilities for Selected
// Central and Noncentral Univariate Probability Functions."
// Morgan C. Wang; William J. Kennedy
// Journal of the American Statistical Association,
// Vol. 89, No. 427. (Sep., 1994), pp. 878-887.
//
test_spot(
static_cast<RealType>(1), // degrees of freedom
static_cast<RealType>(6), // non centrality
static_cast<RealType>(0.00393), // Chi Squared statistic
static_cast<RealType>(0.2498463724258039e-2), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.2498463724258039e-2), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(5), // degrees of freedom
static_cast<RealType>(1), // non centrality
static_cast<RealType>(9.23636), // Chi Squared statistic
static_cast<RealType>(0.8272918751175548), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.8272918751175548), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(11), // degrees of freedom
static_cast<RealType>(21), // non centrality
static_cast<RealType>(24.72497), // Chi Squared statistic
static_cast<RealType>(0.2539481822183126), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.2539481822183126), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(31), // degrees of freedom
static_cast<RealType>(6), // non centrality
static_cast<RealType>(44.98534), // Chi Squared statistic
static_cast<RealType>(0.8125198785064969), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.8125198785064969), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(51), // degrees of freedom
static_cast<RealType>(1), // non centrality
static_cast<RealType>(38.56038), // Chi Squared statistic
static_cast<RealType>(0.8519497361859118e-1), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.8519497361859118e-1), // Q = 1 - P
tolerance * 2);
test_spot(
static_cast<RealType>(100), // degrees of freedom
static_cast<RealType>(16), // non centrality
static_cast<RealType>(82.35814), // Chi Squared statistic
static_cast<RealType>(0.1184348822747824e-1), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.1184348822747824e-1), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(300), // degrees of freedom
static_cast<RealType>(16), // non centrality
static_cast<RealType>(331.78852), // Chi Squared statistic
static_cast<RealType>(0.7355956710306709), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.7355956710306709), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(500), // degrees of freedom
static_cast<RealType>(21), // non centrality
static_cast<RealType>(459.92612), // Chi Squared statistic
static_cast<RealType>(0.2797023600800060e-1), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.2797023600800060e-1), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(1), // degrees of freedom
static_cast<RealType>(1), // non centrality
static_cast<RealType>(0.00016), // Chi Squared statistic
static_cast<RealType>(0.6121428929881423e-2), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.6121428929881423e-2), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(1), // degrees of freedom
static_cast<RealType>(1), // non centrality
static_cast<RealType>(0.00393), // Chi Squared statistic
static_cast<RealType>(0.3033814229753780e-1), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.3033814229753780e-1), // Q = 1 - P
tolerance);
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
boost::math::non_central_chi_squared_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(12));
RealType x = 7;
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE(
mean(dist)
, static_cast<RealType>(8 + 12), tol2);
// variance:
BOOST_CHECK_CLOSE(
variance(dist)
, static_cast<RealType>(64), tol2);
// std deviation:
BOOST_CHECK_CLOSE(
standard_deviation(dist)
, static_cast<RealType>(8), tol2);
// hazard:
BOOST_CHECK_CLOSE(
hazard(dist, x)
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
// cumulative hazard:
BOOST_CHECK_CLOSE(
chf(dist, x)
, -log(cdf(complement(dist, x))), tol2);
// coefficient_of_variation:
BOOST_CHECK_CLOSE(
coefficient_of_variation(dist)
, standard_deviation(dist) / mean(dist), tol2);
// mode:
BOOST_CHECK_CLOSE(
mode(dist)
, static_cast<RealType>(17.184201184730857030170788677340294070728990862663L), sqrt(tolerance * 500));
BOOST_CHECK_CLOSE(
median(dist),
quantile(
boost::math::non_central_chi_squared_distribution<RealType>(
static_cast<RealType>(8),
static_cast<RealType>(12)),
static_cast<RealType>(0.5)), static_cast<RealType>(tol2));
// skewness:
BOOST_CHECK_CLOSE(
skewness(dist)
, static_cast<RealType>(0.6875), tol2);
// kurtosis:
BOOST_CHECK_CLOSE(
kurtosis(dist)
, static_cast<RealType>(3.65625), tol2);
// kurtosis excess:
BOOST_CHECK_CLOSE(
kurtosis_excess(dist)
, static_cast<RealType>(0.65625), tol2);
// Error handling checks:
check_out_of_range<boost::math::non_central_chi_squared_distribution<RealType> >(1, 1);
BOOST_MATH_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution<RealType>(0, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution<RealType>(-1, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution<RealType>(1, -1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(boost::math::non_central_chi_squared_distribution<RealType>(1, 1), -1), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(boost::math::non_central_chi_squared_distribution<RealType>(1, 1), 2), std::domain_error);
#endif
} // template <class RealType>void test_spots(RealType)
template <class T>
T nccs_cdf(T df, T nc, T x)
{
return cdf(boost::math::non_central_chi_squared_distribution<T>(df, nc), x);
}
template <class T>
T nccs_ccdf(T df, T nc, T x)
{
return cdf(complement(boost::math::non_central_chi_squared_distribution<T>(df, nc), x));
}
template <typename Real, typename T>
void do_test_nc_chi_squared(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef Real value_type;
std::cout << "Testing: " << test << std::endl;
#ifdef NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST
value_type(*fp1)(value_type, value_type, value_type) = NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST;
#else
value_type(*fp1)(value_type, value_type, value_type) = nccs_cdf;
#endif
boost::math::tools::test_result<value_type> result;
#if !(defined(ERROR_REPORTING_MODE) && !defined(NC_CHI_SQUARED_CDF_FUNCTION_TO_TEST))
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp1, 0, 1, 2),
extract_result<Real>(3));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "non central chi squared CDF", test);
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST))
#ifdef NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST
fp1 = NC_CHI_SQUARED_CCDF_FUNCTION_TO_TEST;
#else
fp1 = nccs_ccdf;
#endif
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp1, 0, 1, 2),
extract_result<Real>(4));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "non central chi squared CDF complement", test);
std::cout << std::endl;
#endif
}
template <typename Real, typename T>
void quantile_sanity_check(T& data, const char* type_name, const char* test)
{
#ifndef ERROR_REPORTING_MODE
typedef typename T::value_type row_type;
typedef Real value_type;
//
// Tests with type real_concept take rather too long to run, so
// for now we'll disable them:
//
if(!boost::is_floating_point<value_type>::value)
return;
std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
//
// These sanity checks test for a round trip accuracy of one half
// of the bits in T, unless T is type float, in which case we check
// for just one decimal digit. The problem here is the sensitivity
// of the functions, not their accuracy. This test data was generated
// for the forward functions, which means that when it is used as
// the input to the inverses then it is necessarily inexact. This rounding
// of the input is what makes the data unsuitable for use as an accuracy check,
// and also demonstrates that you can't in general round-trip these functions.
// It is however a useful sanity check.
//
value_type precision = static_cast<value_type>(ldexp(1.0, 1 - boost::math::policies::digits<value_type, boost::math::policies::policy<> >() / 2)) * 100;
if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float
for(unsigned i = 0; i < data.size(); ++i)
{
if(Real(data[i][3]) == 0)
{
BOOST_CHECK(0 == quantile(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][3]));
}
else if(data[i][3] < 0.9999f)
{
value_type p = quantile(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][3]);
value_type pt = data[i][2];
BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
}
if(data[i][4] == 0)
{
BOOST_CHECK(0 == quantile(complement(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][3])));
}
else if(data[i][4] < 0.9999f)
{
value_type p = quantile(complement(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), data[i][4]));
value_type pt = data[i][2];
BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
}
if(boost::math::tools::digits<value_type>() > 50)
{
//
// Sanity check mode, the accuracy of
// the mode is at *best* the square root of the accuracy of the PDF:
//
#ifndef BOOST_NO_EXCEPTIONS
try{
value_type m = mode(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]));
value_type p = pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m);
BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m * (1 + sqrt(precision) * 50)) <= p, i);
BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m * (1 - sqrt(precision)) * 50) <= p, i);
}
catch(const boost::math::evaluation_error&) {}
#endif
//
// Sanity check degrees-of-freedom finder, don't bother at float
// precision though as there's not enough data in the probability
// values to get back to the correct degrees of freedom or
// non-cenrality parameter:
//
#ifndef BOOST_NO_EXCEPTIONS
try{
#endif
if((data[i][3] < 0.99) && (data[i][3] != 0))
{
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_chi_squared_distribution<value_type>::find_degrees_of_freedom(data[i][1], data[i][2], data[i][3]),
data[i][0], precision, i);
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_chi_squared_distribution<value_type>::find_non_centrality(data[i][0], data[i][2], data[i][3]),
data[i][1], precision, i);
}
if((data[i][4] < 0.99) && (data[i][4] != 0))
{
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_chi_squared_distribution<value_type>::find_degrees_of_freedom(boost::math::complement(data[i][1], data[i][2], data[i][4])),
data[i][0], precision, i);
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_chi_squared_distribution<value_type>::find_non_centrality(boost::math::complement(data[i][0], data[i][2], data[i][4])),
data[i][1], precision, i);
}
#ifndef BOOST_NO_EXCEPTIONS
}
catch(const std::exception& e)
{
BOOST_ERROR(e.what());
}
#endif
}
}
#endif
}
template <typename T>
void test_accuracy(T, const char* type_name)
{
#include "nccs.ipp"
do_test_nc_chi_squared<T>(nccs, type_name, "Non Central Chi Squared, medium parameters");
quantile_sanity_check<T>(nccs, type_name, "Non Central Chi Squared, medium parameters");
#include "nccs_big.ipp"
do_test_nc_chi_squared<T>(nccs_big, type_name, "Non Central Chi Squared, large parameters");
quantile_sanity_check<T>(nccs_big, type_name, "Non Central Chi Squared, large parameters");
}