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Diffstat (limited to 'src/third_party/boost-1.60.0/boost/math/distributions/extreme_value.hpp')
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diff --git a/src/third_party/boost-1.60.0/boost/math/distributions/extreme_value.hpp b/src/third_party/boost-1.60.0/boost/math/distributions/extreme_value.hpp new file mode 100644 index 00000000000..cb86de66122 --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/math/distributions/extreme_value.hpp @@ -0,0 +1,300 @@ +// 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) + +#ifndef BOOST_STATS_EXTREME_VALUE_HPP +#define BOOST_STATS_EXTREME_VALUE_HPP + +#include <boost/math/distributions/fwd.hpp> +#include <boost/math/constants/constants.hpp> +#include <boost/math/special_functions/log1p.hpp> +#include <boost/math/special_functions/expm1.hpp> +#include <boost/math/distributions/complement.hpp> +#include <boost/math/distributions/detail/common_error_handling.hpp> +#include <boost/config/no_tr1/cmath.hpp> + +// +// This is the maximum extreme value distribution, see +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm +// and http://mathworld.wolfram.com/ExtremeValueDistribution.html +// Also known as a Fisher-Tippett distribution, a log-Weibull +// distribution or a Gumbel distribution. + +#include <utility> + +#ifdef BOOST_MSVC +# pragma warning(push) +# pragma warning(disable: 4702) // unreachable code (return after domain_error throw). +#endif + +namespace boost{ namespace math{ + +namespace detail{ +// +// Error check: +// +template <class RealType, class Policy> +inline bool verify_scale_b(const char* function, RealType b, RealType* presult, const Policy& pol) +{ + if((b <= 0) || !(boost::math::isfinite)(b)) + { + *presult = policies::raise_domain_error<RealType>( + function, + "The scale parameter \"b\" must be finite and > 0, but was: %1%.", b, pol); + return false; + } + return true; +} + +} // namespace detail + +template <class RealType = double, class Policy = policies::policy<> > +class extreme_value_distribution +{ +public: + typedef RealType value_type; + typedef Policy policy_type; + + extreme_value_distribution(RealType a = 0, RealType b = 1) + : m_a(a), m_b(b) + { + RealType err; + detail::verify_scale_b("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", b, &err, Policy()); + detail::check_finite("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", a, &err, Policy()); + } // extreme_value_distribution + + RealType location()const { return m_a; } + RealType scale()const { return m_b; } + +private: + RealType m_a, m_b; +}; + +typedef extreme_value_distribution<double> extreme_value; + +template <class RealType, class Policy> +inline const std::pair<RealType, RealType> range(const extreme_value_distribution<RealType, Policy>& /*dist*/) +{ // Range of permissible values for random variable x. + using boost::math::tools::max_value; + return std::pair<RealType, RealType>( + std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), + std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); +} + +template <class RealType, class Policy> +inline const std::pair<RealType, RealType> support(const extreme_value_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. + using boost::math::tools::max_value; + return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); +} + +template <class RealType, class Policy> +inline RealType pdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + static const char* function = "boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)"; + + RealType a = dist.location(); + RealType b = dist.scale(); + RealType result = 0; + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if((boost::math::isinf)(x)) + return 0.0f; + if(0 == detail::check_x(function, x, &result, Policy())) + return result; + RealType e = (a - x) / b; + if(e < tools::log_max_value<RealType>()) + result = exp(e) * exp(-exp(e)) / b; + // else.... result *must* be zero since exp(e) is infinite... + return result; +} // pdf + +template <class RealType, class Policy> +inline RealType cdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)"; + + if((boost::math::isinf)(x)) + return x < 0 ? 0.0f : 1.0f; + RealType a = dist.location(); + RealType b = dist.scale(); + RealType result = 0; + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_x("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", x, &result, Policy())) + return result; + + result = exp(-exp((a-x)/b)); + + return result; +} // cdf + +template <class RealType, class Policy> +RealType quantile(const extreme_value_distribution<RealType, Policy>& dist, const RealType& p) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)"; + + RealType a = dist.location(); + RealType b = dist.scale(); + RealType result = 0; + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_probability(function, p, &result, Policy())) + return result; + + if(p == 0) + return -policies::raise_overflow_error<RealType>(function, 0, Policy()); + if(p == 1) + return policies::raise_overflow_error<RealType>(function, 0, Policy()); + + result = a - log(-log(p)) * b; + + return result; +} // quantile + +template <class RealType, class Policy> +inline RealType cdf(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)"; + + if((boost::math::isinf)(c.param)) + return c.param < 0 ? 1.0f : 0.0f; + RealType a = c.dist.location(); + RealType b = c.dist.scale(); + RealType result = 0; + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_x(function, c.param, &result, Policy())) + return result; + + result = -boost::math::expm1(-exp((a-c.param)/b), Policy()); + + return result; +} + +template <class RealType, class Policy> +RealType quantile(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)"; + + RealType a = c.dist.location(); + RealType b = c.dist.scale(); + RealType q = c.param; + RealType result = 0; + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_probability(function, q, &result, Policy())) + return result; + + if(q == 0) + return policies::raise_overflow_error<RealType>(function, 0, Policy()); + if(q == 1) + return -policies::raise_overflow_error<RealType>(function, 0, Policy()); + + result = a - log(-boost::math::log1p(-q, Policy())) * b; + + return result; +} + +template <class RealType, class Policy> +inline RealType mean(const extreme_value_distribution<RealType, Policy>& dist) +{ + RealType a = dist.location(); + RealType b = dist.scale(); + RealType result = 0; + if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy())) + return result; + if(0 == detail::check_scale("boost::math::mean(const extreme_value_distribution<%1%>&)", a, &result, Policy())) + return result; + return a + constants::euler<RealType>() * b; +} + +template <class RealType, class Policy> +inline RealType standard_deviation(const extreme_value_distribution<RealType, Policy>& dist) +{ + BOOST_MATH_STD_USING // for ADL of std functions. + + RealType b = dist.scale(); + RealType result = 0; + if(0 == detail::verify_scale_b("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", b, &result, Policy())) + return result; + if(0 == detail::check_scale("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", dist.location(), &result, Policy())) + return result; + return constants::pi<RealType>() * b / sqrt(static_cast<RealType>(6)); +} + +template <class RealType, class Policy> +inline RealType mode(const extreme_value_distribution<RealType, Policy>& dist) +{ + return dist.location(); +} + +template <class RealType, class Policy> +inline RealType median(const extreme_value_distribution<RealType, Policy>& dist) +{ + using constants::ln_ln_two; + return dist.location() - dist.scale() * ln_ln_two<RealType>(); +} + +template <class RealType, class Policy> +inline RealType skewness(const extreme_value_distribution<RealType, Policy>& /*dist*/) +{ + // + // This is 12 * sqrt(6) * zeta(3) / pi^3: + // See http://mathworld.wolfram.com/ExtremeValueDistribution.html + // + return static_cast<RealType>(1.1395470994046486574927930193898461120875997958366L); +} + +template <class RealType, class Policy> +inline RealType kurtosis(const extreme_value_distribution<RealType, Policy>& /*dist*/) +{ + // See http://mathworld.wolfram.com/ExtremeValueDistribution.html + return RealType(27) / 5; +} + +template <class RealType, class Policy> +inline RealType kurtosis_excess(const extreme_value_distribution<RealType, Policy>& /*dist*/) +{ + // See http://mathworld.wolfram.com/ExtremeValueDistribution.html + return RealType(12) / 5; +} + + +} // namespace math +} // namespace boost + +#ifdef BOOST_MSVC +# pragma warning(pop) +#endif + +// 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_STATS_EXTREME_VALUE_HPP |