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