Chris@16: /* boost random/piecewise_constant_distribution.hpp header file
Chris@16:  *
Chris@16:  * Copyright Steven Watanabe 2011
Chris@16:  * Distributed under the Boost Software License, Version 1.0. (See
Chris@16:  * accompanying file LICENSE_1_0.txt or copy at
Chris@16:  * http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  *
Chris@16:  * See http://www.boost.org for most recent version including documentation.
Chris@16:  *
Chris@101:  * $Id$
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_PIECEWISE_CONSTANT_DISTRIBUTION_HPP_INCLUDED
Chris@16: #define BOOST_RANDOM_PIECEWISE_CONSTANT_DISTRIBUTION_HPP_INCLUDED
Chris@16: 
Chris@16: #include <vector>
Chris@16: #include <numeric>
Chris@16: #include <boost/assert.hpp>
Chris@16: #include <boost/random/uniform_real.hpp>
Chris@16: #include <boost/random/discrete_distribution.hpp>
Chris@16: #include <boost/random/detail/config.hpp>
Chris@16: #include <boost/random/detail/operators.hpp>
Chris@16: #include <boost/random/detail/vector_io.hpp>
Chris@16: 
Chris@16: #ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
Chris@16: #include <initializer_list>
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/range/begin.hpp>
Chris@16: #include <boost/range/end.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace random {
Chris@16: 
Chris@16: /**
Chris@16:  * The class @c piecewise_constant_distribution models a \random_distribution.
Chris@16:  */
Chris@16: template<class RealType = double, class WeightType = double>
Chris@16: class piecewise_constant_distribution {
Chris@16: public:
Chris@16:     typedef std::size_t input_type;
Chris@16:     typedef RealType result_type;
Chris@16: 
Chris@16:     class param_type {
Chris@16:     public:
Chris@16: 
Chris@16:         typedef piecewise_constant_distribution distribution_type;
Chris@16: 
Chris@16:         /**
Chris@16:          * Constructs a @c param_type object, representing a distribution
Chris@16:          * that produces values uniformly distributed in the range [0, 1).
Chris@16:          */
Chris@16:         param_type()
Chris@16:         {
Chris@16:             _weights.push_back(WeightType(1));
Chris@16:             _intervals.push_back(RealType(0));
Chris@16:             _intervals.push_back(RealType(1));
Chris@16:         }
Chris@16:         /**
Chris@16:          * Constructs a @c param_type object from two iterator ranges
Chris@16:          * containing the interval boundaries and the interval weights.
Chris@16:          * If there are less than two boundaries, then this is equivalent to
Chris@16:          * the default constructor and creates a single interval, [0, 1).
Chris@16:          *
Chris@16:          * The values of the interval boundaries must be strictly
Chris@16:          * increasing, and the number of weights must be one less than
Chris@16:          * the number of interval boundaries.  If there are extra
Chris@16:          * weights, they are ignored.
Chris@16:          */
Chris@16:         template<class IntervalIter, class WeightIter>
Chris@16:         param_type(IntervalIter intervals_first, IntervalIter intervals_last,
Chris@16:                    WeightIter weight_first)
Chris@16:           : _intervals(intervals_first, intervals_last)
Chris@16:         {
Chris@16:             if(_intervals.size() < 2) {
Chris@16:                 _intervals.clear();
Chris@16:                 _intervals.push_back(RealType(0));
Chris@16:                 _intervals.push_back(RealType(1));
Chris@16:                 _weights.push_back(WeightType(1));
Chris@16:             } else {
Chris@16:                 _weights.reserve(_intervals.size() - 1);
Chris@16:                 for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
Chris@16:                     _weights.push_back(*weight_first++);
Chris@16:                 }
Chris@16:             }
Chris@16:         }
Chris@16: #ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
Chris@16:         /**
Chris@16:          * Constructs a @c param_type object from an
Chris@16:          * initializer_list containing the interval boundaries
Chris@16:          * and a unary function specifying the weights.  Each
Chris@16:          * weight is determined by calling the function at the
Chris@16:          * midpoint of the corresponding interval.
Chris@16:          *
Chris@16:          * If the initializer_list contains less than two elements,
Chris@16:          * this is equivalent to the default constructor and the
Chris@16:          * distribution will produce values uniformly distributed
Chris@16:          * in the range [0, 1).
Chris@16:          */
Chris@16:         template<class T, class F>
Chris@16:         param_type(const std::initializer_list<T>& il, F f)
Chris@16:           : _intervals(il.begin(), il.end())
Chris@16:         {
Chris@16:             if(_intervals.size() < 2) {
Chris@16:                 _intervals.clear();
Chris@16:                 _intervals.push_back(RealType(0));
Chris@16:                 _intervals.push_back(RealType(1));
Chris@16:                 _weights.push_back(WeightType(1));
Chris@16:             } else {
Chris@16:                 _weights.reserve(_intervals.size() - 1);
Chris@16:                 for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
Chris@16:                     RealType midpoint = (_intervals[i] + _intervals[i + 1]) / 2;
Chris@16:                     _weights.push_back(f(midpoint));
Chris@16:                 }
Chris@16:             }
Chris@16:         }
Chris@16: #endif
Chris@16:         /**
Chris@16:          * Constructs a @c param_type object from Boost.Range
Chris@16:          * ranges holding the interval boundaries and the weights.  If
Chris@16:          * there are less than two interval boundaries, this is equivalent
Chris@16:          * to the default constructor and the distribution will produce
Chris@16:          * values uniformly distributed in the range [0, 1).  The
Chris@16:          * number of weights must be one less than the number of
Chris@16:          * interval boundaries.
Chris@16:          */
Chris@16:         template<class IntervalRange, class WeightRange>
Chris@16:         param_type(const IntervalRange& intervals_arg,
Chris@16:                    const WeightRange& weights_arg)
Chris@16:           : _intervals(boost::begin(intervals_arg), boost::end(intervals_arg)),
Chris@16:             _weights(boost::begin(weights_arg), boost::end(weights_arg))
Chris@16:         {
Chris@16:             if(_intervals.size() < 2) {
Chris@16:                 _intervals.clear();
Chris@16:                 _intervals.push_back(RealType(0));
Chris@16:                 _intervals.push_back(RealType(1));
Chris@16:                 _weights.push_back(WeightType(1));
Chris@16:             }
Chris@16:         }
Chris@16: 
Chris@16:         /**
Chris@16:          * Constructs the parameters for a distribution that approximates a
Chris@16:          * function.  The range of the distribution is [xmin, xmax).  This
Chris@16:          * range is divided into nw equally sized intervals and the weights
Chris@16:          * are found by calling the unary function f on the midpoints of the
Chris@16:          * intervals.
Chris@16:          */
Chris@16:         template<class F>
Chris@16:         param_type(std::size_t nw, RealType xmin, RealType xmax, F f)
Chris@16:         {
Chris@16:             std::size_t n = (nw == 0) ? 1 : nw;
Chris@16:             double delta = (xmax - xmin) / n;
Chris@16:             BOOST_ASSERT(delta > 0);
Chris@16:             for(std::size_t k = 0; k < n; ++k) {
Chris@16:                 _weights.push_back(f(xmin + k*delta + delta/2));
Chris@16:                 _intervals.push_back(xmin + k*delta);
Chris@16:             }
Chris@16:             _intervals.push_back(xmax);
Chris@16:         }
Chris@16: 
Chris@16:         /**  Returns a vector containing the interval boundaries. */
Chris@16:         std::vector<RealType> intervals() const { return _intervals; }
Chris@16: 
Chris@16:         /**
Chris@16:          * Returns a vector containing the probability densities
Chris@16:          * over all the intervals of the distribution.
Chris@16:          */
Chris@16:         std::vector<RealType> densities() const
Chris@16:         {
Chris@16:             RealType sum = std::accumulate(_weights.begin(), _weights.end(),
Chris@16:                                              static_cast<RealType>(0));
Chris@16:             std::vector<RealType> result;
Chris@16:             result.reserve(_weights.size());
Chris@16:             for(std::size_t i = 0; i < _weights.size(); ++i) {
Chris@16:                 RealType width = _intervals[i + 1] - _intervals[i];
Chris@16:                 result.push_back(_weights[i] / (sum * width));
Chris@16:             }
Chris@16:             return result;
Chris@16:         }
Chris@16: 
Chris@16:         /** Writes the parameters to a @c std::ostream. */
Chris@16:         BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
Chris@16:         {
Chris@16:             detail::print_vector(os, parm._intervals);
Chris@16:             detail::print_vector(os, parm._weights);
Chris@16:             return os;
Chris@16:         }
Chris@16:         
Chris@16:         /** Reads the parameters from a @c std::istream. */
Chris@16:         BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
Chris@16:         {
Chris@16:             std::vector<RealType> new_intervals;
Chris@16:             std::vector<WeightType> new_weights;
Chris@16:             detail::read_vector(is, new_intervals);
Chris@16:             detail::read_vector(is, new_weights);
Chris@16:             if(is) {
Chris@16:                 parm._intervals.swap(new_intervals);
Chris@16:                 parm._weights.swap(new_weights);
Chris@16:             }
Chris@16:             return is;
Chris@16:         }
Chris@16: 
Chris@16:         /** Returns true if the two sets of parameters are the same. */
Chris@16:         BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
Chris@16:         {
Chris@16:             return lhs._intervals == rhs._intervals
Chris@16:                 && lhs._weights == rhs._weights;
Chris@16:         }
Chris@16:         /** Returns true if the two sets of parameters are different. */
Chris@16:         BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
Chris@16: 
Chris@16:     private:
Chris@16: 
Chris@16:         friend class piecewise_constant_distribution;
Chris@16: 
Chris@16:         std::vector<RealType> _intervals;
Chris@16:         std::vector<WeightType> _weights;
Chris@16:     };
Chris@16: 
Chris@16:     /**
Chris@16:      * Creates a new @c piecewise_constant_distribution with
Chris@16:      * a single interval, [0, 1).
Chris@16:      */
Chris@16:     piecewise_constant_distribution()
Chris@16:     {
Chris@16:         _intervals.push_back(RealType(0));
Chris@16:         _intervals.push_back(RealType(1));
Chris@16:     }
Chris@16:     /**
Chris@16:      * Constructs a piecewise_constant_distribution from two iterator ranges
Chris@16:      * containing the interval boundaries and the interval weights.
Chris@16:      * If there are less than two boundaries, then this is equivalent to
Chris@16:      * the default constructor and creates a single interval, [0, 1).
Chris@16:      *
Chris@16:      * The values of the interval boundaries must be strictly
Chris@16:      * increasing, and the number of weights must be one less than
Chris@16:      * the number of interval boundaries.  If there are extra
Chris@16:      * weights, they are ignored.
Chris@16:      *
Chris@16:      * For example,
Chris@16:      *
Chris@16:      * @code
Chris@16:      * double intervals[] = { 0.0, 1.0, 4.0 };
Chris@16:      * double weights[] = { 1.0, 1.0 };
Chris@16:      * piecewise_constant_distribution<> dist(
Chris@16:      *     &intervals[0], &intervals[0] + 3, &weights[0]);
Chris@16:      * @endcode
Chris@16:      *
Chris@16:      * The distribution has a 50% chance of producing a
Chris@16:      * value between 0 and 1 and a 50% chance of producing
Chris@16:      * a value between 1 and 4.
Chris@16:      */
Chris@16:     template<class IntervalIter, class WeightIter>
Chris@16:     piecewise_constant_distribution(IntervalIter first_interval,
Chris@16:                                     IntervalIter last_interval,
Chris@16:                                     WeightIter first_weight)
Chris@16:       : _intervals(first_interval, last_interval)
Chris@16:     {
Chris@16:         if(_intervals.size() < 2) {
Chris@16:             _intervals.clear();
Chris@16:             _intervals.push_back(RealType(0));
Chris@16:             _intervals.push_back(RealType(1));
Chris@16:         } else {
Chris@16:             std::vector<WeightType> actual_weights;
Chris@16:             actual_weights.reserve(_intervals.size() - 1);
Chris@16:             for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
Chris@16:                 actual_weights.push_back(*first_weight++);
Chris@16:             }
Chris@16:             typedef discrete_distribution<std::size_t, WeightType> bins_type;
Chris@16:             typename bins_type::param_type bins_param(actual_weights);
Chris@16:             _bins.param(bins_param);
Chris@16:         }
Chris@16:     }
Chris@16: #ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
Chris@16:     /**
Chris@16:      * Constructs a piecewise_constant_distribution from an
Chris@16:      * initializer_list containing the interval boundaries
Chris@16:      * and a unary function specifying the weights.  Each
Chris@16:      * weight is determined by calling the function at the
Chris@16:      * midpoint of the corresponding interval.
Chris@16:      *
Chris@16:      * If the initializer_list contains less than two elements,
Chris@16:      * this is equivalent to the default constructor and the
Chris@16:      * distribution will produce values uniformly distributed
Chris@16:      * in the range [0, 1).
Chris@16:      */
Chris@16:     template<class T, class F>
Chris@16:     piecewise_constant_distribution(std::initializer_list<T> il, F f)
Chris@16:       : _intervals(il.begin(), il.end())
Chris@16:     {
Chris@16:         if(_intervals.size() < 2) {
Chris@16:             _intervals.clear();
Chris@16:             _intervals.push_back(RealType(0));
Chris@16:             _intervals.push_back(RealType(1));
Chris@16:         } else {
Chris@16:             std::vector<WeightType> actual_weights;
Chris@16:             actual_weights.reserve(_intervals.size() - 1);
Chris@16:             for(std::size_t i = 0; i < _intervals.size() - 1; ++i) {
Chris@16:                 RealType midpoint = (_intervals[i] + _intervals[i + 1]) / 2;
Chris@16:                 actual_weights.push_back(f(midpoint));
Chris@16:             }
Chris@16:             typedef discrete_distribution<std::size_t, WeightType> bins_type;
Chris@16:             typename bins_type::param_type bins_param(actual_weights);
Chris@16:             _bins.param(bins_param);
Chris@16:         }
Chris@16:     }
Chris@16: #endif
Chris@16:     /**
Chris@16:      * Constructs a piecewise_constant_distribution from Boost.Range
Chris@16:      * ranges holding the interval boundaries and the weights.  If
Chris@16:      * there are less than two interval boundaries, this is equivalent
Chris@16:      * to the default constructor and the distribution will produce
Chris@16:      * values uniformly distributed in the range [0, 1).  The
Chris@16:      * number of weights must be one less than the number of
Chris@16:      * interval boundaries.
Chris@16:      */
Chris@16:     template<class IntervalsRange, class WeightsRange>
Chris@16:     piecewise_constant_distribution(const IntervalsRange& intervals_arg,
Chris@16:                                     const WeightsRange& weights_arg)
Chris@16:       : _bins(weights_arg),
Chris@16:         _intervals(boost::begin(intervals_arg), boost::end(intervals_arg))
Chris@16:     {
Chris@16:         if(_intervals.size() < 2) {
Chris@16:             _intervals.clear();
Chris@16:             _intervals.push_back(RealType(0));
Chris@16:             _intervals.push_back(RealType(1));
Chris@16:         }
Chris@16:     }
Chris@16:     /**
Chris@16:      * Constructs a piecewise_constant_distribution that approximates a
Chris@16:      * function.  The range of the distribution is [xmin, xmax).  This
Chris@16:      * range is divided into nw equally sized intervals and the weights
Chris@16:      * are found by calling the unary function f on the midpoints of the
Chris@16:      * intervals.
Chris@16:      */
Chris@16:     template<class F>
Chris@16:     piecewise_constant_distribution(std::size_t nw,
Chris@16:                                     RealType xmin,
Chris@16:                                     RealType xmax,
Chris@16:                                     F f)
Chris@16:       : _bins(nw, xmin, xmax, f)
Chris@16:     {
Chris@16:         if(nw == 0) { nw = 1; }
Chris@16:         RealType delta = (xmax - xmin) / nw;
Chris@16:         _intervals.reserve(nw + 1);
Chris@16:         for(std::size_t i = 0; i < nw; ++i) {
Chris@16:             _intervals.push_back(xmin + i * delta);
Chris@16:         }
Chris@16:         _intervals.push_back(xmax);
Chris@16:     }
Chris@16:     /**
Chris@16:      * Constructs a piecewise_constant_distribution from its parameters.
Chris@16:      */
Chris@16:     explicit piecewise_constant_distribution(const param_type& parm)
Chris@16:       : _bins(parm._weights),
Chris@16:         _intervals(parm._intervals)
Chris@16:     {
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns a value distributed according to the parameters of the
Chris@16:      * piecewist_constant_distribution.
Chris@16:      */
Chris@16:     template<class URNG>
Chris@16:     RealType operator()(URNG& urng) const
Chris@16:     {
Chris@16:         std::size_t i = _bins(urng);
Chris@16:         return uniform_real<RealType>(_intervals[i], _intervals[i+1])(urng);
Chris@16:     }
Chris@16:     
Chris@16:     /**
Chris@16:      * Returns a value distributed according to the parameters
Chris@16:      * specified by param.
Chris@16:      */
Chris@16:     template<class URNG>
Chris@16:     RealType operator()(URNG& urng, const param_type& parm) const
Chris@16:     {
Chris@16:         return piecewise_constant_distribution(parm)(urng);
Chris@16:     }
Chris@16:     
Chris@16:     /** Returns the smallest value that the distribution can produce. */
Chris@16:     result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const
Chris@16:     { return _intervals.front(); }
Chris@16:     /** Returns the largest value that the distribution can produce. */
Chris@16:     result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const
Chris@16:     { return _intervals.back(); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns a vector containing the probability density
Chris@16:      * over each interval.
Chris@16:      */
Chris@16:     std::vector<RealType> densities() const
Chris@16:     {
Chris@16:         std::vector<RealType> result(_bins.probabilities());
Chris@16:         for(std::size_t i = 0; i < result.size(); ++i) {
Chris@16:             result[i] /= (_intervals[i+1] - _intervals[i]);
Chris@16:         }
Chris@16:         return(result);
Chris@16:     }
Chris@16:     /**  Returns a vector containing the interval boundaries. */
Chris@16:     std::vector<RealType> intervals() const { return _intervals; }
Chris@16: 
Chris@16:     /** Returns the parameters of the distribution. */
Chris@16:     param_type param() const
Chris@16:     {
Chris@16:         return param_type(_intervals, _bins.probabilities());
Chris@16:     }
Chris@16:     /** Sets the parameters of the distribution. */
Chris@16:     void param(const param_type& parm)
Chris@16:     {
Chris@16:         std::vector<RealType> new_intervals(parm._intervals);
Chris@16:         typedef discrete_distribution<std::size_t, RealType> bins_type;
Chris@16:         typename bins_type::param_type bins_param(parm._weights);
Chris@16:         _bins.param(bins_param);
Chris@16:         _intervals.swap(new_intervals);
Chris@16:     }
Chris@16:     
Chris@16:     /**
Chris@16:      * Effects: Subsequent uses of the distribution do not depend
Chris@16:      * on values produced by any engine prior to invoking reset.
Chris@16:      */
Chris@16:     void reset() { _bins.reset(); }
Chris@16: 
Chris@16:     /** Writes a distribution to a @c std::ostream. */
Chris@16:     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(
Chris@16:         os, piecewise_constant_distribution, pcd)
Chris@16:     {
Chris@16:         os << pcd.param();
Chris@16:         return os;
Chris@16:     }
Chris@16: 
Chris@16:     /** Reads a distribution from a @c std::istream */
Chris@16:     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(
Chris@16:         is, piecewise_constant_distribution, pcd)
Chris@16:     {
Chris@16:         param_type parm;
Chris@16:         if(is >> parm) {
Chris@16:             pcd.param(parm);
Chris@16:         }
Chris@16:         return is;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns true if the two distributions will return the
Chris@16:      * same sequence of values, when passed equal generators.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(
Chris@16:         piecewise_constant_distribution, lhs,  rhs)
Chris@16:     {
Chris@16:         return lhs._bins == rhs._bins && lhs._intervals == rhs._intervals;
Chris@16:     }
Chris@16:     /**
Chris@16:      * Returns true if the two distributions may return different
Chris@16:      * sequences of values, when passed equal generators.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(piecewise_constant_distribution)
Chris@16: 
Chris@16: private:
Chris@16:     discrete_distribution<std::size_t, WeightType> _bins;
Chris@16:     std::vector<RealType> _intervals;
Chris@16: };
Chris@16: 
Chris@16: }
Chris@16: }
Chris@16: 
Chris@16: #endif