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Diffstat (limited to 'boost/accumulators/statistics/weighted_variance.hpp')
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1 files changed, 186 insertions, 0 deletions
diff --git a/boost/accumulators/statistics/weighted_variance.hpp b/boost/accumulators/statistics/weighted_variance.hpp new file mode 100644 index 0000000000..e91fdc1bc6 --- /dev/null +++ b/boost/accumulators/statistics/weighted_variance.hpp @@ -0,0 +1,186 @@ +/////////////////////////////////////////////////////////////////////////////// +// 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::average<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 smaples. 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::average<weighted_sample, Weight>::result_type result_type; + + template<typename Args> + weighted_variance_impl(Args const &args) + : weighted_variance(numeric::average(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::average(this->weighted_variance * (sum_of_weights(args) - args[weight]), sum_of_weights(args)) + + numeric::average(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 |