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/usr/include/boost/accumulators/statistics/

/usr/include/boost/accumulators/statistics

Name	Size	Mode	Actions
parameters/	-	0755	rm
variates/	-	0755	rm
count.hpp	2013	0644	edit dl rm
covariance.hpp	7137	0644	edit dl rm
density.hpp	10007	0644	edit dl rm
error_of.hpp	2588	0644	edit dl rm
error_of_mean.hpp	2193	0644	edit dl rm
extended_p_square.hpp	11633	0644	edit dl rm
extended_p_square_quantile.hpp	12522	0644	edit dl rm
kurtosis.hpp	3864	0644	edit dl rm
max.hpp	2294	0644	edit dl rm
mean.hpp	9334	0644	edit dl rm
median.hpp	10242	0644	edit dl rm
min.hpp	2294	0644	edit dl rm
moment.hpp	3436	0644	edit dl rm
peaks_over_threshold.hpp	17525	0644	edit dl rm
pot_quantile.hpp	7336	0644	edit dl rm
pot_tail_mean.hpp	7802	0644	edit dl rm
p_square_cumulative_distribution.hpp	955	0644	edit dl rm
p_square_cumul_dist.hpp	10365	0644	edit dl rm
p_square_quantile.hpp	10086	0644	edit dl rm
rolling_count.hpp	2574	0644	edit dl rm
rolling_mean.hpp	6753	0644	edit dl rm
rolling_moment.hpp	3741	0644	edit dl rm
rolling_sum.hpp	2871	0644	edit dl rm
rolling_variance.hpp	9486	0644	edit dl rm
rolling_window.hpp	7254	0644	edit dl rm
skewness.hpp	3691	0644	edit dl rm
stats.hpp	972	0644	edit dl rm
sum.hpp	3884	0644	edit dl rm
sum_kahan.hpp	5104	0644	edit dl rm
tail.hpp	11012	0644	edit dl rm
tail_mean.hpp	9158	0644	edit dl rm
tail_quantile.hpp	5535	0644	edit dl rm
tail_variate.hpp	4504	0644	edit dl rm
tail_variate_means.hpp	10463	0644	edit dl rm
times2_iterator.hpp	1965	0644	edit dl rm
variance.hpp	7522	0644	edit dl rm
weighted_covariance.hpp	5244	0644	edit dl rm
weighted_density.hpp	9518	0644	edit dl rm
weighted_extended_p_square.hpp	12842	0644	edit dl rm
weighted_kurtosis.hpp	4147	0644	edit dl rm
weighted_mean.hpp	6637	0644	edit dl rm
weighted_median.hpp	8667	0644	edit dl rm
weighted_moment.hpp	3384	0644	edit dl rm
weighted_peaks_over_threshold.hpp	12352	0644	edit dl rm
weighted_p_square_cumulative_distribution.hpp	1009	0644	edit dl rm
weighted_p_square_cumul_dist.hpp	11058	0644	edit dl rm
weighted_p_square_quantile.hpp	11110	0644	edit dl rm
weighted_skewness.hpp	3844	0644	edit dl rm
weighted_sum.hpp	3639	0644	edit dl rm
weighted_sum_kahan.hpp	4559	0644	edit dl rm
weighted_tail_mean.hpp	5788	0644	edit dl rm
weighted_tail_quantile.hpp	5135	0644	edit dl rm
weighted_tail_variate_means.hpp	10052	0644	edit dl rm
weighted_variance.hpp	6774	0644	edit dl rm
with_error.hpp	1277	0644	edit dl rm

Edit: /usr/include/boost/accumulators/statistics/p_square_quantile.hpp (10086B)

///////////////////////////////////////////////////////////////////////////////
// p_square_quantile.hpp
//
//  Copyright 2005 Daniel Egloff. 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_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_QUANTILE_HPP_DE_01_01_2006

#include <cmath>
#include <functional>
#include <boost/array.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/parameter/keyword.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/parameters/quantile_probability.hpp>
#include <boost/serialization/boost_array.hpp>

namespace boost { namespace accumulators
{

namespace impl
{
    ///////////////////////////////////////////////////////////////////////////////
    // p_square_quantile_impl
    //  single quantile estimation
    /**
        @brief Single quantile estimation with the \f$P^2\f$ algorithm

The \f$P^2\f$ algorithm estimates a quantile dynamically without storing samples. Instead of
        storing the whole sample cumulative distribution, only five points (markers) are stored. The heights
        of these markers are the minimum and the maximum of the samples and the current estimates of the
        \f$(p/2)\f$-, \f$p\f$- and \f$(1+p)/2\f$-quantiles. Their positions are equal to the number
        of samples that are smaller or equal to the markers. Each time a new samples is recorded, the
        positions of the markers are updated and if necessary their heights are adjusted using a piecewise-
        parabolic formula.

For further details, see

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

@param quantile_probability
    */
    template<typename Sample, typename Impl>
    struct p_square_quantile_impl
      : accumulator_base
    {
        typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
        typedef array<float_type, 5> array_type;
        // for boost::result_of
        typedef float_type result_type;

template<typename Args>
        p_square_quantile_impl(Args const &args)
          : p(is_same<Impl, for_median>::value ? float_type(0.5) : args[quantile_probability | float_type(0.5)])
          , heights()
          , actual_positions()
          , desired_positions()
          , positions_increments()
        {
            for(std::size_t i = 0; i < 5; ++i)
            {
                this->actual_positions[i] = i + float_type(1.);
            }

this->desired_positions[0] = float_type(1.);
            this->desired_positions[1] = float_type(1.) + float_type(2.) * this->p;
            this->desired_positions[2] = float_type(1.) + float_type(4.) * this->p;
            this->desired_positions[3] = float_type(3.) + float_type(2.) * this->p;
            this->desired_positions[4] = float_type(5.);

this->positions_increments[0] = float_type(0.);
            this->positions_increments[1] = this->p / float_type(2.);
            this->positions_increments[2] = this->p;
            this->positions_increments[3] = (float_type(1.) + this->p) / float_type(2.);
            this->positions_increments[4] = float_type(1.);
        }

template<typename Args>
        void operator ()(Args const &args)
        {
            std::size_t cnt = count(args);

// accumulate 5 first samples
            if(cnt <= 5)
            {
                this->heights[cnt - 1] = args[sample];

// complete the initialization of heights by sorting
                if(cnt == 5)
                {
                    std::sort(this->heights.begin(), this->heights.end());
                }
            }
            else
            {
                std::size_t sample_cell = 1; // k

// 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[4] <= args[sample])
                {
                    this->heights[4] = args[sample];
                    sample_cell = 4;
                }
                else
                {
                    typedef typename array_type::iterator iterator;
                    iterator it = std::upper_bound(
                        this->heights.begin()
                      , this->heights.end()
                      , args[sample]
                    );

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

// update positions of markers above sample_cell
                for(std::size_t i = sample_cell; i < 5; ++i)
                {
                    ++this->actual_positions[i];
                }

// update desired positions of all markers
                for(std::size_t i = 0; i < 5; ++i)
                {
                    this->desired_positions[i] += this->positions_increments[i];
                }

// adjust heights and actual positions of markers 1 to 3 if necessary
                for(std::size_t i = 1; i <= 3; ++i)
                {
                    // offset to desired positions
                    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 >= float_type(1.) && dp > float_type(1.)) || (d <= float_type(-1.) && dm < float_type(-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 > float_type(0))
                            {
                                this->heights[i] += hp;
                            }
                            if(d < float_type(0))
                            {
                                this->heights[i] -= hm;
                            }
                        }
                        this->actual_positions[i] += sign_d;
                    }
                }
            }
        }

result_type result(dont_care) const
        {
            return this->heights[2];
        }

// make this accumulator serializeable
        // TODO: do we need to split to load/save and verify that P did not change?
        template<class Archive>
        void serialize(Archive & ar, const unsigned int file_version)
        { 
            ar & p;
            ar & heights;
            ar & actual_positions;
            ar & desired_positions;
            ar & positions_increments;
        }

private:
        float_type p;                    // the quantile probability p
        array_type heights;              // q_i
        array_type actual_positions;     // n_i
        array_type desired_positions;    // n'_i
        array_type positions_increments; // dn'_i
    };

} // namespace detail

///////////////////////////////////////////////////////////////////////////////
// tag::p_square_quantile
//
namespace tag
{
    struct p_square_quantile
      : depends_on<count>
    {
        /// INTERNAL ONLY
        ///
        typedef accumulators::impl::p_square_quantile_impl<mpl::_1, regular> impl;
    };
    struct p_square_quantile_for_median
      : depends_on<count>
    {
        /// INTERNAL ONLY
        ///
        typedef accumulators::impl::p_square_quantile_impl<mpl::_1, for_median> impl;
    };
}

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

BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile)
    BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile_for_median)
}

using extract::p_square_quantile;
using extract::p_square_quantile_for_median;

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

template<>
struct feature_of<tag::weighted_p_square_quantile>
  : feature_of<tag::p_square_quantile>
{
};

}} // namespace boost::accumulators

#endif

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