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Diffstat (limited to 'boost/accumulators/statistics/p_square_cumul_dist.hpp')
-rw-r--r-- | boost/accumulators/statistics/p_square_cumul_dist.hpp | 260 |
1 files changed, 260 insertions, 0 deletions
diff --git a/boost/accumulators/statistics/p_square_cumul_dist.hpp b/boost/accumulators/statistics/p_square_cumul_dist.hpp new file mode 100644 index 0000000000..b9e24f676c --- /dev/null +++ b/boost/accumulators/statistics/p_square_cumul_dist.hpp @@ -0,0 +1,260 @@ +/////////////////////////////////////////////////////////////////////////////// +// p_square_cumulative_distribution.hpp +// +// Copyright 2005 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_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006 +#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006 + +#include <vector> +#include <functional> +#include <boost/parameter/keyword.hpp> +#include <boost/range.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/statistics_fwd.hpp> +#include <boost/accumulators/statistics/count.hpp> + +namespace boost { namespace accumulators +{ +/////////////////////////////////////////////////////////////////////////////// +// num_cells named parameter +// +BOOST_PARAMETER_NESTED_KEYWORD(tag, p_square_cumulative_distribution_num_cells, num_cells) + +namespace impl +{ + /////////////////////////////////////////////////////////////////////////////// + // p_square_cumulative_distribution_impl + // cumulative_distribution calculation (as histogram) + /** + @brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm + + A histogram of the sample cumulative distribution is computed dynamically without storing samples + based on the \f$ P^2 \f$ algorithm. The returned histogram has a specifiable amount (num_cells) + equiprobable (and not equal-sized) cells. + + 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> + struct p_square_cumulative_distribution_impl + : accumulator_base + { + typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type; + typedef std::vector<float_type> array_type; + typedef std::vector<std::pair<float_type, float_type> > histogram_type; + // for boost::result_of + typedef iterator_range<typename histogram_type::iterator> result_type; + + template<typename Args> + 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) + , positions_increments(num_cells + 1) + , histogram(num_cells + 1) + , is_dirty(true) + { + std::size_t b = this->num_cells; + + for (std::size_t i = 0; i < b + 1; ++i) + { + this->actual_positions[i] = i + 1.; + this->desired_positions[i] = i + 1.; + this->positions_increments[i] = numeric::average(i, b); + } + } + + 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]; + + // complete the initialization of heights by sorting + if (cnt == b + 1) + { + std::sort(this->heights.begin(), this->heights.end()); + } + } + 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]; + 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]; + } + + // update desired position of markers 2 to num_cells + 1 + // (desired position of first marker is always 1) + for (std::size_t i = 1; i < b + 1; ++i) + { + this->desired_positions[i] += this->positions_increments[i]; + } + + // 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] / cnt (y-axis of histogram) + + std::size_t cnt = count(args); + + 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], cnt)); + } + } + //return histogram; + 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 + array_type positions_increments; // dn'_i + mutable histogram_type histogram; // histogram + mutable bool is_dirty; + }; + +} // namespace detail + +/////////////////////////////////////////////////////////////////////////////// +// tag::p_square_cumulative_distribution +// +namespace tag +{ + struct p_square_cumulative_distribution + : depends_on<count> + , p_square_cumulative_distribution_num_cells + { + /// INTERNAL ONLY + /// + typedef accumulators::impl::p_square_cumulative_distribution_impl<mpl::_1> impl; + }; +} + +/////////////////////////////////////////////////////////////////////////////// +// extract::p_square_cumulative_distribution +// +namespace extract +{ + extractor<tag::p_square_cumulative_distribution> const p_square_cumulative_distribution = {}; + + BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_cumulative_distribution) +} + +using extract::p_square_cumulative_distribution; + +// So that p_square_cumulative_distribution can be automatically substituted with +// weighted_p_square_cumulative_distribution when the weight parameter is non-void +template<> +struct as_weighted_feature<tag::p_square_cumulative_distribution> +{ + typedef tag::weighted_p_square_cumulative_distribution type; +}; + +template<> +struct feature_of<tag::weighted_p_square_cumulative_distribution> + : feature_of<tag::p_square_cumulative_distribution> +{ +}; + +}} // namespace boost::accumulators + +#endif |