p_square_cumulative_distribution.hpp

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///////////////////////////////////////////////////////////////////////////////
// p_square_cumulative_distribution.hpp
//
//  Copyright 2005 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_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_DE_01_01_2006

#include <vector>
#include <functional>
#include <boost/parameter/keyword.hpp>
#include <boost/range.hpp>
#include <boost/mpl/placeholders.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>

namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// num_cells named parameter
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, p_square_cumulative_distribution_num_cells, num_cells)

namespace impl
{
    ///////////////////////////////////////////////////////////////////////////////
    // p_square_cumulative_distribution_impl
    //  cumulative_distribution calculation (as histogram)
    /**
        @brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm

        A histogram of the sample cumulative distribution is computed dynamically without storing samples
        based on the \f$ P^2 \f$ algorithm. The returned histogram has a specifiable amount (num_cells)
        equiprobable (and not equal-sized) cells.

        For further details, see

        R. Jain and I. Chlamtac, The P^2 algorithmus for dynamic calculation of quantiles and
        histograms without storing observations, Communications of the ACM,
        Volume 28 (October), Number 10, 1985, p. 1076-1085.

        @param p_square_cumulative_distribution_num_cells.
    */
    template<typename Sample>
    struct p_square_cumulative_distribution_impl
      : accumulator_base
    {
        typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
        typedef std::vector<float_type> array_type;
        typedef std::vector<std::pair<float_type, float_type> > histogram_type;
        // for boost::result_of
        typedef iterator_range<typename histogram_type::iterator> result_type;

        template<typename Args>
        p_square_cumulative_distribution_impl(Args const &args)
          : num_cells(args[p_square_cumulative_distribution_num_cells])
          , heights(num_cells + 1)
          , actual_positions(num_cells + 1)
          , desired_positions(num_cells + 1)
          , positions_increments(num_cells + 1)
          , histogram(num_cells + 1)
          , is_dirty(true)
        {
            std::size_t b = this->num_cells;

            for (std::size_t i = 0; i < b + 1; ++i)
            {
                this->actual_positions[i] = i + 1.;
                this->desired_positions[i] = i + 1.;
                this->positions_increments[i] = numeric::average(i, b);
            }
        }

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

            std::size_t cnt = count(args);
            std::size_t sample_cell = 1; // k
            std::size_t b = this->num_cells;

            // accumulate num_cells + 1 first samples
            if (cnt <= b + 1)
            {
                this->heights[cnt - 1] = args[sample];

                // complete the initialization of heights by sorting
                if (cnt == b + 1)
                {
                    std::sort(this->heights.begin(), this->heights.end());
                }
            }
            else
            {
                // find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
                if (args[sample] < this->heights[0])
                {
                    this->heights[0] = args[sample];
                    sample_cell = 1;
                }
                else if (this->heights[b] <= args[sample])
                {
                    this->heights[b] = args[sample];
                    sample_cell = b;
                }
                else
                {
                    typename array_type::iterator it;
                    it = std::upper_bound(
                        this->heights.begin()
                      , this->heights.end()
                      , args[sample]
                    );

                    sample_cell = std::distance(this->heights.begin(), it);
                }

                // increment positions of markers above sample_cell
                for (std::size_t i = sample_cell; i < b + 1; ++i)
                {
                    ++this->actual_positions[i];
                }

                // update desired position of markers 2 to num_cells + 1
                // (desired position of first marker is always 1)
                for (std::size_t i = 1; i < b + 1; ++i)
                {
                    this->desired_positions[i] += this->positions_increments[i];
                }

                // adjust heights of markers 2 to num_cells if necessary
                for (std::size_t i = 1; i < b; ++i)
                {
                    // offset to desire position
                    float_type d = this->desired_positions[i] - this->actual_positions[i];

                    // offset to next position
                    float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];

                    // offset to previous position
                    float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];

                    // height ds
                    float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
                    float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;

                    if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) )
                    {
                        short sign_d = static_cast<short>(d / std::abs(d));

                        // try adjusting heights[i] using p-squared formula
                        float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm );

                        if ( this->heights[i - 1] < h && h < this->heights[i + 1] )
                        {
                            this->heights[i] = h;
                        }
                        else
                        {
                            // use linear formula
                            if (d>0)
                            {
                                this->heights[i] += hp;
                            }
                            if (d<0)
                            {
                                this->heights[i] -= hm;
                            }
                        }
                        this->actual_positions[i] += sign_d;
                    }
                }
            }
        }

        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 heights[i] (x-axis of histogram) and
                // actual_positions[i] / cnt (y-axis of histogram)

                std::size_t cnt = count(args);

                for (std::size_t i = 0; i < this->histogram.size(); ++i)
                {
                    this->histogram[i] = std::make_pair(this->heights[i], numeric::average(this->actual_positions[i], cnt));
                }
            }
            //return histogram;
            return make_iterator_range(this->histogram);
        }

    private:
        std::size_t num_cells;            // number of cells b
        array_type  heights;              // q_i
        array_type  actual_positions;     // n_i
        array_type  desired_positions;    // n'_i
        array_type  positions_increments; // dn'_i
        mutable histogram_type histogram; // histogram
        mutable bool is_dirty;
    };

} // namespace detail

///////////////////////////////////////////////////////////////////////////////
// tag::p_square_cumulative_distribution
//
namespace tag
{
    struct p_square_cumulative_distribution
      : depends_on<count>
      , p_square_cumulative_distribution_num_cells
    {
        /// INTERNAL ONLY
        ///
        typedef accumulators::impl::p_square_cumulative_distribution_impl<mpl::_1> impl;
    };
}

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

using extract::p_square_cumulative_distribution;

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

template<>
struct feature_of<tag::weighted_p_square_cumulative_distribution>
  : feature_of<tag::p_square_cumulative_distribution>
{
};

}} // namespace boost::accumulators

#endif