Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // weighted_variance.hpp
Chris@16: //
Chris@16: //  Copyright 2005 Daniel Egloff, Eric Niebler. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
Chris@16: 
Chris@16: #include <boost/mpl/placeholders.hpp>
Chris@16: #include <boost/accumulators/framework/accumulator_base.hpp>
Chris@16: #include <boost/accumulators/framework/extractor.hpp>
Chris@16: #include <boost/accumulators/numeric/functional.hpp>
Chris@16: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@16: #include <boost/accumulators/framework/depends_on.hpp>
Chris@16: #include <boost/accumulators/statistics_fwd.hpp>
Chris@16: #include <boost/accumulators/statistics/count.hpp>
Chris@16: #include <boost/accumulators/statistics/variance.hpp>
Chris@16: #include <boost/accumulators/statistics/weighted_sum.hpp>
Chris@16: #include <boost/accumulators/statistics/weighted_mean.hpp>
Chris@16: #include <boost/accumulators/statistics/weighted_moment.hpp>
Chris@16: 
Chris@16: namespace boost { namespace accumulators
Chris@16: {
Chris@16: 
Chris@16: namespace impl
Chris@16: {
Chris@16:     //! Lazy calculation of variance of weighted samples.
Chris@16:     /*!
Chris@16:         The default implementation of the variance of weighted samples is based on the second moment
Chris@16:         \f$\widehat{m}_n^{(2)}\f$ (weighted_moment<2>) and the mean\f$ \hat{\mu}_n\f$ (weighted_mean):
Chris@16:         \f[
Chris@16:             \hat{\sigma}_n^2 = \widehat{m}_n^{(2)}-\hat{\mu}_n^2,
Chris@16:         \f]
Chris@16:         where \f$n\f$ is the number of samples.
Chris@16:     */
Chris@16:     template<typename Sample, typename Weight, typename MeanFeature>
Chris@16:     struct lazy_weighted_variance_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
Chris@16: 
Chris@16:         lazy_weighted_variance_impl(dont_care) {}
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         result_type result(Args const &args) const
Chris@16:         {
Chris@16:             extractor<MeanFeature> const some_mean = {};
Chris@16:             result_type tmp = some_mean(args);
Chris@16:             return accumulators::weighted_moment<2>(args) - tmp * tmp;
Chris@16:         }
Chris@16:     };
Chris@16: 
Chris@16:     //! Iterative calculation of variance of weighted samples.
Chris@16:     /*!
Chris@16:         Iterative calculation of variance of weighted samples:
Chris@16:         \f[
Chris@16:             \hat{\sigma}_n^2 =
Chris@16:                 \frac{\bar{w}_n - w_n}{\bar{w}_n}\hat{\sigma}_{n - 1}^2
Chris@16:               + \frac{w_n}{\bar{w}_n - w_n}\left(X_n - \hat{\mu}_n\right)^2
Chris@16:             ,\quad n\ge2,\quad\hat{\sigma}_0^2 = 0.
Chris@16:         \f]
Chris@16:         where \f$\bar{w}_n\f$ is the sum of the \f$n\f$ weights \f$w_i\f$ and \f$\hat{\mu}_n\f$
Chris@16:         the estimate of the mean of the weighted samples. Note that the sample variance is not defined for
Chris@16:         \f$n <= 1\f$.
Chris@16:     */
Chris@16:     template<typename Sample, typename Weight, typename MeanFeature, typename Tag>
Chris@16:     struct weighted_variance_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         weighted_variance_impl(Args const &args)
Chris@16:           : weighted_variance(numeric::fdiv(args[sample | Sample()], numeric::one<Weight>::value))
Chris@16:         {
Chris@16:         }
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         void operator ()(Args const &args)
Chris@16:         {
Chris@16:             std::size_t cnt = count(args);
Chris@16: 
Chris@16:             if(cnt > 1)
Chris@16:             {
Chris@16:                 extractor<MeanFeature> const some_mean = {};
Chris@16: 
Chris@16:                 result_type tmp = args[parameter::keyword<Tag>::get()] - some_mean(args);
Chris@16: 
Chris@16:                 this->weighted_variance =
Chris@16:                     numeric::fdiv(this->weighted_variance * (sum_of_weights(args) - args[weight]), sum_of_weights(args))
Chris@16:                   + numeric::fdiv(tmp * tmp * args[weight], sum_of_weights(args) - args[weight] );
Chris@16:             }
Chris@16:         }
Chris@16: 
Chris@16:         result_type result(dont_care) const
Chris@16:         {
Chris@16:             return this->weighted_variance;
Chris@16:         }
Chris@16: 
Chris@16:     private:
Chris@16:         result_type weighted_variance;
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::weighted_variance
Chris@16: // tag::immediate_weighted_variance
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     struct lazy_weighted_variance
Chris@16:       : depends_on<weighted_moment<2>, weighted_mean>
Chris@16:     {
Chris@16:         /// INTERNAL ONLY
Chris@16:         ///
Chris@16:         typedef accumulators::impl::lazy_weighted_variance_impl<mpl::_1, mpl::_2, weighted_mean> impl;
Chris@16:     };
Chris@16: 
Chris@16:     struct weighted_variance
Chris@16:       : depends_on<count, immediate_weighted_mean>
Chris@16:     {
Chris@16:         /// INTERNAL ONLY
Chris@16:         ///
Chris@16:         typedef accumulators::impl::weighted_variance_impl<mpl::_1, mpl::_2, immediate_weighted_mean, sample> impl;
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::weighted_variance
Chris@16: // extract::immediate_weighted_variance
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::lazy_weighted_variance> const lazy_weighted_variance = {};
Chris@16:     extractor<tag::weighted_variance> const weighted_variance = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_weighted_variance)
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_variance)
Chris@16: }
Chris@16: 
Chris@16: using extract::lazy_weighted_variance;
Chris@16: using extract::weighted_variance;
Chris@16: 
Chris@16: // weighted_variance(lazy) -> lazy_weighted_variance
Chris@16: template<>
Chris@16: struct as_feature<tag::weighted_variance(lazy)>
Chris@16: {
Chris@16:     typedef tag::lazy_weighted_variance type;
Chris@16: };
Chris@16: 
Chris@16: // weighted_variance(immediate) -> weighted_variance
Chris@16: template<>
Chris@16: struct as_feature<tag::weighted_variance(immediate)>
Chris@16: {
Chris@16:     typedef tag::weighted_variance type;
Chris@16: };
Chris@16: 
Chris@16: ////////////////////////////////////////////////////////////////////////////
Chris@16: //// droppable_accumulator<weighted_variance_impl>
Chris@16: ////  need to specialize droppable lazy weighted_variance to cache the result at the
Chris@16: ////  point the accumulator is dropped.
Chris@16: ///// INTERNAL ONLY
Chris@16: /////
Chris@16: //template<typename Sample, typename Weight, typename MeanFeature>
Chris@16: //struct droppable_accumulator<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
Chris@16: //  : droppable_accumulator_base<
Chris@16: //        with_cached_result<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
Chris@16: //    >
Chris@16: //{
Chris@16: //    template<typename Args>
Chris@16: //    droppable_accumulator(Args const &args)
Chris@16: //      : droppable_accumulator::base(args)
Chris@16: //    {
Chris@16: //    }
Chris@16: //};
Chris@16: 
Chris@16: }} // namespace boost::accumulators
Chris@16: 
Chris@16: #endif