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// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 2009
// 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>
#include <boost/math/special_functions/math_fwd.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/tools/stats.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/tools/big_constant.hpp>
#include <boost/math/constants/constants.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 <boost/math/special_functions/hypergeometric_pFq.hpp>
#include <boost/math/special_functions/relative_difference.hpp>
#ifdef BOOST_MSVC
#pragma warning(disable:4127)
#endif
#ifndef SC_
#define SC_(x) BOOST_MATH_BIG_CONSTANT(T, 1000000, x)
#endif
template <class Seq>
bool is_small_a(const Seq& a)
{
if (a.size() == 1)
{
auto v = *a.begin();
if ((v > -14) && (v < 1))
return true;
}
return false;
}
template <class Seq>
bool has_negative_ab(const Seq& a, const Seq& b)
{
for(auto p = a.begin(); p != a.end(); ++p)
{
if(*p < 0)
return true;
}
for(auto p = b.begin(); p != b.end(); ++p)
{
if(*p < 0)
return true;
}
return false;
}
template <class T>
void check_pFq_result(const T& result, const T& norm, const T& expect, const std::initializer_list<T>& a, const std::initializer_list<T>& b, const T& z)
{
//
// Ideally the error rate we calculate from comparing norm to result
// should be larger than the actual error. However, in practice even
// if all the terms are positive and norm == result there will still
// be a small error from the actual summation (we could work out how
// much from the number of terms summed, but that's overkill for this)
// so we add a small fudge factor when comparing errors:
//
T err = boost::math::relative_difference(result, expect);
T found_err = norm / fabs(result);
T fudge_factor = 25;
if (is_small_a(a))
fudge_factor *= 4; // not sure why??
if ((has_negative_ab(a, b)) || ((a.size() == 2) && (b.size() == 1)) || (boost::math::tools::epsilon<T>() < boost::math::tools::epsilon<double>()))
{
T min_err = boost::math::tools::epsilon<T>() * 600 / found_err;
fudge_factor = (std::max)(fudge_factor, min_err);
}
if ((((err > fudge_factor * found_err) && (found_err < 1)) || (boost::math::isnan)(found_err)) && (!(boost::math::isinf)(result)))
{
std::cout << "Found error = " << err << " error from norm = " << found_err << std::endl;
std::cout << "Testing fudge factor = " << fudge_factor << std::endl;
std::cout << " a = ";
for (auto pa = a.begin(); pa != a.end(); ++pa)
std::cout << *pa << ",";
std::cout << "\n b = ";
for (auto pb = b.begin(); pb != b.end(); ++pb)
std::cout << *pb << ",";
std::cout << "\n z = " << z << std::endl;
//
// This will fail if we've got here:
//
BOOST_CHECK_LE(err, fudge_factor * found_err);
BOOST_CHECK(!(boost::math::isnan)(found_err));
}
}
template <class T>
void test_spots_1F0(T, const char*)
{
using std::pow;
T tolerance = boost::math::tools::epsilon<T>() * 1000;
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(2)), T(-1), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(4)), T(-27), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(0.5)), T(0.125), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(3) }, {}, T(0.5)), T(8), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(3) }, {}, T(2)), T(-1), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(3) }, {}, T(4)), T(T(-1) / 27), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(3) }, {}, T(-0.5)), pow(T(1.5), -3), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(3) }, {}, T(-2)), T(1 / T(27)), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(3) }, {}, T(-4)), T(T(1) / 125), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(-0.5)), pow(T(1.5), 3), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(-2)), T(27), tolerance);
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(-4)), T(125), tolerance);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({ T(3) }, {}, T(1)), std::domain_error);
//BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({ T(-3) }, {}, T(1)), std::domain_error);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({ T(3.25) }, {}, T(1)), std::domain_error);
//BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({ T(-3.25) }, {}, T(1)), std::domain_error);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({ T(3.25) }, {}, T(2)), std::domain_error);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({ T(-3.25) }, {}, T(2)), std::domain_error);
}
template <class T>
void test_spots_0F1(T, const char*)
{
T tolerance = boost::math::tools::epsilon<T>() * 50000;
BOOST_CHECK_EQUAL(boost::math::hypergeometric_pFq({}, { T(3) }, T(0)), 1);
BOOST_CHECK_EQUAL(boost::math::hypergeometric_pFq({}, { T(-3) }, T(0)), 1);
//BOOST_CHECK_EQUAL(boost::math::hypergeometric_pFq({}, { T(0) }, T(0)), 1);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({}, { T(0) }, T(-1)), std::domain_error);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({}, { T(-1) }, T(-1)), std::domain_error);
BOOST_CHECK_THROW(boost::math::hypergeometric_pFq({}, { T(-10) }, T(-5)), std::domain_error);
static const boost::array<boost::array<T, 3>, 35> hypergeometric_pFq_integer_data = { {
{ SC_(4.0), SC_(-20.0), SC_(-0.012889714201783047561923257996127233830940165138385) },
{ SC_(8.0), SC_(-20.0), SC_(0.046498609282365144223175012935939437508273248399881) },
{ SC_(12.0), SC_(-20.0), SC_(0.16608847431869756642136191351311569335145459224622) },
{ SC_(16.0), SC_(-20.0), SC_(0.27230484709157170329168048388841880599105216477631) },
//{ SC_(20.0), SC_(-20.0), SC_(0.35865872656868844615709101792040025253126126604266) },
{ SC_(4.0), SC_(-16.0), SC_(-0.027293644412433023379286103818840667403690937153604) },
{ SC_(8.0), SC_(-16.0), SC_(0.098618710511372349330666801041676087431136532039702) },
{ SC_(12.0), SC_(-16.0), SC_(0.24360114226383905073379763460037817885919457531523) },
//{ SC_(16.0), SC_(-16.0), SC_(0.35635186318802906043824855864337727878754460163525) },
//{ SC_(20.0), SC_(-16.0), SC_(0.44218381382689101428948260613085371477815110358789) },
{ SC_(4.0), SC_(-12.0), SC_(-0.021743572290699436419371120781513860006290363262907) },
{ SC_(8.0), SC_(-12.0), SC_(0.19025625754362006866949730683824627505504067855043) },
//{ SC_(12.0), SC_(-12.0), SC_(0.35251228238278927379621049815222218665165551016489) },
//{ SC_(16.0), SC_(-12.0), SC_(0.46415411486674623230458980010115972932474705884865) },
//{ SC_(20.0), SC_(-12.0), SC_(0.54394918325286018927327004362535051310016558628741) },
{ SC_(4.0), SC_(-8.0), SC_(0.056818744289274872033266550620647787396712125304880) },
//{ SC_(8.0), SC_(-8.0), SC_(0.34487371876996263249797701802458885718691612997456) },
//{ SC_(12.0), SC_(-8.0), SC_(0.50411654015891701804499796523449656998841355305043) },
//{ SC_(16.0), SC_(-8.0), SC_(0.60191459981670594041254437708158847428118361245442) },
//{ SC_(20.0), SC_(-8.0), SC_(0.66770752550930138035694866478078941681114294465418) },
//{ SC_(4.0), SC_(-4.0), SC_(0.32262860540671645526863760914000166725449779629143) },
//{ SC_(8.0), SC_(-4.0), SC_(0.59755773349355150397404772151441126513126998265958) },
//{ SC_(12.0), SC_(-4.0), SC_(0.71337465206009117934071859694314971137807212605147) },
//{ SC_(16.0), SC_(-4.0), SC_(0.77734333649378860739496954157535257278092349684783) },
//{ SC_(20.0), SC_(-4.0), SC_(0.81794177985447769150469288350369205683856312760890) },
{ SC_(4.0), SC_(4.0), SC_(2.5029568338152582758923890008139391395035041790831) },
{ SC_(8.0), SC_(4.0), SC_(1.6273673128576761227855719910743734060605725722129) },
{ SC_(12.0), SC_(4.0), SC_(1.3898419290864057799739567227851793491657442624207) },
{ SC_(16.0), SC_(4.0), SC_(1.2817098157957427946677711269410726972209834860612) },
{ SC_(20.0), SC_(4.0), SC_(1.2202539302152377230940386181201477276788392792437) },
{ SC_(4.0), SC_(8.0), SC_(5.5616961007411965409200003309686924059253894118586) },
{ SC_(8.0), SC_(8.0), SC_(2.5877053985451664722152913482683136948296873738479) },
{ SC_(12.0), SC_(8.0), SC_(1.9166410733572697158003086323981583993970490592046) },
{ SC_(16.0), SC_(8.0), SC_(1.6370675016890669952237854163997946987362497613701) },
{ SC_(20.0), SC_(8.0), SC_(1.4862852701827990444915220582410007454379891584086) },
{ SC_(4.0), SC_(12.0), SC_(11.419268276211177842169936131590385979116019595164) },
{ SC_(8.0), SC_(12.0), SC_(4.0347215359576567066789638314925802225312840819037) },
{ SC_(12.0), SC_(12.0), SC_(2.6242497527837800417573064942486918368886996538285) },
{ SC_(16.0), SC_(12.0), SC_(2.0840468784170876805932772732753387258909164486511) },
{ SC_(20.0), SC_(12.0), SC_(1.8071042457762091748544382847762106786633952487005) },
{ SC_(4.0), SC_(16.0), SC_(22.132051970576036053853444648907108439504682530918) },
{ SC_(8.0), SC_(16.0), SC_(6.1850485247748975008808779795786699492711191898792) },
{ SC_(12.0), SC_(16.0), SC_(3.5694322843488018916484224923627864928705138154372) },
{ SC_(16.0), SC_(16.0), SC_(2.6447371137201451261118187672029372265909501355722) },
{ SC_(20.0), SC_(16.0), SC_(2.1934058398888071720297525592515838555602675797235) },
{ SC_(4.0), SC_(20.0), SC_(41.021743268279206331672552645354782698296383424328) },
{ SC_(8.0), SC_(20.0), SC_(9.3414225299809886395081381945971250426599939097753) },
{ SC_(12.0), SC_(20.0), SC_(4.8253866205826406499959001774187695527272168375992) },
{ SC_(16.0), SC_(20.0), SC_(3.3462305133519485784864062004430532216764447939942) },
{ SC_(20.0), SC_(20.0), SC_(2.6578698872220394617444624241257799193518140676691) },
} };
for (auto row = hypergeometric_pFq_integer_data.begin(); row != hypergeometric_pFq_integer_data.end(); ++row)
{
BOOST_CHECK_CLOSE(boost::math::hypergeometric_pFq({}, { (*row)[0] }, (*row)[1]), (*row)[2], tolerance);
}
}
template <class T>
void test_spots_1F1(T, const char*)
{
#include "hypergeometric_1F1.ipp"
for (auto row = hypergeometric_1F1.begin(); row != hypergeometric_1F1.end(); ++row)
{
try {
T norm;
T result = boost::math::hypergeometric_pFq({ (*row)[0] }, { (*row)[1] }, (*row)[2], &norm);
check_pFq_result(result, norm, (*row)[3], { (*row)[0] }, { (*row)[1] }, (*row)[2]);
}
catch (const boost::math::evaluation_error&) {}
}
}
template <class T>
void test_spots_1F1_b(T, const char*)
{
#include "hypergeometric_1F1_big.ipp"
for (auto row = hypergeometric_1F1_big.begin(); row != hypergeometric_1F1_big.end(); ++row)
{
try {
T norm;
T result = boost::math::hypergeometric_pFq({ (*row)[0] }, { (*row)[1] }, (*row)[2], &norm);
check_pFq_result(result, norm, (*row)[3], { (*row)[0] }, { (*row)[1] }, (*row)[2]);
}
catch (const boost::math::evaluation_error&) {}
}
}
template <class T>
void test_spots_2F1(T, const char*)
{
#include "hypergeometric_2F1.ipp"
for (auto row = hypergeometric_2F1.begin(); row != hypergeometric_2F1.end(); ++row)
{
try {
T norm;
T result = boost::math::hypergeometric_pFq({ (*row)[0], (*row)[1] }, { (*row)[2] }, (*row)[3], &norm);
check_pFq_result(result, norm, (*row)[4], { (*row)[0], (*row)[1] }, { (*row)[2] }, (*row)[3]);
}
catch (const boost::math::evaluation_error&) {}
}
}
template <class T>
void test_spots_0F2(T, const char*)
{
#include "hypergeometric_0F2.ipp"
for (auto row = hypergeometric_0F2.begin(); row != hypergeometric_0F2.end(); ++row)
{
try {
T norm;
T result = boost::math::hypergeometric_pFq({}, { (*row)[0], (*row)[1] }, (*row)[2], &norm);
check_pFq_result(result, norm, (*row)[3], {}, { (*row)[0], (*row)[1] }, (*row)[2]);
}
catch (const boost::math::evaluation_error&) {}
}
}
template <class T>
void test_spots_1F2(T, const char*)
{
#include "hypergeometric_1F2.ipp"
for (auto row = hypergeometric_1F2.begin(); row != hypergeometric_1F2.end(); ++row)
{
try {
T norm;
T result = boost::math::hypergeometric_pFq({ (*row)[0] }, { (*row)[1], (*row)[2] }, (*row)[3], &norm);
check_pFq_result(result, norm, (*row)[4], { (*row)[0] }, { (*row)[1], (*row)[2] }, (*row)[3]);
}
catch (const boost::math::evaluation_error&) {}
}
}
template <class T>
void test_spots_2F2(T, const char*)
{
#include "hypergeometric_2F2.ipp"
for (auto row = hypergeometric_2F2.begin(); row != hypergeometric_2F2.end(); ++row)
{
try {
T norm;
T result = boost::math::hypergeometric_pFq({ (*row)[0], (*row)[1] }, { (*row)[2], (*row)[3] }, (*row)[4], &norm);
check_pFq_result(result, norm, (*row)[5], { (*row)[0], (*row)[1] }, { (*row)[2], (*row)[3] }, (*row)[4]);
}
catch (const boost::math::evaluation_error&) {}
}
}
template <class T>
void test_spots(T z, const char* type_name)
{
test_spots_1F0(z, type_name);
test_spots_0F1(z, type_name);
test_spots_1F1(z, type_name);
test_spots_1F1_b(z, type_name);
test_spots_0F2(z, type_name);
test_spots_1F2(z, type_name);
test_spots_2F2(z, type_name);
test_spots_2F1(z, type_name);
}
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