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diff --git a/boost/math/distributions/hyperexponential.hpp b/boost/math/distributions/hyperexponential.hpp new file mode 100644 index 0000000000..4ed281c662 --- /dev/null +++ b/boost/math/distributions/hyperexponential.hpp @@ -0,0 +1,634 @@ +// Copyright 2014 Marco Guazzone (marco.guazzone@gmail.com) +// +// 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) +// +// This module implements the Hyper-Exponential distribution. +// +// References: +// - "Queueing Theory in Manufacturing Systems Analysis and Design" by H.T. Papadopolous, C. Heavey and J. Browne (Chapman & Hall/CRC, 1993) +// - http://reference.wolfram.com/language/ref/HyperexponentialDistribution.html +// - http://en.wikipedia.org/wiki/Hyperexponential_distribution +// + +#ifndef BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL_HPP +#define BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL_HPP + + +#include <boost/config.hpp> +#include <boost/math/distributions/complement.hpp> +#include <boost/math/distributions/detail/common_error_handling.hpp> +#include <boost/math/distributions/exponential.hpp> +#include <boost/math/policies/policy.hpp> +#include <boost/math/special_functions/fpclassify.hpp> +#include <boost/math/tools/precision.hpp> +#include <boost/math/tools/roots.hpp> +#include <boost/range/begin.hpp> +#include <boost/range/end.hpp> +#include <boost/range/size.hpp> +#include <boost/type_traits/has_pre_increment.hpp> +#include <cstddef> +#include <iterator> +#include <limits> +#include <numeric> +#include <utility> +#include <vector> + +#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) +# include <initializer_list> +#endif + +#ifdef _MSC_VER +# pragma warning (push) +# pragma warning(disable:4127) // conditional expression is constant +# pragma warning(disable:4389) // '==' : signed/unsigned mismatch in test_tools +#endif // _MSC_VER + +namespace boost { namespace math { + +namespace detail { + +template <typename Dist> +typename Dist::value_type generic_quantile(const Dist& dist, const typename Dist::value_type& p, const typename Dist::value_type& guess, bool comp, const char* function); + +} // Namespace detail + + +template <typename RealT, typename PolicyT> +class hyperexponential_distribution; + + +namespace /*<unnamed>*/ { namespace hyperexp_detail { + +template <typename T> +void normalize(std::vector<T>& v) +{ + if(!v.size()) + return; // Our error handlers will get this later + const T sum = std::accumulate(v.begin(), v.end(), static_cast<T>(0)); + T final_sum = 0; + const typename std::vector<T>::iterator end = --v.end(); + for (typename std::vector<T>::iterator it = v.begin(); + it != end; + ++it) + { + *it /= sum; + final_sum += *it; + } + *end = 1 - final_sum; // avoids round off errors, ensures the probs really do sum to 1. +} + +template <typename RealT, typename PolicyT> +bool check_probabilities(char const* function, std::vector<RealT> const& probabilities, RealT* presult, PolicyT const& pol) +{ + BOOST_MATH_STD_USING + const std::size_t n = probabilities.size(); + RealT sum = 0; + for (std::size_t i = 0; i < n; ++i) + { + if (probabilities[i] < 0 + || probabilities[i] > 1 + || !(boost::math::isfinite)(probabilities[i])) + { + *presult = policies::raise_domain_error<RealT>(function, + "The elements of parameter \"probabilities\" must be >= 0 and <= 1, but at least one of them was: %1%.", + probabilities[i], + pol); + return false; + } + sum += probabilities[i]; + } + + // + // We try to keep phase probabilities correctly normalized in the distribution constructors, + // however in practice we have to allow for a very slight divergence from a sum of exactly 1: + // + if (fabs(sum - 1) > tools::epsilon<RealT>() * 2) + { + *presult = policies::raise_domain_error<RealT>(function, + "The elements of parameter \"probabilities\" must sum to 1, but their sum is: %1%.", + sum, + pol); + return false; + } + + return true; +} + +template <typename RealT, typename PolicyT> +bool check_rates(char const* function, std::vector<RealT> const& rates, RealT* presult, PolicyT const& pol) +{ + const std::size_t n = rates.size(); + for (std::size_t i = 0; i < n; ++i) + { + if (rates[i] <= 0 + || !(boost::math::isfinite)(rates[i])) + { + *presult = policies::raise_domain_error<RealT>(function, + "The elements of parameter \"rates\" must be > 0, but at least one of them is: %1%.", + rates[i], + pol); + return false; + } + } + return true; +} + +template <typename RealT, typename PolicyT> +bool check_dist(char const* function, std::vector<RealT> const& probabilities, std::vector<RealT> const& rates, RealT* presult, PolicyT const& pol) +{ + BOOST_MATH_STD_USING + if (probabilities.size() != rates.size()) + { + *presult = policies::raise_domain_error<RealT>(function, + "The parameters \"probabilities\" and \"rates\" must have the same length, but their size differ by: %1%.", + fabs(static_cast<RealT>(probabilities.size())-static_cast<RealT>(rates.size())), + pol); + return false; + } + + return check_probabilities(function, probabilities, presult, pol) + && check_rates(function, rates, presult, pol); +} + +template <typename RealT, typename PolicyT> +bool check_x(char const* function, RealT x, RealT* presult, PolicyT const& pol) +{ + if (x < 0 || (boost::math::isnan)(x)) + { + *presult = policies::raise_domain_error<RealT>(function, "The random variable must be >= 0, but is: %1%.", x, pol); + return false; + } + return true; +} + +template <typename RealT, typename PolicyT> +bool check_probability(char const* function, RealT p, RealT* presult, PolicyT const& pol) +{ + if (p < 0 || p > 1 || (boost::math::isnan)(p)) + { + *presult = policies::raise_domain_error<RealT>(function, "The probability be >= 0 and <= 1, but is: %1%.", p, pol); + return false; + } + return true; +} + +template <typename RealT, typename PolicyT> +RealT quantile_impl(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& p, bool comp) +{ + // Don't have a closed form so try to numerically solve the inverse CDF... + + typedef typename policies::evaluation<RealT, PolicyT>::type value_type; + typedef typename policies::normalise<PolicyT, + policies::promote_float<false>, + policies::promote_double<false>, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + + static const char* function = comp ? "boost::math::quantile(const boost::math::complemented2_type<boost::math::hyperexponential_distribution<%1%>, %1%>&)" + : "boost::math::quantile(const boost::math::hyperexponential_distribution<%1%>&, %1%)"; + + RealT result = 0; + + if (!check_probability(function, p, &result, PolicyT())) + { + return result; + } + + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + // A possible (but inaccurate) approximation is given below, where the + // quantile is given by the weighted sum of exponential quantiles: + RealT guess = 0; + if (comp) + { + for (std::size_t i = 0; i < n; ++i) + { + const exponential_distribution<RealT,PolicyT> exp(rates[i]); + + guess += probs[i]*quantile(complement(exp, p)); + } + } + else + { + for (std::size_t i = 0; i < n; ++i) + { + const exponential_distribution<RealT,PolicyT> exp(rates[i]); + + guess += probs[i]*quantile(exp, p); + } + } + + // Fast return in case the Hyper-Exponential is essentially an Exponential + if (n == 1) + { + return guess; + } + + value_type q; + q = detail::generic_quantile(hyperexponential_distribution<RealT,forwarding_policy>(probs, rates), + p, + guess, + comp, + function); + + result = policies::checked_narrowing_cast<RealT,forwarding_policy>(q, function); + + return result; +} + +}} // Namespace <unnamed>::hyperexp_detail + + +template <typename RealT = double, typename PolicyT = policies::policy<> > +class hyperexponential_distribution +{ + public: typedef RealT value_type; + public: typedef PolicyT policy_type; + + + public: hyperexponential_distribution() + : probs_(1, 1), + rates_(1, 1) + { + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } + + // Four arg constructor: no ambiguity here, the arguments must be two pairs of iterators: + public: template <typename ProbIterT, typename RateIterT> + hyperexponential_distribution(ProbIterT prob_first, ProbIterT prob_last, + RateIterT rate_first, RateIterT rate_last) + : probs_(prob_first, prob_last), + rates_(rate_first, rate_last) + { + hyperexp_detail::normalize(probs_); + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } + + // Two arg constructor from 2 ranges, we SFINAE this out of existance if + // either argument type is incrementable as in that case the type is + // probably an iterator: + public: template <typename ProbRangeT, typename RateRangeT> + hyperexponential_distribution(ProbRangeT const& prob_range, + RateRangeT const& rate_range, + typename boost::disable_if_c<boost::has_pre_increment<ProbRangeT>::value || boost::has_pre_increment<RateRangeT>::value>::type* = 0) + : probs_(boost::begin(prob_range), boost::end(prob_range)), + rates_(boost::begin(rate_range), boost::end(rate_range)) + { + hyperexp_detail::normalize(probs_); + + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } + + // Two arg constructor for a pair of iterators: we SFINAE this out of + // existance if neither argument types are incrementable. + // Note that we allow different argument types here to allow for + // construction from an array plus a pointer into that array. + public: template <typename RateIterT, typename RateIterT2> + hyperexponential_distribution(RateIterT const& rate_first, + RateIterT2 const& rate_last, + typename boost::enable_if_c<boost::has_pre_increment<RateIterT>::value || boost::has_pre_increment<RateIterT2>::value>::type* = 0) + : probs_(std::distance(rate_first, rate_last), 1), // will be normalized below + rates_(rate_first, rate_last) + { + hyperexp_detail::normalize(probs_); + + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } + +#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) + // Initializer list constructor: allows for construction from array literals: +public: hyperexponential_distribution(std::initializer_list<RealT> l1, std::initializer_list<RealT> l2) + : probs_(l1.begin(), l1.end()), + rates_(l2.begin(), l2.end()) + { + hyperexp_detail::normalize(probs_); + + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } + +public: hyperexponential_distribution(std::initializer_list<RealT> l1) + : probs_(l1.size(), 1), + rates_(l1.begin(), l1.end()) + { + hyperexp_detail::normalize(probs_); + + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } +#endif // !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) + + // Single argument constructor: argument must be a range. + public: template <typename RateRangeT> + hyperexponential_distribution(RateRangeT const& rate_range) + : probs_(boost::size(rate_range), 1), // will be normalized below + rates_(boost::begin(rate_range), boost::end(rate_range)) + { + hyperexp_detail::normalize(probs_); + + RealT err; + hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", + probs_, + rates_, + &err, + PolicyT()); + } + + public: std::vector<RealT> probabilities() const + { + return probs_; + } + + public: std::vector<RealT> rates() const + { + return rates_; + } + + public: std::size_t num_phases() const + { + return rates_.size(); + } + + + private: std::vector<RealT> probs_; + private: std::vector<RealT> rates_; +}; // class hyperexponential_distribution + + +// Convenient type synonym for double. +typedef hyperexponential_distribution<double> hyperexponential; + + +// Range of permissible values for random variable x +template <typename RealT, typename PolicyT> +std::pair<RealT,RealT> range(hyperexponential_distribution<RealT,PolicyT> const&) +{ + if (std::numeric_limits<RealT>::has_infinity) + { + return std::make_pair(static_cast<RealT>(0), std::numeric_limits<RealT>::infinity()); // 0 to +inf. + } + + return std::make_pair(static_cast<RealT>(0), tools::max_value<RealT>()); // 0 to +<max value> +} + +// 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. +template <typename RealT, typename PolicyT> +std::pair<RealT,RealT> support(hyperexponential_distribution<RealT,PolicyT> const&) +{ + return std::make_pair(tools::min_value<RealT>(), tools::max_value<RealT>()); // <min value> to +<max value>. +} + +template <typename RealT, typename PolicyT> +RealT pdf(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& x) +{ + BOOST_MATH_STD_USING + RealT result = 0; + + if (!hyperexp_detail::check_x("boost::math::pdf(const boost::math::hyperexponential_distribution<%1%>&, %1%)", x, &result, PolicyT())) + { + return result; + } + + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + for (std::size_t i = 0; i < n; ++i) + { + const exponential_distribution<RealT,PolicyT> exp(rates[i]); + + result += probs[i]*pdf(exp, x); + //result += probs[i]*rates[i]*exp(-rates[i]*x); + } + + return result; +} + +template <typename RealT, typename PolicyT> +RealT cdf(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& x) +{ + RealT result = 0; + + if (!hyperexp_detail::check_x("boost::math::cdf(const boost::math::hyperexponential_distribution<%1%>&, %1%)", x, &result, PolicyT())) + { + return result; + } + + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + for (std::size_t i = 0; i < n; ++i) + { + const exponential_distribution<RealT,PolicyT> exp(rates[i]); + + result += probs[i]*cdf(exp, x); + } + + return result; +} + +template <typename RealT, typename PolicyT> +RealT quantile(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& p) +{ + return hyperexp_detail::quantile_impl(dist, p , false); +} + +template <typename RealT, typename PolicyT> +RealT cdf(complemented2_type<hyperexponential_distribution<RealT,PolicyT>, RealT> const& c) +{ + RealT const& x = c.param; + hyperexponential_distribution<RealT,PolicyT> const& dist = c.dist; + + RealT result = 0; + + if (!hyperexp_detail::check_x("boost::math::cdf(boost::math::complemented2_type<const boost::math::hyperexponential_distribution<%1%>&, %1%>)", x, &result, PolicyT())) + { + return result; + } + + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + for (std::size_t i = 0; i < n; ++i) + { + const exponential_distribution<RealT,PolicyT> exp(rates[i]); + + result += probs[i]*cdf(complement(exp, x)); + } + + return result; +} + + +template <typename RealT, typename PolicyT> +RealT quantile(complemented2_type<hyperexponential_distribution<RealT, PolicyT>, RealT> const& c) +{ + RealT const& p = c.param; + hyperexponential_distribution<RealT,PolicyT> const& dist = c.dist; + + return hyperexp_detail::quantile_impl(dist, p , true); +} + +template <typename RealT, typename PolicyT> +RealT mean(hyperexponential_distribution<RealT, PolicyT> const& dist) +{ + RealT result = 0; + + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + for (std::size_t i = 0; i < n; ++i) + { + const exponential_distribution<RealT,PolicyT> exp(rates[i]); + + result += probs[i]*mean(exp); + } + + return result; +} + +template <typename RealT, typename PolicyT> +RealT variance(hyperexponential_distribution<RealT, PolicyT> const& dist) +{ + RealT result = 0; + + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + for (std::size_t i = 0; i < n; ++i) + { + result += probs[i]/(rates[i]*rates[i]); + } + + const RealT mean = boost::math::mean(dist); + + result = 2*result-mean*mean; + + return result; +} + +template <typename RealT, typename PolicyT> +RealT skewness(hyperexponential_distribution<RealT,PolicyT> const& dist) +{ + BOOST_MATH_STD_USING + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + RealT s1 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i} + RealT s2 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^2} + RealT s3 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^3} + for (std::size_t i = 0; i < n; ++i) + { + const RealT p = probs[i]; + const RealT r = rates[i]; + const RealT r2 = r*r; + const RealT r3 = r2*r; + + s1 += p/r; + s2 += p/r2; + s3 += p/r3; + } + + const RealT s1s1 = s1*s1; + + const RealT num = (6*s3 - (3*(2*s2 - s1s1) + s1s1)*s1); + const RealT den = (2*s2 - s1s1); + + return num / pow(den, static_cast<RealT>(1.5)); +} + +template <typename RealT, typename PolicyT> +RealT kurtosis(hyperexponential_distribution<RealT,PolicyT> const& dist) +{ + const std::size_t n = dist.num_phases(); + const std::vector<RealT> probs = dist.probabilities(); + const std::vector<RealT> rates = dist.rates(); + + RealT s1 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i} + RealT s2 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^2} + RealT s3 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^3} + RealT s4 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^4} + for (std::size_t i = 0; i < n; ++i) + { + const RealT p = probs[i]; + const RealT r = rates[i]; + const RealT r2 = r*r; + const RealT r3 = r2*r; + const RealT r4 = r3*r; + + s1 += p/r; + s2 += p/r2; + s3 += p/r3; + s4 += p/r4; + } + + const RealT s1s1 = s1*s1; + + const RealT num = (24*s4 - 24*s3*s1 + 3*(2*(2*s2 - s1s1) + s1s1)*s1s1); + const RealT den = (2*s2 - s1s1); + + return num/(den*den); +} + +template <typename RealT, typename PolicyT> +RealT kurtosis_excess(hyperexponential_distribution<RealT,PolicyT> const& dist) +{ + return kurtosis(dist) - 3; +} + +template <typename RealT, typename PolicyT> +RealT mode(hyperexponential_distribution<RealT,PolicyT> const& /*dist*/) +{ + return 0; +} + +}} // namespace boost::math + +#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> +#include <boost/math/distributions/detail/generic_quantile.hpp> + +#endif // BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL |