mirror of
https://github.com/boostorg/math.git
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4bdf0dd8f0
Added new optimisation config options (still need documenting). Tidied up use of instrumentation code so they all use BOOST_MATH_INSTRUMENT now. Various tweaks to inverse incomplete beta and gamma to reduce number of iterations. Changed incomplete gamma and beta to calculate derivative at the same time as the function (performance optimisation for inverses). Fixed MinGW failures. Refactored and extended rational / polynomial test cases. [SVN r4172]
325 lines
12 KiB
C++
325 lines
12 KiB
C++
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/concepts/real_concept.hpp>
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#include <boost/test/included/test_exec_monitor.hpp>
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/special_functions/beta.hpp>
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#include <boost/math/tools/stats.hpp>
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#include <boost/math/tools/test.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/type_traits/is_floating_point.hpp>
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#include <boost/array.hpp>
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#include <boost/lambda/lambda.hpp>
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#include <boost/lambda/bind.hpp>
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#include "test_beta_hooks.hpp"
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#include "handle_test_result.hpp"
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//
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// DESCRIPTION:
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// ~~~~~~~~~~~~
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//
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// This file tests the incomplete beta function inverses
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// ibeta_inv and ibetac_inv. There are three sets of tests:
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// 1) Spot tests which compare our results with selected values
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// computed using the online special function calculator at
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// functions.wolfram.com,
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// 2) TODO!!!! Accuracy tests use values generated with NTL::RR at
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// 1000-bit precision and our generic versions of these functions.
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// 3) Round trip sanity checks, use the test data for the forward
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// functions, and verify that we can get (approximately) back
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// where we started.
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//
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// Note that when this file is first run on a new platform many of
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// these tests will fail: the default accuracy is 1 epsilon which
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// is too tight for most platforms. In this situation you will
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// need to cast a human eye over the error rates reported and make
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// a judgement as to whether they are acceptable. Either way please
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// report the results to the Boost mailing list. Acceptable rates of
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// error are marked up below as a series of regular expressions that
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// identify the compiler/stdlib/platform/data-type/test-data/test-function
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// along with the maximum expected peek and RMS mean errors for that
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// test.
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//
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void expected_results()
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{
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//
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// Define the max and mean errors expected for
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// various compilers and platforms.
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//
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// Note that permitted max errors are really pretty high
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// at around 10000eps. The reason for this is that even
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// if the forward function is off by 1eps, it's enough to
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// throw out the inverse by ~7000eps. In other words the
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// forward function may flatline, so that many x-values
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// all map to about the same p. Trying to invert in this
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// region is almost futile.
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//
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const char* largest_type;
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
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{
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largest_type = "(long\\s+)?double";
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}
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else
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{
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largest_type = "long double";
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}
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#else
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largest_type = "(long\\s+)?double";
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#endif
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//
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// Linux,
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// Extended exponent range of long double
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// causes more extreme test cases to be executed:
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//
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"linux", // platform
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"double", // test type(s)
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".*", // test data group
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".*", 20, 10); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"linux", // platform
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"long double", // test type(s)
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".*", // test data group
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".*", 200000, 100000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"linux", // platform
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"real_concept", // test type(s)
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".*", // test data group
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".*", 5000000L, 500000); // test function
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//
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// MinGW,
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// Extended exponent range of long double
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// causes more extreme test cases to be executed:
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//
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add_expected_result(
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".*mingw.*", // compiler
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".*", // stdlib
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".*", // platform
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"double", // test type(s)
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".*", // test data group
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".*", 10, 10); // test function
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add_expected_result(
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".*mingw.*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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".*", // test data group
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".*", 300000, 20000); // test function
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//
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// HP-UX
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// Extended exponent range of long double
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// causes more extreme test cases to be executed:
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//
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"HP-UX", // platform
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"long double", // test type(s)
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".*", // test data group
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".*", 200000, 100000); // test function
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//
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// Catch all cases come last:
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//
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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".*", // test data group
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".*", 10000, 1000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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".*", // test data group
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".*", 500000, 500000); // test function
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//
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// Finish off by printing out the compiler/stdlib/platform names,
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// we do this to make it easier to mark up expected error rates.
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//
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std::cout << "Tests run with " << BOOST_COMPILER << ", "
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<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
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}
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template <class T>
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void test_inverses(const T& data)
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{
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using namespace std;
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::tools::digits<value_type>()/2)) * 100;
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if(boost::math::tools::digits<value_type>() < 50)
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precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated
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for(unsigned i = 0; i < data.size(); ++i)
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{
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//
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// These inverse tests are thrown off if the output of the
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// incomplete beta is too close to 1: basically there is insuffient
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// information left in the value we're using as input to the inverse
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// to be able to get back to the original value.
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//
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if(data[i][5] == 0)
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BOOST_CHECK_EQUAL(boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]), value_type(0));
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else if((1 - data[i][5] > 0.001) && (fabs(data[i][5]) >= boost::math::tools::min_value<value_type>()))
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{
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value_type inv = boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]);
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BOOST_CHECK_CLOSE(data[i][2], inv, precision);
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}
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else if(1 == data[i][5])
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BOOST_CHECK_EQUAL(boost::math::ibeta_inv(data[i][0], data[i][1], data[i][5]), value_type(1));
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if(data[i][6] == 0)
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BOOST_CHECK_EQUAL(boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]), value_type(1));
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else if((1 - data[i][6] > 0.001) && (fabs(data[i][6]) >= boost::math::tools::min_value<value_type>()))
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{
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value_type inv = boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]);
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BOOST_CHECK_CLOSE(data[i][2], inv, precision);
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}
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else if(data[i][6] == 1)
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BOOST_CHECK_EQUAL(boost::math::ibetac_inv(data[i][0], data[i][1], data[i][6]), value_type(0));
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}
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}
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template <class T>
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void test_inverses2(const T& data, const char* type_name, const char* test_name)
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{
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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typedef value_type (*pg)(value_type, value_type, value_type);
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pg funcp = boost::math::ibeta_inv;
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using namespace boost::lambda;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test ibeta_inv(T, T, T) against data:
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//
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1]), ret<value_type>(_1[2])),
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ret<value_type>(_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibeta_inv", test_name);
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//
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// test ibetac_inv(T, T, T) against data:
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//
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funcp = boost::math::ibetac_inv;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1]), ret<value_type>(_1[2])),
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ret<value_type>(_1[4]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibetac_inv", test_name);
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}
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template <class T>
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void test_beta(T, const char* name)
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{
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//
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// The actual test data is rather verbose, so it's in a separate file
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//
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// The contents are as follows, each row of data contains
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// five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
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//
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# include "ibeta_small_data.ipp"
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test_inverses(ibeta_small_data);
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# include "ibeta_data.ipp"
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test_inverses(ibeta_data);
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# include "ibeta_large_data.ipp"
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test_inverses(ibeta_large_data);
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# include "ibeta_inv_data.ipp"
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test_inverses2(ibeta_inv_data, name, "Inverse incomplete beta");
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}
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template <class T>
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void test_spots(T)
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{
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//
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// basic sanity checks, tolerance is 100 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 10000;
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(1),
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static_cast<T>(2),
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static_cast<T>(0.5)),
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static_cast<T>(0.29289321881345247559915563789515096071516406231153L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(3),
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static_cast<T>(0.5),
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static_cast<T>(0.5)),
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static_cast<T>(0.92096723292382700385142816696980724853063433975470L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(20.125),
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static_cast<T>(0.5),
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static_cast<T>(0.5)),
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static_cast<T>(0.98862133312917003480022776106012775747685870929920L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::ibeta_inv(
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static_cast<T>(40),
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static_cast<T>(80),
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static_cast<T>(0.5)),
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static_cast<T>(0.33240456430025026300937492802591128972548660643778L), tolerance);
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}
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int test_main(int, char* [])
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{
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expected_results();
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#ifdef TEST_GSL
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gsl_set_error_handler_off();
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#endif
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test_spots(0.0F);
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test_spots(0.0);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L);
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test_spots(boost::math::concepts::real_concept(0.1));
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#endif
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test_beta(0.1F, "float");
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test_beta(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_beta(0.1L, "long double");
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test_beta(boost::math::concepts::real_concept(0.1), "real_concept");
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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"either because the long double overloads of the usual math functions are "
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"not available at all, or because they are too inaccurate for these tests "
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"to pass.</note>" << std::cout;
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#endif
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return 0;
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}
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