accumulators/statistics/density.hpp

///////////////////////////////////////////////////////////////////////////////
// density.hpp
//
//  Copyright 2006 Daniel Egloff, Olivier Gygi. 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)

#ifndef BOOST_ACCUMULATORS_STATISTICS_DENSITY_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_DENSITY_HPP_DE_01_01_2006

#include <vector>
#include <limits>
#include <functional>
#include <boost/range.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/max.hpp>
#include <boost/accumulators/statistics/min.hpp>

namespace boost { namespace accumulators
{

///////////////////////////////////////////////////////////////////////////////
// cache_size and num_bins named parameters
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, density_cache_size, cache_size)
BOOST_PARAMETER_NESTED_KEYWORD(tag, density_num_bins, num_bins)

BOOST_ACCUMULATORS_IGNORE_GLOBAL(density_cache_size)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(density_num_bins)

namespace impl
{
    ///////////////////////////////////////////////////////////////////////////////
    // density_impl
    //  density histogram
    /**
        @brief Histogram density estimator

        The histogram density estimator returns a histogram of the sample distribution. The positions and sizes of the bins
        are determined using a specifiable number of cached samples (cache_size). The range between the minimum and the
        maximum of the cached samples is subdivided into a specifiable number of bins (num_bins) of same size. Additionally,
        an under- and an overflow bin is added to capture future under- and overflow samples. Once the bins are determined,
        the cached samples and all subsequent samples are added to the correct bins. At the end, a range of std::pair is
        return, where each pair contains the position of the bin (lower bound) and the samples count (normalized with the
        total number of samples).

        @param  density_cache_size Number of first samples used to determine min and max.
        @param  density_num_bins Number of bins (two additional bins collect under- and overflow samples).
    */
    template<typename Sample>
    struct density_impl
      : accumulator_base
    {
        typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
        typedef std::vector<std::pair<float_type, float_type> > histogram_type;
        typedef std::vector<float_type> array_type;
        // for boost::result_of
        typedef iterator_range<typename histogram_type::iterator> result_type;

        template<typename Args>
        density_impl(Args const &args)
            : cache_size(args[density_cache_size])
            , cache(cache_size)
            , num_bins(args[density_num_bins])
            , samples_in_bin(num_bins + 2, 0.)
            , bin_positions(num_bins + 2)
            , histogram(
                num_bins + 2
              , std::make_pair(
                    numeric::fdiv(args[sample | Sample()],(std::size_t)1)
                  , numeric::fdiv(args[sample | Sample()],(std::size_t)1)
                )
              )
            , is_dirty(true)
        {
        }

        template<typename Args>
        void operator ()(Args const &args)
        {
            this->is_dirty = true;

            std::size_t cnt = count(args);

            // Fill up cache with cache_size first samples
            if (cnt <= this->cache_size)
            {
                this->cache[cnt - 1] = args[sample];
            }

            // Once cache_size samples have been accumulated, create num_bins bins of same size between
            // the minimum and maximum of the cached samples as well as under and overflow bins.
            // Store their lower bounds (bin_positions) and fill the bins with the cached samples (samples_in_bin).
            if (cnt == this->cache_size)
            {
                float_type minimum = numeric::fdiv((min)(args), (std::size_t)1);
                float_type maximum = numeric::fdiv((max)(args), (std::size_t)1);
                float_type bin_size = numeric::fdiv(maximum - minimum, this->num_bins );

                // determine bin positions (their lower bounds)
                for (std::size_t i = 0; i < this->num_bins + 2; ++i)
                {
                    this->bin_positions[i] = minimum + (i - 1.) * bin_size;
                }

                for (typename array_type::const_iterator iter = this->cache.begin(); iter != this->cache.end(); ++iter)
                {
                    if (*iter < this->bin_positions[1])
                    {
                        ++(this->samples_in_bin[0]);
                    }
                    else if (*iter >= this->bin_positions[this->num_bins + 1])
                    {
                        ++(this->samples_in_bin[this->num_bins + 1]);
                    }
                    else
                    {
                        typename array_type::iterator it = std::upper_bound(
                            this->bin_positions.begin()
                          , this->bin_positions.end()
                          , *iter
                        );

                        std::size_t d = std::distance(this->bin_positions.begin(), it);
                        ++(this->samples_in_bin[d - 1]);
                    }
                }
            }
            // Add each subsequent sample to the correct bin
            else if (cnt > this->cache_size)
            {
                if (args[sample] < this->bin_positions[1])
                {
                    ++(this->samples_in_bin[0]);
                }
                else if (args[sample] >= this->bin_positions[this->num_bins + 1])
                {
                    ++(this->samples_in_bin[this->num_bins + 1]);
                }
                else
                {
                    typename array_type::iterator it = std::upper_bound(
                        this->bin_positions.begin()
                      , this->bin_positions.end()
                      , args[sample]
                    );

                    std::size_t d = std::distance(this->bin_positions.begin(), it);
                    ++(this->samples_in_bin[d - 1]);
                }
            }
        }

        /**
            @pre The number of samples must meet or exceed the cache size
        */
        template<typename Args>
        result_type result(Args const &args) const
        {
            if (this->is_dirty)
            {
                this->is_dirty = false;

                // creates a vector of std::pair where each pair i holds
                // the values bin_positions[i] (x-axis of histogram) and
                // samples_in_bin[i] / cnt (y-axis of histogram).

                for (std::size_t i = 0; i < this->num_bins + 2; ++i)
                {
                    this->histogram[i] = std::make_pair(this->bin_positions[i], numeric::fdiv(this->samples_in_bin[i], count(args)));
                }
            }
            // returns a range of pairs
            return make_iterator_range(this->histogram);
        }

    private:
        std::size_t            cache_size;      // number of cached samples
        array_type             cache;           // cache to store the first cache_size samples
        std::size_t            num_bins;        // number of bins
        array_type             samples_in_bin;  // number of samples in each bin
        array_type             bin_positions;   // lower bounds of bins
        mutable histogram_type histogram;       // histogram
        mutable bool is_dirty;
    };

} // namespace impl

///////////////////////////////////////////////////////////////////////////////
// tag::density
//
namespace tag
{
    struct density
      : depends_on<count, min, max>
      , density_cache_size
      , density_num_bins
    {
        /// INTERNAL ONLY
        ///
        typedef accumulators::impl::density_impl<mpl::_1> impl;

        #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
        /// tag::density::cache_size named parameter
        /// tag::density::num_bins named parameter
        static boost::parameter::keyword<density_cache_size> const cache_size;
        static boost::parameter::keyword<density_num_bins> const num_bins;
        #endif
    };
}

///////////////////////////////////////////////////////////////////////////////
// extract::density
//
namespace extract
{
    extractor<tag::density> const density = {};

    BOOST_ACCUMULATORS_IGNORE_GLOBAL(density)
}

using extract::density;

// So that density can be automatically substituted
// with weighted_density when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::density>
{
    typedef tag::weighted_density type;
};

template<>
struct feature_of<tag::weighted_density>
  : feature_of<tag::density>
{
};

}} // namespace boost::accumulators

#endif