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Diffstat (limited to 'boost/accumulators/statistics/covariance.hpp')
| -rw-r--r-- | boost/accumulators/statistics/covariance.hpp | 220 |
1 files changed, 220 insertions, 0 deletions
diff --git a/boost/accumulators/statistics/covariance.hpp b/boost/accumulators/statistics/covariance.hpp new file mode 100644 index 0000000000..b34284b046 --- /dev/null +++ b/boost/accumulators/statistics/covariance.hpp @@ -0,0 +1,220 @@ +/////////////////////////////////////////////////////////////////////////////// +// 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_COVARIANCE_HPP_DE_01_01_2006 +#define BOOST_ACCUMULATORS_STATISTICS_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/mean.hpp> + +namespace boost { namespace numeric +{ + namespace functional + { + struct std_vector_tag; + + /////////////////////////////////////////////////////////////////////////////// + // functional::outer_product + template<typename Left, typename Right, typename EnableIf = void> + struct outer_product_base + : functional::multiplies<Left, Right> + {}; + + template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type> + struct outer_product + : outer_product_base<Left, Right, void> + {}; + + template<typename Left, typename Right> + struct outer_product<Left, Right, std_vector_tag, std_vector_tag> + : std::binary_function< + Left + , Right + , ublas::matrix< + typename functional::multiplies< + typename Left::value_type + , typename Right::value_type + >::result_type + > + > + { + typedef + ublas::matrix< + typename functional::multiplies< + typename Left::value_type + , typename Right::value_type + >::result_type + > + result_type; + + result_type + operator ()(Left & left, Right & right) const + { + std::size_t left_size = left.size(); + std::size_t right_size = right.size(); + result_type result(left_size, right_size); + for (std::size_t i = 0; i < left_size; ++i) + for (std::size_t j = 0; j < right_size; ++j) + result(i,j) = numeric::multiplies(left[i], right[j]); + return result; + } + }; + } + + namespace op + { + struct outer_product + : boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > > + {}; + } + + namespace + { + op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance; + } + +}} + +namespace boost { namespace accumulators +{ + +namespace impl +{ + /////////////////////////////////////////////////////////////////////////////// + // covariance_impl + // + /** + @brief Covariance Estimator + + An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample + and \f$X'\f$ is a variate, is given by: + + \f[ + \hat{c}_n = \frac{n-1}{n} \hat{c}_{n-1} + \frac{1}{n-1}(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 means of the samples and variates. + */ + template<typename Sample, typename VariateType, typename VariateTag> + struct covariance_impl + : accumulator_base + { + typedef typename numeric::functional::average<Sample, std::size_t>::result_type sample_type; + typedef typename numeric::functional::average<VariateType, std::size_t>::result_type variate_type; + // for boost::result_of + typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type; + + template<typename Args> + covariance_impl(Args const &args) + : cov_( + numeric::outer_product( + numeric::average(args[sample | Sample()], (std::size_t)1) + , numeric::average(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1) + ) + ) + { + } + + template<typename Args> + void operator ()(Args const &args) + { + std::size_t cnt = count(args); + + if (cnt > 1) + { + extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {}; + + this->cov_ = this->cov_*(cnt-1.)/cnt + + numeric::outer_product( + some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()] + , mean(args) - args[sample] + ) / (cnt-1.); + } + } + + result_type result(dont_care) const + { + return this->cov_; + } + + private: + result_type cov_; + }; + +} // namespace impl + +/////////////////////////////////////////////////////////////////////////////// +// tag::covariance +// +namespace tag +{ + template<typename VariateType, typename VariateTag> + struct covariance + : depends_on<count, mean, mean_of_variates<VariateType, VariateTag> > + { + typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl; + }; + + struct abstract_covariance + : depends_on<> + { + }; +} + +/////////////////////////////////////////////////////////////////////////////// +// extract::covariance +// +namespace extract +{ + extractor<tag::abstract_covariance> const covariance = {}; + + BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance) +} + +using extract::covariance; + +template<typename VariateType, typename VariateTag> +struct feature_of<tag::covariance<VariateType, VariateTag> > + : feature_of<tag::abstract_covariance> +{ +}; + +// So that covariance can be automatically substituted with +// weighted_covariance when the weight parameter is non-void. +template<typename VariateType, typename VariateTag> +struct as_weighted_feature<tag::covariance<VariateType, VariateTag> > +{ + typedef tag::weighted_covariance<VariateType, VariateTag> type; +}; + +template<typename VariateType, typename VariateTag> +struct feature_of<tag::weighted_covariance<VariateType, VariateTag> > + : feature_of<tag::covariance<VariateType, VariateTag> > +{}; + +}} // namespace boost::accumulators + +#endif |