/////////////////////////////////////////////////////////////////////////////// | |
// 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 |