/////////////////////////////////////////////////////////////////////////////// | |
// weighted_p_square_cumulative_distribution.hpp | |
// | |
// Copyright 2006 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_WEIGHTED_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_DE_01_01_2006 | |
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_DE_01_01_2006 | |
#include <vector> | |
#include <functional> | |
#include <boost/parameter/keyword.hpp> | |
#include <boost/mpl/placeholders.hpp> | |
#include <boost/range.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> | |
#include <boost/accumulators/statistics/sum.hpp> | |
#include <boost/accumulators/statistics/p_square_cumulative_distribution.hpp> // for named parameter p_square_cumulative_distribution_num_cells | |
namespace boost { namespace accumulators | |
{ | |
namespace impl | |
{ | |
/////////////////////////////////////////////////////////////////////////////// | |
// weighted_p_square_cumulative_distribution_impl | |
// cumulative distribution calculation (as histogram) | |
/** | |
@brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm for weighted samples | |
A histogram of the sample cumulative distribution is computed dynamically without storing samples | |
based on the \f$ P^2 \f$ algorithm for weighted samples. The returned histogram has a specifiable | |
amount (num_cells) equiprobable (and not equal-sized) cells. | |
Note that applying importance sampling results in regions to be more and other regions to be less | |
accurately estimated than without importance sampling, i.e., with unweighted samples. | |
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, typename Weight> | |
struct weighted_p_square_cumulative_distribution_impl | |
: accumulator_base | |
{ | |
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type; | |
typedef std::vector<std::pair<float_type, float_type> > histogram_type; | |
typedef std::vector<float_type> array_type; | |
// for boost::result_of | |
typedef iterator_range<typename histogram_type::iterator> result_type; | |
template<typename Args> | |
weighted_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) | |
, histogram(num_cells + 1) | |
, is_dirty(true) | |
{ | |
} | |
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]; | |
this->actual_positions[cnt - 1] = args[weight]; | |
// complete the initialization of heights by sorting | |
if (cnt == b + 1) | |
{ | |
//std::sort(this->heights.begin(), this->heights.end()); | |
// TODO: we need to sort the initial samples (in heights) in ascending order and | |
// sort their weights (in actual_positions) the same way. The following lines do | |
// it, but there must be a better and more efficient way of doing this. | |
typename array_type::iterator it_begin, it_end, it_min; | |
it_begin = this->heights.begin(); | |
it_end = this->heights.end(); | |
std::size_t pos = 0; | |
while (it_begin != it_end) | |
{ | |
it_min = std::min_element(it_begin, it_end); | |
std::size_t d = std::distance(it_begin, it_min); | |
std::swap(*it_begin, *it_min); | |
std::swap(this->actual_positions[pos], this->actual_positions[pos + d]); | |
++it_begin; | |
++pos; | |
} | |
// calculate correct initial actual positions | |
for (std::size_t i = 1; i < b; ++i) | |
{ | |
this->actual_positions[i] += this->actual_positions[i - 1]; | |
} | |
} | |
} | |
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]; | |
this->actual_positions[0] = args[weight]; | |
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] += args[weight]; | |
} | |
// determine desired marker positions | |
for (std::size_t i = 1; i < b + 1; ++i) | |
{ | |
this->desired_positions[i] = this->actual_positions[0] | |
+ numeric::average((i-1) * (sum_of_weights(args) - this->actual_positions[0]), b); | |
} | |
// 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] / sum_of_weights (y-axis of histogram) | |
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], sum_of_weights(args))); | |
} | |
} | |
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 | |
mutable histogram_type histogram; // histogram | |
mutable bool is_dirty; | |
}; | |
} // namespace detail | |
/////////////////////////////////////////////////////////////////////////////// | |
// tag::weighted_p_square_cumulative_distribution | |
// | |
namespace tag | |
{ | |
struct weighted_p_square_cumulative_distribution | |
: depends_on<count, sum_of_weights> | |
, p_square_cumulative_distribution_num_cells | |
{ | |
typedef accumulators::impl::weighted_p_square_cumulative_distribution_impl<mpl::_1, mpl::_2> impl; | |
}; | |
} | |
/////////////////////////////////////////////////////////////////////////////// | |
// extract::weighted_p_square_cumulative_distribution | |
// | |
namespace extract | |
{ | |
extractor<tag::weighted_p_square_cumulative_distribution> const weighted_p_square_cumulative_distribution = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_cumulative_distribution) | |
} | |
using extract::weighted_p_square_cumulative_distribution; | |
}} // namespace boost::accumulators | |
#endif |