532 lines
19 KiB
C++
532 lines
19 KiB
C++
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/* boost random/piecewise_linear_distribution.hpp header file
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*
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* Copyright Steven Watanabe 2011
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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_PIECEWISE_LINEAR_DISTRIBUTION_HPP_INCLUDED
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#define BOOST_RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_HPP_INCLUDED
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#include <vector>
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#include <algorithm>
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#include <cmath>
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#include <cstdlib>
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#include <boost/assert.hpp>
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#include <boost/random/uniform_real.hpp>
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#include <boost/random/discrete_distribution.hpp>
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#include <boost/random/detail/config.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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#ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
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#include <initializer_list>
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#endif
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#include <boost/range/begin.hpp>
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#include <boost/range/end.hpp>
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namespace boost {
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namespace random {
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/**
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* The class @c piecewise_linear_distribution models a \random_distribution.
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*/
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template<class RealType = double>
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class piecewise_linear_distribution {
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public:
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typedef std::size_t input_type;
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typedef RealType result_type;
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class param_type {
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public:
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typedef piecewise_linear_distribution distribution_type;
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/**
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* Constructs a @c param_type object, representing a distribution
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* that produces values uniformly distributed in the range [0, 1).
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*/
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param_type()
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{
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_weights.push_back(RealType(1));
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_weights.push_back(RealType(1));
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_intervals.push_back(RealType(0));
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_intervals.push_back(RealType(1));
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}
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/**
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* Constructs a @c param_type object from two iterator ranges
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* containing the interval boundaries and weights at the boundaries.
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* If there are fewer than two boundaries, then this is equivalent to
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* the default constructor and the distribution will produce values
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* uniformly distributed in the range [0, 1).
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*
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* The values of the interval boundaries must be strictly
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* increasing, and the number of weights must be the same as
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* the number of interval boundaries. If there are extra
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* weights, they are ignored.
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*/
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template<class IntervalIter, class WeightIter>
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param_type(IntervalIter intervals_first, IntervalIter intervals_last,
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WeightIter weight_first)
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: _intervals(intervals_first, intervals_last)
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{
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if(_intervals.size() < 2) {
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_intervals.clear();
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_weights.push_back(RealType(1));
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_weights.push_back(RealType(1));
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_intervals.push_back(RealType(0));
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_intervals.push_back(RealType(1));
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} else {
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_weights.reserve(_intervals.size());
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for(std::size_t i = 0; i < _intervals.size(); ++i) {
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_weights.push_back(*weight_first++);
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}
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}
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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 object from an initializer_list
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* containing the interval boundaries and a unary function
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* specifying the weights at the boundaries. Each weight is
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* determined by calling the function at the corresponding point.
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*
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* If the initializer_list contains fewer than two elements,
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* this is equivalent to the default constructor and the
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* distribution will produce values uniformly distributed
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* in the range [0, 1).
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*/
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template<class T, class F>
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param_type(const std::initializer_list<T>& il, F f)
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: _intervals(il.begin(), il.end())
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{
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if(_intervals.size() < 2) {
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_intervals.clear();
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_weights.push_back(RealType(1));
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_weights.push_back(RealType(1));
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_intervals.push_back(RealType(0));
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_intervals.push_back(RealType(1));
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} else {
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_weights.reserve(_intervals.size());
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for(typename std::vector<RealType>::const_iterator
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iter = _intervals.begin(), end = _intervals.end();
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iter != end; ++iter)
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{
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_weights.push_back(f(*iter));
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}
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}
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}
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#endif
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/**
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* Constructs a @c param_type object from Boost.Range ranges holding
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* the interval boundaries and the weights at the boundaries. If
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* there are fewer than two interval boundaries, this is equivalent
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* to the default constructor and the distribution will produce
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* values uniformly distributed in the range [0, 1). The
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* number of weights must be equal to the number of
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* interval boundaries.
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*/
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template<class IntervalRange, class WeightRange>
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param_type(const IntervalRange& intervals_arg,
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const WeightRange& weights_arg)
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: _intervals(boost::begin(intervals_arg), boost::end(intervals_arg)),
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_weights(boost::begin(weights_arg), boost::end(weights_arg))
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{
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if(_intervals.size() < 2) {
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_weights.clear();
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_weights.push_back(RealType(1));
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_weights.push_back(RealType(1));
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_intervals.clear();
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_intervals.push_back(RealType(0));
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_intervals.push_back(RealType(1));
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}
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}
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/**
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* Constructs the parameters for a distribution that approximates a
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* function. The range of the distribution is [xmin, xmax). This
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* range is divided into nw equally sized intervals and the weights
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* are found by calling the unary function f on the boundaries of the
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* intervals.
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*/
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template<class F>
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param_type(std::size_t nw, RealType xmin, RealType xmax, F f)
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{
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std::size_t n = (nw == 0) ? 1 : nw;
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double delta = (xmax - xmin) / n;
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BOOST_ASSERT(delta > 0);
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for(std::size_t k = 0; k < n; ++k) {
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_weights.push_back(f(xmin + k*delta));
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_intervals.push_back(xmin + k*delta);
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}
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_weights.push_back(f(xmax));
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_intervals.push_back(xmax);
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}
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/** Returns a vector containing the interval boundaries. */
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std::vector<RealType> intervals() const { return _intervals; }
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/**
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* Returns a vector containing the probability densities
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* at all the interval boundaries.
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*/
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std::vector<RealType> densities() const
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{
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RealType sum = static_cast<RealType>(0);
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for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
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RealType width = _intervals[i + 1] - _intervals[i];
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sum += (_weights[i] + _weights[i + 1]) * width / 2;
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}
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std::vector<RealType> result;
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result.reserve(_weights.size());
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for(typename std::vector<RealType>::const_iterator
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iter = _weights.begin(), end = _weights.end();
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iter != end; ++iter)
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{
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result.push_back(*iter / sum);
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}
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return result;
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}
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/** Writes the parameters to a @c std::ostream. */
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BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
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{
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detail::print_vector(os, parm._intervals);
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detail::print_vector(os, parm._weights);
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return os;
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}
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/** Reads the parameters from a @c std::istream. */
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BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
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{
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std::vector<RealType> new_intervals;
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std::vector<RealType> new_weights;
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detail::read_vector(is, new_intervals);
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detail::read_vector(is, new_weights);
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if(is) {
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parm._intervals.swap(new_intervals);
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parm._weights.swap(new_weights);
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}
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return is;
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}
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/** Returns true if the two sets of parameters are the same. */
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BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
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{
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return lhs._intervals == rhs._intervals
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&& lhs._weights == rhs._weights;
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}
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/** Returns true if the two sets of parameters are different. */
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BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
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private:
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friend class piecewise_linear_distribution;
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std::vector<RealType> _intervals;
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std::vector<RealType> _weights;
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};
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/**
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* Creates a new @c piecewise_linear_distribution that
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* produces values uniformly distributed in the range [0, 1).
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*/
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piecewise_linear_distribution()
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{
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default_init();
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}
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/**
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* Constructs a piecewise_linear_distribution from two iterator ranges
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* containing the interval boundaries and the weights at the boundaries.
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* If there are fewer than two boundaries, then this is equivalent to
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* the default constructor and creates a distribution that
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* produces values uniformly distributed in the range [0, 1).
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*
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* The values of the interval boundaries must be strictly
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* increasing, and the number of weights must be equal to
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* the number of interval boundaries. If there are extra
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* weights, they are ignored.
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*
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* For example,
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*
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* @code
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* double intervals[] = { 0.0, 1.0, 2.0 };
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* double weights[] = { 0.0, 1.0, 0.0 };
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* piecewise_constant_distribution<> dist(
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* &intervals[0], &intervals[0] + 3, &weights[0]);
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* @endcode
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*
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* produces a triangle distribution.
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*/
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template<class IntervalIter, class WeightIter>
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piecewise_linear_distribution(IntervalIter first_interval,
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IntervalIter last_interval,
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WeightIter first_weight)
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: _intervals(first_interval, last_interval)
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{
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if(_intervals.size() < 2) {
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default_init();
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} else {
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_weights.reserve(_intervals.size());
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for(std::size_t i = 0; i < _intervals.size(); ++i) {
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_weights.push_back(*first_weight++);
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}
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init();
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}
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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 piecewise_linear_distribution from an
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* initializer_list containing the interval boundaries
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* and a unary function specifying the weights. Each
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* weight is determined by calling the function at the
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* corresponding interval boundary.
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*
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* If the initializer_list contains fewer than two elements,
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* this is equivalent to the default constructor and the
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* distribution will produce values uniformly distributed
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* in the range [0, 1).
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*/
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template<class T, class F>
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piecewise_linear_distribution(std::initializer_list<T> il, F f)
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: _intervals(il.begin(), il.end())
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{
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if(_intervals.size() < 2) {
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default_init();
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} else {
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_weights.reserve(_intervals.size());
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for(typename std::vector<RealType>::const_iterator
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iter = _intervals.begin(), end = _intervals.end();
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iter != end; ++iter)
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{
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_weights.push_back(f(*iter));
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}
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init();
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}
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}
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#endif
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/**
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* Constructs a piecewise_linear_distribution from Boost.Range
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* ranges holding the interval boundaries and the weights. If
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* there are fewer than two interval boundaries, this is equivalent
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* to the default constructor and the distribution will produce
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* values uniformly distributed in the range [0, 1). The
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* number of weights must be equal to the number of
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* interval boundaries.
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*/
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template<class IntervalsRange, class WeightsRange>
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piecewise_linear_distribution(const IntervalsRange& intervals_arg,
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const WeightsRange& weights_arg)
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: _intervals(boost::begin(intervals_arg), boost::end(intervals_arg)),
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_weights(boost::begin(weights_arg), boost::end(weights_arg))
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{
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if(_intervals.size() < 2) {
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default_init();
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} else {
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init();
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}
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}
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/**
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* Constructs a piecewise_linear_distribution that approximates a
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* function. The range of the distribution is [xmin, xmax). This
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* range is divided into nw equally sized intervals and the weights
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* are found by calling the unary function f on the interval boundaries.
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*/
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template<class F>
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piecewise_linear_distribution(std::size_t nw,
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RealType xmin,
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RealType xmax,
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F f)
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{
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if(nw == 0) { nw = 1; }
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RealType delta = (xmax - xmin) / nw;
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_intervals.reserve(nw + 1);
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for(std::size_t i = 0; i < nw; ++i) {
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RealType x = xmin + i * delta;
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_intervals.push_back(x);
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_weights.push_back(f(x));
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}
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_intervals.push_back(xmax);
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_weights.push_back(f(xmax));
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init();
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}
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/**
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* Constructs a piecewise_linear_distribution from its parameters.
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*/
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explicit piecewise_linear_distribution(const param_type& parm)
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: _intervals(parm._intervals),
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_weights(parm._weights)
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{
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init();
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}
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/**
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* Returns a value distributed according to the parameters of the
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* piecewise_linear_distribution.
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*/
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|
|
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)
|
||
|
|
{
|
||
|
|
using std::abs;
|
||
|
|
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(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
|