Chris@102: ///////////////////////////////////////////////////////////////////////////////
Chris@102: // rolling_variance.hpp
Chris@102: // Copyright (C) 2005 Eric Niebler
Chris@102: // Copyright (C) 2014 Pieter Bastiaan Ober (Integricom).
Chris@102: // Distributed under the Boost Software License, Version 1.0.
Chris@102: // (See accompanying file LICENSE_1_0.txt or copy at
Chris@102: // http://www.boost.org/LICENSE_1_0.txt)
Chris@102: 
Chris@102: #ifndef BOOST_ACCUMULATORS_STATISTICS_ROLLING_VARIANCE_HPP_EAN_15_11_2011
Chris@102: #define BOOST_ACCUMULATORS_STATISTICS_ROLLING_VARIANCE_HPP_EAN_15_11_2011
Chris@102: 
Chris@102: #include <boost/accumulators/accumulators.hpp>
Chris@102: #include <boost/accumulators/statistics/stats.hpp>
Chris@102: 
Chris@102: #include <boost/mpl/placeholders.hpp>
Chris@102: #include <boost/accumulators/framework/accumulator_base.hpp>
Chris@102: #include <boost/accumulators/framework/extractor.hpp>
Chris@102: #include <boost/accumulators/numeric/functional.hpp>
Chris@102: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@102: #include <boost/accumulators/framework/depends_on.hpp>
Chris@102: #include <boost/accumulators/statistics_fwd.hpp>
Chris@102: #include <boost/accumulators/statistics/rolling_mean.hpp>
Chris@102: #include <boost/accumulators/statistics/rolling_moment.hpp>
Chris@102: 
Chris@102: #include <boost/type_traits/is_arithmetic.hpp>
Chris@102: #include <boost/utility/enable_if.hpp>
Chris@102: 
Chris@102: namespace boost { namespace accumulators
Chris@102: {
Chris@102: namespace impl
Chris@102: {
Chris@102:     //! Immediate (lazy) calculation of the rolling variance.
Chris@102:     /*!
Chris@102:     Calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
Chris@102:     http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
Chris@102:     For a rolling window of size \f$N\f$, when \f$n <= N\f$, the variance is computed according to the formula
Chris@102:     \f[
Chris@102:     \sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2.
Chris@102:     \f]
Chris@102:     When \f$n > N\f$, the sample variance over the window becomes:
Chris@102:     \f[
Chris@102:     \sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2.
Chris@102:     \f]
Chris@102:     */
Chris@102:     ///////////////////////////////////////////////////////////////////////////////
Chris@102:     // lazy_rolling_variance_impl
Chris@102:     //
Chris@102:     template<typename Sample>
Chris@102:     struct lazy_rolling_variance_impl
Chris@102:         : accumulator_base
Chris@102:     {
Chris@102:         // for boost::result_of
Chris@102:         typedef typename numeric::functional::fdiv<Sample, std::size_t,void,void>::result_type result_type;
Chris@102: 
Chris@102:         lazy_rolling_variance_impl(dont_care) {}
Chris@102: 
Chris@102:         template<typename Args>
Chris@102:         result_type result(Args const &args) const
Chris@102:         {
Chris@102:             result_type mean = rolling_mean(args);
Chris@102:             size_t nr_samples = rolling_count(args);
Chris@102:             if (nr_samples < 2) return result_type();
Chris@102:             return nr_samples*(rolling_moment<2>(args) - mean*mean)/(nr_samples-1);
Chris@102:         }
Chris@102:     };
Chris@102: 
Chris@102:     //! Iterative calculation of the rolling variance.
Chris@102:     /*!
Chris@102:     Iterative calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
Chris@102:     http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
Chris@102:     For a rolling window of size \f$N\f$, for the first \f$N\f$ samples, the variance is computed according to the formula
Chris@102:     \f[
Chris@102:     \sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
Chris@102:     \f]
Chris@102:     where the sum of squares \f$M_{2,n}\f$ can be recursively computed as:
Chris@102:     \f[
Chris@102:     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}),
Chris@102:     \f]
Chris@102:     and the estimate of the sample mean as:
Chris@102:     \f[
Chris@102:     \mu_n = \frac{1}{n} \sum_{i = 1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - \mu_{n-1}).
Chris@102:     \f]
Chris@102:     For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest
Chris@102:     sample \f$x_{n-N}\f$ is dropped from the window. The sample variance over the window now becomes:
Chris@102:     \f[
Chris@102:     \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},
Chris@102:     \f]
Chris@102:     where the sum of squares \f$M_{2,n}\f$ now equals:
Chris@102:     \f[
Chris@102:     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}),
Chris@102:     \f]
Chris@102:     and the estimated mean is:
Chris@102:     \f[
Chris@102:     \mu_n = \frac{1}{N} \sum_{i = n-N+1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - x_{n-N}).
Chris@102:     \f]
Chris@102: 
Chris@102:     Note that the sample variance is not defined for \f$n <= 1\f$.
Chris@102: 
Chris@102:     */
Chris@102:     ///////////////////////////////////////////////////////////////////////////////
Chris@102:     // immediate_rolling_variance_impl
Chris@102:     //
Chris@102:     template<typename Sample>
Chris@102:     struct immediate_rolling_variance_impl
Chris@102:         : accumulator_base
Chris@102:     {
Chris@102:         // for boost::result_of
Chris@102:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
Chris@102: 
Chris@102:         template<typename Args>
Chris@102:         immediate_rolling_variance_impl(Args const &args)
Chris@102:             : previous_mean_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
Chris@102:             , sum_of_squares_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
Chris@102:         {
Chris@102:         }
Chris@102: 
Chris@102:         template<typename Args>
Chris@102:         void operator()(Args const &args)
Chris@102:         {
Chris@102:             Sample added_sample = args[sample];
Chris@102: 
Chris@102:             result_type mean = immediate_rolling_mean(args);
Chris@102:             sum_of_squares_ += (added_sample-mean)*(added_sample-previous_mean_);
Chris@102: 
Chris@102:             if(is_rolling_window_plus1_full(args))
Chris@102:             {
Chris@102:                 Sample removed_sample = rolling_window_plus1(args).front();
Chris@102:                 sum_of_squares_ -= (removed_sample-mean)*(removed_sample-previous_mean_);
Chris@102:                 prevent_underflow(sum_of_squares_);
Chris@102:             }
Chris@102:             previous_mean_ = mean;
Chris@102:         }
Chris@102: 
Chris@102:         template<typename Args>
Chris@102:         result_type result(Args const &args) const
Chris@102:         {
Chris@102:             size_t nr_samples = rolling_count(args);
Chris@102:             if (nr_samples < 2) return result_type();
Chris@102:             return numeric::fdiv(sum_of_squares_,(nr_samples-1));
Chris@102:         }
Chris@102: 
Chris@102:     private:
Chris@102: 
Chris@102:         result_type previous_mean_;
Chris@102:         result_type sum_of_squares_;
Chris@102: 
Chris@102:         template<typename T>
Chris@102:         void prevent_underflow(T &non_negative_number,typename boost::enable_if<boost::is_arithmetic<T>,T>::type* = 0)
Chris@102:         {
Chris@102:             if (non_negative_number < T(0)) non_negative_number = T(0);
Chris@102:         }
Chris@102:         template<typename T>
Chris@102:         void prevent_underflow(T &non_arithmetic_quantity,typename boost::disable_if<boost::is_arithmetic<T>,T>::type* = 0)
Chris@102:         {
Chris@102:         }
Chris@102:     };
Chris@102: } // namespace impl
Chris@102: 
Chris@102: ///////////////////////////////////////////////////////////////////////////////
Chris@102: // tag:: lazy_rolling_variance
Chris@102: // tag:: immediate_rolling_variance
Chris@102: // tag:: rolling_variance
Chris@102: //
Chris@102: namespace tag
Chris@102: {
Chris@102:     struct lazy_rolling_variance
Chris@102:         : depends_on< rolling_count, rolling_mean, rolling_moment<2> >
Chris@102:     {
Chris@102:         /// INTERNAL ONLY
Chris@102:         ///
Chris@102:         typedef accumulators::impl::lazy_rolling_variance_impl< mpl::_1 > impl;
Chris@102: 
Chris@102:         #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
Chris@102:         /// tag::rolling_window::window_size named parameter
Chris@102:         static boost::parameter::keyword<tag::rolling_window_size> const window_size;
Chris@102:         #endif
Chris@102:     };
Chris@102: 
Chris@102:     struct immediate_rolling_variance
Chris@102:         : depends_on< rolling_window_plus1, rolling_count, immediate_rolling_mean>
Chris@102:     {
Chris@102:         /// INTERNAL ONLY
Chris@102:         ///
Chris@102:         typedef accumulators::impl::immediate_rolling_variance_impl< mpl::_1> impl;
Chris@102: 
Chris@102:         #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
Chris@102:         /// tag::rolling_window::window_size named parameter
Chris@102:         static boost::parameter::keyword<tag::rolling_window_size> const window_size;
Chris@102:         #endif
Chris@102:     };
Chris@102: 
Chris@102:     // make immediate_rolling_variance the default implementation
Chris@102:     struct rolling_variance : immediate_rolling_variance {};
Chris@102: } // namespace tag
Chris@102: 
Chris@102: ///////////////////////////////////////////////////////////////////////////////
Chris@102: // extract::lazy_rolling_variance
Chris@102: // extract::immediate_rolling_variance
Chris@102: // extract::rolling_variance
Chris@102: //
Chris@102: namespace extract
Chris@102: {
Chris@102:     extractor<tag::lazy_rolling_variance> const lazy_rolling_variance = {};
Chris@102:     extractor<tag::immediate_rolling_variance> const immediate_rolling_variance = {};
Chris@102:     extractor<tag::rolling_variance> const rolling_variance = {};
Chris@102: 
Chris@102:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_rolling_variance)
Chris@102:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(immediate_rolling_variance)
Chris@102:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_variance)
Chris@102: }
Chris@102: 
Chris@102: using extract::lazy_rolling_variance;
Chris@102: using extract::immediate_rolling_variance;
Chris@102: using extract::rolling_variance;
Chris@102: 
Chris@102: // rolling_variance(lazy) -> lazy_rolling_variance
Chris@102: template<>
Chris@102: struct as_feature<tag::rolling_variance(lazy)>
Chris@102: {
Chris@102:     typedef tag::lazy_rolling_variance type;
Chris@102: };
Chris@102: 
Chris@102: // rolling_variance(immediate) -> immediate_rolling_variance
Chris@102: template<>
Chris@102: struct as_feature<tag::rolling_variance(immediate)>
Chris@102: {
Chris@102:     typedef tag::immediate_rolling_variance type;
Chris@102: };
Chris@102: 
Chris@102: // for the purposes of feature-based dependency resolution,
Chris@102: // lazy_rolling_variance provides the same feature as rolling_variance
Chris@102: template<>
Chris@102: struct feature_of<tag::lazy_rolling_variance>
Chris@102:     : feature_of<tag::rolling_variance>
Chris@102: {
Chris@102: };
Chris@102: 
Chris@102: // for the purposes of feature-based dependency resolution,
Chris@102: // immediate_rolling_variance provides the same feature as rolling_variance
Chris@102: template<>
Chris@102: struct feature_of<tag::immediate_rolling_variance>
Chris@102:   : feature_of<tag::rolling_variance>
Chris@102: {
Chris@102: };
Chris@102: }} // namespace boost::accumulators
Chris@102: 
Chris@102: #endif