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///////////////////////////////////////////////////////////////////////////////
// weighted_variance.hpp
//
// Copyright 2005 Daniel Egloff, Eric Niebler. 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_VARIANCE_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
#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/variance.hpp>
#include <boost/accumulators/statistics/weighted_sum.hpp>
#include <boost/accumulators/statistics/weighted_mean.hpp>
#include <boost/accumulators/statistics/weighted_moment.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
//! Lazy calculation of variance of weighted samples.
/*!
The default implementation of the variance of weighted samples is based on the second moment
\f$\widehat{m}_n^{(2)}\f$ (weighted_moment<2>) and the mean\f$ \hat{\mu}_n\f$ (weighted_mean):
\f[
\hat{\sigma}_n^2 = \widehat{m}_n^{(2)}-\hat{\mu}_n^2,
\f]
where \f$n\f$ is the number of samples.
*/
template<typename Sample, typename Weight, typename MeanFeature>
struct lazy_weighted_variance_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
lazy_weighted_variance_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
extractor<MeanFeature> const some_mean = {};
result_type tmp = some_mean(args);
return accumulators::weighted_moment<2>(args) - tmp * tmp;
}
};
//! Iterative calculation of variance of weighted samples.
/*!
Iterative calculation of variance of weighted samples:
\f[
\hat{\sigma}_n^2 =
\frac{\bar{w}_n - w_n}{\bar{w}_n}\hat{\sigma}_{n - 1}^2
+ \frac{w_n}{\bar{w}_n - w_n}\left(X_n - \hat{\mu}_n\right)^2
,\quad n\ge2,\quad\hat{\sigma}_0^2 = 0.
\f]
where \f$\bar{w}_n\f$ is the sum of the \f$n\f$ weights \f$w_i\f$ and \f$\hat{\mu}_n\f$
the estimate of the mean of the weighted samples. Note that the sample variance is not defined for
\f$n <= 1\f$.
*/
template<typename Sample, typename Weight, typename MeanFeature, typename Tag>
struct weighted_variance_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
template<typename Args>
weighted_variance_impl(Args const &args)
: weighted_variance(numeric::fdiv(args[sample | Sample()], numeric::one<Weight>::value))
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
if(cnt > 1)
{
extractor<MeanFeature> const some_mean = {};
result_type tmp = args[parameter::keyword<Tag>::get()] - some_mean(args);
this->weighted_variance =
numeric::fdiv(this->weighted_variance * (sum_of_weights(args) - args[weight]), sum_of_weights(args))
+ numeric::fdiv(tmp * tmp * args[weight], sum_of_weights(args) - args[weight] );
}
}
result_type result(dont_care) const
{
return this->weighted_variance;
}
private:
result_type weighted_variance;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_variance
// tag::immediate_weighted_variance
//
namespace tag
{
struct lazy_weighted_variance
: depends_on<weighted_moment<2>, weighted_mean>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::lazy_weighted_variance_impl<mpl::_1, mpl::_2, weighted_mean> impl;
};
struct weighted_variance
: depends_on<count, immediate_weighted_mean>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_variance_impl<mpl::_1, mpl::_2, immediate_weighted_mean, sample> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_variance
// extract::immediate_weighted_variance
//
namespace extract
{
extractor<tag::lazy_weighted_variance> const lazy_weighted_variance = {};
extractor<tag::weighted_variance> const weighted_variance = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_weighted_variance)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_variance)
}
using extract::lazy_weighted_variance;
using extract::weighted_variance;
// weighted_variance(lazy) -> lazy_weighted_variance
template<>
struct as_feature<tag::weighted_variance(lazy)>
{
typedef tag::lazy_weighted_variance type;
};
// weighted_variance(immediate) -> weighted_variance
template<>
struct as_feature<tag::weighted_variance(immediate)>
{
typedef tag::weighted_variance type;
};
////////////////////////////////////////////////////////////////////////////
//// droppable_accumulator<weighted_variance_impl>
//// need to specialize droppable lazy weighted_variance to cache the result at the
//// point the accumulator is dropped.
///// INTERNAL ONLY
/////
//template<typename Sample, typename Weight, typename MeanFeature>
//struct droppable_accumulator<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
// : droppable_accumulator_base<
// with_cached_result<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
// >
//{
// template<typename Args>
// droppable_accumulator(Args const &args)
// : droppable_accumulator::base(args)
// {
// }
//};
}} // namespace boost::accumulators
#endif
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