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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
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