260 lines
9.3 KiB
C++
260 lines
9.3 KiB
C++
///////////////////////////////////////////////////////////////////////////////
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// rolling_variance.hpp
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// Copyright (C) 2005 Eric Niebler
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// Copyright (C) 2014 Pieter Bastiaan Ober (Integricom).
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_ACCUMULATORS_STATISTICS_ROLLING_VARIANCE_HPP_EAN_15_11_2011
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#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_VARIANCE_HPP_EAN_15_11_2011
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#include <boost/accumulators/accumulators.hpp>
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#include <boost/accumulators/statistics/stats.hpp>
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#include <boost/mpl/placeholders.hpp>
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#include <boost/accumulators/framework/accumulator_base.hpp>
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#include <boost/accumulators/framework/extractor.hpp>
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#include <boost/accumulators/numeric/functional.hpp>
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#include <boost/accumulators/framework/parameters/sample.hpp>
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#include <boost/accumulators/framework/depends_on.hpp>
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#include <boost/accumulators/statistics_fwd.hpp>
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#include <boost/accumulators/statistics/rolling_mean.hpp>
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#include <boost/accumulators/statistics/rolling_moment.hpp>
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#include <boost/type_traits/is_arithmetic.hpp>
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#include <boost/utility/enable_if.hpp>
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namespace boost { namespace accumulators
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{
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namespace impl
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{
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//! Immediate (lazy) calculation of the rolling variance.
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/*!
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Calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
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http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
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For a rolling window of size \f$N\f$, when \f$n <= N\f$, the variance is computed according to the formula
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\f[
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\sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2.
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\f]
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When \f$n > N\f$, the sample variance over the window becomes:
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\f[
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\sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2.
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\f]
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*/
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///////////////////////////////////////////////////////////////////////////////
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// lazy_rolling_variance_impl
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//
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template<typename Sample>
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struct lazy_rolling_variance_impl
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: accumulator_base
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{
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// for boost::result_of
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typedef typename numeric::functional::fdiv<Sample, std::size_t,void,void>::result_type result_type;
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lazy_rolling_variance_impl(dont_care) {}
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template<typename Args>
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result_type result(Args const &args) const
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{
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result_type mean = rolling_mean(args);
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size_t nr_samples = rolling_count(args);
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if (nr_samples < 2) return result_type();
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return nr_samples*(rolling_moment<2>(args) - mean*mean)/(nr_samples-1);
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}
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// serialization is done by accumulators it depends on
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template<class Archive>
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void serialize(Archive & ar, const unsigned int file_version) {}
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};
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//! Iterative calculation of the rolling variance.
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/*!
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Iterative calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
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http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
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For a rolling window of size \f$N\f$, for the first \f$N\f$ samples, the variance is computed according to the formula
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\f[
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\sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
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\f]
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where the sum of squares \f$M_{2,n}\f$ can be recursively computed as:
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\f[
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M_{2,n} = \sum_{i = 1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}),
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\f]
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and the estimate of the sample mean as:
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\f[
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\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - \mu_{n-1}).
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\f]
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For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest
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sample \f$x_{n-N}\f$ is dropped from the window. The sample variance over the window now becomes:
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\f[
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\sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
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\f]
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where the sum of squares \f$M_{2,n}\f$ now equals:
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\f[
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M_{2,n} = \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}) - (x_{n-N} - \mu_n)(x_{n-N} - \mu_{n-1}),
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\f]
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and the estimated mean is:
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\f[
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\mu_n = \frac{1}{N} \sum_{i = n-N+1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - x_{n-N}).
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\f]
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Note that the sample variance is not defined for \f$n <= 1\f$.
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*/
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///////////////////////////////////////////////////////////////////////////////
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// immediate_rolling_variance_impl
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//
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template<typename Sample>
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struct immediate_rolling_variance_impl
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: accumulator_base
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{
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// for boost::result_of
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typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
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template<typename Args>
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immediate_rolling_variance_impl(Args const &args)
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: previous_mean_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
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, sum_of_squares_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
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{
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}
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template<typename Args>
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void operator()(Args const &args)
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{
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Sample added_sample = args[sample];
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result_type mean = immediate_rolling_mean(args);
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sum_of_squares_ += (added_sample-mean)*(added_sample-previous_mean_);
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if(is_rolling_window_plus1_full(args))
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{
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Sample removed_sample = rolling_window_plus1(args).front();
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sum_of_squares_ -= (removed_sample-mean)*(removed_sample-previous_mean_);
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prevent_underflow(sum_of_squares_);
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}
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previous_mean_ = mean;
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}
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template<typename Args>
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result_type result(Args const &args) const
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{
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size_t nr_samples = rolling_count(args);
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if (nr_samples < 2) return result_type();
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return numeric::fdiv(sum_of_squares_,(nr_samples-1));
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}
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// make this accumulator serializeable
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template<class Archive>
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void serialize(Archive & ar, const unsigned int file_version)
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{
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ar & previous_mean_;
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ar & sum_of_squares_;
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}
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private:
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result_type previous_mean_;
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result_type sum_of_squares_;
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template<typename T>
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void prevent_underflow(T &non_negative_number,typename boost::enable_if<boost::is_arithmetic<T>,T>::type* = 0)
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{
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if (non_negative_number < T(0)) non_negative_number = T(0);
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}
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template<typename T>
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void prevent_underflow(T &non_arithmetic_quantity,typename boost::disable_if<boost::is_arithmetic<T>,T>::type* = 0)
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{
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}
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};
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} // namespace impl
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///////////////////////////////////////////////////////////////////////////////
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// tag:: lazy_rolling_variance
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// tag:: immediate_rolling_variance
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// tag:: rolling_variance
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//
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namespace tag
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{
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struct lazy_rolling_variance
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: depends_on< rolling_count, rolling_mean, rolling_moment<2> >
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{
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/// INTERNAL ONLY
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///
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typedef accumulators::impl::lazy_rolling_variance_impl< mpl::_1 > impl;
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#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
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/// tag::rolling_window::window_size named parameter
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static boost::parameter::keyword<tag::rolling_window_size> const window_size;
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#endif
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};
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struct immediate_rolling_variance
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: depends_on< rolling_window_plus1, rolling_count, immediate_rolling_mean>
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{
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/// INTERNAL ONLY
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///
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typedef accumulators::impl::immediate_rolling_variance_impl< mpl::_1> impl;
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#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
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/// tag::rolling_window::window_size named parameter
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static boost::parameter::keyword<tag::rolling_window_size> const window_size;
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#endif
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};
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// make immediate_rolling_variance the default implementation
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struct rolling_variance : immediate_rolling_variance {};
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} // namespace tag
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///////////////////////////////////////////////////////////////////////////////
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// extract::lazy_rolling_variance
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// extract::immediate_rolling_variance
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// extract::rolling_variance
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//
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namespace extract
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{
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extractor<tag::lazy_rolling_variance> const lazy_rolling_variance = {};
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extractor<tag::immediate_rolling_variance> const immediate_rolling_variance = {};
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extractor<tag::rolling_variance> const rolling_variance = {};
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_rolling_variance)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(immediate_rolling_variance)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_variance)
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}
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using extract::lazy_rolling_variance;
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using extract::immediate_rolling_variance;
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using extract::rolling_variance;
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// rolling_variance(lazy) -> lazy_rolling_variance
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template<>
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struct as_feature<tag::rolling_variance(lazy)>
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{
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typedef tag::lazy_rolling_variance type;
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};
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// rolling_variance(immediate) -> immediate_rolling_variance
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template<>
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struct as_feature<tag::rolling_variance(immediate)>
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{
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typedef tag::immediate_rolling_variance type;
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};
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// for the purposes of feature-based dependency resolution,
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// lazy_rolling_variance provides the same feature as rolling_variance
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template<>
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struct feature_of<tag::lazy_rolling_variance>
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: feature_of<tag::rolling_variance>
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{
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};
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// for the purposes of feature-based dependency resolution,
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// immediate_rolling_variance provides the same feature as rolling_variance
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template<>
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struct feature_of<tag::immediate_rolling_variance>
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: feature_of<tag::rolling_variance>
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{
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};
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}} // namespace boost::accumulators
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#endif
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