435 lines
13 KiB
C++
435 lines
13 KiB
C++
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/* boost random/binomial_distribution.hpp header file
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*
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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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* $Id$
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*/
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#ifndef BOOST_RANDOM_BINOMIAL_DISTRIBUTION_HPP_INCLUDED
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#define BOOST_RANDOM_BINOMIAL_DISTRIBUTION_HPP_INCLUDED
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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/random/detail/config.hpp>
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#include <boost/random/uniform_01.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 binomial_table {
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static const RealType table[10];
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};
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template<class RealType>
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const RealType binomial_table<RealType>::table[10] = {
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0.08106146679532726,
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0.04134069595540929,
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0.02767792568499834,
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0.02079067210376509,
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0.01664469118982119,
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0.01387612882307075,
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0.01189670994589177,
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0.01041126526197209,
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0.009255462182712733,
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0.008330563433362871
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};
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}
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/**
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* The binomial distribution is an integer valued distribution with
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* two parameters, @c t and @c p. The values of the distribution
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* are within the range [0,t].
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*
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* The distribution function is
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* \f$\displaystyle P(k) = {t \choose k}p^k(1-p)^{t-k}\f$.
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*
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* The algorithm used is the BTRD algorithm described in
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*
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* @blockquote
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* "The generation of binomial random variates", Wolfgang Hormann,
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* Journal of Statistical Computation and Simulation, Volume 46,
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* Issue 1 & 2 April 1993 , pages 101 - 110
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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 binomial_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 binomial_distribution distribution_type;
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/**
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* Construct a param_type object. @c t and @c p
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* are the parameters of the distribution.
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*
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* Requires: t >=0 && 0 <= p <= 1
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*/
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explicit param_type(IntType t_arg = 1, RealType p_arg = RealType (0.5))
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: _t(t_arg), _p(p_arg)
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{}
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/** Returns the @c t parameter of the distribution. */
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IntType t() const { return _t; }
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/** Returns the @c p parameter of the distribution. */
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RealType p() const { return _p; }
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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._p << " " << parm._t;
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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._p >> std::ws >> parm._t;
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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._t == rhs._t && lhs._p == rhs._p;
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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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IntType _t;
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RealType _p;
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};
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/**
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* Construct a @c binomial_distribution object. @c t and @c p
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* are the parameters of the distribution.
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*
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* Requires: t >=0 && 0 <= p <= 1
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*/
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explicit binomial_distribution(IntType t_arg = 1,
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RealType p_arg = RealType(0.5))
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: _t(t_arg), _p(p_arg)
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{
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init();
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}
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/**
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* Construct an @c binomial_distribution object from the
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* parameters.
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*/
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explicit binomial_distribution(const param_type& parm)
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: _t(parm.t()), _p(parm.p())
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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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* binomial 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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if(0.5 < _p) {
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return _t - invert(_t, 1-_p, urng);
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} else {
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return invert(_t, _p, urng);
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}
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} else if(0.5 < _p) {
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return _t - generate(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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* binomial distribution with parameters specified by @c 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 binomial_distribution(parm)(urng);
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}
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/** Returns the @c t parameter of the distribution. */
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IntType t() const { return _t; }
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/** Returns the @c p parameter of the distribution. */
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RealType p() const { return _p; }
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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 { return _t; }
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/** Returns the parameters of the distribution. */
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param_type param() const { return param_type(_t, _p); }
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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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_t = parm.t();
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_p = parm.p();
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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 binomial_distribution& bd)
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{
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os << bd.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, binomial_distribution& bd)
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{
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bd.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 binomial_distribution& lhs,
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const binomial_distribution& rhs)
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{
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return lhs._t == rhs._t && lhs._p == rhs._p;
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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 binomial_distribution& lhs,
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const binomial_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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// BTRD is safe when np >= 10
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return m < 11;
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}
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// computes the correction factor for the Stirling approximation
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// for log(k!)
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static RealType fc(IntType k)
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{
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if(k < 10) return detail::binomial_table<RealType>::table[k];
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else {
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RealType ikp1 = RealType(1) / (k + 1);
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return (RealType(1)/12
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- (RealType(1)/360
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- (RealType(1)/1260)*(ikp1*ikp1))*(ikp1*ikp1))*ikp1;
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}
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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::pow;
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RealType p = (0.5 < _p)? (1 - _p) : _p;
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IntType t = _t;
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m = static_cast<IntType>((t+1)*p);
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if(use_inversion()) {
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q_n = pow((1 - p), static_cast<RealType>(t));
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} else {
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btrd.r = p/(1-p);
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btrd.nr = (t+1)*btrd.r;
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btrd.npq = t*p*(1-p);
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RealType sqrt_npq = sqrt(btrd.npq);
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btrd.b = 1.15 + 2.53 * sqrt_npq;
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btrd.a = -0.0873 + 0.0248*btrd.b + 0.01*p;
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btrd.c = t*p + 0.5;
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btrd.alpha = (2.83 + 5.1/btrd.b) * sqrt_npq;
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btrd.v_r = 0.92 - 4.2/btrd.b;
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btrd.u_rv_r = 0.86*btrd.v_r;
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}
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}
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template<class URNG>
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result_type 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 <= btrd.u_rv_r) {
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u = v/btrd.v_r - 0.43;
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return static_cast<IntType>(floor(
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(2*btrd.a/(0.5 - abs(u)) + btrd.b)*u + btrd.c));
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}
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if(v >= btrd.v_r) {
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u = uniform_01<RealType>()(urng) - 0.5;
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} else {
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u = v/btrd.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) * btrd.v_r;
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}
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RealType us = 0.5 - abs(u);
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IntType k = static_cast<IntType>(floor((2*btrd.a/us + btrd.b)*u + btrd.c));
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if(k < 0 || k > _t) continue;
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v = v*btrd.alpha/(btrd.a/(us*us) + btrd.b);
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RealType km = abs(k - m);
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if(km <= 15) {
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RealType f = 1;
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if(m < k) {
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IntType i = m;
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do {
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++i;
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f = f*(btrd.nr/i - btrd.r);
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} while(i != k);
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} else if(m > k) {
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IntType i = k;
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do {
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++i;
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v = v*(btrd.nr/i - btrd.r);
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} while(i != m);
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}
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if(v <= f) return k;
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else continue;
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} else {
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// final acceptance/rejection
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v = log(v);
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RealType rho =
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(km/btrd.npq)*(((km/3. + 0.625)*km + 1./6)/btrd.npq + 0.5);
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RealType t = -km*km/(2*btrd.npq);
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if(v < t - rho) return k;
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if(v > t + rho) continue;
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IntType nm = _t - m + 1;
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RealType h = (m + 0.5)*log((m + 1)/(btrd.r*nm))
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+ fc(m) + fc(_t - m);
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IntType nk = _t - k + 1;
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if(v <= h + (_t+1)*log(static_cast<RealType>(nm)/nk)
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+ (k + 0.5)*log(nk*btrd.r/(k+1))
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- fc(k)
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- fc(_t - k))
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{
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return k;
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} else {
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continue;
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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(IntType t, RealType p, URNG& urng) const
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{
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RealType q = 1 - p;
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RealType s = p / q;
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RealType a = (t + 1) * s;
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RealType r = q_n;
|
||
|
|
RealType u = uniform_01<RealType>()(urng);
|
||
|
|
IntType x = 0;
|
||
|
|
while(u > r) {
|
||
|
|
u = u - r;
|
||
|
|
++x;
|
||
|
|
RealType r1 = ((a/x) - s) * r;
|
||
|
|
// If r gets too small then the round-off error
|
||
|
|
// becomes a problem. At this point, p(i) is
|
||
|
|
// decreasing exponentially, so if we just call
|
||
|
|
// it 0, it's close enough. Note that the
|
||
|
|
// minimum value of q_n is about 1e-7, so we
|
||
|
|
// may need to be a little careful to make sure that
|
||
|
|
// we don't terminate the first time through the loop
|
||
|
|
// for float. (Hence the test that r is decreasing)
|
||
|
|
if(r1 < std::numeric_limits<RealType>::epsilon() && r1 < r) {
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
r = r1;
|
||
|
|
}
|
||
|
|
return x;
|
||
|
|
}
|
||
|
|
|
||
|
|
// parameters
|
||
|
|
IntType _t;
|
||
|
|
RealType _p;
|
||
|
|
|
||
|
|
// common data
|
||
|
|
IntType m;
|
||
|
|
|
||
|
|
union {
|
||
|
|
// for btrd
|
||
|
|
struct {
|
||
|
|
RealType r;
|
||
|
|
RealType nr;
|
||
|
|
RealType npq;
|
||
|
|
RealType b;
|
||
|
|
RealType a;
|
||
|
|
RealType c;
|
||
|
|
RealType alpha;
|
||
|
|
RealType v_r;
|
||
|
|
RealType u_rv_r;
|
||
|
|
} btrd;
|
||
|
|
// for inversion
|
||
|
|
RealType q_n;
|
||
|
|
};
|
||
|
|
|
||
|
|
/// @endcond
|
||
|
|
};
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
// backwards compatibility
|
||
|
|
using random::binomial_distribution;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
#include <boost/random/detail/enable_warnings.hpp>
|
||
|
|
|
||
|
|
#endif
|