add boost on mac

macx64/include/boost/accumulators/statistics/rolling_variance.hpp

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+///////////////////////////////////////////////////////////////////////////////
+// rolling_variance.hpp
+// Copyright (C) 2005 Eric Niebler
+// Copyright (C) 2014 Pieter Bastiaan Ober (Integricom).
+// 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_ROLLING_VARIANCE_HPP_EAN_15_11_2011
+#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_VARIANCE_HPP_EAN_15_11_2011
+
+#include <boost/accumulators/accumulators.hpp>
+#include <boost/accumulators/statistics/stats.hpp>
+
+#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/rolling_mean.hpp>
+#include <boost/accumulators/statistics/rolling_moment.hpp>
+
+#include <boost/type_traits/is_arithmetic.hpp>
+#include <boost/utility/enable_if.hpp>
+
+namespace boost { namespace accumulators
+{
+namespace impl
+{
+    //! Immediate (lazy) calculation of the rolling variance.
+    /*!
+    Calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
+    http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
+    For a rolling window of size \f$N\f$, when \f$n <= N\f$, the variance is computed according to the formula
+    \f[
+    \sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2.
+    \f]
+    When \f$n > N\f$, the sample variance over the window becomes:
+    \f[
+    \sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2.
+    \f]
+    */
+    ///////////////////////////////////////////////////////////////////////////////
+    // lazy_rolling_variance_impl
+    //
+    template<typename Sample>
+    struct lazy_rolling_variance_impl
+        : accumulator_base
+    {
+        // for boost::result_of
+        typedef typename numeric::functional::fdiv<Sample, std::size_t,void,void>::result_type result_type;
+
+        lazy_rolling_variance_impl(dont_care) {}
+
+        template<typename Args>
+        result_type result(Args const &args) const
+        {
+            result_type mean = rolling_mean(args);
+            size_t nr_samples = rolling_count(args);
+            if (nr_samples < 2) return result_type();
+            return nr_samples*(rolling_moment<2>(args) - mean*mean)/(nr_samples-1);
+        }
+    };
+
+    //! Iterative calculation of the rolling variance.
+    /*!
+    Iterative calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
+    http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
+    For a rolling window of size \f$N\f$, for the first \f$N\f$ samples, the variance is computed according to the formula
+    \f[
+    \sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
+    \f]
+    where the sum of squares \f$M_{2,n}\f$ can be recursively computed as:
+    \f[
+    M_{2,n} = \sum_{i = 1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}),
+    \f]
+    and the estimate of the sample mean as:
+    \f[
+    \mu_n = \frac{1}{n} \sum_{i = 1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - \mu_{n-1}).
+    \f]
+    For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest
+    sample \f$x_{n-N}\f$ is dropped from the window. The sample variance over the window now becomes:
+    \f[
+    \sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
+    \f]
+    where the sum of squares \f$M_{2,n}\f$ now equals:
+    \f[
+    M_{2,n} = \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}) - (x_{n-N} - \mu_n)(x_{n-N} - \mu_{n-1}),
+    \f]
+    and the estimated mean is:
+    \f[
+    \mu_n = \frac{1}{N} \sum_{i = n-N+1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - x_{n-N}).
+    \f]
+
+    Note that the sample variance is not defined for \f$n <= 1\f$.
+
+    */
+    ///////////////////////////////////////////////////////////////////////////////
+    // immediate_rolling_variance_impl
+    //
+    template<typename Sample>
+    struct immediate_rolling_variance_impl
+        : accumulator_base
+    {
+        // for boost::result_of
+        typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
+
+        template<typename Args>
+        immediate_rolling_variance_impl(Args const &args)
+            : previous_mean_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
+            , sum_of_squares_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
+        {
+        }
+
+        template<typename Args>
+        void operator()(Args const &args)
+        {
+            Sample added_sample = args[sample];
+
+            result_type mean = immediate_rolling_mean(args);
+            sum_of_squares_ += (added_sample-mean)*(added_sample-previous_mean_);
+
+            if(is_rolling_window_plus1_full(args))
+            {
+                Sample removed_sample = rolling_window_plus1(args).front();
+                sum_of_squares_ -= (removed_sample-mean)*(removed_sample-previous_mean_);
+                prevent_underflow(sum_of_squares_);
+            }
+            previous_mean_ = mean;
+        }
+
+        template<typename Args>
+        result_type result(Args const &args) const
+        {
+            size_t nr_samples = rolling_count(args);
+            if (nr_samples < 2) return result_type();
+            return numeric::fdiv(sum_of_squares_,(nr_samples-1));
+        }
+
+    private:
+
+        result_type previous_mean_;
+        result_type sum_of_squares_;
+
+        template<typename T>
+        void prevent_underflow(T &non_negative_number,typename boost::enable_if<boost::is_arithmetic<T>,T>::type* = 0)
+        {
+            if (non_negative_number < T(0)) non_negative_number = T(0);
+        }
+        template<typename T>
+        void prevent_underflow(T &non_arithmetic_quantity,typename boost::disable_if<boost::is_arithmetic<T>,T>::type* = 0)
+        {
+        }
+    };
+} // namespace impl
+
+///////////////////////////////////////////////////////////////////////////////
+// tag:: lazy_rolling_variance
+// tag:: immediate_rolling_variance
+// tag:: rolling_variance
+//
+namespace tag
+{
+    struct lazy_rolling_variance
+        : depends_on< rolling_count, rolling_mean, rolling_moment<2> >
+    {
+        /// INTERNAL ONLY
+        ///
+        typedef accumulators::impl::lazy_rolling_variance_impl< mpl::_1 > impl;
+
+        #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
+        /// tag::rolling_window::window_size named parameter
+        static boost::parameter::keyword<tag::rolling_window_size> const window_size;
+        #endif
+    };
+
+    struct immediate_rolling_variance
+        : depends_on< rolling_window_plus1, rolling_count, immediate_rolling_mean>
+    {
+        /// INTERNAL ONLY
+        ///
+        typedef accumulators::impl::immediate_rolling_variance_impl< mpl::_1> impl;
+
+        #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
+        /// tag::rolling_window::window_size named parameter
+        static boost::parameter::keyword<tag::rolling_window_size> const window_size;
+        #endif
+    };
+
+    // make immediate_rolling_variance the default implementation
+    struct rolling_variance : immediate_rolling_variance {};
+} // namespace tag
+
+///////////////////////////////////////////////////////////////////////////////
+// extract::lazy_rolling_variance
+// extract::immediate_rolling_variance
+// extract::rolling_variance
+//
+namespace extract
+{
+    extractor<tag::lazy_rolling_variance> const lazy_rolling_variance = {};
+    extractor<tag::immediate_rolling_variance> const immediate_rolling_variance = {};
+    extractor<tag::rolling_variance> const rolling_variance = {};
+
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_rolling_variance)
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(immediate_rolling_variance)
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_variance)
+}
+
+using extract::lazy_rolling_variance;
+using extract::immediate_rolling_variance;
+using extract::rolling_variance;
+
+// rolling_variance(lazy) -> lazy_rolling_variance
+template<>
+struct as_feature<tag::rolling_variance(lazy)>
+{
+    typedef tag::lazy_rolling_variance type;
+};
+
+// rolling_variance(immediate) -> immediate_rolling_variance
+template<>
+struct as_feature<tag::rolling_variance(immediate)>
+{
+    typedef tag::immediate_rolling_variance type;
+};
+
+// for the purposes of feature-based dependency resolution,
+// lazy_rolling_variance provides the same feature as rolling_variance
+template<>
+struct feature_of<tag::lazy_rolling_variance>
+    : feature_of<tag::rolling_variance>
+{
+};
+
+// for the purposes of feature-based dependency resolution,
+// immediate_rolling_variance provides the same feature as rolling_variance
+template<>
+struct feature_of<tag::immediate_rolling_variance>
+  : feature_of<tag::rolling_variance>
+{
+};
+}} // namespace boost::accumulators
+
+#endif