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361 lines
9.9 KiB
C++
361 lines
9.9 KiB
C++
/* boost random/poisson_distribution.hpp header file
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*
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* Copyright Jens Maurer 2002
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* Copyright Steven Watanabe 2010
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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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* $Id: poisson_distribution.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
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*
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*/
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#ifndef BOOST_RANDOM_POISSON_DISTRIBUTION_HPP
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#define BOOST_RANDOM_POISSON_DISTRIBUTION_HPP
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#include <boost/config/no_tr1/cmath.hpp>
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#include <cstdlib>
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#include <iosfwd>
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#include <boost/assert.hpp>
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#include <boost/limits.hpp>
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#include <boost/random/uniform_01.hpp>
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#include <boost/random/detail/config.hpp>
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#include <boost/random/detail/disable_warnings.hpp>
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namespace boost {
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namespace random {
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namespace detail {
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template<class RealType>
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struct poisson_table {
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static RealType value[10];
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};
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template<class RealType>
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RealType poisson_table<RealType>::value[10] = {
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0.0,
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0.0,
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0.69314718055994529,
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1.7917594692280550,
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3.1780538303479458,
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4.7874917427820458,
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6.5792512120101012,
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8.5251613610654147,
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10.604602902745251,
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12.801827480081469
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};
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}
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/**
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* An instantiation of the class template @c poisson_distribution is a
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* model of \random_distribution. The poisson distribution has
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* \f$p(i) = \frac{e^{-\lambda}\lambda^i}{i!}\f$
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*
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* This implementation is based on the PTRD algorithm described
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*
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* @blockquote
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* "The transformed rejection method for generating Poisson random variables",
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* Wolfgang Hormann, Insurance: Mathematics and Economics
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* Volume 12, Issue 1, February 1993, Pages 39-45
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* @endblockquote
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*/
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template<class IntType = int, class RealType = double>
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class poisson_distribution {
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public:
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typedef IntType result_type;
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typedef RealType input_type;
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class param_type {
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public:
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typedef poisson_distribution distribution_type;
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/**
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* Construct a param_type object with the parameter "mean"
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*
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* Requires: mean > 0
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*/
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explicit param_type(RealType mean_arg = RealType(1))
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: _mean(mean_arg)
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{
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BOOST_ASSERT(_mean > 0);
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}
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/* Returns the "mean" parameter of the distribution. */
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RealType mean() const { return _mean; }
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#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
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/** Writes the parameters of the distribution to a @c std::ostream. */
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template<class CharT, class Traits>
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friend std::basic_ostream<CharT, Traits>&
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operator<<(std::basic_ostream<CharT, Traits>& os,
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const param_type& parm)
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{
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os << parm._mean;
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return os;
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}
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/** Reads the parameters of the distribution from a @c std::istream. */
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template<class CharT, class Traits>
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friend std::basic_istream<CharT, Traits>&
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operator>>(std::basic_istream<CharT, Traits>& is, param_type& parm)
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{
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is >> parm._mean;
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return is;
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}
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#endif
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/** Returns true if the parameters have the same values. */
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friend bool operator==(const param_type& lhs, const param_type& rhs)
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{
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return lhs._mean == rhs._mean;
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}
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/** Returns true if the parameters have different values. */
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friend bool operator!=(const param_type& lhs, const param_type& rhs)
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{
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return !(lhs == rhs);
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}
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private:
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RealType _mean;
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};
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/**
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* Constructs a @c poisson_distribution with the parameter @c mean.
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*
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* Requires: mean > 0
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*/
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explicit poisson_distribution(RealType mean_arg = RealType(1))
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: _mean(mean_arg)
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{
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BOOST_ASSERT(_mean > 0);
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init();
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}
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/**
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* Construct an @c poisson_distribution object from the
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* parameters.
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*/
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explicit poisson_distribution(const param_type& parm)
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: _mean(parm.mean())
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{
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init();
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}
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/**
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* Returns a random variate distributed according to the
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* poisson distribution.
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*/
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template<class URNG>
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IntType operator()(URNG& urng) const
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{
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if(use_inversion()) {
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return invert(urng);
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} else {
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return generate(urng);
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}
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}
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/**
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* Returns a random variate distributed according to the
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* poisson distribution with parameters specified by param.
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*/
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template<class URNG>
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IntType operator()(URNG& urng, const param_type& parm) const
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{
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return poisson_distribution(parm)(urng);
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}
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/** Returns the "mean" parameter of the distribution. */
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RealType mean() const { return _mean; }
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/** Returns the smallest value that the distribution can produce. */
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IntType min BOOST_PREVENT_MACRO_SUBSTITUTION() const { return 0; }
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/** Returns the largest value that the distribution can produce. */
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IntType max BOOST_PREVENT_MACRO_SUBSTITUTION() const
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{ return (std::numeric_limits<IntType>::max)(); }
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/** Returns the parameters of the distribution. */
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param_type param() const { return param_type(_mean); }
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/** Sets parameters of the distribution. */
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void param(const param_type& parm)
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{
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_mean = parm.mean();
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init();
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}
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/**
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* Effects: Subsequent uses of the distribution do not depend
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* on values produced by any engine prior to invoking reset.
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*/
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void reset() { }
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#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
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/** Writes the parameters of the distribution to a @c std::ostream. */
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template<class CharT, class Traits>
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friend std::basic_ostream<CharT,Traits>&
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operator<<(std::basic_ostream<CharT,Traits>& os,
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const poisson_distribution& pd)
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{
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os << pd.param();
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return os;
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}
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/** Reads the parameters of the distribution from a @c std::istream. */
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template<class CharT, class Traits>
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friend std::basic_istream<CharT,Traits>&
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operator>>(std::basic_istream<CharT,Traits>& is, poisson_distribution& pd)
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{
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pd.read(is);
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return is;
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}
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#endif
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/** Returns true if the two distributions will produce the same
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sequence of values, given equal generators. */
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friend bool operator==(const poisson_distribution& lhs,
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const poisson_distribution& rhs)
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{
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return lhs._mean == rhs._mean;
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}
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/** Returns true if the two distributions could produce different
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sequences of values, given equal generators. */
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friend bool operator!=(const poisson_distribution& lhs,
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const poisson_distribution& rhs)
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{
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return !(lhs == rhs);
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}
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private:
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/// @cond show_private
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template<class CharT, class Traits>
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void read(std::basic_istream<CharT, Traits>& is) {
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param_type parm;
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if(is >> parm) {
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param(parm);
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}
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}
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bool use_inversion() const
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{
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return _mean < 10;
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}
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static RealType log_factorial(IntType k)
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{
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BOOST_ASSERT(k >= 0);
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BOOST_ASSERT(k < 10);
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return detail::poisson_table<RealType>::value[k];
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}
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void init()
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{
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using std::sqrt;
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using std::exp;
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if(use_inversion()) {
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_exp_mean = exp(-_mean);
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} else {
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_ptrd.smu = sqrt(_mean);
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_ptrd.b = 0.931 + 2.53 * _ptrd.smu;
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_ptrd.a = -0.059 + 0.02483 * _ptrd.b;
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_ptrd.inv_alpha = 1.1239 + 1.1328 / (_ptrd.b - 3.4);
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_ptrd.v_r = 0.9277 - 3.6224 / (_ptrd.b - 2);
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}
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}
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template<class URNG>
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IntType generate(URNG& urng) const
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{
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using std::floor;
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using std::abs;
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using std::log;
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while(true) {
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RealType u;
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RealType v = uniform_01<RealType>()(urng);
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if(v <= 0.86 * _ptrd.v_r) {
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u = v / _ptrd.v_r - 0.43;
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return static_cast<IntType>(floor(
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(2*_ptrd.a/(0.5-abs(u)) + _ptrd.b)*u + _mean + 0.445));
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}
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if(v >= _ptrd.v_r) {
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u = uniform_01<RealType>()(urng) - 0.5;
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} else {
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u = v/_ptrd.v_r - 0.93;
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u = ((u < 0)? -0.5 : 0.5) - u;
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v = uniform_01<RealType>()(urng) * _ptrd.v_r;
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}
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RealType us = 0.5 - abs(u);
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if(us < 0.013 && v > us) {
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continue;
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}
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RealType k = floor((2*_ptrd.a/us + _ptrd.b)*u+_mean+0.445);
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v = v*_ptrd.inv_alpha/(_ptrd.a/(us*us) + _ptrd.b);
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RealType log_sqrt_2pi = 0.91893853320467267;
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if(k >= 10) {
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if(log(v*_ptrd.smu) <= (k + 0.5)*log(_mean/k)
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- _mean
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- log_sqrt_2pi
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+ k
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- (1/12. - (1/360. - 1/(1260.*k*k))/(k*k))/k) {
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return static_cast<IntType>(k);
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}
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} else if(k >= 0) {
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if(log(v) <= k*log(_mean)
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- _mean
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- log_factorial(static_cast<IntType>(k))) {
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return static_cast<IntType>(k);
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}
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}
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}
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}
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template<class URNG>
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IntType invert(URNG& urng) const
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{
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RealType p = _exp_mean;
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IntType x = 0;
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RealType u = uniform_01<RealType>()(urng);
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while(u > p) {
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u = u - p;
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++x;
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p = _mean * p / x;
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}
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return x;
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}
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RealType _mean;
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union {
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// for ptrd
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struct {
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RealType v_r;
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RealType a;
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RealType b;
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RealType smu;
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RealType inv_alpha;
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} _ptrd;
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// for inversion
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RealType _exp_mean;
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};
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/// @endcond
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};
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} // namespace random
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using random::poisson_distribution;
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} // namespace boost
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#include <boost/random/detail/enable_warnings.hpp>
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#endif // BOOST_RANDOM_POISSON_DISTRIBUTION_HPP
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