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Diffstat (limited to 'src/third_party/boost-1.60.0/boost/math/distributions/normal.hpp')
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diff --git a/src/third_party/boost-1.60.0/boost/math/distributions/normal.hpp b/src/third_party/boost-1.60.0/boost/math/distributions/normal.hpp new file mode 100644 index 00000000000..32cf66e3ef0 --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/math/distributions/normal.hpp @@ -0,0 +1,329 @@ +// Copyright John Maddock 2006, 2007. +// Copyright Paul A. Bristow 2006, 2007. + +// 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_NORMAL_HPP +#define BOOST_STATS_NORMAL_HPP + +// http://en.wikipedia.org/wiki/Normal_distribution +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm +// Also: +// Weisstein, Eric W. "Normal Distribution." +// From MathWorld--A Wolfram Web Resource. +// http://mathworld.wolfram.com/NormalDistribution.html + +#include <boost/math/distributions/fwd.hpp> +#include <boost/math/special_functions/erf.hpp> // for erf/erfc. +#include <boost/math/distributions/complement.hpp> +#include <boost/math/distributions/detail/common_error_handling.hpp> + +#include <utility> + +namespace boost{ namespace math{ + +template <class RealType = double, class Policy = policies::policy<> > +class normal_distribution +{ +public: + typedef RealType value_type; + typedef Policy policy_type; + + normal_distribution(RealType l_mean = 0, RealType sd = 1) + : m_mean(l_mean), m_sd(sd) + { // Default is a 'standard' normal distribution N01. + static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution"; + + RealType result; + detail::check_scale(function, sd, &result, Policy()); + detail::check_location(function, l_mean, &result, Policy()); + } + + RealType mean()const + { // alias for location. + return m_mean; + } + + RealType standard_deviation()const + { // alias for scale. + return m_sd; + } + + // Synonyms, provided to allow generic use of find_location and find_scale. + RealType location()const + { // location. + return m_mean; + } + RealType scale()const + { // scale. + return m_sd; + } + +private: + // + // Data members: + // + RealType m_mean; // distribution mean or location. + RealType m_sd; // distribution standard deviation or scale. +}; // class normal_distribution + +typedef normal_distribution<double> normal; + +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) +#endif + +template <class RealType, class Policy> +inline const std::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/) +{ // Range of permissible values for random variable x. + if (std::numeric_limits<RealType>::has_infinity) + { + return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. + } + else + { // Can only use max_value. + using boost::math::tools::max_value; + return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. + } +} + +template <class RealType, class Policy> +inline const std::pair<RealType, RealType> support(const normal_distribution<RealType, Policy>& /*dist*/) +{ // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero. + if (std::numeric_limits<RealType>::has_infinity) + { + return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. + } + else + { // Can only use max_value. + using boost::math::tools::max_value; + return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. + } +} + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +template <class RealType, class Policy> +inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = dist.standard_deviation(); + RealType mean = dist.mean(); + + static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)"; + + RealType result = 0; + if(false == detail::check_scale(function, sd, &result, Policy())) + { + return result; + } + if(false == detail::check_location(function, mean, &result, Policy())) + { + return result; + } + if((boost::math::isinf)(x)) + { + return 0; // pdf + and - infinity is zero. + } + // Below produces MSVC 4127 warnings, so the above used instead. + //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity()) + //{ // pdf + and - infinity is zero. + // return 0; + //} + if(false == detail::check_x(function, x, &result, Policy())) + { + return result; + } + + RealType exponent = x - mean; + exponent *= -exponent; + exponent /= 2 * sd * sd; + + result = exp(exponent); + result /= sd * sqrt(2 * constants::pi<RealType>()); + + return result; +} // pdf + +template <class RealType, class Policy> +inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = dist.standard_deviation(); + RealType mean = dist.mean(); + static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)"; + RealType result = 0; + if(false == detail::check_scale(function, sd, &result, Policy())) + { + return result; + } + if(false == detail::check_location(function, mean, &result, Policy())) + { + return result; + } + if((boost::math::isinf)(x)) + { + if(x < 0) return 0; // -infinity + return 1; // + infinity + } + // These produce MSVC 4127 warnings, so the above used instead. + //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) + //{ // cdf +infinity is unity. + // return 1; + //} + //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) + //{ // cdf -infinity is zero. + // return 0; + //} + if(false == detail::check_x(function, x, &result, Policy())) + { + return result; + } + RealType diff = (x - mean) / (sd * constants::root_two<RealType>()); + result = boost::math::erfc(-diff, Policy()) / 2; + return result; +} // cdf + +template <class RealType, class Policy> +inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = dist.standard_deviation(); + RealType mean = dist.mean(); + static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)"; + + RealType result = 0; + if(false == detail::check_scale(function, sd, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + if(false == detail::check_probability(function, p, &result, Policy())) + return result; + + result= boost::math::erfc_inv(2 * p, Policy()); + result = -result; + result *= sd * constants::root_two<RealType>(); + result += mean; + return result; +} // quantile + +template <class RealType, class Policy> +inline RealType cdf(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = c.dist.standard_deviation(); + RealType mean = c.dist.mean(); + RealType x = c.param; + static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)"; + + RealType result = 0; + if(false == detail::check_scale(function, sd, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + if((boost::math::isinf)(x)) + { + if(x < 0) return 1; // cdf complement -infinity is unity. + return 0; // cdf complement +infinity is zero + } + // These produce MSVC 4127 warnings, so the above used instead. + //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) + //{ // cdf complement +infinity is zero. + // return 0; + //} + //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) + //{ // cdf complement -infinity is unity. + // return 1; + //} + if(false == detail::check_x(function, x, &result, Policy())) + return result; + + RealType diff = (x - mean) / (sd * constants::root_two<RealType>()); + result = boost::math::erfc(diff, Policy()) / 2; + return result; +} // cdf complement + +template <class RealType, class Policy> +inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = c.dist.standard_deviation(); + RealType mean = c.dist.mean(); + static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)"; + RealType result = 0; + if(false == detail::check_scale(function, sd, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + RealType q = c.param; + if(false == detail::check_probability(function, q, &result, Policy())) + return result; + result = boost::math::erfc_inv(2 * q, Policy()); + result *= sd * constants::root_two<RealType>(); + result += mean; + return result; +} // quantile + +template <class RealType, class Policy> +inline RealType mean(const normal_distribution<RealType, Policy>& dist) +{ + return dist.mean(); +} + +template <class RealType, class Policy> +inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist) +{ + return dist.standard_deviation(); +} + +template <class RealType, class Policy> +inline RealType mode(const normal_distribution<RealType, Policy>& dist) +{ + return dist.mean(); +} + +template <class RealType, class Policy> +inline RealType median(const normal_distribution<RealType, Policy>& dist) +{ + return dist.mean(); +} + +template <class RealType, class Policy> +inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/) +{ + return 0; +} + +template <class RealType, class Policy> +inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/) +{ + return 3; +} + +template <class RealType, class Policy> +inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/) +{ + return 0; +} + +} // 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_STATS_NORMAL_HPP + + |