221 lines
7.2 KiB
C++
221 lines
7.2 KiB
C++
///////////////////////////////////////////////////////////////////////////////
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// covariance.hpp
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//
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// Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_ACCUMULATORS_STATISTICS_COVARIANCE_HPP_DE_01_01_2006
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#define BOOST_ACCUMULATORS_STATISTICS_COVARIANCE_HPP_DE_01_01_2006
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#include <vector>
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#include <limits>
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#include <numeric>
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#include <functional>
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#include <complex>
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#include <boost/mpl/assert.hpp>
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#include <boost/mpl/bool.hpp>
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#include <boost/range.hpp>
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#include <boost/parameter/keyword.hpp>
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#include <boost/mpl/placeholders.hpp>
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#include <boost/numeric/ublas/io.hpp>
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#include <boost/numeric/ublas/matrix.hpp>
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#include <boost/type_traits/is_scalar.hpp>
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#include <boost/type_traits/is_same.hpp>
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#include <boost/accumulators/framework/accumulator_base.hpp>
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#include <boost/accumulators/framework/extractor.hpp>
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#include <boost/accumulators/numeric/functional.hpp>
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#include <boost/accumulators/framework/parameters/sample.hpp>
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#include <boost/accumulators/statistics_fwd.hpp>
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#include <boost/accumulators/statistics/count.hpp>
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#include <boost/accumulators/statistics/mean.hpp>
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namespace boost { namespace numeric
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{
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namespace functional
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{
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struct std_vector_tag;
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///////////////////////////////////////////////////////////////////////////////
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// functional::outer_product
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template<typename Left, typename Right, typename EnableIf = void>
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struct outer_product_base
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: functional::multiplies<Left, Right>
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{};
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template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
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struct outer_product
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: outer_product_base<Left, Right, void>
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{};
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template<typename Left, typename Right>
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struct outer_product<Left, Right, std_vector_tag, std_vector_tag>
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: std::binary_function<
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Left
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, Right
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, ublas::matrix<
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typename functional::multiplies<
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typename Left::value_type
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, typename Right::value_type
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>::result_type
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>
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>
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{
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typedef
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ublas::matrix<
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typename functional::multiplies<
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typename Left::value_type
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, typename Right::value_type
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>::result_type
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>
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result_type;
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result_type
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operator ()(Left & left, Right & right) const
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{
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std::size_t left_size = left.size();
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std::size_t right_size = right.size();
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result_type result(left_size, right_size);
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for (std::size_t i = 0; i < left_size; ++i)
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for (std::size_t j = 0; j < right_size; ++j)
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result(i,j) = numeric::multiplies(left[i], right[j]);
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return result;
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}
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};
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}
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namespace op
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{
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struct outer_product
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: boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > >
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{};
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}
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namespace
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{
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op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance;
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}
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}}
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namespace boost { namespace accumulators
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{
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namespace impl
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{
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///////////////////////////////////////////////////////////////////////////////
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// covariance_impl
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//
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/**
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@brief Covariance Estimator
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An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
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and \f$X'\f$ is a variate, is given by:
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\f[
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\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,
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\f]
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\f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates.
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*/
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template<typename Sample, typename VariateType, typename VariateTag>
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struct covariance_impl
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: accumulator_base
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{
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typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type sample_type;
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typedef typename numeric::functional::fdiv<VariateType, std::size_t>::result_type variate_type;
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// for boost::result_of
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typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type;
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template<typename Args>
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covariance_impl(Args const &args)
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: cov_(
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numeric::outer_product(
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numeric::fdiv(args[sample | Sample()], (std::size_t)1)
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, numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
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)
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)
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{
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}
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template<typename Args>
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void operator ()(Args const &args)
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{
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std::size_t cnt = count(args);
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if (cnt > 1)
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{
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extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {};
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this->cov_ = this->cov_*(cnt-1.)/cnt
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+ numeric::outer_product(
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some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
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, mean(args) - args[sample]
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) / (cnt-1.);
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}
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}
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result_type result(dont_care) const
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{
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return this->cov_;
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}
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private:
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result_type cov_;
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};
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} // namespace impl
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///////////////////////////////////////////////////////////////////////////////
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// tag::covariance
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//
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namespace tag
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{
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template<typename VariateType, typename VariateTag>
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struct covariance
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: depends_on<count, mean, mean_of_variates<VariateType, VariateTag> >
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{
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typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl;
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};
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struct abstract_covariance
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: depends_on<>
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{
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};
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}
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///////////////////////////////////////////////////////////////////////////////
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// extract::covariance
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//
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namespace extract
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{
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extractor<tag::abstract_covariance> const covariance = {};
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance)
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}
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using extract::covariance;
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template<typename VariateType, typename VariateTag>
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struct feature_of<tag::covariance<VariateType, VariateTag> >
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: feature_of<tag::abstract_covariance>
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{
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};
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// So that covariance can be automatically substituted with
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// weighted_covariance when the weight parameter is non-void.
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template<typename VariateType, typename VariateTag>
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struct as_weighted_feature<tag::covariance<VariateType, VariateTag> >
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{
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typedef tag::weighted_covariance<VariateType, VariateTag> type;
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};
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template<typename VariateType, typename VariateTag>
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struct feature_of<tag::weighted_covariance<VariateType, VariateTag> >
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: feature_of<tag::covariance<VariateType, VariateTag> >
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{};
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}} // namespace boost::accumulators
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#endif
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