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 /* boost random/piecewise_linear_distribution.hpp header file
  *
  * 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.
  *
  * $Id$
  */
 
 #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_CXX11_HDR_INITIALIZER_LIST
 #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_CXX11_HDR_INITIALIZER_LIST
         /**
          * 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_CXX11_HDR_INITIALIZER_LIST
     /**
      * 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)
     {
         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

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