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https://github.com/saitohirga/WSJT-X.git
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742 lines
29 KiB
C++
742 lines
29 KiB
C++
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// Copyright John Maddock 2006, 2007.
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// Copyright Paul A. Bristow 2007
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// test_cauchy.cpp Test Cauchy distribution
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#ifdef _MSC_VER
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# pragma warning(disable: 4100) // unreferenced formal parameter.
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// Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */
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//# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test)
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// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535.
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# pragma warning(disable: 4127) // conditional expression is constant
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#endif
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// #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false
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// To compile even if Cauchy mean is used.
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#include <boost/math/tools/test.hpp>
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#include <boost/math/distributions/cauchy.hpp>
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using boost::math::cauchy_distribution;
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#include "test_out_of_range.hpp"
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include <iostream>
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using std::cout;
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using std::endl;
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template <class RealType>
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void test_spots(RealType T)
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{
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// Check some bad parameters to construct the distribution,
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#ifndef BOOST_NO_EXCEPTIONS
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BOOST_MATH_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(0, 0), std::domain_error); // zero scale.
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BOOST_MATH_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(0, -1), std::domain_error); // negative scale (shape).
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#else
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BOOST_MATH_CHECK_THROW(boost::math::cauchy_distribution<RealType>(0, 0), std::domain_error); // zero scale.
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BOOST_MATH_CHECK_THROW(boost::math::cauchy_distribution<RealType>(0, -1), std::domain_error); // negative scale (shape).
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#endif
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cauchy_distribution<RealType> C01;
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BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values.
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BOOST_CHECK_EQUAL(C01.scale(), 1);
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// Basic sanity checks.
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// 50eps as a percentage, up to a maximum of double precision
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// (that's the limit of our test data).
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RealType tolerance = (std::max)(
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static_cast<RealType>(boost::math::tools::epsilon<double>()),
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boost::math::tools::epsilon<RealType>());
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tolerance *= 50 * 100;
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cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl;
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// These first sets of test values were calculated by punching numbers
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// into a calculator, and using the formulas on the Mathworld website:
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// http://mathworld.wolfram.com/CauchyDistribution.html
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// and values from MathCAD 200 Professional,
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// CDF:
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//
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.125)), // x
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static_cast<RealType>(0.53958342416056554201085167134004L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-0.125)), // x
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static_cast<RealType>(0.46041657583943445798914832865996L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.5)), // x
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static_cast<RealType>(0.64758361765043327417540107622474L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-0.5)), // x
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static_cast<RealType>(0.35241638234956672582459892377526L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(1.0)), // x
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static_cast<RealType>(0.75), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-1.0)), // x
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static_cast<RealType>(0.25), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(2.0)), // x
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static_cast<RealType>(0.85241638234956672582459892377526L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-2.0)), // x
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static_cast<RealType>(0.14758361765043327417540107622474L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(10.0)), // x
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static_cast<RealType>(0.9682744825694464304850228813987L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-10.0)), // x
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static_cast<RealType>(0.031725517430553569514977118601302L), // probability.
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tolerance); // %
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//
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// Complements:
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//
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.125))), // x
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static_cast<RealType>(0.46041657583943445798914832865996L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(-0.125))), // x
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static_cast<RealType>(0.53958342416056554201085167134004L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.5))), // x
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static_cast<RealType>(0.35241638234956672582459892377526L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(-0.5))), // x
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static_cast<RealType>(0.64758361765043327417540107622474L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(1.0))), // x
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static_cast<RealType>(0.25), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(-1.0))), // x
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static_cast<RealType>(0.75), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(2.0))), // x
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static_cast<RealType>(0.14758361765043327417540107622474L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(-2.0))), // x
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static_cast<RealType>(0.85241638234956672582459892377526L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(10.0))), // x
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static_cast<RealType>(0.031725517430553569514977118601302L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(-10.0))), // x
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static_cast<RealType>(0.9682744825694464304850228813987L), // probability.
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tolerance); // %
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//
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// Quantiles:
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//
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.53958342416056554201085167134004L)),
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static_cast<RealType>(0.125),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.46041657583943445798914832865996L)),
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static_cast<RealType>(-0.125),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.64758361765043327417540107622474L)),
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static_cast<RealType>(0.5),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.35241638234956672582459892377526)),
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static_cast<RealType>(-0.5),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.75)),
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static_cast<RealType>(1.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.25)),
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static_cast<RealType>(-1.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.85241638234956672582459892377526L)),
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static_cast<RealType>(2.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.14758361765043327417540107622474L)),
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static_cast<RealType>(-2.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.9682744825694464304850228813987L)),
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static_cast<RealType>(10.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.031725517430553569514977118601302L)),
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static_cast<RealType>(-10.0),
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tolerance); // %
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//
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// Quantile from complement:
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//
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.46041657583943445798914832865996L))),
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static_cast<RealType>(0.125),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.53958342416056554201085167134004L))),
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static_cast<RealType>(-0.125),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.35241638234956672582459892377526L))),
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static_cast<RealType>(0.5),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.64758361765043327417540107622474L))),
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static_cast<RealType>(-0.5),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.25))),
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static_cast<RealType>(1.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.75))),
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static_cast<RealType>(-1.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.14758361765043327417540107622474L))),
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static_cast<RealType>(2.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.85241638234956672582459892377526L))),
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static_cast<RealType>(-2.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.031725517430553569514977118601302L))),
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static_cast<RealType>(10.0),
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::quantile(
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complement(cauchy_distribution<RealType>(),
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static_cast<RealType>(0.9682744825694464304850228813987L))),
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static_cast<RealType>(-10.0),
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tolerance); // %
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//
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// PDF
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//
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.125)), // x
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static_cast<RealType>(0.31341281101173235351410956479511L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-0.125)), // x
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static_cast<RealType>(0.31341281101173235351410956479511L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(0.5)), // x
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static_cast<RealType>(0.25464790894703253723021402139602L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-0.5)), // x
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static_cast<RealType>(0.25464790894703253723021402139602L), // probability.
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tolerance); // %
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(1.0)), // x
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static_cast<RealType>(0.15915494309189533576888376337251L), // probability.
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tolerance); // %
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||
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BOOST_CHECK_CLOSE(
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::boost::math::pdf(
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-1.0)), // x
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static_cast<RealType>(0.15915494309189533576888376337251L), // probability.
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||
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tolerance); // %
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||
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BOOST_CHECK_CLOSE(
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||
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::boost::math::pdf(
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||
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cauchy_distribution<RealType>(),
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static_cast<RealType>(2.0)), // x
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static_cast<RealType>(0.063661977236758134307553505349006L), // probability.
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||
|
tolerance); // %
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||
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BOOST_CHECK_CLOSE(
|
||
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::boost::math::pdf(
|
||
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cauchy_distribution<RealType>(),
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static_cast<RealType>(-2.0)), // x
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||
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static_cast<RealType>(0.063661977236758134307553505349006L), // probability.
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||
|
tolerance); // %
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||
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BOOST_CHECK_CLOSE(
|
||
|
::boost::math::pdf(
|
||
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cauchy_distribution<RealType>(),
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||
|
static_cast<RealType>(10.0)), // x
|
||
|
static_cast<RealType>(0.0031515830315226799162155200667825L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::pdf(
|
||
|
cauchy_distribution<RealType>(),
|
||
|
static_cast<RealType>(-10.0)), // x
|
||
|
static_cast<RealType>(0.0031515830315226799162155200667825L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::pdf(
|
||
|
cauchy_distribution<RealType>(2, 5),
|
||
|
static_cast<RealType>(1)), // x
|
||
|
static_cast<RealType>(0.061213439650728975295724524374044L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::pdf(
|
||
|
cauchy_distribution<RealType>(-2, 0.25),
|
||
|
static_cast<RealType>(1)), // x
|
||
|
static_cast<RealType>(0.0087809623774838805941453110826215L), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
//
|
||
|
// The following test values were calculated using MathCad,
|
||
|
// precision seems to be about 10^-13.
|
||
|
//
|
||
|
tolerance = (std::max)(tolerance, static_cast<RealType>(1e-11));
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(1, 1),
|
||
|
static_cast<RealType>(0.125)), // x
|
||
|
static_cast<RealType>(0.271189304634946L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
complement(cauchy_distribution<RealType>(1, 1),
|
||
|
static_cast<RealType>(0.125))), // x
|
||
|
static_cast<RealType>(1 - 0.271189304634946L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(1, 1),
|
||
|
static_cast<RealType>(0.271189304634946L)), // x
|
||
|
static_cast<RealType>(0.125), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
complement(cauchy_distribution<RealType>(1, 1),
|
||
|
static_cast<RealType>(1 - 0.271189304634946L))), // x
|
||
|
static_cast<RealType>(0.125), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(0.125)), // x
|
||
|
static_cast<RealType>(0.539583424160566L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(0.5)), // x
|
||
|
static_cast<RealType>(0.647583617650433L), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(1)), // x
|
||
|
static_cast<RealType>(0.750000000000000), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(2)), // x
|
||
|
static_cast<RealType>(0.852416382349567), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(10)), // x
|
||
|
static_cast<RealType>(0.968274482569447), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(100)), // x
|
||
|
static_cast<RealType>(0.996817007235092), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(-0.125)), // x
|
||
|
static_cast<RealType>(0.460416575839434), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(-0.5)), // x
|
||
|
static_cast<RealType>(0.352416382349567), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(-1)), // x
|
||
|
static_cast<RealType>(0.2500000000000000), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(-2)), // x
|
||
|
static_cast<RealType>(0.147583617650433), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(-10)), // x
|
||
|
static_cast<RealType>(0.031725517430554), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(0, 1),
|
||
|
static_cast<RealType>(-100)), // x
|
||
|
static_cast<RealType>(3.18299276490824E-3), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(1, 5),
|
||
|
static_cast<RealType>(1.25)), // x
|
||
|
static_cast<RealType>(0.515902251256176), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(2, 2),
|
||
|
static_cast<RealType>(1.25)), // x
|
||
|
static_cast<RealType>(0.385799748780092), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(4, 0.125),
|
||
|
static_cast<RealType>(3)), // x
|
||
|
static_cast<RealType>(0.039583424160566), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(-2, static_cast<RealType>(0.0001)),
|
||
|
static_cast<RealType>(-3)), // x
|
||
|
static_cast<RealType>(3.1830988512275777e-5), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(4, 50),
|
||
|
static_cast<RealType>(-3)), // x
|
||
|
static_cast<RealType>(0.455724386698215), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(-4, 50),
|
||
|
static_cast<RealType>(-3)), // x
|
||
|
static_cast<RealType>(0.506365349100973), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
complement(cauchy_distribution<RealType>(1, 5),
|
||
|
static_cast<RealType>(1.25))), // x
|
||
|
static_cast<RealType>(1-0.515902251256176), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
complement(cauchy_distribution<RealType>(2, 2),
|
||
|
static_cast<RealType>(1.25))), // x
|
||
|
static_cast<RealType>(1-0.385799748780092), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
complement(cauchy_distribution<RealType>(4, 0.125),
|
||
|
static_cast<RealType>(3))), // x
|
||
|
static_cast<RealType>(1-0.039583424160566), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
cauchy_distribution<RealType>(-2, static_cast<RealType>(0.001)),
|
||
|
static_cast<RealType>(-3)), // x
|
||
|
static_cast<RealType>(0.000318309780080539), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
complement(cauchy_distribution<RealType>(4, 50),
|
||
|
static_cast<RealType>(-3))), // x
|
||
|
static_cast<RealType>(1-0.455724386698215), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::cdf(
|
||
|
complement(cauchy_distribution<RealType>(-4, 50),
|
||
|
static_cast<RealType>(-3))), // x
|
||
|
static_cast<RealType>(1-0.506365349100973), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(1, 5),
|
||
|
static_cast<RealType>(0.515902251256176)), // x
|
||
|
static_cast<RealType>(1.25), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(2, 2),
|
||
|
static_cast<RealType>(0.385799748780092)), // x
|
||
|
static_cast<RealType>(1.25), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(4, 0.125),
|
||
|
static_cast<RealType>(0.039583424160566)), // x
|
||
|
static_cast<RealType>(3), // probability.
|
||
|
tolerance); // %
|
||
|
/*
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(-2, 0.0001),
|
||
|
static_cast<RealType>(-3)), // x
|
||
|
static_cast<RealType>(0.000015915494296), // probability.
|
||
|
tolerance); // %
|
||
|
*/
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(4, 50),
|
||
|
static_cast<RealType>(0.455724386698215)), // x
|
||
|
static_cast<RealType>(-3), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(-4, 50),
|
||
|
static_cast<RealType>(0.506365349100973)), // x
|
||
|
static_cast<RealType>(-3), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
complement(cauchy_distribution<RealType>(1, 5),
|
||
|
static_cast<RealType>(1-0.515902251256176))), // x
|
||
|
static_cast<RealType>(1.25), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
complement(cauchy_distribution<RealType>(2, 2),
|
||
|
static_cast<RealType>(1-0.385799748780092))), // x
|
||
|
static_cast<RealType>(1.25), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
complement(cauchy_distribution<RealType>(4, 0.125),
|
||
|
static_cast<RealType>(1-0.039583424160566))), // x
|
||
|
static_cast<RealType>(3), // probability.
|
||
|
tolerance); // %
|
||
|
/*
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
cauchy_distribution<RealType>(-2, 0.0001),
|
||
|
static_cast<RealType>(-3)), // x
|
||
|
static_cast<RealType>(0.000015915494296), // probability.
|
||
|
tolerance); // %
|
||
|
*/
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
complement(cauchy_distribution<RealType>(4, 50),
|
||
|
static_cast<RealType>(1-0.455724386698215))), // x
|
||
|
static_cast<RealType>(-3), // probability.
|
||
|
tolerance); // %
|
||
|
BOOST_CHECK_CLOSE(
|
||
|
::boost::math::quantile(
|
||
|
complement(cauchy_distribution<RealType>(-4, 50),
|
||
|
static_cast<RealType>(1-0.506365349100973))), // x
|
||
|
static_cast<RealType>(-3), // probability.
|
||
|
tolerance); // %
|
||
|
|
||
|
cauchy_distribution<RealType> dist; // default (0, 1)
|
||
|
BOOST_CHECK_EQUAL(
|
||
|
mode(dist),
|
||
|
static_cast<RealType>(0));
|
||
|
BOOST_CHECK_EQUAL(
|
||
|
median(dist),
|
||
|
static_cast<RealType>(0));
|
||
|
//
|
||
|
// Things that now don't compile (BOOST-STATIC_ASSERT_FAILURE) by default.
|
||
|
// #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false
|
||
|
// To compile even if Cauchy mean is used.
|
||
|
// See policy reference, mathematically undefined function policies
|
||
|
//
|
||
|
//BOOST_MATH_CHECK_THROW(
|
||
|
// mean(dist),
|
||
|
// std::domain_error);
|
||
|
//BOOST_MATH_CHECK_THROW(
|
||
|
// variance(dist),
|
||
|
// std::domain_error);
|
||
|
//BOOST_MATH_CHECK_THROW(
|
||
|
// standard_deviation(dist),
|
||
|
// std::domain_error);
|
||
|
//BOOST_MATH_CHECK_THROW(
|
||
|
// kurtosis(dist),
|
||
|
// std::domain_error);
|
||
|
//BOOST_MATH_CHECK_THROW(
|
||
|
// kurtosis_excess(dist),
|
||
|
// std::domain_error);
|
||
|
//BOOST_MATH_CHECK_THROW(
|
||
|
// skewness(dist),
|
||
|
// std::domain_error);
|
||
|
|
||
|
BOOST_MATH_CHECK_THROW(
|
||
|
quantile(dist, RealType(0.0)),
|
||
|
std::overflow_error);
|
||
|
BOOST_MATH_CHECK_THROW(
|
||
|
quantile(dist, RealType(1.0)),
|
||
|
std::overflow_error);
|
||
|
BOOST_MATH_CHECK_THROW(
|
||
|
quantile(complement(dist, RealType(0.0))),
|
||
|
std::overflow_error);
|
||
|
BOOST_MATH_CHECK_THROW(
|
||
|
quantile(complement(dist, RealType(1.0))),
|
||
|
std::overflow_error);
|
||
|
|
||
|
check_out_of_range<boost::math::cauchy_distribution<RealType> >(0, 1); // (All) valid constructor parameter values.
|
||
|
|
||
|
|
||
|
|
||
|
} // template <class RealType>void test_spots(RealType)
|
||
|
|
||
|
BOOST_AUTO_TEST_CASE( test_main )
|
||
|
{
|
||
|
BOOST_MATH_CONTROL_FP;
|
||
|
// Check that can generate cauchy distribution using the two convenience methods:
|
||
|
boost::math::cauchy mycd1(1.); // Using typedef
|
||
|
cauchy_distribution<> mycd2(1.); // Using default RealType double.
|
||
|
cauchy_distribution<> C01; // Using default RealType double for Standard Cauchy.
|
||
|
BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values.
|
||
|
BOOST_CHECK_EQUAL(C01.scale(), 1);
|
||
|
|
||
|
// Basic sanity-check spot values.
|
||
|
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
||
|
test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
|
||
|
test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
|
||
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
||
|
test_spots(0.0L); // Test long double.
|
||
|
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
|
||
|
test_spots(boost::math::concepts::real_concept(0.)); // Test 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::endl;
|
||
|
#endif
|
||
|
|
||
|
} // BOOST_AUTO_TEST_CASE( test_main )
|
||
|
|
||
|
/*
|
||
|
Output:
|
||
|
|
||
|
Running 1 test case...
|
||
|
Tolerance for type float is 0.000596046 %
|
||
|
Tolerance for type double is 1.11022e-012 %
|
||
|
Tolerance for type long double is 1.11022e-012 %
|
||
|
Tolerance for type class boost::math::concepts::real_concept is 1.11022e-012 %
|
||
|
*** No errors detected
|
||
|
|
||
|
*/
|