mirror of
https://github.com/boostorg/math.git
synced 2026-01-19 04:22:09 +00:00
415 lines
19 KiB
C++
415 lines
19 KiB
C++
// (C) 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)
|
|
|
|
#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/legendre.hpp>
|
|
#include <boost/math/constants/constants.hpp>
|
|
#include <boost/array.hpp>
|
|
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
|
|
#include <boost/lambda/lambda.hpp>
|
|
#include <boost/lambda/bind.hpp>
|
|
#endif
|
|
|
|
#include "handle_test_result.hpp"
|
|
#include "test_legendre_hooks.hpp"
|
|
|
|
//
|
|
// DESCRIPTION:
|
|
// ~~~~~~~~~~~~
|
|
//
|
|
// This file tests the legendre polynomials.
|
|
// 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";
|
|
}
|
|
else
|
|
{
|
|
largest_type = "long double";
|
|
}
|
|
#else
|
|
largest_type = "(long\\s+)?double";
|
|
#endif
|
|
//
|
|
// Linux:
|
|
//
|
|
if((std::numeric_limits<long double>::digits <= 64)
|
|
&& (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
|
|
{
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"double", // test type(s)
|
|
".*", // test data group
|
|
".*", 10, 5); // test function
|
|
#endif
|
|
}
|
|
if(std::numeric_limits<long double>::digits == 64)
|
|
{
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_p", 1000, 200); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_q", 7000, 1000); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_p", 1000, 200); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_q", 7000, 1000); // test function
|
|
}
|
|
//
|
|
// Catch all cases come last:
|
|
//
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_p", 400, 200); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_q", 5400, 500); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Legendre Polynomials.*", // test data group
|
|
"boost::math::legendre_p", 300, 80); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Legendre Polynomials.*", // test data group
|
|
"boost::math::legendre_q", 100, 50); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
largest_type, // test type(s)
|
|
"Associated Legendre Polynomials.*", // test data group
|
|
".*", 200, 20); // test function
|
|
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_p", 400, 200); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Legendre Polynomials.*Large.*", // test data group
|
|
"boost::math::legendre_q", 5400, 500); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Legendre Polynomials.*", // test data group
|
|
"boost::math::legendre_p", 300, 80); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Legendre Polynomials.*", // test data group
|
|
"boost::math::legendre_q", 100, 50); // test function
|
|
add_expected_result(
|
|
".*", // compiler
|
|
".*", // stdlib
|
|
".*", // platform
|
|
"real_concept", // test type(s)
|
|
"Associated Legendre Polynomials.*", // test data group
|
|
".*", 200, 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_legendre_p(const T& data, const char* type_name, const char* test_name)
|
|
{
|
|
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
|
|
typedef typename T::value_type row_type;
|
|
typedef typename row_type::value_type value_type;
|
|
|
|
typedef value_type (*pg)(int, value_type);
|
|
pg funcp = boost::math::legendre_p;
|
|
|
|
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 legendre_p 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::legendre_p", test_name);
|
|
#ifdef TEST_OTHER
|
|
if(::boost::is_floating_point<value_type>::value){
|
|
funcp = other::legendre_p;
|
|
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]));
|
|
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::legendre_p");
|
|
}
|
|
#endif
|
|
|
|
typedef value_type (*pg2)(unsigned, value_type);
|
|
pg2 funcp2 = boost::math::legendre_q;
|
|
|
|
//
|
|
// test legendre_q against data:
|
|
//
|
|
result = boost::math::tools::test(
|
|
data,
|
|
boost::lambda::bind(funcp2,
|
|
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[3]));
|
|
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_q", test_name);
|
|
#ifdef TEST_OTHER
|
|
if(::boost::is_floating_point<value_type>::value){
|
|
funcp = other::legendre_q;
|
|
result = boost::math::tools::test(
|
|
data,
|
|
boost::lambda::bind(funcp2,
|
|
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[3]));
|
|
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::legendre_q");
|
|
}
|
|
#endif
|
|
|
|
|
|
std::cout << std::endl;
|
|
#endif
|
|
}
|
|
|
|
template <class T>
|
|
void do_test_assoc_legendre_p(const T& data, const char* type_name, const char* test_name)
|
|
{
|
|
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
|
|
typedef typename T::value_type row_type;
|
|
typedef typename row_type::value_type value_type;
|
|
|
|
typedef value_type (*pg)(int, int, value_type);
|
|
pg funcp = boost::math::legendre_p;
|
|
|
|
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 legendre_p 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<int>(
|
|
boost::lambda::bind(
|
|
rc,
|
|
boost::lambda::ret<value_type>(boost::lambda::_1[1]))),
|
|
boost::lambda::ret<value_type>(boost::lambda::_1[2])),
|
|
boost::lambda::ret<value_type>(boost::lambda::_1[3]));
|
|
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_p", test_name);
|
|
std::cout << std::endl;
|
|
#endif
|
|
}
|
|
|
|
template <class T>
|
|
void test_legendre_p(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):
|
|
//
|
|
# include "legendre_p.ipp"
|
|
|
|
do_test_legendre_p(legendre_p, name, "Legendre Polynomials: Small Values");
|
|
|
|
# include "legendre_p_large.ipp"
|
|
|
|
do_test_legendre_p(legendre_p_large, name, "Legendre Polynomials: Large Values");
|
|
|
|
# include "assoc_legendre_p.ipp"
|
|
|
|
do_test_assoc_legendre_p(assoc_legendre_p, name, "Associated Legendre Polynomials: Small Values");
|
|
|
|
}
|
|
|
|
template <class T>
|
|
void test_spots(T, const char* t)
|
|
{
|
|
std::cout << "Testing basic sanity checks for type " << t << std::endl;
|
|
//
|
|
// basic sanity checks, tolerance is 100 epsilon:
|
|
//
|
|
T tolerance = boost::math::tools::epsilon<T>() * 100;
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-1, static_cast<T>(0.5L)), static_cast<T>(1L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, static_cast<T>(0.5L)), static_cast<T>(-0.2890625000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, static_cast<T>(0.5L)), static_cast<T>(-0.4375000000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, static_cast<T>(0.5L)), static_cast<T>(0.2231445312500000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, static_cast<T>(0.5L)), static_cast<T>(0.3232421875000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, static_cast<T>(0.5L)), static_cast<T>(-0.09542943523261546936538467572384923220258L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, static_cast<T>(0.5L)), static_cast<T>(-0.1316993126940266257030910566308990611306L), tolerance);
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(0.5L)), static_cast<T>(5.625000000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
|
|
if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
|
|
{
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
|
|
}
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(0.5L)), static_cast<T>(4.966634149702370788037088925152355134665e30L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(-0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(-0.5L)), static_cast<T>(-5.625000000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(-0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(-0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
|
|
if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
|
|
{
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(-0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
|
|
}
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(-0.5L)), static_cast<T>(-4.966634149702370788037088925152355134665e30L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, -2, static_cast<T>(0.5L)), static_cast<T>(0.01171875000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, -2, static_cast<T>(0.5L)), static_cast<T>(0.04687500000000000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, -5, static_cast<T>(0.5L)), static_cast<T>(0.00002378609812640364935569308025139290054701L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, -4, static_cast<T>(0.5L)), static_cast<T>(0.0002563476562500000000000000000000000000000L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, -30, static_cast<T>(0.5L)), static_cast<T>(-2.379819988646847616996471299410611801239e-48L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, -20, static_cast<T>(0.5L)), static_cast<T>(4.356454600748202401657099008867502679122e-33L), tolerance);
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(1, static_cast<T>(0.5L)), static_cast<T>(-0.7253469278329725771511886907693685738381L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(4, static_cast<T>(0.5L)), static_cast<T>(0.4401745259867706044988642951843745400835L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(7, static_cast<T>(0.5L)), static_cast<T>(-0.3439152932669753451878700644212067616780L), tolerance);
|
|
BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(40, static_cast<T>(0.5L)), static_cast<T>(0.1493671665503550095010454949479907886011L), tolerance);
|
|
}
|
|
|
|
int test_main(int, char* [])
|
|
{
|
|
test_spots(0.0F, "float");
|
|
test_spots(0.0, "double");
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_spots(0.0L, "long double");
|
|
test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
|
|
#endif
|
|
|
|
expected_results();
|
|
|
|
test_legendre_p(0.1F, "float");
|
|
test_legendre_p(0.1, "double");
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_legendre_p(0.1L, "long double");
|
|
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
|
|
test_legendre_p(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;
|
|
}
|
|
|
|
|
|
|