Added boost header

test/external/boost/accumulators/statistics/variance.hpp

@@ -0,0 +1,236 @@
+///////////////////////////////////////////////////////////////////////////////
+// variance.hpp
+//
+//  Copyright 2005 Daniel Egloff, Eric Niebler. 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_VARIANCE_HPP_EAN_28_10_2005
+#define BOOST_ACCUMULATORS_STATISTICS_VARIANCE_HPP_EAN_28_10_2005
+
+#include <boost/mpl/placeholders.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/framework/depends_on.hpp>
+#include <boost/accumulators/statistics_fwd.hpp>
+#include <boost/accumulators/statistics/count.hpp>
+#include <boost/accumulators/statistics/sum.hpp>
+#include <boost/accumulators/statistics/mean.hpp>
+#include <boost/accumulators/statistics/moment.hpp>
+
+namespace boost { namespace accumulators
+{
+
+namespace impl
+{
+    //! Lazy calculation of variance.
+    /*!
+        Default sample variance implementation based on the second moment \f$ M_n^{(2)} \f$ moment<2>, mean and count.
+        \f[
+            \sigma_n^2 = M_n^{(2)} - \mu_n^2.
+        \f]
+        where
+        \f[
+            \mu_n = \frac{1}{n} \sum_{i = 1}^n x_i.
+        \f]
+        is the estimate of the sample mean and \f$n\f$ is the number of samples.
+    */
+    template<typename Sample, typename MeanFeature>
+    struct lazy_variance_impl
+      : accumulator_base
+    {
+        // for boost::result_of
+        typedef typename numeric::functional::average<Sample, std::size_t>::result_type result_type;
+
+        lazy_variance_impl(dont_care) {}
+
+        template<typename Args>
+        result_type result(Args const &args) const
+        {
+            extractor<MeanFeature> mean;
+            result_type tmp = mean(args);
+            return accumulators::moment<2>(args) - tmp * tmp;
+        }
+    };
+
+    //! Iterative calculation of variance.
+    /*!
+        Iterative calculation of sample variance \f$\sigma_n^2\f$ according to the formula
+        \f[
+            \sigma_n^2 = \frac{1}{n} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{n-1}{n} \sigma_{n-1}^2 + \frac{1}{n-1}(x_n - \mu_n)^2.
+        \f]
+        where
+        \f[
+            \mu_n = \frac{1}{n} \sum_{i = 1}^n x_i.
+        \f]
+        is the estimate of the sample mean and \f$n\f$ is the number of samples.
+
+        Note that the sample variance is not defined for \f$n <= 1\f$.
+
+        A simplification can be obtained by the approximate recursion
+        \f[
+            \sigma_n^2 \approx \frac{n-1}{n} \sigma_{n-1}^2 + \frac{1}{n}(x_n - \mu_n)^2.
+        \f]
+        because the difference
+        \f[
+            \left(\frac{1}{n-1} - \frac{1}{n}\right)(x_n - \mu_n)^2 = \frac{1}{n(n-1)}(x_n - \mu_n)^2.
+        \f]
+        converges to zero as \f$n \rightarrow \infty\f$. However, for small \f$ n \f$ the difference
+        can be non-negligible.
+    */
+    template<typename Sample, typename MeanFeature, typename Tag>
+    struct variance_impl
+      : accumulator_base
+    {
+        // for boost::result_of
+        typedef typename numeric::functional::average<Sample, std::size_t>::result_type result_type;
+
+        template<typename Args>
+        variance_impl(Args const &args)
+          : variance(numeric::average(args[sample | Sample()], numeric::one<std::size_t>::value))
+        {
+        }
+
+        template<typename Args>
+        void operator ()(Args const &args)
+        {
+            std::size_t cnt = count(args);
+
+            if(cnt > 1)
+            {
+                extractor<MeanFeature> mean;
+                result_type tmp = args[parameter::keyword<Tag>::get()] - mean(args);
+                this->variance =
+                    numeric::average(this->variance * (cnt - 1), cnt)
+                  + numeric::average(tmp * tmp, cnt - 1);
+            }
+        }
+
+        result_type result(dont_care) const
+        {
+            return this->variance;
+        }
+
+    private:
+        result_type variance;
+    };
+
+} // namespace impl
+
+///////////////////////////////////////////////////////////////////////////////
+// tag::variance
+// tag::immediate_variance
+//
+namespace tag
+{
+    struct lazy_variance
+      : depends_on<moment<2>, mean>
+    {
+        /// INTERNAL ONLY
+        ///
+        typedef accumulators::impl::lazy_variance_impl<mpl::_1, mean> impl;
+    };
+
+    struct variance
+      : depends_on<count, immediate_mean>
+    {
+        /// INTERNAL ONLY
+        ///
+        typedef accumulators::impl::variance_impl<mpl::_1, mean, sample> impl;
+    };
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// extract::lazy_variance
+// extract::variance
+//
+namespace extract
+{
+    extractor<tag::lazy_variance> const lazy_variance = {};
+    extractor<tag::variance> const variance = {};
+
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_variance)
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(variance)
+}
+
+using extract::lazy_variance;
+using extract::variance;
+
+// variance(lazy) -> lazy_variance
+template<>
+struct as_feature<tag::variance(lazy)>
+{
+    typedef tag::lazy_variance type;
+};
+
+// variance(immediate) -> variance
+template<>
+struct as_feature<tag::variance(immediate)>
+{
+    typedef tag::variance type;
+};
+
+// for the purposes of feature-based dependency resolution,
+// immediate_variance provides the same feature as variance
+template<>
+struct feature_of<tag::lazy_variance>
+  : feature_of<tag::variance>
+{
+};
+
+// So that variance can be automatically substituted with
+// weighted_variance when the weight parameter is non-void.
+template<>
+struct as_weighted_feature<tag::variance>
+{
+    typedef tag::weighted_variance type;
+};
+
+// for the purposes of feature-based dependency resolution,
+// weighted_variance provides the same feature as variance
+template<>
+struct feature_of<tag::weighted_variance>
+  : feature_of<tag::variance>
+{
+};
+
+// So that immediate_variance can be automatically substituted with
+// immediate_weighted_variance when the weight parameter is non-void.
+template<>
+struct as_weighted_feature<tag::lazy_variance>
+{
+    typedef tag::lazy_weighted_variance type;
+};
+
+// for the purposes of feature-based dependency resolution,
+// immediate_weighted_variance provides the same feature as immediate_variance
+template<>
+struct feature_of<tag::lazy_weighted_variance>
+  : feature_of<tag::lazy_variance>
+{
+};
+
+////////////////////////////////////////////////////////////////////////////
+//// droppable_accumulator<variance_impl>
+////  need to specialize droppable lazy variance to cache the result at the
+////  point the accumulator is dropped.
+///// INTERNAL ONLY
+/////
+//template<typename Sample, typename MeanFeature>
+//struct droppable_accumulator<impl::variance_impl<Sample, MeanFeature> >
+//  : droppable_accumulator_base<
+//        with_cached_result<impl::variance_impl<Sample, MeanFeature> >
+//    >
+//{
+//    template<typename Args>
+//    droppable_accumulator(Args const &args)
+//      : droppable_accumulator::base(args)
+//    {
+//    }
+//};
+
+}} // namespace boost::accumulators
+
+#endif