/usr/include/boost/accumulators/statistics
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
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
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
struct p_square_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv::result_type float_type;
typedef array array_type;
// for boost::result_of
typedef float_type result_type;
template
p_square_quantile_impl(Args const &args)
: p(is_same::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
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(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
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
{
/// INTERNAL ONLY
///
typedef accumulators::impl::p_square_quantile_impl impl;
};
struct p_square_quantile_for_median
: depends_on
{
/// INTERNAL ONLY
///
typedef accumulators::impl::p_square_quantile_impl impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::p_square_quantile
// extract::p_square_quantile_for_median
//
namespace extract
{
extractor const p_square_quantile = {};
extractor 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
{
typedef tag::weighted_p_square_quantile type;
};
template<>
struct feature_of
: feature_of
{
};
}} // namespace boost::accumulators
#endif