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weighted_covariance.hpp
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/////////////////////////////////////////////////////////////////////////////// // weighted_covariance.hpp // // Copyright 2006 Daniel Egloff, Olivier Gygi. 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_COVARIANCE_HPP_DE_01_01_2006 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006 #include <vector> #include <limits> #include <numeric> #include <functional> #include <complex> #include <boost/mpl/assert.hpp> #include <boost/mpl/bool.hpp> #include <boost/range.hpp> #include <boost/parameter/keyword.hpp> #include <boost/mpl/placeholders.hpp> #include <boost/numeric/ublas/io.hpp> #include <boost/numeric/ublas/matrix.hpp> #include <boost/type_traits/is_scalar.hpp> #include <boost/type_traits/is_same.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/statistics_fwd.hpp> #include <boost/accumulators/statistics/count.hpp> #include <boost/accumulators/statistics/covariance.hpp> // for numeric::outer_product() and type traits #include <boost/accumulators/statistics/weighted_mean.hpp> namespace boost { namespace accumulators { namespace impl { /////////////////////////////////////////////////////////////////////////////// // weighted_covariance_impl // /** @brief Weighted Covariance Estimator An iterative Monte Carlo estimator for the weighted covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample and \f$X'\f$ a variate, is given by: \f[ \hat{c}_n = \frac{\bar{w}_n-w_n}{\bar{w}_n} \hat{c}_{n-1} + \frac{w_n}{\bar{w}_n-w_n}(X_n - \hat{\mu}_n)(X_n' - \hat{\mu}_n'), \quad n\ge2,\quad\hat{c}_1 = 0, \f] \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the weighted means of the samples and variates and \f$\bar{w}_n\f$ the sum of the \f$n\f$ first weights \f$w_i\f$. */ template<typename Sample, typename Weight, typename VariateType, typename VariateTag> struct weighted_covariance_impl : accumulator_base { typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<Sample, std::size_t>::result_type>::result_type weighted_sample_type; typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<VariateType, std::size_t>::result_type>::result_type weighted_variate_type; // for boost::result_of typedef typename numeric::functional::outer_product<weighted_sample_type, weighted_variate_type>::result_type result_type; template<typename Args> weighted_covariance_impl(Args const &args) : cov_( numeric::outer_product( numeric::fdiv(args[sample | Sample()], (std::size_t)1) * numeric::one<Weight>::value , numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1) * numeric::one<Weight>::value ) ) { } template<typename Args> void operator ()(Args const &args) { std::size_t cnt = count(args); if (cnt > 1) { extractor<tag::weighted_mean_of_variates<VariateType, VariateTag> > const some_weighted_mean_of_variates = {}; this->cov_ = this->cov_ * (sum_of_weights(args) - args[weight]) / sum_of_weights(args) + numeric::outer_product( some_weighted_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()] , weighted_mean(args) - args[sample] ) * args[weight] / (sum_of_weights(args) - args[weight]); } } result_type result(dont_care) const { return this->cov_; } // make this accumulator serializeable template<class Archive> void serialize(Archive & ar, const unsigned int file_version) { ar & cov_; } private: result_type cov_; }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::weighted_covariance // namespace tag { template<typename VariateType, typename VariateTag> struct weighted_covariance : depends_on<count, sum_of_weights, weighted_mean, weighted_mean_of_variates<VariateType, VariateTag> > { typedef accumulators::impl::weighted_covariance_impl<mpl::_1, mpl::_2, VariateType, VariateTag> impl; }; } /////////////////////////////////////////////////////////////////////////////// // extract::weighted_covariance // namespace extract { extractor<tag::abstract_covariance> const weighted_covariance = {}; BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance) } using extract::weighted_covariance; }} // namespace boost::accumulators #endif