boost/accumulators/statistics/rolling_variance.hpp
/////////////////////////////////////////////////////////////////////////////// // 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