| /////////////////////////////////////////////////////////////////////////////// |
| // 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::average<Sample, std::size_t>::result_type>::result_type weighted_sample_type; |
| typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::average<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::average(args[sample | Sample()], (std::size_t)1) |
| * numeric::one<Weight>::value |
| , numeric::average(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_; |
| } |
| |
| 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 |