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/* boost random/normal_distribution.hpp header file
*
* Copyright Jens Maurer 2000-2001
* Copyright Steven Watanabe 2010-2011
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* See http://www.boost.org for most recent version including documentation.
*
* $Id: normal_distribution.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
*
* Revision history
* 2001-02-18 moved to individual header files
*/
#ifndef BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP
#define BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP
#include <boost/config/no_tr1/cmath.hpp>
#include <istream>
#include <iosfwd>
#include <boost/assert.hpp>
#include <boost/limits.hpp>
#include <boost/static_assert.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/operators.hpp>
#include <boost/random/uniform_01.hpp>
namespace boost {
namespace random {
// deterministic Box-Muller method, uses trigonometric functions
/**
* Instantiations of class template normal_distribution model a
* \random_distribution. Such a distribution produces random numbers
* @c x distributed with probability density function
* \f$\displaystyle p(x) =
* \frac{1}{\sqrt{2\pi\sigma}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
* \f$,
* where mean and sigma are the parameters of the distribution.
*/
template<class RealType = double>
class normal_distribution
{
public:
typedef RealType input_type;
typedef RealType result_type;
class param_type {
public:
typedef normal_distribution distribution_type;
/**
* Constructs a @c param_type with a given mean and
* standard deviation.
*
* Requires: sigma >= 0
*/
explicit param_type(RealType mean_arg = RealType(0.0),
RealType sigma_arg = RealType(1.0))
: _mean(mean_arg),
_sigma(sigma_arg)
{}
/** Returns the mean of the distribution. */
RealType mean() const { return _mean; }
/** Returns the standand deviation of the distribution. */
RealType sigma() const { return _sigma; }
/** Writes a @c param_type to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
{ os << parm._mean << " " << parm._sigma ; return os; }
/** Reads a @c param_type from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
{ is >> parm._mean >> std::ws >> parm._sigma; return is; }
/** Returns true if the two sets of parameters are the same. */
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
{ return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma; }
/** Returns true if the two sets of parameters are the different. */
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
private:
RealType _mean;
RealType _sigma;
};
/**
* Constructs a @c normal_distribution object. @c mean and @c sigma are
* the parameters for the distribution.
*
* Requires: sigma >= 0
*/
explicit normal_distribution(const RealType& mean_arg = RealType(0.0),
const RealType& sigma_arg = RealType(1.0))
: _mean(mean_arg), _sigma(sigma_arg),
_r1(0), _r2(0), _cached_rho(0), _valid(false)
{
BOOST_ASSERT(_sigma >= RealType(0));
}
/**
* Constructs a @c normal_distribution object from its parameters.
*/
explicit normal_distribution(const param_type& parm)
: _mean(parm.mean()), _sigma(parm.sigma()),
_r1(0), _r2(0), _cached_rho(0), _valid(false)
{}
/** Returns the mean of the distribution. */
RealType mean() const { return _mean; }
/** Returns the standard deviation of the distribution. */
RealType sigma() const { return _sigma; }
/** Returns the smallest value that the distribution can produce. */
RealType min BOOST_PREVENT_MACRO_SUBSTITUTION () const
{ return -std::numeric_limits<RealType>::infinity(); }
/** Returns the largest value that the distribution can produce. */
RealType max BOOST_PREVENT_MACRO_SUBSTITUTION () const
{ return std::numeric_limits<RealType>::infinity(); }
/** Returns the parameters of the distribution. */
param_type param() const { return param_type(_mean, _sigma); }
/** Sets the parameters of the distribution. */
void param(const param_type& parm)
{
_mean = parm.mean();
_sigma = parm.sigma();
_valid = false;
}
/**
* Effects: Subsequent uses of the distribution do not depend
* on values produced by any engine prior to invoking reset.
*/
void reset() { _valid = false; }
/** Returns a normal variate. */
template<class Engine>
result_type operator()(Engine& eng)
{
using std::sqrt;
using std::log;
using std::sin;
using std::cos;
if(!_valid) {
_r1 = boost::uniform_01<RealType>()(eng);
_r2 = boost::uniform_01<RealType>()(eng);
_cached_rho = sqrt(-result_type(2) * log(result_type(1)-_r2));
_valid = true;
} else {
_valid = false;
}
// Can we have a boost::mathconst please?
const result_type pi = result_type(3.14159265358979323846);
return _cached_rho * (_valid ?
cos(result_type(2)*pi*_r1) :
sin(result_type(2)*pi*_r1))
* _sigma + _mean;
}
/** Returns a normal variate with parameters specified by @c param. */
template<class URNG>
result_type operator()(URNG& urng, const param_type& parm)
{
return normal_distribution(parm)(urng);
}
/** Writes a @c normal_distribution to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, normal_distribution, nd)
{
os << nd._mean << " " << nd._sigma << " "
<< nd._valid << " " << nd._cached_rho << " " << nd._r1;
return os;
}
/** Reads a @c normal_distribution from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, normal_distribution, nd)
{
is >> std::ws >> nd._mean >> std::ws >> nd._sigma
>> std::ws >> nd._valid >> std::ws >> nd._cached_rho
>> std::ws >> nd._r1;
return is;
}
/**
* Returns true if the two instances of @c normal_distribution will
* return identical sequences of values given equal generators.
*/
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(normal_distribution, lhs, rhs)
{
return lhs._mean == rhs._mean && lhs._sigma == rhs._sigma
&& lhs._valid == rhs._valid
&& (!lhs._valid || (lhs._r1 == rhs._r1 && lhs._r2 == rhs._r2));
}
/**
* Returns true if the two instances of @c normal_distribution will
* return different sequences of values given equal generators.
*/
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(normal_distribution)
private:
RealType _mean, _sigma;
RealType _r1, _r2, _cached_rho;
bool _valid;
};
} // namespace random
using random::normal_distribution;
} // namespace boost
#endif // BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP
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