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math/test/test_bessel_j.cpp
John Maddock be2ccd4e73 Fixed Cygwin failures. 
[SVN r38713]
2007-08-16 13:07:32 +00:00

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// (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)
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/bessel.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#include "handle_test_result.hpp"
#include "test_bessel_hooks.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the bessel functions. There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
{
largest_type = "(long\\s+)?double|real_concept";
}
else
{
largest_type = "long double|real_concept";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// HP-UX specific rates:
//
// Does this need more investigation or is test data limited????
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
"double", // test type(s)
".*Tricky.*", // test data group
".*", 100000, 100000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 80000000000LL, 80000000000LL); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 3000000, 2000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*J.*Tricky.*", // test data group
".*", 3000, 500); // test function
//
// Mac OS X:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
"Bessel JN.*", // test data group
".*", 40000, 20000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
"Bessel J:.*", // test data group
".*", 50000, 20000); // test function
// This shouldn't be required, could be limited test data precision
// i.e. not enough bits in double input to get double result.
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
"double", // test type(s)
".*Tricky.*", // test data group
".*", 100000, 100000); // test function
//
// Linux specific results:
//
// sin and cos appear to have only double precision for large
// arguments on some linux distros:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
".*J:.*", // test data group
".*", 40000, 30000); // test function
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if((std::numeric_limits<double>::digits != std::numeric_limits<long double>::digits)
&& (std::numeric_limits<long double>::digits < 90))
{
// some errors spill over into type double as well:
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000, 400000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*J1.*Tricky.*", // test data group
".*", 5000, 5000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*(JN|j).*|.*Tricky.*", // test data group
".*", 50, 50); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*", // test data group
".*", 30, 30); // test function
//
// and we have a few cases with higher limits as well:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000000, 400000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 5000000, 5000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*(JN|j).*|.*Tricky.*", // test data group
".*", 33000, 20000); // test function
}
#endif
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000000, 400000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 5000000, 5000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*JN.*Integer.*", // test data group
".*", 30000, 10000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*(JN|j).*|.*Tricky.*", // test data group
".*", 1500, 700); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 40, 20); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class T>
void do_test_cyl_bessel_j(const T& data, const char* type_name, const char* test_name)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(value_type, value_type);
pg funcp = boost::math::cyl_bessel_j;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test cyl_bessel_j against data:
//
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_bessel_j", test_name);
std::cout << std::endl;
#ifdef TEST_OTHER
if(boost::is_floating_point<value_type>::value)
{
funcp = other::cyl_bessel_j;
//
// test other::cyl_bessel_j against data:
//
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::cyl_bessel_j", test_name);
std::cout << std::endl;
}
#endif
}
template <class T>
T cyl_bessel_j_int_wrapper(T v, T x)
{
return static_cast<T>(boost::math::cyl_bessel_j(boost::math::tools::real_cast<int>(v), x));
}
template <class T>
void do_test_cyl_bessel_j_int(const T& data, const char* type_name, const char* test_name)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(value_type, value_type);
pg funcp = cyl_bessel_j_int_wrapper;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test cyl_bessel_j against data:
//
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_bessel_j", test_name);
std::cout << std::endl;
}
template <class T>
void do_test_sph_bessel_j(const T& data, const char* type_name, const char* test_name)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(unsigned, value_type);
pg funcp = boost::math::sph_bessel;
typedef int (*cast_t)(value_type);
cast_t rc = &boost::math::tools::real_cast<int, value_type>;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test sph_bessel against data:
//
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp,
boost::lambda::ret<int>(
boost::lambda::bind(
rc,
boost::lambda::ret<value_type>(boost::lambda::_1[0]))),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::sph_bessel", test_name);
std::cout << std::endl;
}
template <class T>
void test_bessel(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
// function values calculated on http://functions.wolfram.com/
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 8> j0_data = {{
{ SC_(0), SC_(0), SC_(1) },
{ SC_(0), SC_(1), SC_(0.7651976865579665514497175261026632209093) },
{ SC_(0), SC_(-2), SC_(0.2238907791412356680518274546499486258252) },
{ SC_(0), SC_(4), SC_(-0.3971498098638473722865907684516980419756) },
{ SC_(0), SC_(-8), SC_(0.1716508071375539060908694078519720010684) },
{ SC_(0), SC_(1e-05), SC_(0.999999999975000000000156249999999565972) },
{ SC_(0), SC_(1e-10), SC_(0.999999999999999999997500000000000000000) },
{ SC_(0), SC_(-1e+01), SC_(-0.2459357644513483351977608624853287538296) },
}};
static const boost::array<boost::array<T, 3>, 6> j0_tricky = {{
// Big numbers make the accuracy of std::sin the limiting factor:
{ SC_(0), SC_(1e+03), SC_(0.02478668615242017456133073111569370878617) },
{ SC_(0), SC_(1e+05), SC_(-0.001719201116235972192570601477073201747532) },
// test at the roots:
{ SC_(0), SC_(2521642)/(1024 * 1024), SC_(1.80208819970046790002973759410972422387259992955354630042138e-7) },
{ SC_(0), SC_(5788221)/(1024 * 1024), SC_(-1.37774249380686777043369399806210229535671843632174587432454e-7) },
{ SC_(0), SC_(9074091)/(1024 * 1024), SC_(1.03553057441100845081018471279571355857520645127532785991335e-7) },
{ SC_(0), SC_(12364320)/(1024 * 1024), SC_(-3.53017140778223781420794006033810387155048392363051866610931e-9) }
}};
static const boost::array<boost::array<T, 3>, 8> j1_data = {
SC_(1), SC_(0), SC_(0),
SC_(1), SC_(1), SC_(0.4400505857449335159596822037189149131274),
SC_(1), SC_(-2), SC_(-0.5767248077568733872024482422691370869203),
SC_(1), SC_(4), SC_(-6.604332802354913614318542080327502872742e-02),
SC_(1), SC_(-8), SC_(-0.2346363468539146243812766515904546115488),
SC_(1), SC_(1e-05), SC_(4.999999999937500000000260416666666124132e-06),
SC_(1), SC_(1e-10), SC_(4.999999999999999999993750000000000000000e-11),
SC_(1), SC_(-1e+01), SC_(-4.347274616886143666974876802585928830627e-02),
};
static const boost::array<boost::array<T, 3>, 5> j1_tricky = {
// Big numbers make the accuracy of std::sin the limiting factor:
SC_(1), SC_(1e+03), SC_(4.728311907089523917576071901216916285418e-03),
SC_(1), SC_(1e+05), SC_(1.846757562882567716362123967114215743694e-03),
// test zeros:
SC_(1), SC_(4017834)/(1024*1024), SC_(3.53149033321258645807835062770856949751958513973522222203044e-7),
SC_(1), SC_(7356375)/(1024*1024), SC_(-2.31227973111067286051984021150135526024117175836722748404342e-7),
SC_(1), SC_(10667654)/(1024*1024), SC_(1.24591331097191900488116495350277530373473085499043086981229e-7),
};
static const boost::array<boost::array<T, 3>, 14> jn_data = {
SC_(2), SC_(0), SC_(0),
SC_(2), SC_(1e-02), SC_(1.249989583365885362413250958437642113452e-05),
SC_(5), SC_(10), SC_(-0.2340615281867936404436949416457777864635),
SC_(5), SC_(-10), SC_(0.2340615281867936404436949416457777864635),
SC_(-5), SC_(1e+06), SC_(7.259643842453285052375779970433848914846e-04),
SC_(5), SC_(1e+06), SC_(-0.000725964384245328505237577997043384891484649290328285235308619),
SC_(-5), SC_(-1), SC_(2.497577302112344313750655409880451981584e-04),
SC_(10), SC_(10), SC_(0.2074861066333588576972787235187534280327),
SC_(10), SC_(-10), SC_(0.2074861066333588576972787235187534280327),
SC_(10), SC_(-5), SC_(1.467802647310474131107532232606627020895e-03),
SC_(-10), SC_(1e+06), SC_(-3.310793117604488741264958559035744460210e-04),
SC_(10), SC_(1e+06), SC_(-0.000331079311760448874126495855903574446020957243277028930713243),
SC_(1e+02), SC_(8e+01), SC_(4.606553064823477354141298259169874909670e-06),
SC_(1e+03), SC_(1e+05), SC_(1.283178112502480365195139312635384057363e-03),
};
do_test_cyl_bessel_j(j0_data, name, "Bessel J0: Mathworld Data");
do_test_cyl_bessel_j(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases)");
do_test_cyl_bessel_j(j1_data, name, "Bessel J1: Mathworld Data");
do_test_cyl_bessel_j(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases)");
do_test_cyl_bessel_j(jn_data, name, "Bessel JN: Mathworld Data");
do_test_cyl_bessel_j_int(j0_data, name, "Bessel J0: Mathworld Data (Integer Version)");
do_test_cyl_bessel_j_int(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases) (Integer Version)");
do_test_cyl_bessel_j_int(j1_data, name, "Bessel J1: Mathworld Data (Integer Version)");
do_test_cyl_bessel_j_int(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases) (Integer Version)");
do_test_cyl_bessel_j_int(jn_data, name, "Bessel JN: Mathworld Data (Integer Version)");
static const boost::array<boost::array<T, 3>, 17> jv_data = {
//SC_(-2.4), SC_(0), std::numeric_limits<T>::infinity(),
SC_(2457)/1024, SC_(1)/1024, SC_(3.80739920118603335646474073457326714709615200130620574875292e-9),
SC_(5.5), SC_(3217)/1024, SC_(0.0281933076257506091621579544064767140470089107926550720453038),
SC_(-5.5), SC_(3217)/1024, SC_(-2.55820064470647911823175836997490971806135336759164272675969),
SC_(-5.5), SC_(1e+04), SC_(2.449843111985605522111159013846599118397e-03),
SC_(5.5), SC_(1e+04), SC_(0.00759343502722670361395585198154817047185480147294665270646578),
SC_(5.5), SC_(1e+06), SC_(-0.000747424248595630177396350688505919533097973148718960064663632),
SC_(5.125), SC_(1e+06), SC_(-0.000776600124835704280633640911329691642748783663198207360238214),
SC_(5.875), SC_(1e+06), SC_(-0.000466322721115193071631008581529503095819705088484386434589780),
SC_(0.5), SC_(101), SC_(0.0358874487875643822020496677692429287863419555699447066226409),
SC_(-5.5), SC_(1e+04), SC_(0.00244984311198560552211115901384659911839737686676766460822577),
SC_(-5.5), SC_(1e+06), SC_(0.000279243200433579511095229508894156656558211060453622750659554),
SC_(-0.5), SC_(101), SC_(0.0708184798097594268482290389188138201440114881159344944791454),
SC_(-10486074) / (1024*1024), SC_(1)/1024, SC_(1.41474013160494695750009004222225969090304185981836460288562e35),
SC_(-10486074) / (1024*1024), SC_(15), SC_(-0.0902239288885423309568944543848111461724911781719692852541489),
SC_(10486074) / (1024*1024), SC_(1e+02), SC_(-0.0547064914615137807616774867984047583596945624129838091326863),
SC_(10486074) / (1024*1024), SC_(2e+04), SC_(-0.00556783614400875611650958980796060611309029233226596737701688),
SC_(-10486074) / (1024*1024), SC_(1e+02), SC_(-0.0547613660316806551338637153942604550779513947674222863858713),
};
do_test_cyl_bessel_j(jv_data, name, "Bessel J: Mathworld Data");
#undef SC_
#include "bessel_j_int_data.ipp"
do_test_cyl_bessel_j(bessel_j_int_data, name, "Bessel JN: Random Data");
#include "bessel_j_data.ipp"
do_test_cyl_bessel_j(bessel_j_data, name, "Bessel J: Random Data");
#include "bessel_j_large_data.ipp"
do_test_cyl_bessel_j(bessel_j_large_data, name, "Bessel J: Random Data (Tricky large values)");
#include "sph_bessel_data.ipp"
do_test_sph_bessel_j(sph_bessel_data, name, "Bessel j: Random Data");
}
int test_main(int, char* [])
{
#ifdef TEST_GSL
gsl_set_error_handler_off();
#endif
expected_results();
test_bessel(0.1F, "float");
test_bessel(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_bessel(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_bessel(boost::math::concepts::real_concept(0.1), "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::cout;
#endif
return 0;
}
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