FM / statistics

/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/extended_p_square.hpp (11633B)

///////////////////////////////////////////////////////////////////////////////
// extended_p_square.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_EXTENDED_SINGLE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_HPP_DE_01_01_2006

#include <vector>
#include <functional>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/accumulators_fwd.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/times2_iterator.hpp>
#include <boost/serialization/vector.hpp>

namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// probabilities named parameter
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, extended_p_square_probabilities, probabilities)

BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_probabilities)

namespace impl
{
    ///////////////////////////////////////////////////////////////////////////////
    // extended_p_square_impl
    //  multiple quantile estimation
    /**
        @brief Multiple quantile estimation with the extended \f$P^2\f$ algorithm

Extended \f$P^2\f$ algorithm for estimation of several quantiles without storing samples.
        Assume that \f$m\f$ quantiles \f$\xi_{p_1}, \ldots, \xi_{p_m}\f$ are to be estimated.
        Instead of storing the whole sample cumulative distribution, the algorithm maintains only
        \f$m+2\f$ principal markers and \f$m+1\f$ middle markers, whose positions are updated
        with each sample and whose heights are adjusted (if necessary) using a piecewise-parablic
        formula. The heights of these central markers are the current estimates of the quantiles
        and returned as an iterator range.

For further details, see

K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49,
        Number 4 (October), 1986, p. 159-164.

The extended \f$ P^2 \f$ algorithm generalizes the \f$ P^2 \f$ algorithm of

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 extended_p_square_probabilities A vector of quantile probabilities.
    */
    template<typename Sample>
    struct extended_p_square_impl
      : accumulator_base
    {
        typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
        typedef std::vector<float_type> array_type;
        // for boost::result_of
        typedef iterator_range<
            detail::lvalue_index_iterator<
                permutation_iterator<
                    typename array_type::const_iterator
                  , detail::times2_iterator
                >
            >
        > result_type;

template<typename Args>
        extended_p_square_impl(Args const &args)
          : probabilities(
                boost::begin(args[extended_p_square_probabilities])
              , boost::end(args[extended_p_square_probabilities])
            )
          , heights(2 * probabilities.size() + 3)
          , actual_positions(heights.size())
          , desired_positions(heights.size())
          , positions_increments(heights.size())
        {
            std::size_t num_quantiles = this->probabilities.size();
            std::size_t num_markers = this->heights.size();

for(std::size_t i = 0; i < num_markers; ++i)
            {
                this->actual_positions[i] = i + 1;
            }

this->positions_increments[0] = 0.;
            this->positions_increments[num_markers - 1] = 1.;

for(std::size_t i = 0; i < num_quantiles; ++i)
            {
                this->positions_increments[2 * i + 2] = probabilities[i];
            }

for(std::size_t i = 0; i <= num_quantiles; ++i)
            {
                this->positions_increments[2 * i + 1] =
                    0.5 * (this->positions_increments[2 * i] + this->positions_increments[2 * i + 2]);
            }

for(std::size_t i = 0; i < num_markers; ++i)
            {
                this->desired_positions[i] = 1. + 2. * (num_quantiles + 1.) * this->positions_increments[i];
            }
        }

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

// m+2 principal markers and m+1 middle markers
            std::size_t num_markers = 2 * this->probabilities.size() + 3;

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

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

// find cell k = sample_cell such that heights[k-1] <= sample < heights[k]
                if(args[sample] < this->heights[0])
                {
                    this->heights[0] = args[sample];
                    sample_cell = 1;
                }
                else if(args[sample] >= this->heights[num_markers - 1])
                {
                    this->heights[num_markers - 1] = args[sample];
                    sample_cell = num_markers - 1;
                }
                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 actual positions of all markers above sample_cell index
                for(std::size_t i = sample_cell; i < num_markers; ++i)
                {
                    ++this->actual_positions[i];
                }

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

// adjust heights and actual positions of markers 1 to num_markers-2 if necessary
                for(std::size_t i = 1; i <= num_markers - 2; ++i)
                {
                    // offset to desired 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));

float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm)*hp
                                     + (dp - sign_d) * hm);

// try adjusting heights[i] using p-squared formula
                        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;
                    }
                }
            }
        }

result_type result(dont_care) const
        {
            // for i in [1,probabilities.size()], return heights[i * 2]
            detail::times2_iterator idx_begin = detail::make_times2_iterator(1);
            detail::times2_iterator idx_end = detail::make_times2_iterator(this->probabilities.size() + 1);

return result_type(
                make_permutation_iterator(this->heights.begin(), idx_begin)
              , make_permutation_iterator(this->heights.begin(), idx_end)
            );
        }

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

private:
        array_type probabilities;         // the quantile probabilities
        array_type heights;               // q_i
        array_type actual_positions;      // n_i
        array_type desired_positions;     // d_i
        array_type positions_increments;  // f_i
    };

} // namespace impl

///////////////////////////////////////////////////////////////////////////////
// tag::extended_p_square
//
namespace tag
{
    struct extended_p_square
      : depends_on<count>
      , extended_p_square_probabilities
    {
        typedef accumulators::impl::extended_p_square_impl<mpl::_1> impl;

#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
        /// tag::extended_p_square::probabilities named parameter
        static boost::parameter::keyword<tag::probabilities> const probabilities;
        #endif
    };
}

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

BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square)
}

using extract::extended_p_square;

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

template<>
struct feature_of<tag::weighted_extended_p_square>
  : feature_of<tag::extended_p_square>
{
};

}} // namespace boost::accumulators

#endif

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