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///////////////////////////////////////////////////////////////////////////////


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// variance.hpp

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//

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// Copyright 2005 Daniel Egloff, Eric Niebler. Distributed under the Boost

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// Software License, Version 1.0. (See accompanying file

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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

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#ifndef BOOST_ACCUMULATORS_STATISTICS_VARIANCE_HPP_EAN_28_10_2005

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#define BOOST_ACCUMULATORS_STATISTICS_VARIANCE_HPP_EAN_28_10_2005

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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/count.hpp> 
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#include <boost/accumulators/statistics/sum.hpp> 
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#include <boost/accumulators/statistics/mean.hpp> 
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#include <boost/accumulators/statistics/moment.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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//! Lazy calculation of variance.

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/*!

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Default sample variance implementation based on the second moment \f$ M_n^{(2)} \f$ moment<2>, mean and count.

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\f[

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\sigma_n^2 = M_n^{(2)}  \mu_n^2.

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\f]

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where

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\f[

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\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i.

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\f]

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is the estimate of the sample mean and \f$n\f$ is the number of samples.

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*/

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template<typename Sample, typename MeanFeature> 
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struct lazy_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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lazy_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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extractor<MeanFeature> mean; 
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result_type tmp = mean(args); 
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return accumulators::moment<2>(args)  tmp * tmp; 
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} 
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}; 
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//! Iterative calculation of variance.

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/*!

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Iterative calculation of sample variance \f$\sigma_n^2\f$ according to the formula

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\f[

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\sigma_n^2 = \frac{1}{n} \sum_{i = 1}^n (x_i  \mu_n)^2 = \frac{n1}{n} \sigma_{n1}^2 + \frac{1}{n1}(x_n  \mu_n)^2.

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\f]

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where

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\f[

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\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i.

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\f]

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is the estimate of the sample mean and \f$n\f$ is the number of samples.

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Note that the sample variance is not defined for \f$n <= 1\f$.

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A simplification can be obtained by the approximate recursion

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\f[

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\sigma_n^2 \approx \frac{n1}{n} \sigma_{n1}^2 + \frac{1}{n}(x_n  \mu_n)^2.

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\f]

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because the difference

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\f[

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\left(\frac{1}{n1}  \frac{1}{n}\right)(x_n  \mu_n)^2 = \frac{1}{n(n1)}(x_n  \mu_n)^2.

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\f]

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converges to zero as \f$n \rightarrow \infty\f$. However, for small \f$ n \f$ the difference

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can be nonnegligible.

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*/

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template<typename Sample, typename MeanFeature, typename Tag> 
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struct 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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variance_impl(Args const &args)

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: variance(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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std::size_t cnt = count(args); 
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if(cnt > 1) 
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{ 
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extractor<MeanFeature> mean; 
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result_type tmp = args[parameter::keyword<Tag>::get()]  mean(args); 
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this>variance =

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numeric::fdiv(this>variance * (cnt  1), cnt) 
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+ numeric::fdiv(tmp * tmp, cnt  1);

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} 
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} 
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result_type result(dont_care) const

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{ 
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return this>variance; 
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} 
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private:

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result_type variance; 
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}; 
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} // namespace impl

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///////////////////////////////////////////////////////////////////////////////

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// tag::variance

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// tag::immediate_variance

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//

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namespace tag

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{ 
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struct lazy_variance

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: depends_on<moment<2>, mean>

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{ 
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/// INTERNAL ONLY

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///

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typedef accumulators::impl::lazy_variance_impl<mpl::_1, mean> impl;

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}; 
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struct variance

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: depends_on<count, immediate_mean> 
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{ 
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/// INTERNAL ONLY

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///

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typedef accumulators::impl::variance_impl<mpl::_1, mean, sample> impl;

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}; 
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} 
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///////////////////////////////////////////////////////////////////////////////

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// extract::lazy_variance

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// extract::variance

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//

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namespace extract

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{ 
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extractor<tag::lazy_variance> const lazy_variance = {};

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extractor<tag::variance> const variance = {};

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BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_variance) 
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(variance) 
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} 
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using extract::lazy_variance;

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using extract::variance;

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// variance(lazy) > lazy_variance

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template<>

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struct as_feature<tag::variance(lazy)>

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{ 
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typedef tag::lazy_variance type;

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}; 
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// variance(immediate) > variance

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template<>

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struct as_feature<tag::variance(immediate)>

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{ 
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typedef tag::variance type;

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}; 
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// for the purposes of featurebased dependency resolution,

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// immediate_variance provides the same feature as variance

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template<>

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struct feature_of<tag::lazy_variance>

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: feature_of<tag::variance> 
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{ 
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}; 
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// So that variance can be automatically substituted with

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// weighted_variance when the weight parameter is nonvoid.

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template<>

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struct as_weighted_feature<tag::variance>

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{ 
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typedef tag::weighted_variance type;

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}; 
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// for the purposes of featurebased dependency resolution,

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// weighted_variance provides the same feature as variance

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template<>

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struct feature_of<tag::weighted_variance>

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: feature_of<tag::variance> 
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{ 
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}; 
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// So that immediate_variance can be automatically substituted with

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// immediate_weighted_variance when the weight parameter is nonvoid.

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template<>

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struct as_weighted_feature<tag::lazy_variance>

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{ 
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typedef tag::lazy_weighted_variance type;

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}; 
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// for the purposes of featurebased dependency resolution,

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// immediate_weighted_variance provides the same feature as immediate_variance

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template<>

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struct feature_of<tag::lazy_weighted_variance>

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: feature_of<tag::lazy_variance> 
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{ 
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}; 
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////////////////////////////////////////////////////////////////////////////

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//// droppable_accumulator<variance_impl>

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//// need to specialize droppable lazy variance to cache the result at the

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//// point the accumulator is dropped.

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///// INTERNAL ONLY

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/////

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//template<typename Sample, typename MeanFeature>

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//struct droppable_accumulator<impl::variance_impl<Sample, MeanFeature> >

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// : droppable_accumulator_base<

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// with_cached_result<impl::variance_impl<Sample, MeanFeature> >

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// >

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//{

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// template<typename Args>

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// droppable_accumulator(Args const &args)

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// : droppable_accumulator::base(args)

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// {

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// }

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//};

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}} // namespace boost::accumulators

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#endif
