/////////////////////////////////////////////////////////////////////////////// | |
// 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/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/times2_iterator.hpp> | |
namespace boost { namespace accumulators | |
{ | |
/////////////////////////////////////////////////////////////////////////////// | |
// probabilities named parameter | |
// | |
BOOST_PARAMETER_NESTED_KEYWORD(tag, extended_p_square_probabilities, 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 generalizess the \f$ P^2 \f$ algorithm of | |
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 extended_p_square_probabilities A vector of quantile probabilities. | |
*/ | |
template<typename Sample> | |
struct extended_p_square_impl | |
: accumulator_base | |
{ | |
typedef typename numeric::functional::average<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) | |
); | |
} | |
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 paramter | |
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 |