boost/accumulators/statistics/variance.hpp
/////////////////////////////////////////////////////////////////////////////// // 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 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 = {}; } 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