Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

This is the documentation for a snapshot of the develop branch, built from commit 10855bc5cc.
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Reference

Accumulators Framework Reference
Statistics Library Reference
Numeric Operators Library Reference

Accumulators Framework Reference

Includes all of the Accumulators Framework


BOOST_ACCUMULATORS_MAX_FEATURES
BOOST_ACCUMULATORS_MAX_ARGS
BOOST_ACCUMULATORS_PROTO_DISABLE_IF_IS_CONST(T)
BOOST_ACCUMULATORS_GCC_VERSION
BOOST_ACCUMULATORS_IGNORE_GLOBAL(X)
namespace boost {
  namespace accumulators {
    template<typename Sample, typename Features, typename Weight> 
      struct accumulator_set;
    template<typename Feature> struct as_feature;
    template<typename Feature> struct as_weighted_feature;
    template<typename Feature1, typename Feature2, ... > struct depends_on;
    template<typename Accumulator> struct droppable_accumulator;
    template<typename Accumulator> struct droppable_accumulator_base;
    template<typename Feature> struct extractor;
    template<typename Feature> struct feature_of;
    template<typename Feature1, typename Feature2, ... > struct features;
    template<typename Accumulator> struct with_cached_result;
    template<typename Feature, typename AccumulatorSet> 
      mpl::apply< AccumulatorSet, Feature >::type::result_type 
      extract_result(AccumulatorSet const & acc);
    namespace impl {
    }
    namespace tag {
      template<typename Feature> struct droppable;
      template<typename Feature, typename Tag, typename AccumulatorSet> 
        struct external;
      template<typename Referent, typename Tag> struct reference;
      template<typename Tag> struct reference_tag;
      template<typename ValueType, typename Tag> struct value;
      template<typename Tag> struct value_tag;
    }
  }
}
namespace boost {
  namespace accumulators {
    struct accumulator_base;
    struct dont_care;
  }
}
namespace boost {
  namespace accumulators {
    template<typename Stat> struct accumulator_concept;
  }
}
namespace boost {
  namespace accumulators {
    template<typename Feature, typename AccumulatorSet> 
      mpl::apply< AccumulatorSet, Feature >::type & 
      find_accumulator(AccumulatorSet &acc  BOOST_ACCUMULATORS_PROTO_DISABLE_IF_IS_CONST);
  }
}
namespace boost {
  namespace accumulators {
    template<typename Feature> struct as_feature<tag::droppable< Feature >>;
    template<typename Feature> 
      struct as_weighted_feature<tag::droppable< Feature >>;
    template<typename Feature> struct feature_of<tag::droppable< Feature >>;
    namespace tag {
      template<typename Feature> struct as_droppable;

      template<typename Feature> struct as_droppable<droppable< Feature >>;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename Feature, typename Tag, typename AccumulatorSet> 
      struct feature_of<tag::external< Feature, Tag, AccumulatorSet >>;
    namespace impl {
    }
    namespace tag {
      template<typename Feature, typename Tag> 
        struct external<Feature, Tag, void>;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename ValueType, typename Tag> 
      struct feature_of<tag::reference< ValueType, Tag >>;
    namespace extract {
    }
    namespace impl {
      template<typename Referent, typename Tag> struct reference_accumulator_impl;
    }
    namespace tag {
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename ValueType, typename Tag> 
      struct feature_of<tag::value< ValueType, Tag >>;
    namespace extract {
    }
    namespace impl {
      template<typename ValueType, typename Tag> struct value_accumulator_impl;
    }
    namespace tag {
    }
  }
}

Statistics Library Reference

Header <boost/accumulators/statistics.hpp>
Header <boost/accumulators/statistics/count.hpp>
Header <boost/accumulators/statistics/covariance.hpp>
Header <boost/accumulators/statistics/density.hpp>
Header <boost/accumulators/statistics/error_of.hpp>
Header <boost/accumulators/statistics/error_of_mean.hpp>
Header <boost/accumulators/statistics/extended_p_square.hpp>
Header <boost/accumulators/statistics/extended_p_square_quantile.hpp>
Header <boost/accumulators/statistics/kurtosis.hpp>
Header <boost/accumulators/statistics/max.hpp>
Header <boost/accumulators/statistics/mean.hpp>
Header <boost/accumulators/statistics/median.hpp>
Header <boost/accumulators/statistics/min.hpp>
Header <boost/accumulators/statistics/moment.hpp>
Header <boost/accumulators/statistics/p_square_cumul_dist.hpp>
Header <boost/accumulators/statistics/p_square_quantile.hpp>
Header <boost/accumulators/statistics/peaks_over_threshold.hpp>
Header <boost/accumulators/statistics/pot_quantile.hpp>
Header <boost/accumulators/statistics/pot_tail_mean.hpp>
Header <boost/accumulators/statistics/rolling_count.hpp>
Header <boost/accumulators/statistics/rolling_mean.hpp>
Header <boost/accumulators/statistics/rolling_moment.hpp>
Header <boost/accumulators/statistics/rolling_sum.hpp>
Header <boost/accumulators/statistics/rolling_variance.hpp>
Header <boost/accumulators/statistics/rolling_window.hpp>
Header <boost/accumulators/statistics/skewness.hpp>
Header <boost/accumulators/statistics/stats.hpp>
Header <boost/accumulators/statistics/sum.hpp>
Header <boost/accumulators/statistics/sum_kahan.hpp>
Header <boost/accumulators/statistics/tail.hpp>
Header <boost/accumulators/statistics/tail_mean.hpp>
Header <boost/accumulators/statistics/tail_quantile.hpp>
Header <boost/accumulators/statistics/tail_variate.hpp>
Header <boost/accumulators/statistics/tail_variate_means.hpp>
Header <boost/accumulators/statistics/times2_iterator.hpp>
Header <boost/accumulators/statistics/variance.hpp>
Header <boost/accumulators/statistics/variates/covariate.hpp>
Header <boost/accumulators/statistics/weighted_covariance.hpp>
Header <boost/accumulators/statistics/weighted_density.hpp>
Header <boost/accumulators/statistics/weighted_extended_p_square.hpp>
Header <boost/accumulators/statistics/weighted_kurtosis.hpp>
Header <boost/accumulators/statistics/weighted_mean.hpp>
Header <boost/accumulators/statistics/weighted_median.hpp>
Header <boost/accumulators/statistics/weighted_moment.hpp>
Header <boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp>
Header <boost/accumulators/statistics/weighted_p_square_quantile.hpp>
Header <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp>
Header <boost/accumulators/statistics/weighted_skewness.hpp>
Header <boost/accumulators/statistics/weighted_sum.hpp>
Header <boost/accumulators/statistics/weighted_sum_kahan.hpp>
Header <boost/accumulators/statistics/weighted_tail_mean.hpp>
Header <boost/accumulators/statistics/weighted_tail_quantile.hpp>
Header <boost/accumulators/statistics/weighted_tail_variate_means.hpp>
Header <boost/accumulators/statistics/weighted_variance.hpp>
Header <boost/accumulators/statistics/with_error.hpp>
Header <boost/accumulators/statistics_fwd.hpp>

Includes all of the Statistical Accumulators Library

namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::count > const count;
    }
    namespace impl {
      struct count_impl;
    }
    namespace tag {
      struct count;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename VariateType, typename VariateTag> 
      struct as_weighted_feature<tag::covariance< VariateType, VariateTag >>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::covariance< VariateType, VariateTag >>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::weighted_covariance< VariateType, VariateTag >>;
    namespace extract {
      extractor< tag::abstract_covariance > const covariance;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_covariance;
    }
  }
  namespace numeric {
    namespace functional {
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct outer_product;

      template<typename Left, typename Right> 
        struct outer_product<Left, Right, std_vector_tag, std_vector_tag>;

      template<typename Left, typename Right, typename EnableIf = void> 
        struct outer_product_base;
    }
    namespace op {
      struct outer_product;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_weighted_feature<tag::density>;
    template<> struct feature_of<tag::weighted_density>;
    namespace extract {
      extractor< tag::density > const density;
    }
    namespace impl {
    }
    namespace tag {
      struct density;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename Feature> struct as_feature<tag::error_of< Feature >>;
    template<typename Feature> 
      struct as_weighted_feature<tag::error_of< Feature >>;
    namespace extract {
    }
    namespace impl {
    }
    namespace tag {
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_weighted_feature<tag::extended_p_square>;
    template<> struct feature_of<tag::weighted_extended_p_square>;
    namespace extract {
      extractor< tag::extended_p_square > const extended_p_square;
    }
    namespace impl {
    }
    namespace tag {
      struct extended_p_square;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::extended_p_square_quantile(linear)>;
    template<> struct as_feature<tag::extended_p_square_quantile(quadratic)>;
    template<> 
      struct as_feature<tag::weighted_extended_p_square_quantile(linear)>;
    template<> 
      struct as_feature<tag::weighted_extended_p_square_quantile(quadratic)>;
    template<> struct as_weighted_feature<tag::extended_p_square_quantile>;
    template<> 
      struct as_weighted_feature<tag::extended_p_square_quantile_quadratic>;
    template<> struct feature_of<tag::extended_p_square_quantile>;
    template<> struct feature_of<tag::extended_p_square_quantile_quadratic>;
    template<> struct feature_of<tag::weighted_extended_p_square_quantile>;
    template<> 
      struct feature_of<tag::weighted_extended_p_square_quantile_quadratic>;
    namespace extract {
      extractor< tag::extended_p_square_quantile > const extended_p_square_quantile;
      extractor< tag::extended_p_square_quantile_quadratic > const extended_p_square_quantile_quadratic;
      extractor< tag::weighted_extended_p_square_quantile > const weighted_extended_p_square_quantile;
      extractor< tag::weighted_extended_p_square_quantile_quadratic > const weighted_extended_p_square_quantile_quadratic;
    }
    namespace impl {
    }
    namespace tag {
      struct extended_p_square_quantile;
      struct extended_p_square_quantile_quadratic;
      struct weighted_extended_p_square_quantile;
      struct weighted_extended_p_square_quantile_quadratic;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_weighted_feature<tag::kurtosis>;
    template<> struct feature_of<tag::weighted_kurtosis>;
    namespace extract {
      extractor< tag::kurtosis > const kurtosis;
    }
    namespace impl {
    }
    namespace tag {
      struct kurtosis;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::max > const max;
    }
    namespace impl {
    }
    namespace tag {
      struct max;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::mean(immediate)>;
    template<> struct as_feature<tag::mean(lazy)>;
    template<typename VariateType, typename VariateTag> 
      struct as_feature<tag::mean_of_variates< VariateType, VariateTag >(immediate)>;
    template<typename VariateType, typename VariateTag> 
      struct as_feature<tag::mean_of_variates< VariateType, VariateTag >(lazy)>;
    template<> struct as_feature<tag::mean_of_weights(immediate)>;
    template<> struct as_feature<tag::mean_of_weights(lazy)>;
    template<> struct as_weighted_feature<tag::immediate_mean>;
    template<typename VariateType, typename VariateTag> 
      struct as_weighted_feature<tag::immediate_mean_of_variates< VariateType, VariateTag >>;
    template<> struct as_weighted_feature<tag::mean>;
    template<typename VariateType, typename VariateTag> 
      struct as_weighted_feature<tag::mean_of_variates< VariateType, VariateTag >>;
    template<> struct feature_of<tag::immediate_mean>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::immediate_mean_of_variates< VariateType, VariateTag >>;
    template<> struct feature_of<tag::immediate_mean_of_weights>;
    template<> struct feature_of<tag::immediate_weighted_mean>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::immediate_weighted_mean_of_variates< VariateType, VariateTag >>;
    template<> struct feature_of<tag::weighted_mean>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::weighted_mean_of_variates< VariateType, VariateTag >>;
    namespace extract {
      extractor< tag::mean > const mean;
      extractor< tag::mean_of_weights > const mean_of_weights;
    }
    namespace impl {
    }
    namespace tag {
      struct immediate_mean;
      struct immediate_mean_of_weights;
      struct mean;
      struct mean_of_weights;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::median(with_density)>;
    template<> 
      struct as_feature<tag::median(with_p_square_cumulative_distribution)>;
    template<> struct as_feature<tag::median(with_p_square_quantile)>;
    template<> struct as_weighted_feature<tag::median>;
    template<> struct as_weighted_feature<tag::with_density_median>;
    template<> 
      struct as_weighted_feature<tag::with_p_square_cumulative_distribution_median>;
    template<> struct feature_of<tag::weighted_median>;
    template<> struct feature_of<tag::with_density_median>;
    template<> struct feature_of<tag::with_density_weighted_median>;
    template<> 
      struct feature_of<tag::with_p_square_cumulative_distribution_median>;
    template<> 
      struct feature_of<tag::with_p_square_cumulative_distribution_weighted_median>;
    namespace extract {
      extractor< tag::median > const median;
      extractor< tag::with_density_median > const with_density_median;
      extractor< tag::with_p_square_cumulative_distribution_median > const with_p_square_cumulative_distribution_median;
    }
    namespace impl {
    }
    namespace tag {
      struct median;
      struct with_density_median;
      struct with_p_square_cumulative_distribution_median;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::min > const min;
    }
    namespace impl {
    }
    namespace tag {
      struct min;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<int N> struct as_weighted_feature<tag::moment< N >>;
    template<int N> struct feature_of<tag::weighted_moment< N >>;
    namespace extract {
    }
    namespace impl {
    }
    namespace tag {
    }
  }
  namespace numeric {
  }
}
namespace boost {
  namespace accumulators {
    template<> 
      struct as_weighted_feature<tag::p_square_cumulative_distribution>;
    template<> 
      struct feature_of<tag::weighted_p_square_cumulative_distribution>;
    namespace extract {
      extractor< tag::p_square_cumulative_distribution > const p_square_cumulative_distribution;
    }
    namespace impl {
    }
    namespace tag {
      struct p_square_cumulative_distribution;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_weighted_feature<tag::p_square_quantile>;
    template<> struct feature_of<tag::weighted_p_square_quantile>;
    namespace extract {
      extractor< tag::p_square_quantile > const p_square_quantile;
      extractor< tag::p_square_quantile_for_median > const p_square_quantile_for_median;
    }
    namespace impl {
    }
    namespace tag {
      struct p_square_quantile;
      struct p_square_quantile_for_median;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> 
      struct as_feature<tag::peaks_over_threshold< LeftRight >(with_threshold_probability)>;
    template<typename LeftRight> 
      struct as_feature<tag::peaks_over_threshold< LeftRight >(with_threshold_value)>;
    template<typename LeftRight> 
      struct as_weighted_feature<tag::peaks_over_threshold< LeftRight >>;
    template<typename LeftRight> 
      struct as_weighted_feature<tag::peaks_over_threshold_prob< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::peaks_over_threshold< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::peaks_over_threshold_prob< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_peaks_over_threshold< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_peaks_over_threshold_prob< LeftRight >>;
    namespace extract {
      extractor< tag::abstract_peaks_over_threshold > const peaks_over_threshold;
    }
    namespace impl {
      template<typename Sample, typename LeftRight> 
        struct peaks_over_threshold_impl;
    }
    namespace tag {
      struct abstract_peaks_over_threshold;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> 
      struct as_feature<tag::pot_quantile< LeftRight >(with_threshold_probability)>;
    template<typename LeftRight> 
      struct as_feature<tag::pot_quantile< LeftRight >(with_threshold_value)>;
    template<typename LeftRight> 
      struct as_feature<tag::weighted_pot_quantile< LeftRight >(with_threshold_probability)>;
    template<typename LeftRight> 
      struct as_feature<tag::weighted_pot_quantile< LeftRight >(with_threshold_value)>;
    template<typename LeftRight> 
      struct as_weighted_feature<tag::pot_quantile< LeftRight >>;
    template<typename LeftRight> 
      struct as_weighted_feature<tag::pot_quantile_prob< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::pot_quantile< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::pot_quantile_prob< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_pot_quantile< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_pot_quantile_prob< LeftRight >>;
    namespace impl {
    }
    namespace tag {
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> 
      struct as_feature<tag::pot_tail_mean< LeftRight >(with_threshold_probability)>;
    template<typename LeftRight> 
      struct as_feature<tag::pot_tail_mean< LeftRight >(with_threshold_value)>;
    template<typename LeftRight> 
      struct as_feature<tag::weighted_pot_tail_mean< LeftRight >(with_threshold_probability)>;
    template<typename LeftRight> 
      struct as_feature<tag::weighted_pot_tail_mean< LeftRight >(with_threshold_value)>;
    template<typename LeftRight> 
      struct as_weighted_feature<tag::pot_tail_mean< LeftRight >>;
    template<typename LeftRight> 
      struct as_weighted_feature<tag::pot_tail_mean_prob< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::pot_tail_mean< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::pot_tail_mean_prob< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_pot_tail_mean< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_pot_tail_mean_prob< LeftRight >>;
    namespace impl {
    }
    namespace tag {
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::rolling_count > const rolling_count;
    }
    namespace impl {
    }
    namespace tag {
      struct rolling_count;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::rolling_mean(immediate)>;
    template<> struct as_feature<tag::rolling_mean(lazy)>;
    template<> struct feature_of<tag::immediate_rolling_mean>;
    template<> struct feature_of<tag::lazy_rolling_mean>;
    namespace extract {
      extractor< tag::lazy_rolling_mean > const lazy_rolling_mean;
      extractor< tag::immediate_rolling_mean > const immediate_rolling_mean;
      extractor< tag::rolling_mean > const rolling_mean;
    }
    namespace impl {
      template<typename Sample> struct immediate_rolling_mean_impl;
      template<typename Sample> struct lazy_rolling_mean_impl;
    }
    namespace tag {
      struct immediate_rolling_mean;
      struct lazy_rolling_mean;
      struct rolling_mean;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
    }
    namespace impl {
      template<typename N, typename Sample> struct rolling_moment_impl;
    }
    namespace tag {
      template<int N> struct rolling_moment;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::rolling_sum > const rolling_sum;
    }
    namespace impl {
    }
    namespace tag {
      struct rolling_sum;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::rolling_variance(immediate)>;
    template<> struct as_feature<tag::rolling_variance(lazy)>;
    template<> struct feature_of<tag::immediate_rolling_variance>;
    template<> struct feature_of<tag::lazy_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;
    }
    namespace impl {
      template<typename Sample> struct immediate_rolling_variance_impl;
      template<typename Sample> struct lazy_rolling_variance_impl;
    }
    namespace tag {
      struct immediate_rolling_variance;
      struct lazy_rolling_variance;
      struct rolling_variance;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::rolling_window_plus1 > const rolling_window_plus1;
      extractor< tag::rolling_window > const rolling_window;
    }
    namespace impl {
      template<typename Args> 
        bool is_rolling_window_plus1_full(Args const & args);
    }
    namespace tag {
      struct rolling_window;
      struct rolling_window_plus1;
    }
  }
  namespace serialization {
    template<typename Archive, typename T> 
      void save(Archive & ar, const circular_buffer< T > & b, 
                const unsigned int);
    template<typename Archive, typename T> 
      void load(Archive & ar, circular_buffer< T > & b, const unsigned int);
    template<typename Archive, typename T> 
      void serialize(Archive & ar, circular_buffer< T > & b, 
                     const unsigned int version);
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_weighted_feature<tag::skewness>;
    template<> struct feature_of<tag::weighted_skewness>;
    namespace extract {
      extractor< tag::skewness > const skewness;
    }
    namespace impl {
    }
    namespace tag {
      struct skewness;
    }
  }
}

Contains the stats<> template.

namespace boost {
  namespace accumulators {
    template<> struct as_weighted_feature<tag::sum>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::sum_of_variates< VariateType, VariateTag >>;
    template<> struct feature_of<tag::weighted_sum>;
    namespace extract {
      extractor< tag::sum > const sum;
      extractor< tag::sum_of_weights > const sum_of_weights;
      extractor< tag::abstract_sum_of_variates > const sum_of_variates;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_sum_of_variates;
      struct sum;
      struct sum_of_weights;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::sum(kahan)>;
    template<> struct as_feature<tag::sum_of_weights(kahan)>;
    template<> struct as_weighted_feature<tag::sum_kahan>;
    template<> struct feature_of<tag::sum_kahan>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::sum_of_variates_kahan< VariateType, VariateTag >>;
    template<> struct feature_of<tag::sum_of_weights_kahan>;
    template<> struct feature_of<tag::weighted_sum_kahan>;
    namespace extract {
      extractor< tag::sum_kahan > const sum_kahan;
      extractor< tag::sum_of_weights_kahan > const sum_of_weights_kahan;
      extractor< tag::abstract_sum_of_variates > const sum_of_variates_kahan;
    }
    namespace impl {
    }
    namespace tag {
      struct sum_kahan;
      struct sum_of_weights_kahan;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> struct feature_of<tag::tail< LeftRight >>;

    template<typename T> struct tail_cache_size_named_arg;

    template<> struct tail_cache_size_named_arg<left>;
    template<> struct tail_cache_size_named_arg<right>;
    namespace extract {
      extractor< tag::abstract_tail > const tail;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_tail;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> 
      struct as_weighted_feature<tag::non_coherent_tail_mean< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::coherent_tail_mean< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::non_coherent_tail_mean< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::non_coherent_weighted_tail_mean< LeftRight >>;
    namespace extract {
      extractor< tag::abstract_non_coherent_tail_mean > const non_coherent_tail_mean;
      extractor< tag::tail_mean > const coherent_tail_mean;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_non_coherent_tail_mean;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> 
      struct as_weighted_feature<tag::tail_quantile< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::tail_quantile< LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::weighted_tail_quantile< LeftRight >>;
    namespace extract {
      extractor< tag::quantile > const tail_quantile;
    }
    namespace impl {
    }
    namespace tag {
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename VariateType, typename VariateTag, typename LeftRight> 
      struct feature_of<tag::tail_variate< VariateType, VariateTag, LeftRight >>;
    template<typename LeftRight> 
      struct feature_of<tag::tail_weights< LeftRight >>;
    namespace extract {
      extractor< tag::abstract_tail_variate > const tail_variate;
      extractor< tag::abstract_tail_weights > const tail_weights;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_tail_variate;
      struct abstract_tail_weights;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct as_feature<tag::tail_variate_means< LeftRight, VariateType, VariateTag >(absolute)>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct as_feature<tag::tail_variate_means< LeftRight, VariateType, VariateTag >(relative)>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct as_weighted_feature<tag::absolute_tail_variate_means< LeftRight, VariateType, VariateTag >>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct as_weighted_feature<tag::relative_tail_variate_means< LeftRight, VariateType, VariateTag >>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct feature_of<tag::absolute_tail_variate_means< LeftRight, VariateType, VariateTag >>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct feature_of<tag::absolute_weighted_tail_variate_means< LeftRight, VariateType, VariateTag >>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct feature_of<tag::relative_tail_variate_means< LeftRight, VariateType, VariateTag >>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct feature_of<tag::relative_weighted_tail_variate_means< LeftRight, VariateType, VariateTag >>;
    namespace extract {
      extractor< tag::abstract_absolute_tail_variate_means > const tail_variate_means;
      extractor< tag::abstract_relative_tail_variate_means > const relative_tail_variate_means;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_absolute_tail_variate_means;
      struct abstract_relative_tail_variate_means;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::variance(immediate)>;
    template<> struct as_feature<tag::variance(lazy)>;
    template<> struct as_weighted_feature<tag::lazy_variance>;
    template<> struct as_weighted_feature<tag::variance>;
    template<> struct feature_of<tag::lazy_variance>;
    template<> struct feature_of<tag::lazy_weighted_variance>;
    template<> struct feature_of<tag::weighted_variance>;
    namespace extract {
      extractor< tag::lazy_variance > const lazy_variance;
      extractor< tag::variance > const variance;
    }
    namespace impl {
    }
    namespace tag {
      struct lazy_variance;
      struct variance;
    }
  }
}
namespace boost {
  namespace accumulators {
    boost::parameter::keyword< tag ::covariate1 > const covariate1;
    boost::parameter::keyword< tag ::covariate2 > const covariate2;
    namespace tag {
      struct covariate1;
      struct covariate2;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::density > const weighted_density;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_density;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::weighted_extended_p_square > const weighted_extended_p_square;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_extended_p_square;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::weighted_kurtosis > const weighted_kurtosis;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_kurtosis;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::weighted_mean(immediate)>;
    template<> struct as_feature<tag::weighted_mean(lazy)>;
    template<typename VariateType, typename VariateTag> 
      struct as_feature<tag::weighted_mean_of_variates< VariateType, VariateTag >(immediate)>;
    template<typename VariateType, typename VariateTag> 
      struct as_feature<tag::weighted_mean_of_variates< VariateType, VariateTag >(lazy)>;
    namespace extract {
      extractor< tag::mean > const weighted_mean;
    }
    namespace impl {
    }
    namespace tag {
      struct immediate_weighted_mean;
      struct weighted_mean;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::weighted_median(with_density)>;
    template<> 
      struct as_feature<tag::weighted_median(with_p_square_cumulative_distribution)>;
    template<> struct as_feature<tag::weighted_median(with_p_square_quantile)>;
    namespace extract {
      extractor< tag::median > const weighted_median;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_median;
      struct with_density_weighted_median;
      struct with_p_square_cumulative_distribution_weighted_median;
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::weighted_p_square_cumulative_distribution > const weighted_p_square_cumulative_distribution;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_p_square_cumulative_distribution;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight> 
      struct as_feature<tag::weighted_peaks_over_threshold< LeftRight >(with_threshold_probability)>;
    template<typename LeftRight> 
      struct as_feature<tag::weighted_peaks_over_threshold< LeftRight >(with_threshold_value)>;
    namespace extract {
      extractor< tag::abstract_peaks_over_threshold > const weighted_peaks_over_threshold;
    }
    namespace impl {
    }
    namespace tag {
    }
  }
}
namespace boost {
  namespace accumulators {
    namespace extract {
      extractor< tag::weighted_skewness > const weighted_skewness;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_skewness;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::weighted_sum_of_variates< VariateType, VariateTag >>;
    namespace extract {
      extractor< tag::weighted_sum > const weighted_sum;
      extractor< tag::abstract_weighted_sum_of_variates > const weighted_sum_of_variates;
    }
    namespace impl {
    }
    namespace tag {
      struct abstract_weighted_sum_of_variates;
      struct weighted_sum;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::weighted_sum(kahan)>;
    template<typename VariateType, typename VariateTag> 
      struct feature_of<tag::weighted_sum_of_variates_kahan< VariateType, VariateTag >>;
    namespace extract {
      extractor< tag::weighted_sum_kahan > const weighted_sum_kahan;
      extractor< tag::abstract_weighted_sum_of_variates > const weighted_sum_of_variates_kahan;
    }
    namespace impl {
    }
    namespace tag {
      struct weighted_sum_kahan;
      template<typename VariateType, typename VariateTag> 
        struct weighted_sum_of_variates_kahan;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct as_feature<tag::weighted_tail_variate_means< LeftRight, VariateType, VariateTag >(absolute)>;
    template<typename LeftRight, typename VariateType, typename VariateTag> 
      struct as_feature<tag::weighted_tail_variate_means< LeftRight, VariateType, VariateTag >(relative)>;
    namespace extract {
      extractor< tag::abstract_absolute_tail_variate_means > const weighted_tail_variate_means;
      extractor< tag::abstract_relative_tail_variate_means > const relative_weighted_tail_variate_means;
    }
    namespace impl {
    }
    namespace tag {
    }
  }
  namespace numeric {
    namespace functional {
      template<typename T, typename U> struct multiply_and_promote_to_double;
    }
  }
}
namespace boost {
  namespace accumulators {
    template<> struct as_feature<tag::weighted_variance(immediate)>;
    template<> struct as_feature<tag::weighted_variance(lazy)>;
    namespace extract {
      extractor< tag::lazy_weighted_variance > const lazy_weighted_variance;
      extractor< tag::weighted_variance > const weighted_variance;
    }
    namespace impl {
    }
    namespace tag {
      struct lazy_weighted_variance;
      struct weighted_variance;
    }
  }
}
namespace boost {
  namespace accumulators {
    struct absolute;
    struct for_median;
    struct immediate;
    struct kahan;
    struct lazy;
    struct left;
    struct linear;
    struct quadratic;
    struct regular;
    struct relative;
    struct right;
    template<typename Stat1, typename Stat2, ... > struct stats;
    struct unweighted;
    struct weighted;
    struct with_density;
    template<typename Feature1, typename Feature2, ... > struct with_error;
    struct with_p_square_cumulative_distribution;
    struct with_p_square_quantile;
    struct with_threshold_probability;
    struct with_threshold_value;
    namespace extract {
      extractor< tag::quantile > const quantile;
      extractor< tag::tail_mean > const tail_mean;
    }
    namespace impl {
      template<typename Sample, typename LeftRight> 
        struct coherent_tail_mean_impl;
      template<typename Sample, typename VariateType, typename VariateTag> 
        struct covariance_impl;
      template<typename Sample> struct density_impl;
      template<typename Sample, typename Variance> struct error_of_mean_impl;
      template<typename Sample> struct extended_p_square_impl;
      template<typename Sample, typename Impl1, typename Impl2> 
        struct extended_p_square_quantile_impl;
      template<typename Sample, typename Tag> struct immediate_mean_impl;
      template<typename Sample, typename Weight, typename Tag> 
        struct immediate_weighted_mean_impl;
      template<typename Sample> struct kurtosis_impl;
      template<typename Sample, typename MeanFeature> struct lazy_variance_impl;
      template<typename Sample, typename Weight, typename MeanFeature> 
        struct lazy_weighted_variance_impl;
      template<typename Sample> struct max_impl;
      template<typename Sample, typename SumFeature> struct mean_impl;
      template<typename Sample> struct median_impl;
      template<typename Sample> struct min_impl;
      template<typename N, typename Sample> struct moment_impl;
      template<typename Sample, typename LeftRight> 
        struct non_coherent_tail_mean_impl;
      template<typename Sample, typename Weight, typename LeftRight> 
        struct non_coherent_weighted_tail_mean_impl;
      template<typename Sample> struct p_square_cumulative_distribution_impl;
      template<typename Sample, typename Impl> struct p_square_quantile_impl;
      template<typename Sample, typename LeftRight> 
        struct peaks_over_threshold_prob_impl;
      template<typename Sample, typename Impl, typename LeftRight> 
        struct pot_quantile_impl;
      template<typename Sample, typename Impl, typename LeftRight> 
        struct pot_tail_mean_impl;
      template<typename Sample> struct rolling_count_impl;
      template<typename Sample> struct rolling_mean_impl;
      template<typename Sample> struct rolling_sum_impl;
      template<typename Sample> struct rolling_window_impl;
      template<typename Sample> struct rolling_window_plus1_impl;
      template<typename Sample> struct skewness_impl;
      template<typename Sample, typename Tag> struct sum_impl;
      template<typename Sample, typename Tag> struct sum_kahan_impl;
      template<typename Sample, typename LeftRight> struct tail_impl;
      template<typename Sample, typename LeftRight> struct tail_quantile_impl;
      template<typename VariateType, typename VariateTag, typename LeftRight> 
        struct tail_variate_impl;
      template<typename Sample, typename Impl, typename LeftRight, 
               typename VariateTag> 
        struct tail_variate_means_impl;
      template<typename Sample, typename MeanFeature, typename Tag> 
        struct variance_impl;
      template<typename Sample, typename Weight, typename VariateType, 
               typename VariateTag> 
        struct weighted_covariance_impl;
      template<typename Sample, typename Weight> struct weighted_density_impl;
      template<typename Sample, typename Weight> 
        struct weighted_extended_p_square_impl;
      template<typename Sample, typename Weight> struct weighted_kurtosis_impl;
      template<typename Sample, typename Weight, typename Tag> 
        struct weighted_mean_impl;
      template<typename Sample> struct weighted_median_impl;
      template<typename N, typename Sample, typename Weight> 
        struct weighted_moment_impl;
      template<typename Sample, typename Weight> 
        struct weighted_p_square_cumulative_distribution_impl;
      template<typename Sample, typename Weight, typename Impl> 
        struct weighted_p_square_quantile_impl;
      template<typename Sample, typename Weight, typename LeftRight> 
        struct weighted_peaks_over_threshold_impl;
      template<typename Sample, typename Weight, typename LeftRight> 
        struct weighted_peaks_over_threshold_prob_impl;
      template<typename Sample, typename Weight> struct weighted_skewness_impl;
      template<typename Sample, typename Weight, typename Tag> 
        struct weighted_sum_impl;
      template<typename Sample, typename Weight, typename Tag> 
        struct weighted_sum_kahan_impl;
      template<typename Sample, typename Weight, typename LeftRight> 
        struct weighted_tail_quantile_impl;
      template<typename Sample, typename Weight, typename Impl, 
               typename LeftRight, typename VariateType> 
        struct weighted_tail_variate_means_impl;
      template<typename Sample, typename Weight, typename MeanFeature, 
               typename Tag> 
        struct weighted_variance_impl;
      template<typename Sample> struct with_density_median_impl;
      template<typename Sample> struct with_density_weighted_median_impl;
      template<typename Sample> 
        struct with_p_square_cumulative_distribution_median_impl;
      template<typename Sample, typename Weight> 
        struct with_p_square_cumulative_distribution_weighted_median_impl;
    }
    namespace tag {
      template<typename LeftRight, typename VariateType, typename VariateTag> 
        struct absolute_tail_variate_means;
      template<typename LeftRight, typename VariateType, typename VariateTag> 
        struct absolute_weighted_tail_variate_means;
      template<typename LeftRight> struct coherent_tail_mean;
      template<typename VariateType, typename VariateTag> struct covariance;
      template<typename Feature> struct error_of;
      template<typename VariateType, typename VariateTag> 
        struct immediate_mean_of_variates;
      template<typename VariateType, typename VariateTag> 
        struct immediate_weighted_mean_of_variates;
      template<typename VariateType, typename VariateTag, typename LeftRight> 
        struct left_tail_variate;
      template<typename VariateType, typename VariateTag> struct mean_of_variates;
      template<int N> struct moment;
      template<typename LeftRight> struct non_coherent_tail_mean;
      template<typename LeftRight> struct non_coherent_weighted_tail_mean;
      template<typename LeftRight> struct peaks_over_threshold;
      template<typename LeftRight> struct peaks_over_threshold_prob;
      template<typename LeftRight> struct pot_quantile;
      template<typename LeftRight> struct pot_quantile_prob;
      template<typename LeftRight> struct pot_tail_mean;
      template<typename LeftRight> struct pot_tail_mean_prob;
      struct quantile;
      template<typename LeftRight, typename VariateType, typename VariateTag> 
        struct relative_tail_variate_means;
      template<typename LeftRight, typename VariateType, typename VariateTag> 
        struct relative_weighted_tail_variate_means;
      template<typename VariateType, typename VariateTag, typename LeftRight> 
        struct right_tail_variate;
      template<typename VariateType, typename VariateTag> struct sum_of_variates;
      template<typename VariateType, typename VariateTag> 
        struct sum_of_variates_kahan;
      template<typename LeftRight> struct tail;
      struct tail_mean;
      template<typename LeftRight> struct tail_quantile;
      template<typename VariateType, typename VariateTag, typename LeftRight> 
        struct tail_variate;
      template<typename LeftRight, typename VariateType, typename VariateTag> 
        struct tail_variate_means;
      template<typename LeftRight> struct tail_weights;
      template<typename VariateType, typename VariateTag> 
        struct weighted_covariance;
      template<typename VariateType, typename VariateTag> 
        struct weighted_mean_of_variates;
      template<int N> struct weighted_moment;
      template<typename LeftRight> struct weighted_peaks_over_threshold;
      template<typename LeftRight> struct weighted_peaks_over_threshold_prob;
      template<typename LeftRight> struct weighted_pot_quantile;
      template<typename LeftRight> struct weighted_pot_quantile_prob;
      template<typename LeftRight> struct weighted_pot_tail_mean;
      template<typename LeftRight> struct weighted_pot_tail_mean_prob;
      template<typename VariateType, typename VariateTag> 
        struct weighted_sum_of_variates;
      template<typename LeftRight> struct weighted_tail_quantile;
      template<typename LeftRight, typename VariateType, typename VariateTag> 
        struct weighted_tail_variate_means;
    }
  }
}

Numeric Operators Library Reference

namespace boost {
  namespace numeric {
    template<typename T> struct default_;
    template<typename T> struct one;
    template<typename T> struct one_or_default;
    template<typename T> struct zero;
    template<typename T> struct zero_or_default;
    template<typename To, typename From> 
      lazy_disable_if< is_const< From >, mpl::if_< is_same< To, From >, To &, To > >::type 
      promote(From & from);
    template<typename To, typename From> 
      mpl::if_< is_same< To const, From const  >, To const &, To const  >::type 
      promote(From const & from);
    namespace functional {
      template<typename Arg, typename Tag> struct as_max;
      template<typename Arg, typename EnableIf> struct as_max_base;
      template<typename Arg, typename Tag> struct as_min;
      template<typename Arg, typename EnableIf> struct as_min_base;

      template<typename Arg> 
        struct as_min_base<Arg, typename enable_if< is_floating_point< Arg > >::type>;

      template<typename Arg, typename Tag> struct as_one;
      template<typename Arg, typename EnableIf> struct as_one_base;
      template<typename Arg, typename Tag> struct as_zero;
      template<typename Arg, typename EnableIf> struct as_zero_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct assign;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct assign_base;
      template<typename Arg, typename Tag = typename tag<Arg>::type> 
        struct complement;
      template<typename Arg, typename EnableIf = void> struct complement_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct divides;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct divides_assign;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct divides_assign_base;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct divides_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct equal_to;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct equal_to_base;
      template<typename Left, typename Right, typename LeftTag, 
               typename RightTag> 
        struct fdiv;
      template<typename Left, typename Right, typename EnableIf> struct fdiv_base;

      template<typename Left, typename Right> 
        struct fdiv_base<Left, Right, typename enable_if< are_integral< Left, Right > >::type>;

      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct greater;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct greater_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct greater_equal;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct greater_equal_base;
      template<typename Left, typename Right> struct left_ref;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct less;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct less_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct less_equal;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct less_equal_base;
      template<typename Arg, typename Tag = typename tag<Arg>::type> 
        struct logical_not;
      template<typename Arg, typename EnableIf = void> struct logical_not_base;
      template<typename Left, typename Right, typename LeftTag, 
               typename RightTag> 
        struct max_assign;
      template<typename Left, typename Right, typename EnableIf> 
        struct max_assign_base;
      template<typename Left, typename Right, typename LeftTag, 
               typename RightTag> 
        struct min_assign;
      template<typename Left, typename Right, typename EnableIf> 
        struct min_assign_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct minus;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct minus_assign;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct minus_assign_base;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct minus_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct modulus;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct modulus_assign;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct modulus_assign_base;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct modulus_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct multiplies;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct multiplies_assign;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct multiplies_assign_base;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct multiplies_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct not_equal_to;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct not_equal_to_base;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct plus;
      template<typename Left, typename Right, 
               typename LeftTag = typename tag<Left>::type, 
               typename RightTag = typename tag<Right>::type> 
        struct plus_assign;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct plus_assign_base;
      template<typename Left, typename Right, typename EnableIf = void> 
        struct plus_base;
      template<typename To, typename From, typename ToTag, typename FromTag> 
        struct promote;
      template<typename To, typename From, typename EnableIf> struct promote_base;

      template<typename ToFrom> struct promote_base<ToFrom, ToFrom, void>;

      template<typename Arg, typename Tag = typename tag<Arg>::type> 
        struct unary_minus;
      template<typename Arg, typename EnableIf = void> struct unary_minus_base;
      template<typename Arg, typename Tag = typename tag<Arg>::type> 
        struct unary_plus;
      template<typename Arg, typename EnableIf = void> struct unary_plus_base;
    }
    namespace op {
      struct as_max;
      struct as_min;
      struct as_one;
      struct as_zero;
      struct assign;
      struct complement;
      struct divides;
      struct divides_assign;
      struct equal_to;
      struct fdiv;
      struct greater;
      struct greater_equal;
      struct less;
      struct less_equal;
      struct logical_not;
      struct max_assign;
      struct min_assign;
      struct minus;
      struct minus_assign;
      struct modulus;
      struct modulus_assign;
      struct multiplies;
      struct multiplies_assign;
      struct not_equal_to;
      struct plus;
      struct plus_assign;
      template<typename To> struct promote;
      struct unary_minus;
      struct unary_plus;
    }
  }
}
namespace boost {
  namespace numeric {
    namespace operators {
      template<typename T, typename U> 
        disable_if< mpl::or_< is_same< T, U >, is_same< std::complex< T >, U > >, std::complex< T > >::type 
        operator*(std::complex< T > ri, U const & u);
      template<typename T, typename U> 
        disable_if< mpl::or_< is_same< T, U >, is_same< std::complex< T >, U > >, std::complex< T > >::type 
        operator/(std::complex< T > ri, U const & u);
    }
  }
}
namespace boost {
  namespace numeric {
    namespace functional {
      template<typename T> struct as_max<T, std_valarray_tag>;
      template<typename T> struct as_min<T, std_valarray_tag>;
      template<typename T> struct as_one<T, std_valarray_tag>;
      template<typename T> struct as_zero<T, std_valarray_tag>;
      template<typename Left, typename Right, typename RightTag> 
        struct fdiv<Left, Right, std_valarray_tag, RightTag>;
      template<typename Left, typename Right> 
        struct max_assign<Left, Right, std_valarray_tag, std_valarray_tag>;
      template<typename Left, typename Right> 
        struct min_assign<Left, Right, std_valarray_tag, std_valarray_tag>;
      template<typename From> 
        struct promote<bool const, From, void, std_valarray_tag>;
      template<typename From> struct promote<bool, From, void, std_valarray_tag>;
      template<typename To, typename From> 
        struct promote<To, From, std_valarray_tag, std_valarray_tag>;
      template<typename ToFrom> 
        struct promote<ToFrom, ToFrom, std_valarray_tag, std_valarray_tag>;
      template<typename T> struct tag<std::valarray< T >>;
    }
    namespace operators {
      template<typename Left, typename Right> 
        unspecified operator/(std::valarray< Left > const & left, 
                              Right const & right);
      template<typename Left, typename Right> 
        unspecified operator*(std::valarray< Left > const & left, 
                              Right const & right);
      template<typename Left, typename Right> 
        unspecified operator+(std::valarray< Left > const & left, 
                              std::valarray< Right > const & right);
    }
  }
}
namespace boost {
  namespace numeric {
    namespace functional {
      template<typename T> struct as_max<T, std_vector_tag>;
      template<typename T> struct as_min<T, std_vector_tag>;
      template<typename T> struct as_one<T, std_vector_tag>;
      template<typename T> struct as_zero<T, std_vector_tag>;
      template<typename Left, typename Right> 
        struct fdiv<Left, Right, std_vector_tag, void>;
      template<typename Left, typename Right> 
        struct max_assign<Left, Right, std_vector_tag, std_vector_tag>;
      template<typename Left, typename Right> 
        struct min_assign<Left, Right, std_vector_tag, std_vector_tag>;
      template<typename To, typename From> 
        struct promote<To, From, std_vector_tag, std_vector_tag>;
      template<typename ToFrom> 
        struct promote<ToFrom, ToFrom, std_vector_tag, std_vector_tag>;
      template<typename T, typename Al> struct tag<std::vector< T, Al >>;
    }
    namespace operators {
      template<typename Left, typename Right> 
        unspecified operator/(std::vector< Left > const & left, 
                              Right const & right);
      template<typename Left, typename Right> 
        std::vector< typename functional::divides< Left, Right >::result_type > 
        operator/(std::vector< Left > const & left, 
                  std::vector< Right > const & right);
      template<typename Left, typename Right> 
        unspecified operator*(std::vector< Left > const & left, 
                              Right const & right);
      template<typename Left, typename Right> 
        unspecified operator*(Left const & left, 
                              std::vector< Right > const & right);
      template<typename Left, typename Right> 
        std::vector< typename functional::multiplies< Left, Right >::result_type > 
        operator*(std::vector< Left > const & left, 
                  std::vector< Right > const & right);
      template<typename Left, typename Right> 
        std::vector< typename functional::plus< Left, Right >::result_type > 
        operator+(std::vector< Left > const & left, 
                  std::vector< Right > const & right);
      template<typename Left, typename Right> 
        std::vector< typename functional::minus< Left, Right >::result_type > 
        operator-(std::vector< Left > const & left, 
                  std::vector< Right > const & right);
      template<typename Left> 
        std::vector< Left > & 
        operator+=(std::vector< Left > & left, 
                   std::vector< Left > const & right);
      template<typename Arg> 
        std::vector< typename functional::unary_minus< Arg >::result_type > 
        operator-(std::vector< Arg > const & arg);
    }
  }
}

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