Added boost header

test/external/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