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*
* Copyright Steven Watanabe 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: piecewise_linear_distribution.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
*/
#ifndef BOOST_RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_HPP_INCLUDED
#define BOOST_RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_HPP_INCLUDED
#include <vector>
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <boost/assert.hpp>
#include <boost/random/uniform_real.hpp>
#include <boost/random/discrete_distribution.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/operators.hpp>
#include <boost/random/detail/vector_io.hpp>
#ifndef BOOST_NO_INITIALIZER_LISTS
#include <initializer_list>
#endif
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost {
namespace random {
/**
* The class @c piecewise_linear_distribution models a \random_distribution.
*/
template<class RealType = double>
class piecewise_linear_distribution {
public:
typedef std::size_t input_type;
typedef RealType result_type;
class param_type {
public:
typedef piecewise_linear_distribution distribution_type;
/**
* Constructs a @c param_type object, representing a distribution
* that produces values uniformly distributed in the range [0, 1).
*/
param_type()
{
_weights.push_back(RealType(1));
_weights.push_back(RealType(1));
_intervals.push_back(RealType(0));
_intervals.push_back(RealType(1));
}
/**
* Constructs a @c param_type object from two iterator ranges
* containing the interval boundaries and weights at the boundaries.
* If there are fewer than two boundaries, then this is equivalent to
* the default constructor and the distribution will produce values
* uniformly distributed in the range [0, 1).
*
* The values of the interval boundaries must be strictly
* increasing, and the number of weights must be the same as
* the number of interval boundaries. If there are extra
* weights, they are ignored.
*/
template<class IntervalIter, class WeightIter>
param_type(IntervalIter intervals_first, IntervalIter intervals_last,
WeightIter weight_first)
: _intervals(intervals_first, intervals_last)
{
if(_intervals.size() < 2) {
_intervals.clear();
_weights.push_back(RealType(1));
_weights.push_back(RealType(1));
_intervals.push_back(RealType(0));
_intervals.push_back(RealType(1));
} else {
_weights.reserve(_intervals.size());
for(std::size_t i = 0; i < _intervals.size(); ++i) {
_weights.push_back(*weight_first++);
}
}
}
#ifndef BOOST_NO_INITIALIZER_LISTS
/**
* Constructs a @c param_type object from an initializer_list
* containing the interval boundaries and a unary function
* specifying the weights at the boundaries. Each weight is
* determined by calling the function at the corresponding point.
*
* If the initializer_list contains fewer than two elements,
* this is equivalent to the default constructor and the
* distribution will produce values uniformly distributed
* in the range [0, 1).
*/
template<class T, class F>
param_type(const std::initializer_list<T>& il, F f)
: _intervals(il.begin(), il.end())
{
if(_intervals.size() < 2) {
_intervals.clear();
_weights.push_back(RealType(1));
_weights.push_back(RealType(1));
_intervals.push_back(RealType(0));
_intervals.push_back(RealType(1));
} else {
_weights.reserve(_intervals.size());
for(typename std::vector<RealType>::const_iterator
iter = _intervals.begin(), end = _intervals.end();
iter != end; ++iter)
{
_weights.push_back(f(*iter));
}
}
}
#endif
/**
* Constructs a @c param_type object from Boost.Range ranges holding
* the interval boundaries and the weights at the boundaries. If
* there are fewer than two interval boundaries, this is equivalent
* to the default constructor and the distribution will produce
* values uniformly distributed in the range [0, 1). The
* number of weights must be equal to the number of
* interval boundaries.
*/
template<class IntervalRange, class WeightRange>
param_type(const IntervalRange& intervals_arg,
const WeightRange& weights_arg)
: _intervals(boost::begin(intervals_arg), boost::end(intervals_arg)),
_weights(boost::begin(weights_arg), boost::end(weights_arg))
{
if(_intervals.size() < 2) {
_weights.clear();
_weights.push_back(RealType(1));
_weights.push_back(RealType(1));
_intervals.clear();
_intervals.push_back(RealType(0));
_intervals.push_back(RealType(1));
}
}
/**
* Constructs the parameters for a distribution that approximates a
* function. The range of the distribution is [xmin, xmax). This
* range is divided into nw equally sized intervals and the weights
* are found by calling the unary function f on the boundaries of the
* intervals.
*/
template<class F>
param_type(std::size_t nw, RealType xmin, RealType xmax, F f)
{
std::size_t n = (nw == 0) ? 1 : nw;
double delta = (xmax - xmin) / n;
BOOST_ASSERT(delta > 0);
for(std::size_t k = 0; k < n; ++k) {
_weights.push_back(f(xmin + k*delta));
_intervals.push_back(xmin + k*delta);
}
_weights.push_back(f(xmax));
_intervals.push_back(xmax);
}
/** Returns a vector containing the interval boundaries. */
std::vector<RealType> intervals() const { return _intervals; }
/**
* Returns a vector containing the probability densities
* at all the interval boundaries.
*/
std::vector<RealType> densities() const
{
RealType sum = static_cast<RealType>(0);
for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
RealType width = _intervals[i + 1] - _intervals[i];
sum += (_weights[i] + _weights[i + 1]) * width / 2;
}
std::vector<RealType> result;
result.reserve(_weights.size());
for(typename std::vector<RealType>::const_iterator
iter = _weights.begin(), end = _weights.end();
iter != end; ++iter)
{
result.push_back(*iter / sum);
}
return result;
}
/** Writes the parameters to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
{
detail::print_vector(os, parm._intervals);
detail::print_vector(os, parm._weights);
return os;
}
/** Reads the parameters from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
{
std::vector<RealType> new_intervals;
std::vector<RealType> new_weights;
detail::read_vector(is, new_intervals);
detail::read_vector(is, new_weights);
if(is) {
parm._intervals.swap(new_intervals);
parm._weights.swap(new_weights);
}
return is;
}
/** Returns true if the two sets of parameters are the same. */
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
{
return lhs._intervals == rhs._intervals
&& lhs._weights == rhs._weights;
}
/** Returns true if the two sets of parameters are different. */
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
private:
friend class piecewise_linear_distribution;
std::vector<RealType> _intervals;
std::vector<RealType> _weights;
};
/**
* Creates a new @c piecewise_linear_distribution that
* produces values uniformly distributed in the range [0, 1).
*/
piecewise_linear_distribution()
{
default_init();
}
/**
* Constructs a piecewise_linear_distribution from two iterator ranges
* containing the interval boundaries and the weights at the boundaries.
* If there are fewer than two boundaries, then this is equivalent to
* the default constructor and creates a distribution that
* produces values uniformly distributed in the range [0, 1).
*
* The values of the interval boundaries must be strictly
* increasing, and the number of weights must be equal to
* the number of interval boundaries. If there are extra
* weights, they are ignored.
*
* For example,
*
* @code
* double intervals[] = { 0.0, 1.0, 2.0 };
* double weights[] = { 0.0, 1.0, 0.0 };
* piecewise_constant_distribution<> dist(
* &intervals[0], &intervals[0] + 3, &weights[0]);
* @endcode
*
* produces a triangle distribution.
*/
template<class IntervalIter, class WeightIter>
piecewise_linear_distribution(IntervalIter first_interval,
IntervalIter last_interval,
WeightIter first_weight)
: _intervals(first_interval, last_interval)
{
if(_intervals.size() < 2) {
default_init();
} else {
_weights.reserve(_intervals.size());
for(std::size_t i = 0; i < _intervals.size(); ++i) {
_weights.push_back(*first_weight++);
}
init();
}
}
#ifndef BOOST_NO_INITIALIZER_LISTS
/**
* Constructs a piecewise_linear_distribution from an
* initializer_list containing the interval boundaries
* and a unary function specifying the weights. Each
* weight is determined by calling the function at the
* corresponding interval boundary.
*
* If the initializer_list contains fewer than two elements,
* this is equivalent to the default constructor and the
* distribution will produce values uniformly distributed
* in the range [0, 1).
*/
template<class T, class F>
piecewise_linear_distribution(std::initializer_list<T> il, F f)
: _intervals(il.begin(), il.end())
{
if(_intervals.size() < 2) {
default_init();
} else {
_weights.reserve(_intervals.size());
for(typename std::vector<RealType>::const_iterator
iter = _intervals.begin(), end = _intervals.end();
iter != end; ++iter)
{
_weights.push_back(f(*iter));
}
init();
}
}
#endif
/**
* Constructs a piecewise_linear_distribution from Boost.Range
* ranges holding the interval boundaries and the weights. If
* there are fewer than two interval boundaries, this is equivalent
* to the default constructor and the distribution will produce
* values uniformly distributed in the range [0, 1). The
* number of weights must be equal to the number of
* interval boundaries.
*/
template<class IntervalsRange, class WeightsRange>
piecewise_linear_distribution(const IntervalsRange& intervals_arg,
const WeightsRange& weights_arg)
: _intervals(boost::begin(intervals_arg), boost::end(intervals_arg)),
_weights(boost::begin(weights_arg), boost::end(weights_arg))
{
if(_intervals.size() < 2) {
default_init();
} else {
init();
}
}
/**
* Constructs a piecewise_linear_distribution that approximates a
* function. The range of the distribution is [xmin, xmax). This
* range is divided into nw equally sized intervals and the weights
* are found by calling the unary function f on the interval boundaries.
*/
template<class F>
piecewise_linear_distribution(std::size_t nw,
RealType xmin,
RealType xmax,
F f)
{
if(nw == 0) { nw = 1; }
RealType delta = (xmax - xmin) / nw;
_intervals.reserve(nw + 1);
for(std::size_t i = 0; i < nw; ++i) {
RealType x = xmin + i * delta;
_intervals.push_back(x);
_weights.push_back(f(x));
}
_intervals.push_back(xmax);
_weights.push_back(f(xmax));
init();
}
/**
* Constructs a piecewise_linear_distribution from its parameters.
*/
explicit piecewise_linear_distribution(const param_type& parm)
: _intervals(parm._intervals),
_weights(parm._weights)
{
init();
}
/**
* Returns a value distributed according to the parameters of the
* piecewise_linear_distribution.
*/
template<class URNG>
RealType operator()(URNG& urng) const
{
std::size_t i = _bins(urng);
bool is_in_rectangle = (i % 2 == 0);
i = i / 2;
uniform_real<RealType> dist(_intervals[i], _intervals[i+1]);
if(is_in_rectangle) {
return dist(urng);
} else if(_weights[i] < _weights[i+1]) {
return (std::max)(dist(urng), dist(urng));
} else {
return (std::min)(dist(urng), dist(urng));
}
}
/**
* Returns a value distributed according to the parameters
* specified by param.
*/
template<class URNG>
RealType operator()(URNG& urng, const param_type& parm) const
{
return piecewise_linear_distribution(parm)(urng);
}
/** Returns the smallest value that the distribution can produce. */
result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const
{ return _intervals.front(); }
/** Returns the largest value that the distribution can produce. */
result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const
{ return _intervals.back(); }
/**
* Returns a vector containing the probability densities
* at the interval boundaries.
*/
std::vector<RealType> densities() const
{
RealType sum = static_cast<RealType>(0);
for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
RealType width = _intervals[i + 1] - _intervals[i];
sum += (_weights[i] + _weights[i + 1]) * width / 2;
}
std::vector<RealType> result;
result.reserve(_weights.size());
for(typename std::vector<RealType>::const_iterator
iter = _weights.begin(), end = _weights.end();
iter != end; ++iter)
{
result.push_back(*iter / sum);
}
return result;
}
/** Returns a vector containing the interval boundaries. */
std::vector<RealType> intervals() const { return _intervals; }
/** Returns the parameters of the distribution. */
param_type param() const
{
return param_type(_intervals, _weights);
}
/** Sets the parameters of the distribution. */
void param(const param_type& parm)
{
std::vector<RealType> new_intervals(parm._intervals);
std::vector<RealType> new_weights(parm._weights);
init(new_intervals, new_weights);
_intervals.swap(new_intervals);
_weights.swap(new_weights);
}
/**
* Effects: Subsequent uses of the distribution do not depend
* on values produced by any engine prior to invoking reset.
*/
void reset() { _bins.reset(); }
/** Writes a distribution to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(
os, piecewise_linear_distribution, pld)
{
os << pld.param();
return os;
}
/** Reads a distribution from a @c std::istream */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(
is, piecewise_linear_distribution, pld)
{
param_type parm;
if(is >> parm) {
pld.param(parm);
}
return is;
}
/**
* Returns true if the two distributions will return the
* same sequence of values, when passed equal generators.
*/
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(
piecewise_linear_distribution, lhs, rhs)
{
return lhs._intervals == rhs._intervals && lhs._weights == rhs._weights;
}
/**
* Returns true if the two distributions may return different
* sequences of values, when passed equal generators.
*/
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(piecewise_linear_distribution)
private:
/// @cond \show_private
void init(const std::vector<RealType>& intervals_arg,
const std::vector<RealType>& weights_arg)
{
std::vector<RealType> bin_weights;
bin_weights.reserve((intervals_arg.size() - 1) * 2);
for(std::size_t i = 0; i < intervals_arg.size() - 1; ++i) {
RealType width = intervals_arg[i + 1] - intervals_arg[i];
RealType w1 = weights_arg[i];
RealType w2 = weights_arg[i + 1];
bin_weights.push_back((std::min)(w1, w2) * width);
bin_weights.push_back(std::abs(w1 - w2) * width / 2);
}
typedef discrete_distribution<std::size_t, RealType> bins_type;
typename bins_type::param_type bins_param(bin_weights);
_bins.param(bins_param);
}
void init()
{
init(_intervals, _weights);
}
void default_init()
{
_intervals.clear();
_intervals.push_back(RealType(0));
_intervals.push_back(RealType(1));
_weights.clear();
_weights.push_back(RealType(1));
_weights.push_back(RealType(1));
init();
}
discrete_distribution<std::size_t, RealType> _bins;
std::vector<RealType> _intervals;
std::vector<RealType> _weights;
/// @endcond
};
}
}
#endif
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