884 lines
37 KiB
C++
884 lines
37 KiB
C++
/* boost random/hyperexponential_distribution.hpp header file
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*
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* Copyright Marco Guazzone 2014
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* Much of the code here taken by boost::math::hyperexponential_distribution.
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* To this end, we would like to thank Paul Bristow and John Maddock for their
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* valuable feedback.
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*
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* \author Marco Guazzone (marco.guazzone@gmail.com)
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*/
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#ifndef BOOST_RANDOM_HYPEREXPONENTIAL_DISTRIBUTION_HPP
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#define BOOST_RANDOM_HYPEREXPONENTIAL_DISTRIBUTION_HPP
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#include <boost/config.hpp>
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#include <boost/math/special_functions/fpclassify.hpp>
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#include <boost/random/detail/operators.hpp>
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#include <boost/random/detail/vector_io.hpp>
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#include <boost/random/discrete_distribution.hpp>
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#include <boost/random/exponential_distribution.hpp>
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#include <boost/range/begin.hpp>
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#include <boost/range/end.hpp>
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#include <boost/range/size.hpp>
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#include <boost/type_traits/has_pre_increment.hpp>
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#include <cassert>
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#include <cmath>
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#include <cstddef>
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#include <iterator>
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#ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
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# include <initializer_list>
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#endif // BOOST_NO_CXX11_HDR_INITIALIZER_LIST
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#include <iostream>
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#include <limits>
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#include <numeric>
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#include <vector>
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namespace boost { namespace random {
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namespace hyperexp_detail {
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template <typename T>
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std::vector<T>& normalize(std::vector<T>& v)
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{
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if (v.size() == 0)
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{
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return v;
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}
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const T sum = std::accumulate(v.begin(), v.end(), static_cast<T>(0));
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T final_sum = 0;
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const typename std::vector<T>::iterator end = --v.end();
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for (typename std::vector<T>::iterator it = v.begin();
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it != end;
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++it)
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{
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*it /= sum;
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final_sum += *it;
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}
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*end = 1-final_sum; // avoids round off errors thus ensuring the probabilities really sum to 1
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return v;
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}
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template <typename RealT>
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bool check_probabilities(std::vector<RealT> const& probabilities)
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{
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const std::size_t n = probabilities.size();
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RealT sum = 0;
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for (std::size_t i = 0; i < n; ++i)
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{
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if (probabilities[i] < 0
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|| probabilities[i] > 1
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|| !(boost::math::isfinite)(probabilities[i]))
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{
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return false;
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}
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sum += probabilities[i];
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}
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//NOTE: the check below seems to fail on some architectures.
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// So we commented it.
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//// - We try to keep phase probabilities correctly normalized in the distribution constructors
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//// - However in practice we have to allow for a very slight divergence from a sum of exactly 1:
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////if (std::abs(sum-1) > (std::numeric_limits<RealT>::epsilon()*2))
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//// This is from Knuth "The Art of Computer Programming: Vol.2, 3rd Ed", and can be used to
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//// check is two numbers are approximately equal
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//const RealT one = 1;
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//const RealT tol = std::numeric_limits<RealT>::epsilon()*2.0;
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//if (std::abs(sum-one) > (std::max(std::abs(sum), std::abs(one))*tol))
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//{
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// return false;
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//}
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return true;
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}
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template <typename RealT>
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bool check_rates(std::vector<RealT> const& rates)
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{
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const std::size_t n = rates.size();
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for (std::size_t i = 0; i < n; ++i)
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{
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if (rates[i] <= 0
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|| !(boost::math::isfinite)(rates[i]))
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{
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return false;
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}
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}
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return true;
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}
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template <typename RealT>
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bool check_params(std::vector<RealT> const& probabilities, std::vector<RealT> const& rates)
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{
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if (probabilities.size() != rates.size())
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{
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return false;
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}
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return check_probabilities(probabilities)
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&& check_rates(rates);
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}
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} // Namespace hyperexp_detail
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/**
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* The hyperexponential distribution is a real-valued continuous distribution
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* with two parameters, the <em>phase probability vector</em> \c probs and the
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* <em>rate vector</em> \c rates.
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*
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* A \f$k\f$-phase hyperexponential distribution is a mixture of \f$k\f$
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* exponential distributions.
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* For this reason, it is also referred to as <em>mixed exponential
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* distribution</em> or <em>parallel \f$k\f$-phase exponential
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* distribution</em>.
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*
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* A \f$k\f$-phase hyperexponential distribution is characterized by two
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* parameters, namely a <em>phase probability vector</em> \f$\mathbf{\alpha}=(\alpha_1,\ldots,\alpha_k)\f$ and a <em>rate vector</em> \f$\mathbf{\lambda}=(\lambda_1,\ldots,\lambda_k)\f$.
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*
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* A \f$k\f$-phase hyperexponential distribution is frequently used in
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* <em>queueing theory</em> to model the distribution of the superposition of
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* \f$k\f$ independent events, like, for instance, the service time distribution
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* of a queueing station with \f$k\f$ servers in parallel where the \f$i\f$-th
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* server is chosen with probability \f$\alpha_i\f$ and its service time
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* distribution is an exponential distribution with rate \f$\lambda_i\f$
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* (Allen,1990; Papadopolous et al.,1993; Trivedi,2002).
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*
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* For instance, CPUs service-time distribution in a computing system has often
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* been observed to possess such a distribution (Rosin,1965).
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* Also, the arrival of different types of customer to a single queueing station
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* is often modeled as a hyperexponential distribution (Papadopolous et al.,1993).
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* Similarly, if a product manufactured in several parallel assemply lines and
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* the outputs are merged, the failure density of the overall product is likely
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* to be hyperexponential (Trivedi,2002).
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*
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* Finally, since the hyperexponential distribution exhibits a high Coefficient
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* of Variation (CoV), that is a CoV > 1, it is especially suited to fit
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* empirical data with large CoV (Feitelson,2014; Wolski et al.,2013) and to
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* approximate <em>long-tail probability distributions</em> (Feldmann et al.,1998).
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*
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* See (Boost,2014) for more information and examples.
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*
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* A \f$k\f$-phase hyperexponential distribution has a probability density
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* function
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* \f[
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* f(x) = \sum_{i=1}^k \alpha_i \lambda_i e^{-x\lambda_i}
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* \f]
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* where:
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* - \f$k\f$ is the <em>number of phases</em> and also the size of the input
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* vector parameters,
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* - \f$\mathbf{\alpha}=(\alpha_1,\ldots,\alpha_k)\f$ is the <em>phase probability
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* vector</em> parameter, and
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* - \f$\mathbf{\lambda}=(\lambda_1,\ldots,\lambda_k)\f$ is the <em>rate vector</em>
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* parameter.
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* .
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*
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* Given a \f$k\f$-phase hyperexponential distribution with phase probability
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* vector \f$\mathbf{\alpha}\f$ and rate vector \f$\mathbf{\lambda}\f$, the
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* random variate generation algorithm consists of the following steps (Tyszer,1999):
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* -# Generate a random variable \f$U\f$ uniformly distribution on the interval \f$(0,1)\f$.
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* -# Use \f$U\f$ to select the appropriate \f$\lambda_i\f$ (e.g., the
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* <em>alias method</em> can possibly be used for this step).
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* -# Generate an exponentially distributed random variable \f$X\f$ with rate parameter \f$\lambda_i\f$.
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* -# Return \f$X\f$.
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* .
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*
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* References:
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* -# A.O. Allen, <em>Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition</em>, Academic Press, 1990.
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* -# Boost C++ Libraries, <em>Boost.Math / Statistical Distributions: Hyperexponential Distribution</em>, Online: http://www.boost.org/doc/libs/release/libs/math/doc/html/dist.html , 2014.
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* -# D.G. Feitelson, <em>Workload Modeling for Computer Systems Performance Evaluation</em>, Cambridge University Press, 2014
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* -# A. Feldmann and W. Whitt, <em>Fitting mixtures of exponentials to long-tail distributions to analyze network performance models</em>, Performance Evaluation 31(3-4):245, doi:10.1016/S0166-5316(97)00003-5, 1998.
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* -# H.T. Papadopolous, C. Heavey and J. Browne, <em>Queueing Theory in Manufacturing Systems Analysis and Design</em>, Chapman & Hall/CRC, 1993, p. 35.
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* -# R.F. Rosin, <em>Determining a computing center environment</em>, Communications of the ACM 8(7):463-468, 1965.
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* -# K.S. Trivedi, <em>Probability and Statistics with Reliability, Queueing, and Computer Science Applications</em>, John Wiley & Sons, Inc., 2002.
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* -# J. Tyszer, <em>Object-Oriented Computer Simulation of Discrete-Event Systems</em>, Springer, 1999.
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* -# Wikipedia, <em>Hyperexponential Distribution</em>, Online: http://en.wikipedia.org/wiki/Hyperexponential_distribution , 2014.
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* -# Wolfram Mathematica, <em>Hyperexponential Distribution</em>, Online: http://reference.wolfram.com/language/ref/HyperexponentialDistribution.html , 2014.
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* .
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*
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* \author Marco Guazzone (marco.guazzone@gmail.com)
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*/
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template<class RealT = double>
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class hyperexponential_distribution
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{
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public: typedef RealT result_type;
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public: typedef RealT input_type;
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/**
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* The parameters of a hyperexponential distribution.
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*
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* Stores the <em>phase probability vector</em> and the <em>rate vector</em>
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* of the hyperexponential distribution.
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*
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* \author Marco Guazzone (marco.guazzone@gmail.com)
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*/
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public: class param_type
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{
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public: typedef hyperexponential_distribution distribution_type;
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/**
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* Constructs a \c param_type with the default parameters
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* of the distribution.
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*/
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public: param_type()
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: probs_(1, 1),
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rates_(1, 1)
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{
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}
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/**
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* Constructs a \c param_type from the <em>phase probability vector</em>
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* and <em>rate vector</em> parameters of the distribution.
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*
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* The <em>phase probability vector</em> parameter is given by the range
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* defined by [\a prob_first, \a prob_last) iterator pair, and the
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* <em>rate vector</em> parameter is given by the range defined by
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* [\a rate_first, \a rate_last) iterator pair.
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*
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* \tparam ProbIterT Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
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* \tparam RateIterT Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
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*
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* \param prob_first The iterator to the beginning of the range of non-negative real elements representing the phase probabilities; if elements don't sum to 1, they are normalized.
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* \param prob_last The iterator to the ending of the range of non-negative real elements representing the phase probabilities; if elements don't sum to 1, they are normalized.
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* \param rate_first The iterator to the beginning of the range of non-negative real elements representing the rates.
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* \param rate_last The iterator to the ending of the range of non-negative real elements representing the rates.
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*
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* References:
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* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
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* .
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*/
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public: template <typename ProbIterT, typename RateIterT>
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param_type(ProbIterT prob_first, ProbIterT prob_last,
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RateIterT rate_first, RateIterT rate_last)
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: probs_(prob_first, prob_last),
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rates_(rate_first, rate_last)
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{
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hyperexp_detail::normalize(probs_);
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assert( hyperexp_detail::check_params(probs_, rates_) );
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}
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/**
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* Constructs a \c param_type from the <em>phase probability vector</em>
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* and <em>rate vector</em> parameters of the distribution.
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*
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* The <em>phase probability vector</em> parameter is given by the range
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* defined by \a prob_range, and the <em>rate vector</em> parameter is
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* given by the range defined by \a rate_range.
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*
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* \tparam ProbRangeT Must meet the requirements of <a href="boost:/libs/range/doc/html/range/concepts.html">Range</a> concept.
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* \tparam RateRangeT Must meet the requirements of <a href="boost:/libs/range/doc/html/range/concepts.html">Range</a> concept.
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*
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* \param prob_range The range of non-negative real elements representing the phase probabilities; if elements don't sum to 1, they are normalized.
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* \param rate_range The range of positive real elements representing the rates.
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*
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* \note
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* The final \c disable_if parameter is an implementation detail that
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* differentiates between this two argument constructor and the
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* iterator-based two argument constructor described below.
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*/
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// We SFINAE this out of existance if either argument type is
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// incrementable as in that case the type is probably an iterator:
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public: template <typename ProbRangeT, typename RateRangeT>
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param_type(ProbRangeT const& prob_range,
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RateRangeT const& rate_range,
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typename boost::disable_if_c<boost::has_pre_increment<ProbRangeT>::value || boost::has_pre_increment<RateRangeT>::value>::type* = 0)
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: probs_(boost::begin(prob_range), boost::end(prob_range)),
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rates_(boost::begin(rate_range), boost::end(rate_range))
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{
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hyperexp_detail::normalize(probs_);
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assert( hyperexp_detail::check_params(probs_, rates_) );
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}
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/**
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* Constructs a \c param_type from the <em>rate vector</em> parameter of
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* the distribution and with equal phase probabilities.
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*
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* The <em>rate vector</em> parameter is given by the range defined by
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* [\a rate_first, \a rate_last) iterator pair, and the <em>phase
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* probability vector</em> parameter is set to the equal phase
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* probabilities (i.e., to a vector of the same length \f$k\f$ of the
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* <em>rate vector</em> and with each element set to \f$1.0/k\f$).
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*
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* \tparam RateIterT Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
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* \tparam RateIterT2 Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
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*
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* \param rate_first The iterator to the beginning of the range of non-negative real elements representing the rates.
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* \param rate_last The iterator to the ending of the range of non-negative real elements representing the rates.
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*
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* \note
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* The final \c disable_if parameter is an implementation detail that
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* differentiates between this two argument constructor and the
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* range-based two argument constructor described above.
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*
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* References:
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* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
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* .
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*/
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// We SFINAE this out of existance if the argument type is
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// incrementable as in that case the type is probably an iterator.
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public: template <typename RateIterT>
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param_type(RateIterT rate_first,
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RateIterT rate_last,
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typename boost::enable_if_c<boost::has_pre_increment<RateIterT>::value>::type* = 0)
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: probs_(std::distance(rate_first, rate_last), 1), // will be normalized below
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rates_(rate_first, rate_last)
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{
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assert(probs_.size() == rates_.size());
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}
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/**
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* Constructs a @c param_type from the "rates" parameters
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* of the distribution and with equal phase probabilities.
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*
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* The <em>rate vector</em> parameter is given by the range defined by
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* \a rate_range, and the <em>phase probability vector</em> parameter is
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* set to the equal phase probabilities (i.e., to a vector of the same
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* length \f$k\f$ of the <em>rate vector</em> and with each element set
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* to \f$1.0/k\f$).
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*
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* \tparam RateRangeT Must meet the requirements of <a href="boost:/libs/range/doc/html/range/concepts.html">Range</a> concept.
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*
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* \param rate_range The range of positive real elements representing the rates.
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*/
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public: template <typename RateRangeT>
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param_type(RateRangeT const& rate_range)
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: probs_(boost::size(rate_range), 1), // Will be normalized below
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rates_(boost::begin(rate_range), boost::end(rate_range))
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{
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hyperexp_detail::normalize(probs_);
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assert( hyperexp_detail::check_params(probs_, rates_) );
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}
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#ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
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/**
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* Constructs a \c param_type from the <em>phase probability vector</em>
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* and <em>rate vector</em> parameters of the distribution.
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*
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* The <em>phase probability vector</em> parameter is given by the
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* <em>brace-init-list</em> (ISO,2014,sec. 8.5.4 [dcl.init.list])
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* defined by \a l1, and the <em>rate vector</em> parameter is given by the
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* <em>brace-init-list</em> (ISO,2014,sec. 8.5.4 [dcl.init.list])
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* defined by \a l2.
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*
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* \param l1 The initializer list for inizializing the phase probability vector.
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* \param l2 The initializer list for inizializing the rate vector.
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*
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* References:
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* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
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* .
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*/
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public: param_type(std::initializer_list<RealT> l1, std::initializer_list<RealT> l2)
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: probs_(l1.begin(), l1.end()),
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rates_(l2.begin(), l2.end())
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{
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hyperexp_detail::normalize(probs_);
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assert( hyperexp_detail::check_params(probs_, rates_) );
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}
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/**
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* Constructs a \c param_type from the <em>rate vector</em> parameter
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* of the distribution and with equal phase probabilities.
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*
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* The <em>rate vector</em> parameter is given by the
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* <em>brace-init-list</em> (ISO,2014,sec. 8.5.4 [dcl.init.list])
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* defined by \a l1, and the <em>phase probability vector</em> parameter is
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* set to the equal phase probabilities (i.e., to a vector of the same
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* length \f$k\f$ of the <em>rate vector</em> and with each element set
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* to \f$1.0/k\f$).
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*
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* \param l1 The initializer list for inizializing the rate vector.
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*
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* References:
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* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
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* .
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*/
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public: param_type(std::initializer_list<RealT> l1)
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: probs_(std::distance(l1.begin(), l1.end()), 1), // Will be normalized below
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rates_(l1.begin(), l1.end())
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{
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hyperexp_detail::normalize(probs_);
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assert( hyperexp_detail::check_params(probs_, rates_) );
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}
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#endif // BOOST_NO_CXX11_HDR_INITIALIZER_LIST
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/**
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* Gets the <em>phase probability vector</em> parameter of the distribtuion.
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*
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* \return The <em>phase probability vector</em> parameter of the distribution.
|
|
*
|
|
* \note
|
|
* The returned probabilities are the normalized version of the ones
|
|
* passed at construction time.
|
|
*/
|
|
public: std::vector<RealT> probabilities() const
|
|
{
|
|
return probs_;
|
|
}
|
|
|
|
/**
|
|
* Gets the <em>rate vector</em> parameter of the distribtuion.
|
|
*
|
|
* \return The <em>rate vector</em> parameter of the distribution.
|
|
*/
|
|
public: std::vector<RealT> rates() const
|
|
{
|
|
return rates_;
|
|
}
|
|
|
|
/** Writes a \c param_type to a \c std::ostream. */
|
|
public: BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, param)
|
|
{
|
|
detail::print_vector(os, param.probs_);
|
|
os << ' ';
|
|
detail::print_vector(os, param.rates_);
|
|
|
|
return os;
|
|
}
|
|
|
|
/** Reads a \c param_type from a \c std::istream. */
|
|
public: BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, param)
|
|
{
|
|
// NOTE: if \c std::ios_base::exceptions is set, the code below may
|
|
// throw in case of a I/O failure.
|
|
// To prevent leaving the state of \c param inconsistent:
|
|
// - if an exception is thrown, the state of \c param is left
|
|
// unchanged (i.e., is the same as the one at the beginning
|
|
// of the function's execution), and
|
|
// - the state of \c param only after reading the whole input.
|
|
|
|
std::vector<RealT> probs;
|
|
std::vector<RealT> rates;
|
|
|
|
// Reads probability and rate vectors
|
|
detail::read_vector(is, probs);
|
|
if (!is)
|
|
{
|
|
return is;
|
|
}
|
|
is >> std::ws;
|
|
detail::read_vector(is, rates);
|
|
if (!is)
|
|
{
|
|
return is;
|
|
}
|
|
|
|
// Update the state of the param_type object
|
|
if (probs.size() > 0)
|
|
{
|
|
param.probs_.swap(probs);
|
|
probs.clear();
|
|
}
|
|
if (rates.size() > 0)
|
|
{
|
|
param.rates_.swap(rates);
|
|
rates.clear();
|
|
}
|
|
|
|
bool fail = false;
|
|
|
|
// Adjust vector sizes (if needed)
|
|
if (param.probs_.size() != param.rates_.size()
|
|
|| param.probs_.size() == 0)
|
|
{
|
|
fail = true;
|
|
|
|
const std::size_t np = param.probs_.size();
|
|
const std::size_t nr = param.rates_.size();
|
|
|
|
if (np > nr)
|
|
{
|
|
param.rates_.resize(np, 1);
|
|
}
|
|
else if (nr > np)
|
|
{
|
|
param.probs_.resize(nr, 1);
|
|
}
|
|
else
|
|
{
|
|
param.probs_.resize(1, 1);
|
|
param.rates_.resize(1, 1);
|
|
}
|
|
}
|
|
|
|
// Normalize probabilities
|
|
// NOTE: this cannot be done earlier since the probability vector
|
|
// can be changed due to size conformance
|
|
hyperexp_detail::normalize(param.probs_);
|
|
|
|
// Set the error state in the underlying stream in case of invalid input
|
|
if (fail)
|
|
{
|
|
// This throws an exception if ios_base::exception(failbit) is enabled
|
|
is.setstate(std::ios_base::failbit);
|
|
}
|
|
|
|
//post: vector size conformance
|
|
assert(param.probs_.size() == param.rates_.size());
|
|
|
|
return is;
|
|
}
|
|
|
|
/** Returns true if the two sets of parameters are the same. */
|
|
public: BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
|
|
{
|
|
return lhs.probs_ == rhs.probs_
|
|
&& lhs.rates_ == rhs.rates_;
|
|
}
|
|
|
|
/** Returns true if the two sets of parameters are the different. */
|
|
public: BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
|
|
|
|
|
|
private: std::vector<RealT> probs_; ///< The <em>phase probability vector</em> parameter of the distribution
|
|
private: std::vector<RealT> rates_; ///< The <em>rate vector</em> parameter of the distribution
|
|
}; // param_type
|
|
|
|
|
|
/**
|
|
* Constructs a 1-phase \c hyperexponential_distribution (i.e., an
|
|
* exponential distribution) with rate 1.
|
|
*/
|
|
public: hyperexponential_distribution()
|
|
: dd_(std::vector<RealT>(1, 1)),
|
|
rates_(1, 1)
|
|
{
|
|
// empty
|
|
}
|
|
|
|
/**
|
|
* Constructs a \c hyperexponential_distribution from the <em>phase
|
|
* probability vector</em> and <em>rate vector</em> parameters of the
|
|
* distribution.
|
|
*
|
|
* The <em>phase probability vector</em> parameter is given by the range
|
|
* defined by [\a prob_first, \a prob_last) iterator pair, and the
|
|
* <em>rate vector</em> parameter is given by the range defined by
|
|
* [\a rate_first, \a rate_last) iterator pair.
|
|
*
|
|
* \tparam ProbIterT Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
|
|
* \tparam RateIterT Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
|
|
*
|
|
* \param prob_first The iterator to the beginning of the range of non-negative real elements representing the phase probabilities; if elements don't sum to 1, they are normalized.
|
|
* \param prob_last The iterator to the ending of the range of non-negative real elements representing the phase probabilities; if elements don't sum to 1, they are normalized.
|
|
* \param rate_first The iterator to the beginning of the range of non-negative real elements representing the rates.
|
|
* \param rate_last The iterator to the ending of the range of non-negative real elements representing the rates.
|
|
*
|
|
* References:
|
|
* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
|
|
* .
|
|
*/
|
|
public: template <typename ProbIterT, typename RateIterT>
|
|
hyperexponential_distribution(ProbIterT prob_first, ProbIterT prob_last,
|
|
RateIterT rate_first, RateIterT rate_last)
|
|
: dd_(prob_first, prob_last),
|
|
rates_(rate_first, rate_last)
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
|
|
/**
|
|
* Constructs a \c hyperexponential_distribution from the <em>phase
|
|
* probability vector</em> and <em>rate vector</em> parameters of the
|
|
* distribution.
|
|
*
|
|
* The <em>phase probability vector</em> parameter is given by the range
|
|
* defined by \a prob_range, and the <em>rate vector</em> parameter is
|
|
* given by the range defined by \a rate_range.
|
|
*
|
|
* \tparam ProbRangeT Must meet the requirements of <a href="boost:/libs/range/doc/html/range/concepts.html">Range</a> concept.
|
|
* \tparam RateRangeT Must meet the requirements of <a href="boost:/libs/range/doc/html/range/concepts.html">Range</a> concept.
|
|
*
|
|
* \param prob_range The range of non-negative real elements representing the phase probabilities; if elements don't sum to 1, they are normalized.
|
|
* \param rate_range The range of positive real elements representing the rates.
|
|
*
|
|
* \note
|
|
* The final \c disable_if parameter is an implementation detail that
|
|
* differentiates between this two argument constructor and the
|
|
* iterator-based two argument constructor described below.
|
|
*/
|
|
// 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)
|
|
: dd_(prob_range),
|
|
rates_(boost::begin(rate_range), boost::end(rate_range))
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
|
|
/**
|
|
* Constructs a \c hyperexponential_distribution from the <em>rate
|
|
* vector</em> parameter of the distribution and with equal phase
|
|
* probabilities.
|
|
*
|
|
* The <em>rate vector</em> parameter is given by the range defined by
|
|
* [\a rate_first, \a rate_last) iterator pair, and the <em>phase
|
|
* probability vector</em> parameter is set to the equal phase
|
|
* probabilities (i.e., to a vector of the same length \f$k\f$ of the
|
|
* <em>rate vector</em> and with each element set to \f$1.0/k\f$).
|
|
*
|
|
* \tparam RateIterT Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
|
|
* \tparam RateIterT2 Must meet the requirements of \c InputIterator concept (ISO,2014,sec. 24.2.3 [input.iterators]).
|
|
*
|
|
* \param rate_first The iterator to the beginning of the range of non-negative real elements representing the rates.
|
|
* \param rate_last The iterator to the ending of the range of non-negative real elements representing the rates.
|
|
*
|
|
* \note
|
|
* The final \c disable_if parameter is an implementation detail that
|
|
* differentiates between this two argument constructor and the
|
|
* range-based two argument constructor described above.
|
|
*
|
|
* References:
|
|
* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
|
|
* .
|
|
*/
|
|
// We SFINAE this out of existance if the argument type is
|
|
// incrementable as in that case the type is probably an iterator.
|
|
public: template <typename RateIterT>
|
|
hyperexponential_distribution(RateIterT rate_first,
|
|
RateIterT rate_last,
|
|
typename boost::enable_if_c<boost::has_pre_increment<RateIterT>::value>::type* = 0)
|
|
: dd_(std::vector<RealT>(std::distance(rate_first, rate_last), 1)),
|
|
rates_(rate_first, rate_last)
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
|
|
/**
|
|
* Constructs a @c param_type from the "rates" parameters
|
|
* of the distribution and with equal phase probabilities.
|
|
*
|
|
* The <em>rate vector</em> parameter is given by the range defined by
|
|
* \a rate_range, and the <em>phase probability vector</em> parameter is
|
|
* set to the equal phase probabilities (i.e., to a vector of the same
|
|
* length \f$k\f$ of the <em>rate vector</em> and with each element set
|
|
* to \f$1.0/k\f$).
|
|
*
|
|
* \tparam RateRangeT Must meet the requirements of <a href="boost:/libs/range/doc/html/range/concepts.html">Range</a> concept.
|
|
*
|
|
* \param rate_range The range of positive real elements representing the rates.
|
|
*/
|
|
public: template <typename RateRangeT>
|
|
hyperexponential_distribution(RateRangeT const& rate_range)
|
|
: dd_(std::vector<RealT>(boost::size(rate_range), 1)),
|
|
rates_(boost::begin(rate_range), boost::end(rate_range))
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
|
|
/**
|
|
* Constructs a \c hyperexponential_distribution from its parameters.
|
|
*
|
|
* \param param The parameters of the distribution.
|
|
*/
|
|
public: explicit hyperexponential_distribution(param_type const& param)
|
|
: dd_(param.probabilities()),
|
|
rates_(param.rates())
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
|
|
#ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
|
|
/**
|
|
* Constructs a \c hyperexponential_distribution from the <em>phase
|
|
* probability vector</em> and <em>rate vector</em> parameters of the
|
|
* distribution.
|
|
*
|
|
* The <em>phase probability vector</em> parameter is given by the
|
|
* <em>brace-init-list</em> (ISO,2014,sec. 8.5.4 [dcl.init.list])
|
|
* defined by \a l1, and the <em>rate vector</em> parameter is given by the
|
|
* <em>brace-init-list</em> (ISO,2014,sec. 8.5.4 [dcl.init.list])
|
|
* defined by \a l2.
|
|
*
|
|
* \param l1 The initializer list for inizializing the phase probability vector.
|
|
* \param l2 The initializer list for inizializing the rate vector.
|
|
*
|
|
* References:
|
|
* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
|
|
* .
|
|
*/
|
|
public: hyperexponential_distribution(std::initializer_list<RealT> const& l1, std::initializer_list<RealT> const& l2)
|
|
: dd_(l1.begin(), l1.end()),
|
|
rates_(l2.begin(), l2.end())
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
|
|
/**
|
|
* Constructs a \c hyperexponential_distribution from the <em>rate
|
|
* vector</em> parameter of the distribution and with equal phase
|
|
* probabilities.
|
|
*
|
|
* The <em>rate vector</em> parameter is given by the
|
|
* <em>brace-init-list</em> (ISO,2014,sec. 8.5.4 [dcl.init.list])
|
|
* defined by \a l1, and the <em>phase probability vector</em> parameter is
|
|
* set to the equal phase probabilities (i.e., to a vector of the same
|
|
* length \f$k\f$ of the <em>rate vector</em> and with each element set
|
|
* to \f$1.0/k\f$).
|
|
*
|
|
* \param l1 The initializer list for inizializing the rate vector.
|
|
*
|
|
* References:
|
|
* -# ISO, <em>ISO/IEC 14882-2014: Information technology - Programming languages - C++</em>, 2014
|
|
* .
|
|
*/
|
|
public: hyperexponential_distribution(std::initializer_list<RealT> const& l1)
|
|
: dd_(std::vector<RealT>(std::distance(l1.begin(), l1.end()), 1)),
|
|
rates_(l1.begin(), l1.end())
|
|
{
|
|
assert( hyperexp_detail::check_params(dd_.probabilities(), rates_) );
|
|
}
|
|
#endif
|
|
|
|
/**
|
|
* Gets a random variate distributed according to the
|
|
* hyperexponential distribution.
|
|
*
|
|
* \tparam URNG Must meet the requirements of \uniform_random_number_generator.
|
|
*
|
|
* \param urng A uniform random number generator object.
|
|
*
|
|
* \return A random variate distributed according to the hyperexponential distribution.
|
|
*/
|
|
public: template<class URNG>\
|
|
RealT operator()(URNG& urng) const
|
|
{
|
|
const int i = dd_(urng);
|
|
|
|
return boost::random::exponential_distribution<RealT>(rates_[i])(urng);
|
|
}
|
|
|
|
/**
|
|
* Gets a random variate distributed according to the hyperexponential
|
|
* distribution with parameters specified by \c param.
|
|
*
|
|
* \tparam URNG Must meet the requirements of \uniform_random_number_generator.
|
|
*
|
|
* \param urng A uniform random number generator object.
|
|
* \param param A distribution parameter object.
|
|
*
|
|
* \return A random variate distributed according to the hyperexponential distribution.
|
|
* distribution with parameters specified by \c param.
|
|
*/
|
|
public: template<class URNG>
|
|
RealT operator()(URNG& urng, const param_type& param) const
|
|
{
|
|
return hyperexponential_distribution(param)(urng);
|
|
}
|
|
|
|
/** Returns the number of phases of the distribution. */
|
|
public: std::size_t num_phases() const
|
|
{
|
|
return rates_.size();
|
|
}
|
|
|
|
/** Returns the <em>phase probability vector</em> parameter of the distribution. */
|
|
public: std::vector<RealT> probabilities() const
|
|
{
|
|
return dd_.probabilities();
|
|
}
|
|
|
|
/** Returns the <em>rate vector</em> parameter of the distribution. */
|
|
public: std::vector<RealT> rates() const
|
|
{
|
|
return rates_;
|
|
}
|
|
|
|
/** Returns the smallest value that the distribution can produce. */
|
|
public: RealT min BOOST_PREVENT_MACRO_SUBSTITUTION () const
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
/** Returns the largest value that the distribution can produce. */
|
|
public: RealT max BOOST_PREVENT_MACRO_SUBSTITUTION () const
|
|
{
|
|
return std::numeric_limits<RealT>::infinity();
|
|
}
|
|
|
|
/** Returns the parameters of the distribution. */
|
|
public: param_type param() const
|
|
{
|
|
std::vector<RealT> probs = dd_.probabilities();
|
|
|
|
return param_type(probs.begin(), probs.end(), rates_.begin(), rates_.end());
|
|
}
|
|
|
|
/** Sets the parameters of the distribution. */
|
|
public: void param(param_type const& param)
|
|
{
|
|
dd_.param(typename boost::random::discrete_distribution<int,RealT>::param_type(param.probabilities()));
|
|
rates_ = param.rates();
|
|
}
|
|
|
|
/**
|
|
* Effects: Subsequent uses of the distribution do not depend
|
|
* on values produced by any engine prior to invoking reset.
|
|
*/
|
|
public: void reset()
|
|
{
|
|
// empty
|
|
}
|
|
|
|
/** Writes an @c hyperexponential_distribution to a @c std::ostream. */
|
|
public: BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, hyperexponential_distribution, hd)
|
|
{
|
|
os << hd.param();
|
|
return os;
|
|
}
|
|
|
|
/** Reads an @c hyperexponential_distribution from a @c std::istream. */
|
|
public: BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, hyperexponential_distribution, hd)
|
|
{
|
|
param_type param;
|
|
if(is >> param)
|
|
{
|
|
hd.param(param);
|
|
}
|
|
return is;
|
|
}
|
|
|
|
/**
|
|
* Returns true if the two instances of @c hyperexponential_distribution will
|
|
* return identical sequences of values given equal generators.
|
|
*/
|
|
public: BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(hyperexponential_distribution, lhs, rhs)
|
|
{
|
|
return lhs.dd_ == rhs.dd_
|
|
&& lhs.rates_ == rhs.rates_;
|
|
}
|
|
|
|
/**
|
|
* Returns true if the two instances of @c hyperexponential_distribution will
|
|
* return different sequences of values given equal generators.
|
|
*/
|
|
public: BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(hyperexponential_distribution)
|
|
|
|
|
|
private: boost::random::discrete_distribution<int,RealT> dd_; ///< The \c discrete_distribution used to sample the phase probability and choose the rate
|
|
private: std::vector<RealT> rates_; ///< The <em>rate vector</em> parameter of the distribution
|
|
}; // hyperexponential_distribution
|
|
|
|
}} // namespace boost::random
|
|
|
|
|
|
#endif // BOOST_RANDOM_HYPEREXPONENTIAL_DISTRIBUTION_HPP
|