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-// Copyright John Maddock 2006, 2007.
-// Copyright Paul A. Bristow 2008, 2010.
-
-// 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)
-
-#ifndef BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
-#define BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
-
-#include <boost/math/distributions/fwd.hpp>
-#include <boost/math/special_functions/gamma.hpp> // for incomplete beta.
-#include <boost/math/distributions/complement.hpp> // complements
-#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
-#include <boost/math/special_functions/fpclassify.hpp>
-
-#include <utility>
-
-namespace boost{ namespace math{
-
-template <class RealType = double, class Policy = policies::policy<> >
-class chi_squared_distribution
-{
-public:
- typedef RealType value_type;
- typedef Policy policy_type;
-
- chi_squared_distribution(RealType i) : m_df(i)
- {
- RealType result;
- detail::check_df(
- "boost::math::chi_squared_distribution<%1%>::chi_squared_distribution", m_df, &result, Policy());
- } // chi_squared_distribution
-
- RealType degrees_of_freedom()const
- {
- return m_df;
- }
-
- // Parameter estimation:
- static RealType find_degrees_of_freedom(
- RealType difference_from_variance,
- RealType alpha,
- RealType beta,
- RealType variance,
- RealType hint = 100);
-
-private:
- //
- // Data member:
- //
- RealType m_df; // degrees of freedom is a positive real number.
-}; // class chi_squared_distribution
-
-typedef chi_squared_distribution<double> chi_squared;
-
-#ifdef BOOST_MSVC
-#pragma warning(push)
-#pragma warning(disable:4127)
-#endif
-
-template <class RealType, class Policy>
-inline const std::pair<RealType, RealType> range(const chi_squared_distribution<RealType, Policy>& /*dist*/)
-{ // Range of permissible values for random variable x.
- if (std::numeric_limits<RealType>::has_infinity)
- {
- return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity.
- }
- else
- {
- using boost::math::tools::max_value;
- return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max.
- }
-}
-
-#ifdef BOOST_MSVC
-#pragma warning(pop)
-#endif
-
-template <class RealType, class Policy>
-inline const std::pair<RealType, RealType> support(const chi_squared_distribution<RealType, Policy>& /*dist*/)
-{ // Range of supported values for random variable x.
- // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
- return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity.
-}
-
-template <class RealType, class Policy>
-RealType pdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)
-{
- BOOST_MATH_STD_USING // for ADL of std functions
- RealType degrees_of_freedom = dist.degrees_of_freedom();
- // Error check:
- RealType error_result;
-
- static const char* function = "boost::math::pdf(const chi_squared_distribution<%1%>&, %1%)";
-
- if(false == detail::check_df(
- function, degrees_of_freedom, &error_result, Policy()))
- return error_result;
-
- if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
- {
- return policies::raise_domain_error<RealType>(
- function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
- }
-
- if(chi_square == 0)
- {
- // Handle special cases:
- if(degrees_of_freedom < 2)
- {
- return policies::raise_overflow_error<RealType>(
- function, 0, Policy());
- }
- else if(degrees_of_freedom == 2)
- {
- return 0.5f;
- }
- else
- {
- return 0;
- }
- }
-
- return gamma_p_derivative(degrees_of_freedom / 2, chi_square / 2, Policy()) / 2;
-} // pdf
-
-template <class RealType, class Policy>
-inline RealType cdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)
-{
- RealType degrees_of_freedom = dist.degrees_of_freedom();
- // Error check:
- RealType error_result;
- static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)";
-
- if(false == detail::check_df(
- function, degrees_of_freedom, &error_result, Policy()))
- return error_result;
-
- if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
- {
- return policies::raise_domain_error<RealType>(
- function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
- }
-
- return boost::math::gamma_p(degrees_of_freedom / 2, chi_square / 2, Policy());
-} // cdf
-
-template <class RealType, class Policy>
-inline RealType quantile(const chi_squared_distribution<RealType, Policy>& dist, const RealType& p)
-{
- RealType degrees_of_freedom = dist.degrees_of_freedom();
- static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)";
- // Error check:
- RealType error_result;
- if(false ==
- (
- detail::check_df(function, degrees_of_freedom, &error_result, Policy())
- && detail::check_probability(function, p, &error_result, Policy()))
- )
- return error_result;
-
- return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy());
-} // quantile
-
-template <class RealType, class Policy>
-inline RealType cdf(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c)
-{
- RealType const& degrees_of_freedom = c.dist.degrees_of_freedom();
- RealType const& chi_square = c.param;
- static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)";
- // Error check:
- RealType error_result;
- if(false == detail::check_df(
- function, degrees_of_freedom, &error_result, Policy()))
- return error_result;
-
- if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
- {
- return policies::raise_domain_error<RealType>(
- function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
- }
-
- return boost::math::gamma_q(degrees_of_freedom / 2, chi_square / 2, Policy());
-}
-
-template <class RealType, class Policy>
-inline RealType quantile(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c)
-{
- RealType const& degrees_of_freedom = c.dist.degrees_of_freedom();
- RealType const& q = c.param;
- static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)";
- // Error check:
- RealType error_result;
- if(false == (
- detail::check_df(function, degrees_of_freedom, &error_result, Policy())
- && detail::check_probability(function, q, &error_result, Policy()))
- )
- return error_result;
-
- return 2 * boost::math::gamma_q_inv(degrees_of_freedom / 2, q, Policy());
-}
-
-template <class RealType, class Policy>
-inline RealType mean(const chi_squared_distribution<RealType, Policy>& dist)
-{ // Mean of Chi-Squared distribution = v.
- return dist.degrees_of_freedom();
-} // mean
-
-template <class RealType, class Policy>
-inline RealType variance(const chi_squared_distribution<RealType, Policy>& dist)
-{ // Variance of Chi-Squared distribution = 2v.
- return 2 * dist.degrees_of_freedom();
-} // variance
-
-template <class RealType, class Policy>
-inline RealType mode(const chi_squared_distribution<RealType, Policy>& dist)
-{
- RealType df = dist.degrees_of_freedom();
- static const char* function = "boost::math::mode(const chi_squared_distribution<%1%>&)";
- // Most sources only define mode for df >= 2,
- // but for 0 <= df <= 2, the pdf maximum actually occurs at random variate = 0;
- // So one could extend the definition of mode thus:
- //if(df < 0)
- //{
- // return policies::raise_domain_error<RealType>(
- // function,
- // "Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
- // df, Policy());
- //}
- //return (df <= 2) ? 0 : df - 2;
-
- if(df < 2)
- return policies::raise_domain_error<RealType>(
- function,
- "Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
- df, Policy());
- return df - 2;
-}
-
-//template <class RealType, class Policy>
-//inline RealType median(const chi_squared_distribution<RealType, Policy>& dist)
-//{ // Median is given by Quantile[dist, 1/2]
-// RealType df = dist.degrees_of_freedom();
-// if(df <= 1)
-// return tools::domain_error<RealType>(
-// BOOST_CURRENT_FUNCTION,
-// "The Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
-// df);
-// return df - RealType(2)/3;
-//}
-// Now implemented via quantile(half) in derived accessors.
-
-template <class RealType, class Policy>
-inline RealType skewness(const chi_squared_distribution<RealType, Policy>& dist)
-{
- BOOST_MATH_STD_USING // For ADL
- RealType df = dist.degrees_of_freedom();
- return sqrt (8 / df); // == 2 * sqrt(2 / df);
-}
-
-template <class RealType, class Policy>
-inline RealType kurtosis(const chi_squared_distribution<RealType, Policy>& dist)
-{
- RealType df = dist.degrees_of_freedom();
- return 3 + 12 / df;
-}
-
-template <class RealType, class Policy>
-inline RealType kurtosis_excess(const chi_squared_distribution<RealType, Policy>& dist)
-{
- RealType df = dist.degrees_of_freedom();
- return 12 / df;
-}
-
-//
-// Parameter estimation comes last:
-//
-namespace detail
-{
-
-template <class RealType, class Policy>
-struct df_estimator
-{
- df_estimator(RealType a, RealType b, RealType variance, RealType delta)
- : alpha(a), beta(b), ratio(delta/variance)
- { // Constructor
- }
-
- RealType operator()(const RealType& df)
- {
- if(df <= tools::min_value<RealType>())
- return 1;
- chi_squared_distribution<RealType, Policy> cs(df);
-
- RealType result;
- if(ratio > 0)
- {
- RealType r = 1 + ratio;
- result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta;
- }
- else
- { // ratio <= 0
- RealType r = 1 + ratio;
- result = cdf(complement(cs, quantile(cs, alpha) / r)) - beta;
- }
- return result;
- }
-private:
- RealType alpha;
- RealType beta;
- RealType ratio; // Difference from variance / variance, so fractional.
-};
-
-} // namespace detail
-
-template <class RealType, class Policy>
-RealType chi_squared_distribution<RealType, Policy>::find_degrees_of_freedom(
- RealType difference_from_variance,
- RealType alpha,
- RealType beta,
- RealType variance,
- RealType hint)
-{
- static const char* function = "boost::math::chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)";
- // Check for domain errors:
- RealType error_result;
- if(false ==
- detail::check_probability(function, alpha, &error_result, Policy())
- && detail::check_probability(function, beta, &error_result, Policy()))
- { // Either probability is outside 0 to 1.
- return error_result;
- }
-
- if(hint <= 0)
- { // No hint given, so guess df = 1.
- hint = 1;
- }
-
- detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance);
- tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
- boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
- std::pair<RealType, RealType> r =
- tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());
- RealType result = r.first + (r.second - r.first) / 2;
- if(max_iter >= policies::get_max_root_iterations<Policy>())
- {
- policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
- " either there is no answer to how many degrees of freedom are required"
- " or the answer is infinite. Current best guess is %1%", result, Policy());
- }
- return result;
-}
-
-} // namespace math
-} // namespace boost
-
-// This include must be at the end, *after* the accessors
-// for this distribution have been defined, in order to
-// keep compilers that support two-phase lookup happy.
-#include <boost/math/distributions/detail/derived_accessors.hpp>
-
-#endif // BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP