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Edouard DUPIN 2018-01-12 21:47:58 +01:00
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23
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Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
execute, and transmit the Software, and to prepare derivative works of the
Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:
The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

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///////////////////////////////////////////////////////////////////////////////
/// \file accumulators.hpp
/// Includes all of the Accumulators Framework
//
// Copyright 2005 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_ACCUMULATORS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_ACCUMULATORS_HPP_EAN_28_10_2005
#include <boost/accumulators/framework/accumulator_set.hpp>
#include <boost/accumulators/framework/accumulator_concept.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/external.hpp>
#include <boost/accumulators/framework/features.hpp>
#include <boost/accumulators/framework/parameters/accumulator.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/framework/parameters/weight.hpp>
#include <boost/accumulators/framework/parameters/weights.hpp>
#include <boost/accumulators/framework/accumulators/external_accumulator.hpp>
#include <boost/accumulators/framework/accumulators/droppable_accumulator.hpp>
#include <boost/accumulators/framework/accumulators/reference_accumulator.hpp>
#include <boost/accumulators/framework/accumulators/value_accumulator.hpp>
#endif

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///////////////////////////////////////////////////////////////////////////////
// accumulators_fwd.hpp
//
// Copyright 2005 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_ACCUMULATORS_FWD_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_ACCUMULATORS_FWD_HPP_EAN_28_10_2005
#include <boost/config.hpp>
#include <boost/mpl/apply_fwd.hpp> // for mpl::na
#include <boost/mpl/limits/vector.hpp>
#include <boost/preprocessor/cat.hpp>
#include <boost/preprocessor/arithmetic/inc.hpp>
#include <boost/preprocessor/repetition/enum_params_with_a_default.hpp>
#include <boost/preprocessor/repetition/enum_trailing_params.hpp>
#include <boost/preprocessor/repetition/enum_trailing_binary_params.hpp>
#include <boost/preprocessor/repetition/repeat_from_to.hpp>
#include <boost/accumulators/numeric/functional_fwd.hpp>
#ifndef BOOST_ACCUMULATORS_MAX_FEATURES
/// The maximum number of accumulators that may be put in an accumulator_set.
/// Defaults to BOOST_MPL_LIMIT_VECTOR_SIZE (which defaults to 20).
# define BOOST_ACCUMULATORS_MAX_FEATURES BOOST_MPL_LIMIT_VECTOR_SIZE
#endif
#if BOOST_ACCUMULATORS_MAX_FEATURES > BOOST_MPL_LIMIT_VECTOR_SIZE
# error BOOST_ACCUMULATORS_MAX_FEATURES cannot be larger than BOOST_MPL_LIMIT_VECTOR_SIZE
#endif
#ifndef BOOST_ACCUMULATORS_MAX_ARGS
/// The maximum number of arguments that may be specified to an accumulator_set's
/// accumulation function. Defaults to 15.
# define BOOST_ACCUMULATORS_MAX_ARGS 15
#endif
#if BOOST_WORKAROUND(__GNUC__, == 3) \
|| BOOST_WORKAROUND(__EDG_VERSION__, BOOST_TESTED_AT(306))
# define BOOST_ACCUMULATORS_BROKEN_CONST_OVERLOADS
#endif
#ifdef BOOST_ACCUMULATORS_BROKEN_CONST_OVERLOADS
# include <boost/utility/enable_if.hpp>
# include <boost/type_traits/is_const.hpp>
# define BOOST_ACCUMULATORS_PROTO_DISABLE_IF_IS_CONST(T)\
, typename boost::disable_if<boost::is_const<T> >::type * = 0
#else
# define BOOST_ACCUMULATORS_PROTO_DISABLE_IF_IS_CONST(T)
#endif
#define BOOST_ACCUMULATORS_GCC_VERSION \
(__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// Named parameters tags
//
namespace tag
{
struct sample;
struct weight;
struct accumulator;
struct weights;
}
///////////////////////////////////////////////////////////////////////////////
// User-level features
//
namespace tag
{
template<typename ValueType, typename Tag>
struct value;
template<typename Tag>
struct value_tag;
template<typename Referent, typename Tag>
struct reference;
template<typename Tag>
struct reference_tag;
template<typename Type, typename Tag = void, typename AccumulatorSet = void>
struct external;
template<typename Feature>
struct droppable;
}
template<typename Accumulator>
struct droppable_accumulator_base;
template<typename Accumulator>
struct droppable_accumulator;
template<typename Accumulator>
struct with_cached_result;
template<typename Sample, typename Features, typename Weight = void>
struct accumulator_set;
template<typename Feature>
struct extractor;
template<typename Feature>
struct feature_of;
template<typename Feature>
struct as_feature;
template<typename Feature>
struct as_weighted_feature;
template<BOOST_PP_ENUM_PARAMS_WITH_A_DEFAULT(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature, mpl::na)>
struct depends_on;
template<BOOST_PP_ENUM_PARAMS_WITH_A_DEFAULT(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature, mpl::na)>
struct features;
template<typename Feature, typename AccumulatorSet>
typename mpl::apply<AccumulatorSet, Feature>::type const &
find_accumulator(AccumulatorSet const &acc);
template<typename Feature, typename AccumulatorSet>
typename mpl::apply<AccumulatorSet, Feature>::type::result_type
extract_result(AccumulatorSet const &acc);
template<typename Feature, typename AccumulatorSet, typename A1>
typename mpl::apply<AccumulatorSet, Feature>::type::result_type
extract_result(AccumulatorSet const &acc, A1 const &a1);
// ... other overloads generated by Boost.Preprocessor:
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_EXTRACT_RESULT_FWD(z, n, _) \
template< \
typename Feature \
, typename AccumulatorSet \
BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, typename A) \
> \
typename mpl::apply<AccumulatorSet, Feature>::type::result_type \
extract_result( \
AccumulatorSet const &acc \
BOOST_PP_ENUM_TRAILING_BINARY_PARAMS_Z(z, n, A, const &a) \
);
/// INTERNAL ONLY
///
BOOST_PP_REPEAT_FROM_TO(
2
, BOOST_PP_INC(BOOST_ACCUMULATORS_MAX_ARGS)
, BOOST_ACCUMULATORS_EXTRACT_RESULT_FWD
, _
)
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
template<typename Feature, typename AccumulatorSet, typename A1, typename A2 ...>
typename mpl::apply<AccumulatorSet, Feature>::type::result_type
extract_result(AccumulatorSet const &acc, A1 const &a1, A2 const &a2 ...);
#endif
namespace impl
{
using namespace numeric::operators;
template<typename Accumulator, typename Tag>
struct external_impl;
}
namespace detail
{
template<typename Accumulator>
struct feature_tag;
template<typename Feature, typename Sample, typename Weight>
struct to_accumulator;
struct accumulator_set_base;
template<typename T>
struct is_accumulator_set;
inline void ignore_variable(void const *) {}
#define BOOST_ACCUMULATORS_IGNORE_GLOBAL(X) \
namespace detail \
{ \
struct BOOST_PP_CAT(ignore_, X) \
{ \
void ignore() \
{ \
boost::accumulators::detail::ignore_variable(&X); \
} \
}; \
} \
/**/
}
}} // namespace boost::accumulators
// For defining boost::parameter keywords that can be inherited from to
// get a nested, class-scoped keyword with the requested alias
#define BOOST_PARAMETER_NESTED_KEYWORD(tag_namespace, name, alias) \
namespace tag_namespace \
{ \
template<int Dummy = 0> \
struct name ## _ \
{ \
static char const* keyword_name() \
{ \
return #name; \
} \
static ::boost::parameter::keyword<name ## _<Dummy> > &alias; \
}; \
template<int Dummy> \
::boost::parameter::keyword<name ## _<Dummy> > &name ## _<Dummy>::alias = \
::boost::parameter::keyword<name ## _<Dummy> >::get(); \
typedef name ## _ <> name; \
} \
namespace \
{ \
::boost::parameter::keyword<tag_namespace::name> &name = \
::boost::parameter::keyword<tag_namespace::name>::get(); \
}
#endif

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///////////////////////////////////////////////////////////////////////////////
// accumulator_base.hpp
//
// Copyright 2005 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_FRAMEWORK_ACCUMULATORS_BASE_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATORS_BASE_HPP_EAN_28_10_2005
#include <boost/mpl/placeholders.hpp>
#include <boost/mpl/joint_view.hpp>
#include <boost/mpl/single_view.hpp>
#include <boost/mpl/fold.hpp>
#include <boost/mpl/contains.hpp>
#include <boost/mpl/empty_sequence.hpp>
#include <boost/accumulators/framework/accumulator_concept.hpp>
namespace boost { namespace accumulators
{
namespace detail
{
typedef void void_;
}
///////////////////////////////////////////////////////////////////////////////
// dont_care
//
struct dont_care
{
template<typename Args>
dont_care(Args const &)
{
}
};
///////////////////////////////////////////////////////////////////////////////
// accumulator_base
//
struct accumulator_base
{
// hidden if defined in derived classes
detail::void_ operator ()(dont_care)
{
}
typedef mpl::false_ is_droppable;
detail::void_ add_ref(dont_care)
{
}
detail::void_ drop(dont_care)
{
}
detail::void_ on_drop(dont_care)
{
}
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// accumulator_concept.hpp
//
// Copyright 2005 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_FRAMEWORK_ACCUMULATOR_CONCEPT_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATOR_CONCEPT_HPP_EAN_28_10_2005
#include <boost/concept_check.hpp>
namespace boost { namespace accumulators
{
template<typename Stat>
struct accumulator_concept
{
void constraints()
{
// TODO: define the stat concept
}
Stat stat;
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// accumulator_set.hpp
//
// Copyright 2005 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_FRAMEWORK_ACCUMULATOR_SET_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATOR_SET_HPP_EAN_28_10_2005
#include <boost/version.hpp>
#include <boost/mpl/apply.hpp>
#include <boost/mpl/assert.hpp>
#include <boost/mpl/protect.hpp>
#include <boost/mpl/identity.hpp>
#include <boost/mpl/is_sequence.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/is_base_and_derived.hpp>
#include <boost/parameter/parameters.hpp>
#include <boost/preprocessor/repetition/repeat_from_to.hpp>
#include <boost/preprocessor/repetition/enum_binary_params.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/framework/accumulator_concept.hpp>
#include <boost/accumulators/framework/parameters/accumulator.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/framework/accumulators/external_accumulator.hpp>
#include <boost/accumulators/framework/accumulators/droppable_accumulator.hpp>
#include <boost/fusion/include/any.hpp>
#include <boost/fusion/include/find_if.hpp>
#include <boost/fusion/include/for_each.hpp>
#include <boost/fusion/include/filter_view.hpp>
namespace boost { namespace accumulators
{
namespace detail
{
///////////////////////////////////////////////////////////////////////////////
// accumulator_visitor
// wrap a boost::parameter argument pack in a Fusion extractor object
template<typename Args>
struct accumulator_visitor
{
explicit accumulator_visitor(Args const &a)
: args(a)
{
}
template<typename Accumulator>
void operator ()(Accumulator &accumulator) const
{
accumulator(this->args);
}
private:
accumulator_visitor &operator =(accumulator_visitor const &);
Args const &args;
};
template<typename Args>
inline accumulator_visitor<Args> const make_accumulator_visitor(Args const &args)
{
return accumulator_visitor<Args>(args);
}
typedef
parameter::parameters<
parameter::required<tag::accumulator>
, parameter::optional<tag::sample>
// ... and others which are not specified here...
>
accumulator_params;
///////////////////////////////////////////////////////////////////////////////
// accumulator_set_base
struct accumulator_set_base
{
};
///////////////////////////////////////////////////////////////////////////////
// is_accumulator_set
template<typename T>
struct is_accumulator_set
: is_base_and_derived<accumulator_set_base, T>
{
};
} // namespace detail
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable: 4355) // warning C4355: 'this' : used in base member initializer list
#endif
///////////////////////////////////////////////////////////////////////////////
/// \brief A set of accumulators.
///
/// accumulator_set resolves the dependencies between features and ensures that
/// the accumulators in the set are updated in the proper order.
///
/// acccumulator_set provides a general mechanism to visit the accumulators
/// in the set in order, with or without a filter. You can also fetch a reference
/// to an accumulator that corresponds to a feature.
///
template<typename Sample, typename Features, typename Weight>
struct accumulator_set
: detail::accumulator_set_base
{
typedef Sample sample_type; ///< The type of the samples that will be accumulated
typedef Features features_type; ///< An MPL sequence of the features that should be accumulated.
typedef Weight weight_type; ///< The type of the weight parameter. Must be a scalar. Defaults to void.
/// INTERNAL ONLY
///
typedef
typename detail::make_accumulator_tuple<
Features
, Sample
, Weight
>::type
accumulators_mpl_vector;
// generate a fusion::list of accumulators
/// INTERNAL ONLY
///
typedef
typename detail::meta::make_acc_list<
accumulators_mpl_vector
>::type
accumulators_type;
/// INTERNAL ONLY
///
//BOOST_MPL_ASSERT((mpl::is_sequence<accumulators_type>));
///////////////////////////////////////////////////////////////////////////////
/// default-construct all contained accumulators
accumulator_set()
: accumulators(
detail::make_acc_list(
accumulators_mpl_vector()
, detail::accumulator_params()(*this)
)
)
{
// Add-ref the Features that the user has specified
this->template visit_if<detail::contains_feature_of_<Features> >(
detail::make_add_ref_visitor(detail::accumulator_params()(*this))
);
}
/// \overload
///
/// \param a1 Optional named parameter to be passed to all the accumulators
template<typename A1>
explicit accumulator_set(A1 const &a1)
: accumulators(
detail::make_acc_list(
accumulators_mpl_vector()
, detail::accumulator_params()(*this, a1)
)
)
{
// Add-ref the Features that the user has specified
this->template visit_if<detail::contains_feature_of_<Features> >(
detail::make_add_ref_visitor(detail::accumulator_params()(*this))
);
}
// ... other overloads generated by Boost.Preprocessor:
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_ACCUMULATOR_SET_CTOR(z, n, _) \
template<BOOST_PP_ENUM_PARAMS_Z(z, n, typename A)> \
accumulator_set(BOOST_PP_ENUM_BINARY_PARAMS_Z(z, n, A, const &a)) \
: accumulators( \
detail::make_acc_list( \
accumulators_mpl_vector() \
, detail::accumulator_params()( \
*this BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, a) \
) \
) \
) \
{ \
/* Add-ref the Features that the user has specified */ \
this->template visit_if<detail::contains_feature_of_<Features> >( \
detail::make_add_ref_visitor(detail::accumulator_params()(*this)) \
); \
}
/// INTERNAL ONLY
///
BOOST_PP_REPEAT_FROM_TO(
2
, BOOST_PP_INC(BOOST_ACCUMULATORS_MAX_ARGS)
, BOOST_ACCUMULATORS_ACCUMULATOR_SET_CTOR
, _
)
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// \overload
///
template<typename A1, typename A2, ...>
accumulator_set(A1 const &a1, A2 const &a2, ...);
#endif
// ... other overloads generated by Boost.Preprocessor below ...
///////////////////////////////////////////////////////////////////////////////
/// Visitation
/// \param func UnaryFunction which is invoked with each accumulator in turn.
template<typename UnaryFunction>
void visit(UnaryFunction const &func)
{
fusion::for_each(this->accumulators, func);
}
///////////////////////////////////////////////////////////////////////////////
/// Conditional visitation
/// \param func UnaryFunction which is invoked with each accumulator in turn,
/// provided the accumulator satisfies the MPL predicate FilterPred.
template<typename FilterPred, typename UnaryFunction>
void visit_if(UnaryFunction const &func)
{
fusion::filter_view<accumulators_type, FilterPred> filtered_accs(this->accumulators);
fusion::for_each(filtered_accs, func);
}
///////////////////////////////////////////////////////////////////////////////
/// The return type of the operator() overloads is void.
typedef void result_type;
///////////////////////////////////////////////////////////////////////////////
/// Accumulation
/// \param a1 Optional named parameter to be passed to all the accumulators
void operator ()()
{
this->visit(
detail::make_accumulator_visitor(
detail::accumulator_params()(*this)
)
);
}
template<typename A1>
void operator ()(A1 const &a1)
{
this->visit(
detail::make_accumulator_visitor(
detail::accumulator_params()(*this, a1)
)
);
}
// ... other overloads generated by Boost.Preprocessor:
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_ACCUMULATOR_SET_FUN_OP(z, n, _) \
template<BOOST_PP_ENUM_PARAMS_Z(z, n, typename A)> \
void operator ()(BOOST_PP_ENUM_BINARY_PARAMS_Z(z, n, A, const &a)) \
{ \
this->visit( \
detail::make_accumulator_visitor( \
detail::accumulator_params()( \
*this BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, a) \
) \
) \
); \
}
/// INTERNAL ONLY
///
BOOST_PP_REPEAT_FROM_TO(
2
, BOOST_PP_INC(BOOST_ACCUMULATORS_MAX_ARGS)
, BOOST_ACCUMULATORS_ACCUMULATOR_SET_FUN_OP
, _
)
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// \overload
///
template<typename A1, typename A2, ...>
void operator ()(A1 const &a1, A2 const &a2, ...);
#endif
///////////////////////////////////////////////////////////////////////////////
/// Extraction
template<typename Feature>
struct apply
: fusion::result_of::value_of<
typename fusion::result_of::find_if<
accumulators_type
, detail::matches_feature<Feature>
>::type
>
{
};
///////////////////////////////////////////////////////////////////////////////
/// Extraction
template<typename Feature>
typename apply<Feature>::type &extract()
{
return *fusion::find_if<detail::matches_feature<Feature> >(this->accumulators);
}
/// \overload
template<typename Feature>
typename apply<Feature>::type const &extract() const
{
return *fusion::find_if<detail::matches_feature<Feature> >(this->accumulators);
}
///////////////////////////////////////////////////////////////////////////////
/// Drop
template<typename Feature>
void drop()
{
// You can only drop the features that you have specified explicitly
typedef typename apply<Feature>::type the_accumulator;
BOOST_MPL_ASSERT((detail::contains_feature_of<Features, the_accumulator>));
typedef
typename feature_of<typename as_feature<Feature>::type>::type
the_feature;
(*fusion::find_if<detail::matches_feature<Feature> >(this->accumulators))
.drop(detail::accumulator_params()(*this));
// Also drop accumulators that this feature depends on
typedef typename the_feature::dependencies dependencies;
this->template visit_if<detail::contains_feature_of_<dependencies> >(
detail::make_drop_visitor(detail::accumulator_params()(*this))
);
}
private:
accumulators_type accumulators;
};
#ifdef _MSC_VER
#pragma warning(pop)
#endif
///////////////////////////////////////////////////////////////////////////////
// find_accumulator
// find an accumulator in an accumulator_set corresponding to a feature
template<typename Feature, typename AccumulatorSet>
typename mpl::apply<AccumulatorSet, Feature>::type &
find_accumulator(AccumulatorSet &acc BOOST_ACCUMULATORS_PROTO_DISABLE_IF_IS_CONST(AccumulatorSet))
{
return acc.template extract<Feature>();
}
/// \overload
template<typename Feature, typename AccumulatorSet>
typename mpl::apply<AccumulatorSet, Feature>::type const &
find_accumulator(AccumulatorSet const &acc)
{
return acc.template extract<Feature>();
}
///////////////////////////////////////////////////////////////////////////////
// extract_result
// extract a result from an accumulator set
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_EXTRACT_RESULT_FUN(z, n, _) \
template< \
typename Feature \
, typename AccumulatorSet \
BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, typename A) \
> \
typename mpl::apply<AccumulatorSet, Feature>::type::result_type \
extract_result( \
AccumulatorSet const &acc \
BOOST_PP_ENUM_TRAILING_BINARY_PARAMS_Z(z, n, A, const &a) \
) \
{ \
return find_accumulator<Feature>(acc).result( \
detail::accumulator_params()( \
acc \
BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, a) \
) \
); \
}
BOOST_PP_REPEAT(
BOOST_PP_INC(BOOST_ACCUMULATORS_MAX_ARGS)
, BOOST_ACCUMULATORS_EXTRACT_RESULT_FUN
, _
)
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// droppable_accumulator.hpp
//
// Copyright 2005 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_FRAMEWORK_ACCUMULATORS_DROPPABLE_ACCUMULATOR_HPP_EAN_13_12_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATORS_DROPPABLE_ACCUMULATOR_HPP_EAN_13_12_2005
#include <new>
#include <boost/assert.hpp>
#include <boost/mpl/apply.hpp>
#include <boost/aligned_storage.hpp>
#include <boost/accumulators/framework/depends_on.hpp> // for feature_of
#include <boost/accumulators/framework/parameters/accumulator.hpp> // for accumulator
namespace boost { namespace accumulators
{
template<typename Accumulator>
struct droppable_accumulator;
namespace detail
{
///////////////////////////////////////////////////////////////////////////////
// add_ref_visitor
// a fusion function object for add_ref'ing accumulators
template<typename Args>
struct add_ref_visitor
{
explicit add_ref_visitor(Args const &args)
: args_(args)
{
}
template<typename Accumulator>
void operator ()(Accumulator &acc) const
{
typedef typename Accumulator::feature_tag::dependencies dependencies;
acc.add_ref(this->args_);
// Also add_ref accumulators that this feature depends on
this->args_[accumulator].template
visit_if<detail::contains_feature_of_<dependencies> >(
*this
);
}
private:
add_ref_visitor &operator =(add_ref_visitor const &);
Args const &args_;
};
template<typename Args>
add_ref_visitor<Args> make_add_ref_visitor(Args const &args)
{
return add_ref_visitor<Args>(args);
}
///////////////////////////////////////////////////////////////////////////////
// drop_visitor
// a fusion function object for dropping accumulators
template<typename Args>
struct drop_visitor
{
explicit drop_visitor(Args const &args)
: args_(args)
{
}
template<typename Accumulator>
void operator ()(Accumulator &acc) const
{
if(typename Accumulator::is_droppable())
{
typedef typename Accumulator::feature_tag::dependencies dependencies;
acc.drop(this->args_);
// Also drop accumulators that this feature depends on
this->args_[accumulator].template
visit_if<detail::contains_feature_of_<dependencies> >(
*this
);
}
}
private:
drop_visitor &operator =(drop_visitor const &);
Args const &args_;
};
template<typename Args>
drop_visitor<Args> make_drop_visitor(Args const &args)
{
return drop_visitor<Args>(args);
}
}
//////////////////////////////////////////////////////////////////////////
// droppable_accumulator_base
template<typename Accumulator>
struct droppable_accumulator_base
: Accumulator
{
typedef droppable_accumulator_base base;
typedef mpl::true_ is_droppable;
typedef typename Accumulator::result_type result_type;
template<typename Args>
droppable_accumulator_base(Args const &args)
: Accumulator(args)
, ref_count_(0)
{
}
droppable_accumulator_base(droppable_accumulator_base const &that)
: Accumulator(*static_cast<Accumulator const *>(&that))
, ref_count_(that.ref_count_)
{
}
template<typename Args>
void operator ()(Args const &args)
{
if(!this->is_dropped())
{
this->Accumulator::operator ()(args);
}
}
template<typename Args>
void add_ref(Args const &)
{
++this->ref_count_;
}
template<typename Args>
void drop(Args const &args)
{
BOOST_ASSERT(0 < this->ref_count_);
if(1 == this->ref_count_)
{
static_cast<droppable_accumulator<Accumulator> *>(this)->on_drop(args);
}
--this->ref_count_;
}
bool is_dropped() const
{
return 0 == this->ref_count_;
}
private:
int ref_count_;
};
//////////////////////////////////////////////////////////////////////////
// droppable_accumulator
// this can be specialized for any type that needs special handling
template<typename Accumulator>
struct droppable_accumulator
: droppable_accumulator_base<Accumulator>
{
template<typename Args>
droppable_accumulator(Args const &args)
: droppable_accumulator::base(args)
{
}
droppable_accumulator(droppable_accumulator const &that)
: droppable_accumulator::base(*static_cast<typename droppable_accumulator::base const *>(&that))
{
}
};
//////////////////////////////////////////////////////////////////////////
// with_cached_result
template<typename Accumulator>
struct with_cached_result
: Accumulator
{
typedef typename Accumulator::result_type result_type;
template<typename Args>
with_cached_result(Args const &args)
: Accumulator(args)
, cache()
{
}
with_cached_result(with_cached_result const &that)
: Accumulator(*static_cast<Accumulator const *>(&that))
, cache()
{
if(that.has_result())
{
this->set(that.get());
}
}
~with_cached_result()
{
// Since this is a base class of droppable_accumulator_base,
// this destructor is called before any of droppable_accumulator_base's
// members get cleaned up, including is_dropped, so the following
// call to has_result() is valid.
if(this->has_result())
{
this->get().~result_type();
}
}
template<typename Args>
void on_drop(Args const &args)
{
// cache the result at the point this calculation was dropped
BOOST_ASSERT(!this->has_result());
this->set(this->Accumulator::result(args));
}
template<typename Args>
result_type result(Args const &args) const
{
return this->has_result() ? this->get() : this->Accumulator::result(args);
}
private:
with_cached_result &operator =(with_cached_result const &);
void set(result_type const &r)
{
::new(this->cache.address()) result_type(r);
}
result_type const &get() const
{
return *static_cast<result_type const *>(this->cache.address());
}
bool has_result() const
{
typedef with_cached_result<Accumulator> this_type;
typedef droppable_accumulator_base<this_type> derived_type;
return static_cast<derived_type const *>(this)->is_dropped();
}
aligned_storage<sizeof(result_type)> cache;
};
namespace tag
{
template<typename Feature>
struct as_droppable
{
typedef droppable<Feature> type;
};
template<typename Feature>
struct as_droppable<droppable<Feature> >
{
typedef droppable<Feature> type;
};
//////////////////////////////////////////////////////////////////////////
// droppable
template<typename Feature>
struct droppable
: as_feature<Feature>::type
{
typedef typename as_feature<Feature>::type feature_type;
typedef typename feature_type::dependencies tmp_dependencies_;
typedef
typename mpl::transform<
typename feature_type::dependencies
, as_droppable<mpl::_1>
>::type
dependencies;
struct impl
{
template<typename Sample, typename Weight>
struct apply
{
typedef
droppable_accumulator<
typename mpl::apply2<typename feature_type::impl, Sample, Weight>::type
>
type;
};
};
};
}
// make droppable<tag::feature(modifier)> work
template<typename Feature>
struct as_feature<tag::droppable<Feature> >
{
typedef tag::droppable<typename as_feature<Feature>::type> type;
};
// make droppable<tag::mean> work with non-void weights (should become
// droppable<tag::weighted_mean>
template<typename Feature>
struct as_weighted_feature<tag::droppable<Feature> >
{
typedef tag::droppable<typename as_weighted_feature<Feature>::type> type;
};
// for the purposes of feature-based dependency resolution,
// droppable<Foo> provides the same feature as Foo
template<typename Feature>
struct feature_of<tag::droppable<Feature> >
: feature_of<Feature>
{
};
// Note: Usually, the extractor is pulled into the accumulators namespace with
// a using directive, not the tag. But the droppable<> feature doesn't have an
// extractor, so we can put the droppable tag in the accumulators namespace
// without fear of a name conflict.
using tag::droppable;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// external_accumulator.hpp
//
// Copyright 2005 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_FRAMEWORK_ACCUMULATORS_EXTERNAL_ACCUMULATOR_HPP_EAN_01_12_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATORS_EXTERNAL_ACCUMULATOR_HPP_EAN_01_12_2005
#include <boost/mpl/placeholders.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/depends_on.hpp> // for feature_tag
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/accumulators/reference_accumulator.hpp>
namespace boost { namespace accumulators { namespace impl
{
//////////////////////////////////////////////////////////////////////////
// external_impl
/// INTERNAL ONLY
///
template<typename Accumulator, typename Tag>
struct external_impl
: accumulator_base
{
typedef typename Accumulator::result_type result_type;
typedef typename detail::feature_tag<Accumulator>::type feature_tag;
external_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
return this->extract_(args, args[parameter::keyword<Tag>::get() | 0]);
}
private:
template<typename Args>
static result_type extract_(Args const &args, int)
{
// No named parameter passed to the extractor. Maybe the external
// feature is held by reference<>.
extractor<feature_tag> extract;
return extract(accumulators::reference_tag<Tag>(args));
}
template<typename Args, typename AccumulatorSet>
static result_type extract_(Args const &, AccumulatorSet const &acc)
{
// OK, a named parameter for this external feature was passed to the
// extractor, so use that.
extractor<feature_tag> extract;
return extract(acc);
}
};
} // namespace impl
namespace tag
{
//////////////////////////////////////////////////////////////////////////
// external
template<typename Feature, typename Tag, typename AccumulatorSet>
struct external
: depends_on<reference<AccumulatorSet, Tag> >
{
typedef
accumulators::impl::external_impl<
detail::to_accumulator<Feature, mpl::_1, mpl::_2>
, Tag
>
impl;
};
template<typename Feature, typename Tag>
struct external<Feature, Tag, void>
: depends_on<>
{
typedef
accumulators::impl::external_impl<
detail::to_accumulator<Feature, mpl::_1, mpl::_2>
, Tag
>
impl;
};
}
// for the purposes of feature-based dependency resolution,
// external_accumulator<Feature, Tag> provides the same feature as Feature
template<typename Feature, typename Tag, typename AccumulatorSet>
struct feature_of<tag::external<Feature, Tag, AccumulatorSet> >
: feature_of<Feature>
{
};
// Note: Usually, the extractor is pulled into the accumulators namespace with
// a using directive, not the tag. But the external<> feature doesn't have an
// extractor, so we can put the external tag in the accumulators namespace
// without fear of a name conflict.
using tag::external;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// reference_accumulator.hpp
//
// Copyright 2005 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_FRAMEWORK_ACCUMULATORS_REFERENCE_ACCUMULATOR_HPP_EAN_03_23_2006
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATORS_REFERENCE_ACCUMULATOR_HPP_EAN_03_23_2006
#include <boost/ref.hpp>
#include <boost/mpl/always.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/framework/depends_on.hpp> // for feature_tag
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
//////////////////////////////////////////////////////////////////////////
// reference_accumulator_impl
//
template<typename Referent, typename Tag>
struct reference_accumulator_impl
: accumulator_base
{
typedef Referent &result_type;
template<typename Args>
reference_accumulator_impl(Args const &args)
: ref(args[parameter::keyword<Tag>::get()])
{
}
result_type result(dont_care) const
{
return this->ref;
}
private:
reference_wrapper<Referent> ref;
};
} // namespace impl
namespace tag
{
//////////////////////////////////////////////////////////////////////////
// reference_tag
template<typename Tag>
struct reference_tag
{
};
//////////////////////////////////////////////////////////////////////////
// reference
template<typename Referent, typename Tag>
struct reference
: depends_on<>
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::reference_accumulator_impl<Referent, Tag> > impl;
};
}
namespace extract
{
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, reference, (typename)(typename))
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, reference_tag, (typename))
}
using extract::reference;
using extract::reference_tag;
// Map all reference<V,T> features to reference_tag<T> so
// that references can be extracted using reference_tag<T>
// without specifying the referent type.
template<typename ValueType, typename Tag>
struct feature_of<tag::reference<ValueType, Tag> >
: feature_of<tag::reference_tag<Tag> >
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// value_accumulator.hpp
//
// Copyright 2005 Eric Niebler, Daniel Egloff. 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_FRAMEWORK_ACCUMULATORS_VALUE_ACCUMULATOR_HPP_EAN_03_23_2006
#define BOOST_ACCUMULATORS_FRAMEWORK_ACCUMULATORS_VALUE_ACCUMULATOR_HPP_EAN_03_23_2006
#include <boost/mpl/always.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/framework/depends_on.hpp> // for feature_tag
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
//////////////////////////////////////////////////////////////////////////
// value_accumulator_impl
template<typename ValueType, typename Tag>
struct value_accumulator_impl
: accumulator_base
{
typedef ValueType result_type;
template<typename Args>
value_accumulator_impl(Args const &args)
: val(args[parameter::keyword<Tag>::get()])
{
}
result_type result(dont_care) const
{
return this->val;
}
private:
ValueType val;
};
} // namespace impl
namespace tag
{
//////////////////////////////////////////////////////////////////////////
// value_tag
template<typename Tag>
struct value_tag
{
};
//////////////////////////////////////////////////////////////////////////
// value
template<typename ValueType, typename Tag>
struct value
: depends_on<>
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::value_accumulator_impl<ValueType, Tag> > impl;
};
}
namespace extract
{
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, value, (typename)(typename))
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, value_tag, (typename))
}
using extract::value;
using extract::value_tag;
// Map all value<V,T> features to value_tag<T> so
// that values can be extracted using value_tag<T>
// without specifying the value type.
template<typename ValueType, typename Tag>
struct feature_of<tag::value<ValueType, Tag> >
: feature_of<tag::value_tag<Tag> >
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// depends_on.hpp
//
// Copyright 2005 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_FRAMEWORK_DEPENDS_ON_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_DEPENDS_ON_HPP_EAN_28_10_2005
#include <boost/version.hpp>
#include <boost/mpl/end.hpp>
#include <boost/mpl/map.hpp>
#include <boost/mpl/set.hpp>
#include <boost/mpl/copy.hpp>
#include <boost/mpl/fold.hpp>
#include <boost/mpl/size.hpp>
#include <boost/mpl/sort.hpp>
#include <boost/mpl/insert.hpp>
#include <boost/mpl/assert.hpp>
#include <boost/mpl/remove.hpp>
#include <boost/mpl/vector.hpp>
#include <boost/mpl/inherit.hpp>
#include <boost/mpl/identity.hpp>
#include <boost/mpl/equal_to.hpp>
#include <boost/mpl/contains.hpp>
#include <boost/mpl/transform.hpp>
#include <boost/mpl/is_sequence.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/mpl/insert_range.hpp>
#include <boost/mpl/back_inserter.hpp>
#include <boost/mpl/transform_view.hpp>
#include <boost/mpl/inherit_linearly.hpp>
#include <boost/type_traits/is_base_and_derived.hpp>
#include <boost/preprocessor/repetition/repeat.hpp>
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/preprocessor/facilities/intercept.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/fusion/include/next.hpp>
#include <boost/fusion/include/equal_to.hpp>
#include <boost/fusion/include/value_of.hpp>
#include <boost/fusion/include/mpl.hpp>
#include <boost/fusion/include/end.hpp>
#include <boost/fusion/include/begin.hpp>
#include <boost/fusion/include/cons.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////
// as_feature
template<typename Feature>
struct as_feature
{
typedef Feature type;
};
///////////////////////////////////////////////////////////////////////////
// weighted_feature
template<typename Feature>
struct as_weighted_feature
{
typedef Feature type;
};
///////////////////////////////////////////////////////////////////////////
// feature_of
template<typename Feature>
struct feature_of
{
typedef Feature type;
};
namespace detail
{
///////////////////////////////////////////////////////////////////////////
// feature_tag
template<typename Accumulator>
struct feature_tag
{
typedef typename Accumulator::feature_tag type;
};
template<typename Feature>
struct undroppable
{
typedef Feature type;
};
template<typename Feature>
struct undroppable<tag::droppable<Feature> >
{
typedef Feature type;
};
// For the purpose of determining whether one feature depends on another,
// disregard whether the feature is droppable or not.
template<typename A, typename B>
struct is_dependent_on
: is_base_and_derived<
typename feature_of<typename undroppable<B>::type>::type
, typename undroppable<A>::type
>
{};
template<typename Feature>
struct dependencies_of
{
typedef typename Feature::dependencies type;
};
// Should use mpl::insert_range, but doesn't seem to work with mpl sets
template<typename Set, typename Range>
struct set_insert_range
: mpl::fold<
Range
, Set
, mpl::insert<mpl::_1, mpl::_2>
>
{};
template<typename Features>
struct collect_abstract_features
: mpl::fold<
Features
, mpl::set0<>
, set_insert_range<
mpl::insert<mpl::_1, feature_of<mpl::_2> >
, collect_abstract_features<dependencies_of<mpl::_2> >
>
>
{};
template<typename Features>
struct depends_on_base
: mpl::inherit_linearly<
typename mpl::sort<
typename mpl::copy<
typename collect_abstract_features<Features>::type
, mpl::back_inserter<mpl::vector0<> >
>::type
, is_dependent_on<mpl::_1, mpl::_2>
>::type
// Don't inherit multiply from a feature
, mpl::if_<
is_dependent_on<mpl::_1, mpl::_2>
, mpl::_1
, mpl::inherit<mpl::_1, mpl::_2>
>
>::type
{
};
}
///////////////////////////////////////////////////////////////////////////
/// depends_on
template<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature)>
struct depends_on
: detail::depends_on_base<
typename mpl::transform<
mpl::vector<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, Feature)>
, as_feature<mpl::_1>
>::type
>
{
typedef mpl::false_ is_weight_accumulator;
typedef
typename mpl::transform<
mpl::vector<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, Feature)>
, as_feature<mpl::_1>
>::type
dependencies;
};
namespace detail
{
template<typename Feature>
struct matches_feature
{
template<typename Accumulator>
struct apply
: is_same<
typename feature_of<typename as_feature<Feature>::type>::type
, typename feature_of<typename as_feature<typename feature_tag<Accumulator>::type>::type>::type
>
{};
};
template<typename Features, typename Accumulator>
struct contains_feature_of
{
typedef
mpl::transform_view<Features, feature_of<as_feature<mpl::_> > >
features_list;
typedef
typename feature_of<typename feature_tag<Accumulator>::type>::type
the_feature;
typedef
typename mpl::contains<features_list, the_feature>::type
type;
};
// This is to work around a bug in early versions of Fusion which caused
// a compile error if contains_feature_of<List, mpl::_> is used as a
// predicate to fusion::find_if
template<typename Features>
struct contains_feature_of_
{
template<typename Accumulator>
struct apply
: contains_feature_of<Features, Accumulator>
{};
};
template<
typename First
, typename Last
, bool is_empty = fusion::result_of::equal_to<First, Last>::value
>
struct build_acc_list;
template<typename First, typename Last>
struct build_acc_list<First, Last, true>
{
typedef fusion::nil_ type;
template<typename Args>
static fusion::nil_
call(Args const &, First const&, Last const&)
{
return fusion::nil_();
}
};
template<typename First, typename Last>
struct build_acc_list<First, Last, false>
{
typedef
build_acc_list<typename fusion::result_of::next<First>::type, Last>
next_build_acc_list;
typedef fusion::cons<
typename fusion::result_of::value_of<First>::type
, typename next_build_acc_list::type>
type;
template<typename Args>
static type
call(Args const &args, First const& f, Last const& l)
{
return type(args, next_build_acc_list::call(args, fusion::next(f), l));
}
};
namespace meta
{
template<typename Sequence>
struct make_acc_list
: build_acc_list<
typename fusion::result_of::begin<Sequence>::type
, typename fusion::result_of::end<Sequence>::type
>
{};
}
template<typename Sequence, typename Args>
typename meta::make_acc_list<Sequence>::type
make_acc_list(Sequence const &seq, Args const &args)
{
return meta::make_acc_list<Sequence>::call(args, fusion::begin(seq), fusion::end(seq));
}
///////////////////////////////////////////////////////////////////////////
// checked_as_weighted_feature
template<typename Feature>
struct checked_as_weighted_feature
{
typedef typename as_feature<Feature>::type feature_type;
typedef typename as_weighted_feature<feature_type>::type type;
// weighted and non-weighted flavors should provide the same feature.
BOOST_MPL_ASSERT((
is_same<
typename feature_of<feature_type>::type
, typename feature_of<type>::type
>
));
};
///////////////////////////////////////////////////////////////////////////
// as_feature_list
template<typename Features, typename Weight>
struct as_feature_list
: mpl::transform_view<Features, checked_as_weighted_feature<mpl::_1> >
{
};
template<typename Features>
struct as_feature_list<Features, void>
: mpl::transform_view<Features, as_feature<mpl::_1> >
{
};
///////////////////////////////////////////////////////////////////////////
// accumulator_wrapper
template<typename Accumulator, typename Feature>
struct accumulator_wrapper
: Accumulator
{
typedef Feature feature_tag;
accumulator_wrapper(accumulator_wrapper const &that)
: Accumulator(*static_cast<Accumulator const *>(&that))
{
}
template<typename Args>
accumulator_wrapper(Args const &args)
: Accumulator(args)
{
}
};
///////////////////////////////////////////////////////////////////////////
// to_accumulator
template<typename Feature, typename Sample, typename Weight>
struct to_accumulator
{
typedef
accumulator_wrapper<
typename mpl::apply2<typename Feature::impl, Sample, Weight>::type
, Feature
>
type;
};
template<typename Feature, typename Sample, typename Weight, typename Tag, typename AccumulatorSet>
struct to_accumulator<Feature, Sample, tag::external<Weight, Tag, AccumulatorSet> >
{
BOOST_MPL_ASSERT((is_same<Tag, void>));
BOOST_MPL_ASSERT((is_same<AccumulatorSet, void>));
typedef
accumulator_wrapper<
typename mpl::apply2<typename Feature::impl, Sample, Weight>::type
, Feature
>
accumulator_type;
typedef
typename mpl::if_<
typename Feature::is_weight_accumulator
, accumulator_wrapper<impl::external_impl<accumulator_type, tag::weights>, Feature>
, accumulator_type
>::type
type;
};
// BUGBUG work around an MPL bug wrt map insertion
template<typename FeatureMap, typename Feature>
struct insert_feature
: mpl::eval_if<
mpl::has_key<FeatureMap, typename feature_of<Feature>::type>
, mpl::identity<FeatureMap>
, mpl::insert<FeatureMap, mpl::pair<typename feature_of<Feature>::type, Feature> >
>
{
};
template<typename FeatureMap, typename Feature, typename Weight>
struct insert_dependencies
: mpl::fold<
as_feature_list<typename Feature::dependencies, Weight>
, FeatureMap
, insert_dependencies<
insert_feature<mpl::_1, mpl::_2>
, mpl::_2
, Weight
>
>
{
};
template<typename FeatureMap, typename Features, typename Weight>
struct insert_sequence
: mpl::fold< // BUGBUG should use insert_range, but doesn't seem to work for maps
as_feature_list<Features, Weight>
, FeatureMap
, insert_feature<mpl::_1, mpl::_2>
>
{
};
template<typename Features, typename Sample, typename Weight>
struct make_accumulator_tuple
{
typedef
typename mpl::fold<
as_feature_list<Features, Weight>
, mpl::map0<>
, mpl::if_<
mpl::is_sequence<mpl::_2>
, insert_sequence<mpl::_1, mpl::_2, Weight>
, insert_feature<mpl::_1, mpl::_2>
>
>::type
feature_map;
// for each element in the map, add its dependencies also
typedef
typename mpl::fold<
feature_map
, feature_map
, insert_dependencies<mpl::_1, mpl::second<mpl::_2>, Weight>
>::type
feature_map_with_dependencies;
// turn the map into a vector so we can sort it
typedef
typename mpl::insert_range<
mpl::vector<>
, mpl::end<mpl::vector<> >::type
, mpl::transform_view<feature_map_with_dependencies, mpl::second<mpl::_1> >
>::type
feature_vector_with_dependencies;
// sort the features according to which is derived from which
typedef
typename mpl::sort<
feature_vector_with_dependencies
, is_dependent_on<mpl::_2, mpl::_1>
>::type
sorted_feature_vector;
// From the vector of features, construct a vector of accumulators
typedef
typename mpl::transform<
sorted_feature_vector
, to_accumulator<mpl::_1, Sample, Weight>
>::type
type;
};
} // namespace detail
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// external.hpp
//
// Copyright 2005 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_FRAMEWORK_EXTERNAL_HPP_EAN_01_12_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_EXTERNAL_HPP_EAN_01_12_2005
#include <boost/mpl/apply.hpp>
#include <boost/accumulators/framework/accumulators/external_accumulator.hpp>
//namespace boost { namespace accumulators
//{
//
/////////////////////////////////////////////////////////////////////////////////
//// external
////
//template<typename Type>
//struct external
//{
//};
//
//}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// extractor.hpp
//
// Copyright 2005 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_FRAMEWORK_EXTRACTOR_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_EXTRACTOR_HPP_EAN_28_10_2005
#include <boost/preprocessor/tuple/rem.hpp>
#include <boost/preprocessor/array/size.hpp>
#include <boost/preprocessor/array/data.hpp>
#include <boost/preprocessor/array/elem.hpp>
#include <boost/preprocessor/seq/to_array.hpp>
#include <boost/preprocessor/seq/transform.hpp>
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/preprocessor/repetition/enum_trailing_params.hpp>
#include <boost/preprocessor/repetition/enum_trailing_binary_params.hpp>
#include <boost/parameter/binding.hpp>
#include <boost/mpl/apply.hpp>
#include <boost/mpl/eval_if.hpp>
#include <boost/type_traits/remove_reference.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/accumulators/framework/parameters/accumulator.hpp>
namespace boost { namespace accumulators
{
namespace detail
{
template<typename AccumulatorSet, typename Feature>
struct accumulator_set_result
{
typedef typename as_feature<Feature>::type feature_type;
typedef typename mpl::apply<AccumulatorSet, feature_type>::type::result_type type;
};
template<typename Args, typename Feature>
struct argument_pack_result
: accumulator_set_result<
typename remove_reference<
typename parameter::binding<Args, tag::accumulator>::type
>::type
, Feature
>
{
};
template<typename A, typename Feature>
struct extractor_result
: mpl::eval_if<
detail::is_accumulator_set<A>
, accumulator_set_result<A, Feature>
, argument_pack_result<A, Feature>
>
{
};
template<typename Feature, typename AccumulatorSet>
typename extractor_result<AccumulatorSet, Feature>::type
do_extract(AccumulatorSet const &acc, mpl::true_)
{
typedef typename as_feature<Feature>::type feature_type;
return extract_result<feature_type>(acc);
}
template<typename Feature, typename Args>
typename extractor_result<Args, Feature>::type
do_extract(Args const &args, mpl::false_)
{
typedef typename as_feature<Feature>::type feature_type;
return find_accumulator<feature_type>(args[accumulator]).result(args);
}
} // namespace detail
///////////////////////////////////////////////////////////////////////////////
/// Extracts the result associated with Feature from the specified accumulator_set.
template<typename Feature>
struct extractor
{
typedef extractor<Feature> this_type;
/// The result meta-function for determining the return type of the extractor
template<typename F>
struct result;
template<typename A1>
struct result<this_type(A1)>
: detail::extractor_result<A1, Feature>
{
};
/// Extract the result associated with Feature from the accumulator set
/// \param acc The accumulator set object from which to extract the result
template<typename Arg1>
typename detail::extractor_result<Arg1, Feature>::type
operator ()(Arg1 const &arg1) const
{
// Arg1 could be an accumulator_set or an argument pack containing
// an accumulator_set. Dispatch accordingly.
return detail::do_extract<Feature>(arg1, detail::is_accumulator_set<Arg1>());
}
/// \overload
///
/// \param a1 Optional named parameter to be passed to the accumulator's result() function.
template<typename AccumulatorSet, typename A1>
typename detail::extractor_result<AccumulatorSet, Feature>::type
operator ()(AccumulatorSet const &acc, A1 const &a1) const
{
BOOST_MPL_ASSERT((detail::is_accumulator_set<AccumulatorSet>));
typedef typename as_feature<Feature>::type feature_type;
return extract_result<feature_type>(acc, a1);
}
// ... other overloads generated by Boost.Preprocessor:
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_EXTRACTOR_FUN_OP(z, n, _) \
template<BOOST_PP_ENUM_PARAMS_Z(z, n, typename A)> \
struct result<this_type(BOOST_PP_ENUM_PARAMS_Z(z, n, A))> \
: detail::extractor_result<A1, Feature> \
{}; \
template< \
typename AccumulatorSet \
BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, typename A) \
> \
typename detail::extractor_result<AccumulatorSet, Feature>::type \
operator ()( \
AccumulatorSet const &acc \
BOOST_PP_ENUM_TRAILING_BINARY_PARAMS_Z(z, n, A, const &a) \
) const \
{ \
BOOST_MPL_ASSERT((detail::is_accumulator_set<AccumulatorSet>)); \
typedef typename as_feature<Feature>::type feature_type; \
return extract_result<feature_type>(acc BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, a));\
}
BOOST_PP_REPEAT_FROM_TO(
2
, BOOST_PP_INC(BOOST_ACCUMULATORS_MAX_ARGS)
, BOOST_ACCUMULATORS_EXTRACTOR_FUN_OP
, _
)
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// \overload
///
template<typename AccumulatorSet, typename A1, typename A2, ...>
typename detail::extractor_result<AccumulatorSet, Feature>::type
operator ()(AccumulatorSet const &acc, A1 const &a1, A2 const &a2, ...);
#endif
};
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_ARRAY_REM(Array) \
BOOST_PP_TUPLE_REM_CTOR(BOOST_PP_ARRAY_SIZE(Array), BOOST_PP_ARRAY_DATA(Array))
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_SEQ_REM(Seq) \
BOOST_ACCUMULATORS_ARRAY_REM(BOOST_PP_SEQ_TO_ARRAY(Seq))
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_ARGS_OP(s, data, elem) \
T ## s
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_PARAMS_OP(s, data, elem) \
elem T ## s
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_MAKE_FEATURE(Tag, Feature, ParamsSeq) \
Tag::Feature< \
BOOST_ACCUMULATORS_SEQ_REM( \
BOOST_PP_SEQ_TRANSFORM(BOOST_ACCUMULATORS_ARGS_OP, ~, ParamsSeq) \
) \
>
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_DEFINE_EXTRACTOR_FUN_IMPL(z, n, Tag, Feature, ParamsSeq) \
template< \
BOOST_ACCUMULATORS_SEQ_REM( \
BOOST_PP_SEQ_TRANSFORM(BOOST_ACCUMULATORS_PARAMS_OP, ~, ParamsSeq) \
) \
, typename Arg1 \
BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, typename A) \
> \
typename boost::accumulators::detail::extractor_result< \
Arg1 \
, BOOST_ACCUMULATORS_MAKE_FEATURE(Tag, Feature, ParamsSeq) \
>::type \
Feature(Arg1 const &arg1 BOOST_PP_ENUM_TRAILING_BINARY_PARAMS_Z(z, n, A, const &a) ) \
{ \
typedef BOOST_ACCUMULATORS_MAKE_FEATURE(Tag, Feature, ParamsSeq) feature_type; \
return boost::accumulators::extractor<feature_type>()( \
arg1 BOOST_PP_ENUM_TRAILING_PARAMS_Z(z, n, a)); \
}
/// INTERNAL ONLY
///
#define BOOST_ACCUMULATORS_DEFINE_EXTRACTOR_FUN(z, n, _) \
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR_FUN_IMPL( \
z \
, n \
, BOOST_PP_ARRAY_ELEM(0, _) \
, BOOST_PP_ARRAY_ELEM(1, _) \
, BOOST_PP_ARRAY_ELEM(2, _) \
)
#define BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(Tag, Feature, ParamSeq) \
BOOST_PP_REPEAT( \
BOOST_PP_INC(BOOST_ACCUMULATORS_MAX_ARGS) \
, BOOST_ACCUMULATORS_DEFINE_EXTRACTOR_FUN \
, (3, (Tag, Feature, ParamSeq)) \
)
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// features.hpp
//
// Copyright 2005 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_STATS_HPP_EAN_08_12_2005
#define BOOST_ACCUMULATORS_STATISTICS_STATS_HPP_EAN_08_12_2005
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/mpl/vector.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// features
//
template<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature)>
struct features
: mpl::vector<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, Feature)>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// accumulator.hpp
//
// Copyright 2005 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_FRAMEWORK_PARAMETERS_ACCUMULATOR_HPP_EAN_31_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_PARAMETERS_ACCUMULATOR_HPP_EAN_31_10_2005
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
BOOST_PARAMETER_KEYWORD(tag, accumulator)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(accumulator)
}} // namespace boost::accumulators
#endif

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boost/accumulators/framework/parameters/sample.hpp Normal file
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///////////////////////////////////////////////////////////////////////////////
// sample.hpp
//
// Copyright 2005 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_FRAMEWORK_PARAMETERS_SAMPLE_HPP_EAN_31_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_PARAMETERS_SAMPLE_HPP_EAN_31_10_2005
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
BOOST_PARAMETER_KEYWORD(tag, sample)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sample)
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weight.hpp
//
// Copyright 2005 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_FRAMEWORK_PARAMETERS_WEIGHT_HPP_EAN_31_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_PARAMETERS_WEIGHT_HPP_EAN_31_10_2005
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
// The weight of a single sample
BOOST_PARAMETER_KEYWORD(tag, weight)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weight)
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weights.hpp
//
// Copyright 2005 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_FRAMEWORK_PARAMETERS_WEIGHTS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_FRAMEWORK_PARAMETERS_WEIGHTS_HPP_EAN_28_10_2005
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
// The weight accumulator
BOOST_PARAMETER_KEYWORD(tag, weights)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weights)
}} // namespace boost::accumulators
#endif

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// Copyright David Abrahams 2006. 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_DETAIL_FUNCTION1_DWA200655_HPP
# define BOOST_DETAIL_FUNCTION1_DWA200655_HPP
# include <boost/concept_check.hpp>
# include <boost/type_traits/remove_reference.hpp>
# include <boost/type_traits/add_const.hpp>
# include <boost/mpl/apply.hpp>
namespace boost { namespace detail {
// A utility for creating unary function objects that play nicely with
// boost::result_of and that handle the forwarding problem.
//
// mpl::apply<F, A0>::type is expected to be a stateless function
// object that accepts an argument of type A0&. It is also expected
// to have a nested ::result_type identical to its return type.
template<typename F>
struct function1
{
template<typename Signature>
struct result
{};
template<typename This, typename A0>
struct result<This(A0)>
{
// How adding const to arguments handles rvalues.
//
// if A0 is arg0 is represents actual argument
// -------- ------- --------------------------
// T const & T const const T lvalue
// T & T non-const T lvalue
// T const T const const T rvalue
// T T const non-const T rvalue
typedef typename remove_reference<
typename add_const< A0 >::type
>::type arg0;
typedef typename mpl::apply1<F, arg0>::type impl;
typedef typename impl::result_type type;
};
// Handles mutable lvalues
template<typename A0>
typename result<function1(A0 &)>::type
operator ()(A0 &a0) const
{
typedef typename result<function1(A0 &)>::impl impl;
typedef typename result<function1(A0 &)>::type type;
typedef A0 &arg0;
BOOST_CONCEPT_ASSERT((UnaryFunction<impl, type, arg0>));
//boost::function_requires<UnaryFunctionConcept<impl, type, arg0> >();
return impl()(a0);
}
// Handles const lvalues and all rvalues
template<typename A0>
typename result<function1(A0 const &)>::type
operator ()(A0 const &a0) const
{
typedef typename result<function1(A0 const &)>::impl impl;
typedef typename result<function1(A0 const &)>::type type;
typedef A0 const &arg0;
BOOST_CONCEPT_ASSERT((UnaryFunction<impl, type, arg0>));
//boost::function_requires<UnaryFunctionConcept<impl, type, arg0> >();
return impl()(a0);
}
};
}} // namespace boost::detail
#endif // BOOST_DETAIL_FUNCTION1_DWA200655_HPP

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// Copyright David Abrahams 2006. 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_DETAIL_FUNCTION2_DWA200655_HPP
# define BOOST_DETAIL_FUNCTION2_DWA200655_HPP
# define args (2)
# include <boost/accumulators/numeric/detail/function_n.hpp>
#endif // BOOST_DETAIL_FUNCTION2_DWA200655_HPP

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// Copyright David Abrahams 2006. 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_DETAIL_FUNCTION3_DWA2006514_HPP
# define BOOST_DETAIL_FUNCTION3_DWA2006514_HPP
# define args (3)
# include <boost/accumulators/numeric/detail/function_n.hpp>
#endif // BOOST_DETAIL_FUNCTION3_DWA2006514_HPP

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// Copyright David Abrahams 2006. 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_DETAIL_FUNCTION4_DWA2006514_HPP
# define BOOST_DETAIL_FUNCTION4_DWA2006514_HPP
# define args (4)
# include <boost/accumulators/numeric/detail/function_n.hpp>
#endif // BOOST_DETAIL_FUNCTION4_DWA2006514_HPP

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// Copyright David Abrahams 2006. 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)
//
// #include guards intentionally disabled.
// #ifndef BOOST_DETAIL_FUNCTION_N_DWA2006514_HPP
// # define BOOST_DETAIL_FUNCTION_N_DWA2006514_HPP
#include <boost/mpl/void.hpp>
#include <boost/mpl/apply.hpp>
#include <boost/preprocessor/control/if.hpp>
#include <boost/preprocessor/cat.hpp>
#include <boost/preprocessor/punctuation/comma_if.hpp>
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/preprocessor/repetition/enum_trailing_params.hpp>
#include <boost/preprocessor/repetition/repeat.hpp>
#include <boost/preprocessor/seq/fold_left.hpp>
#include <boost/preprocessor/seq/seq.hpp>
#include <boost/preprocessor/seq/for_each.hpp>
#include <boost/preprocessor/seq/for_each_i.hpp>
#include <boost/preprocessor/seq/for_each_product.hpp>
#include <boost/preprocessor/seq/size.hpp>
#include <boost/type_traits/add_const.hpp>
#include <boost/type_traits/remove_reference.hpp>
namespace boost { namespace detail {
# define BOOST_DETAIL_default_arg(z, n, _) \
typedef mpl::void_ BOOST_PP_CAT(arg, n);
# define BOOST_DETAIL_function_arg(z, n, _) \
typedef typename remove_reference< \
typename add_const< BOOST_PP_CAT(A, n) >::type \
>::type BOOST_PP_CAT(arg, n);
#define BOOST_DETAIL_cat_arg_counts(s, state, n) \
BOOST_PP_IF( \
n \
, BOOST_PP_CAT(state, BOOST_PP_CAT(_, n)) \
, state \
) \
/**/
#define function_name \
BOOST_PP_SEQ_FOLD_LEFT( \
BOOST_DETAIL_cat_arg_counts \
, BOOST_PP_CAT(function, BOOST_PP_SEQ_HEAD(args)) \
, BOOST_PP_SEQ_TAIL(args)(0) \
) \
/**/
template<typename F>
struct function_name
{
BOOST_PP_REPEAT(
BOOST_MPL_LIMIT_METAFUNCTION_ARITY
, BOOST_DETAIL_default_arg
, ~
)
template<typename Signature>
struct result {};
#define BOOST_DETAIL_function_result(r, _, n) \
template<typename This BOOST_PP_ENUM_TRAILING_PARAMS(n, typename A)> \
struct result<This(BOOST_PP_ENUM_PARAMS(n, A))> \
{ \
BOOST_PP_REPEAT(n, BOOST_DETAIL_function_arg, ~) \
typedef \
typename BOOST_PP_CAT(mpl::apply, BOOST_MPL_LIMIT_METAFUNCTION_ARITY)<\
F \
BOOST_PP_ENUM_TRAILING_PARAMS( \
BOOST_MPL_LIMIT_METAFUNCTION_ARITY \
, arg \
) \
>::type \
impl; \
typedef typename impl::result_type type; \
}; \
/**/
BOOST_PP_SEQ_FOR_EACH(BOOST_DETAIL_function_result, _, args)
# define arg_type(r, _, i, is_const) \
BOOST_PP_COMMA_IF(i) BOOST_PP_CAT(A, i) BOOST_PP_CAT(const_if, is_const) &
# define result_(r, n, constness) \
typename result< \
function_name( \
BOOST_PP_SEQ_FOR_EACH_I_R(r, arg_type, ~, constness) \
) \
> \
/**/
# define param(r, _, i, is_const) BOOST_PP_COMMA_IF(i) \
BOOST_PP_CAT(A, i) BOOST_PP_CAT(const_if, is_const) & BOOST_PP_CAT(x, i)
# define param_list(r, n, constness) \
BOOST_PP_SEQ_FOR_EACH_I_R(r, param, ~, constness)
# define call_operator(r, constness) \
template<BOOST_PP_ENUM_PARAMS(BOOST_PP_SEQ_SIZE(constness), typename A)> \
result_(r, BOOST_PP_SEQ_SIZE(constness), constness)::type \
operator ()( param_list(r, BOOST_PP_SEQ_SIZE(constness), constness) ) const \
{ \
typedef result_(r, BOOST_PP_SEQ_SIZE(constness), constness)::impl impl; \
return impl()(BOOST_PP_ENUM_PARAMS(BOOST_PP_SEQ_SIZE(constness), x)); \
} \
/**/
# define const_if0
# define const_if1 const
# define bits(z, n, _) ((0)(1))
# define gen_operator(r, _, n) \
BOOST_PP_SEQ_FOR_EACH_PRODUCT_R( \
r \
, call_operator \
, BOOST_PP_REPEAT(n, bits, ~) \
) \
/**/
BOOST_PP_SEQ_FOR_EACH(
gen_operator
, ~
, args
)
# undef bits
# undef const_if1
# undef const_if0
# undef call_operator
# undef param_list
# undef param
# undef result_
# undef default_
# undef arg_type
# undef gen_operator
# undef function_name
# undef args
};
}} // namespace boost::detail
//#endif // BOOST_DETAIL_FUNCTION_N_DWA2006514_HPP

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// Copyright David Abrahams 2006. 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_DETAIL_POD_SINGLETON_DWA200655_HPP
# define BOOST_DETAIL_POD_SINGLETON_DWA200655_HPP
namespace boost { namespace detail {
template<typename T>
struct pod_singleton
{
static T instance;
};
template<typename T>
T pod_singleton<T>::instance;
}} // namespace boost::detail
#endif // BOOST_DETAIL_POD_SINGLETON_DWA200655_HPP

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///////////////////////////////////////////////////////////////////////////////
/// \file functional.hpp
///
// Copyright 2005 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_NUMERIC_FUNCTIONAL_HPP_EAN_08_12_2005
#define BOOST_NUMERIC_FUNCTIONAL_HPP_EAN_08_12_2005
#include <limits>
#include <functional>
#include <boost/static_assert.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/and.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/type_traits/add_reference.hpp>
#include <boost/type_traits/is_empty.hpp>
#include <boost/type_traits/is_integral.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/typeof/typeof.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/accumulators/numeric/functional_fwd.hpp>
#include <boost/accumulators/numeric/detail/function1.hpp>
#include <boost/accumulators/numeric/detail/function2.hpp>
#include <boost/accumulators/numeric/detail/pod_singleton.hpp>
#ifdef BOOST_NUMERIC_FUNCTIONAL_STD_VECTOR_SUPPORT
# include <boost/accumulators/numeric/functional/vector.hpp>
#endif
#ifdef BOOST_NUMERIC_FUNCTIONAL_STD_VALARRAY_SUPPORT
# include <boost/accumulators/numeric/functional/valarray.hpp>
#endif
#ifdef BOOST_NUMERIC_FUNCTIONAL_STD_COMPLEX_SUPPORT
# include <boost/accumulators/numeric/functional/complex.hpp>
#endif
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_HPP_INCLUDED
#ifdef BOOST_NUMERIC_FUNCTIONAL_DOXYGEN_INVOKED
// Hack to make Doxygen show the inheritance relationships
/// INTERNAL ONLY
///
namespace std
{
/// INTERNAL ONLY
///
template<class Arg, class Ret> struct unary_function {};
/// INTERNAL ONLY
///
template<class Left, class Right, class Ret> struct binary_function {};
}
#endif
namespace boost { namespace numeric
{
namespace functional
{
/// INTERNAL ONLY
///
template<typename A0, typename A1>
struct are_integral
: mpl::and_<is_integral<A0>, is_integral<A1> >
{};
template<typename Left, typename Right>
struct left_ref
{
typedef Left &type;
};
namespace detail
{
template<typename T>
T &lvalue_of();
}
}
// TODO: handle complex weight, valarray, MTL vectors
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_DEFINE_UNARY_OP(Name, Op) \
namespace functional \
{ \
template<typename Arg> \
struct result_of_ ## Name \
{ \
BOOST_TYPEOF_NESTED_TYPEDEF_TPL( \
nested \
, Op boost::numeric::functional::detail::lvalue_of<Arg>() \
) \
typedef typename nested::type type; \
}; \
template<typename Arg, typename EnableIf> \
struct Name ## _base \
{ \
typedef typename remove_const<Arg>::type argument_type; \
typedef typename result_of_ ## Name<Arg>::type result_type; \
typename result_of_ ## Name<Arg>::type operator ()(Arg &arg) const \
{ \
return Op arg; \
} \
}; \
template<typename Arg, typename ArgTag> \
struct Name \
: Name ## _base<Arg, void> \
{}; \
} \
namespace op \
{ \
struct Name \
: boost::detail::function1<functional::Name<_, functional::tag<_> > > \
{}; \
} \
namespace \
{ \
op::Name const &Name = boost::detail::pod_singleton<op::Name>::instance; \
} \
/**/
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(Name, Op, RetType) \
namespace functional \
{ \
template<typename Left, typename Right, typename EnableIf> \
struct result_of_ ## Name \
{ \
RetType(Left, Op, Right) \
}; \
template<typename Left, typename Right, typename EnableIf> \
struct Name ## _base \
{ \
typedef typename remove_const<Left>::type first_argument_type; \
typedef typename remove_const<Right>::type second_argument_type; \
typedef typename result_of_ ## Name<Left, Right>::type result_type; \
typename result_of_ ## Name<Left, Right>::type \
operator ()(Left &left, Right &right) const \
{ \
return left Op right; \
} \
}; \
template<typename Left, typename Right, typename LeftTag, typename RightTag> \
struct Name \
: Name ## _base<Left, Right, void> \
{}; \
} \
namespace op \
{ \
struct Name \
: boost::detail::function2< \
functional::Name<_1, _2, functional::tag<_1>, functional::tag<_2> > \
> \
{}; \
} \
namespace \
{ \
op::Name const &Name = boost::detail::pod_singleton<op::Name>::instance; \
} \
BOOST_ACCUMULATORS_IGNORE_GLOBAL(Name) \
/**/
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_DEDUCED(Left, Op, Right) \
BOOST_TYPEOF_NESTED_TYPEDEF_TPL( \
nested \
, boost::numeric::functional::detail::lvalue_of<Left>() Op \
boost::numeric::functional::detail::lvalue_of<Right>() \
) \
typedef typename nested::type type; \
/**/
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_LEFT(Left, Op, Right) \
typedef Left &type; \
/**/
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(plus, +, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(minus, -, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(multiplies, *, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(divides, /, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(modulus, %, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(greater, >, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(greater_equal, >=, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(less, <, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(less_equal, <=, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(equal_to, ==, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(not_equal_to, !=, BOOST_NUMERIC_FUNCTIONAL_DEDUCED)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(assign, =, BOOST_NUMERIC_FUNCTIONAL_LEFT)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(plus_assign, +=, BOOST_NUMERIC_FUNCTIONAL_LEFT)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(minus_assign, -=, BOOST_NUMERIC_FUNCTIONAL_LEFT)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(multiplies_assign, *=, BOOST_NUMERIC_FUNCTIONAL_LEFT)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(divides_assign, /=, BOOST_NUMERIC_FUNCTIONAL_LEFT)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP(modulus_assign, %=, BOOST_NUMERIC_FUNCTIONAL_LEFT)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_UNARY_OP(unary_plus, +)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_UNARY_OP(unary_minus, -)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_UNARY_OP(complement, ~)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_UNARY_OP(logical_not, !)
#undef BOOST_NUMERIC_FUNCTIONAL_LEFT
#undef BOOST_NUMERIC_FUNCTIONAL_DEDUCED
#undef BOOST_NUMERIC_FUNCTIONAL_DEFINE_UNARY_OP
#undef BOOST_NUMERIC_FUNCTIONAL_DEFINE_BINARY_OP
namespace functional
{
template<typename Left, typename Right, typename EnableIf>
struct min_assign_base
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef void result_type;
void operator ()(Left &left, Right &right) const
{
if(numeric::less(right, left))
{
left = right;
}
}
};
template<typename Left, typename Right, typename EnableIf>
struct max_assign_base
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef void result_type;
void operator ()(Left &left, Right &right) const
{
if(numeric::greater(right, left))
{
left = right;
}
}
};
template<typename Left, typename Right, typename EnableIf>
struct fdiv_base
: functional::divides<Left, Right>
{};
// partial specialization that promotes the arguments to double for
// integral division.
template<typename Left, typename Right>
struct fdiv_base<Left, Right, typename enable_if<are_integral<Left, Right> >::type>
: functional::divides<double const, double const>
{};
template<typename To, typename From, typename EnableIf>
struct promote_base
{
typedef From argument_type;
typedef To result_type;
To operator ()(From &from) const
{
return from;
}
};
template<typename ToFrom>
struct promote_base<ToFrom, ToFrom, void>
{
typedef ToFrom argument_type;
typedef ToFrom result_type;
ToFrom &operator ()(ToFrom &tofrom)
{
return tofrom;
}
};
template<typename Arg, typename EnableIf>
struct as_min_base
{
BOOST_STATIC_ASSERT(std::numeric_limits<typename remove_const<Arg>::type>::is_specialized);
typedef Arg argument_type;
typedef typename remove_const<Arg>::type result_type;
typename remove_const<Arg>::type operator ()(Arg &) const
{
return (std::numeric_limits<typename remove_const<Arg>::type>::min)();
}
};
template<typename Arg>
struct as_min_base<Arg, typename enable_if<is_floating_point<Arg> >::type>
{
BOOST_STATIC_ASSERT(std::numeric_limits<typename remove_const<Arg>::type>::is_specialized);
typedef Arg argument_type;
typedef typename remove_const<Arg>::type result_type;
typename remove_const<Arg>::type operator ()(Arg &) const
{
return -(std::numeric_limits<typename remove_const<Arg>::type>::max)();
}
};
template<typename Arg, typename EnableIf>
struct as_max_base
{
BOOST_STATIC_ASSERT(std::numeric_limits<typename remove_const<Arg>::type>::is_specialized);
typedef Arg argument_type;
typedef typename remove_const<Arg>::type result_type;
typename remove_const<Arg>::type operator ()(Arg &) const
{
return (std::numeric_limits<typename remove_const<Arg>::type>::max)();
}
};
template<typename Arg, typename EnableIf>
struct as_zero_base
{
typedef Arg argument_type;
typedef typename remove_const<Arg>::type result_type;
typename remove_const<Arg>::type operator ()(Arg &) const
{
return numeric::zero<typename remove_const<Arg>::type>::value;
}
};
template<typename Arg, typename EnableIf>
struct as_one_base
{
typedef Arg argument_type;
typedef typename remove_const<Arg>::type result_type;
typename remove_const<Arg>::type operator ()(Arg &) const
{
return numeric::one<typename remove_const<Arg>::type>::value;
}
};
template<typename To, typename From, typename ToTag, typename FromTag>
struct promote
: promote_base<To, From, void>
{};
template<typename Left, typename Right, typename LeftTag, typename RightTag>
struct min_assign
: min_assign_base<Left, Right, void>
{};
template<typename Left, typename Right, typename LeftTag, typename RightTag>
struct max_assign
: max_assign_base<Left, Right, void>
{};
template<typename Left, typename Right, typename LeftTag, typename RightTag>
struct fdiv
: fdiv_base<Left, Right, void>
{};
/// INTERNAL ONLY
/// For back-compat only. Use fdiv.
template<typename Left, typename Right, typename LeftTag, typename RightTag>
struct average
: fdiv<Left, Right, LeftTag, RightTag>
{};
template<typename Arg, typename Tag>
struct as_min
: as_min_base<Arg, void>
{};
template<typename Arg, typename Tag>
struct as_max
: as_max_base<Arg, void>
{};
template<typename Arg, typename Tag>
struct as_zero
: as_zero_base<Arg, void>
{};
template<typename Arg, typename Tag>
struct as_one
: as_one_base<Arg, void>
{};
}
namespace op
{
template<typename To>
struct promote
: boost::detail::function1<functional::promote<To, _, typename functional::tag<To>::type, functional::tag<_> > >
{};
struct min_assign
: boost::detail::function2<functional::min_assign<_1, _2, functional::tag<_1>, functional::tag<_2> > >
{};
struct max_assign
: boost::detail::function2<functional::max_assign<_1, _2, functional::tag<_1>, functional::tag<_2> > >
{};
struct fdiv
: boost::detail::function2<functional::fdiv<_1, _2, functional::tag<_1>, functional::tag<_2> > >
{};
/// INTERNAL ONLY
struct average
: boost::detail::function2<functional::fdiv<_1, _2, functional::tag<_1>, functional::tag<_2> > >
{};
struct as_min
: boost::detail::function1<functional::as_min<_, functional::tag<_> > >
{};
struct as_max
: boost::detail::function1<functional::as_max<_, functional::tag<_> > >
{};
struct as_zero
: boost::detail::function1<functional::as_zero<_, functional::tag<_> > >
{};
struct as_one
: boost::detail::function1<functional::as_one<_, functional::tag<_> > >
{};
}
namespace
{
op::min_assign const &min_assign = boost::detail::pod_singleton<op::min_assign>::instance;
op::max_assign const &max_assign = boost::detail::pod_singleton<op::max_assign>::instance;
op::fdiv const &fdiv = boost::detail::pod_singleton<op::fdiv>::instance;
op::fdiv const &average = boost::detail::pod_singleton<op::fdiv>::instance; ///< INTERNAL ONLY
op::as_min const &as_min = boost::detail::pod_singleton<op::as_min>::instance;
op::as_max const &as_max = boost::detail::pod_singleton<op::as_max>::instance;
op::as_zero const &as_zero = boost::detail::pod_singleton<op::as_zero>::instance;
op::as_one const &as_one = boost::detail::pod_singleton<op::as_one>::instance;
BOOST_ACCUMULATORS_IGNORE_GLOBAL(min_assign)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(max_assign)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(fdiv)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(average)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(as_min)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(as_max)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(as_zero)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(as_one)
}
///////////////////////////////////////////////////////////////////////////////
// promote
template<typename To, typename From>
typename lazy_disable_if<is_const<From>, mpl::if_<is_same<To, From>, To &, To> >::type
promote(From &from)
{
return functional::promote<To, From>()(from);
}
template<typename To, typename From>
typename mpl::if_<is_same<To const, From const>, To const &, To const>::type
promote(From const &from)
{
return functional::promote<To const, From const>()(from);
}
template<typename T>
struct default_
{
typedef default_ type;
typedef T value_type;
static T const value;
operator T const & () const
{
return default_::value;
}
};
template<typename T>
T const default_<T>::value = T();
template<typename T>
struct one
{
typedef one type;
typedef T value_type;
static T const value;
operator T const & () const
{
return one::value;
}
};
template<typename T>
T const one<T>::value = T(1);
template<typename T>
struct zero
{
typedef zero type;
typedef T value_type;
static T const value;
operator T const & () const
{
return zero::value;
}
};
template<typename T>
T const zero<T>::value = T();
template<typename T>
struct one_or_default
: mpl::if_<is_empty<T>, default_<T>, one<T> >::type
{};
template<typename T>
struct zero_or_default
: mpl::if_<is_empty<T>, default_<T>, zero<T> >::type
{};
}} // namespace boost::numeric
#endif

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///////////////////////////////////////////////////////////////////////////////
/// \file complex.hpp
///
// Copyright 2005 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_NUMERIC_FUNCTIONAL_COMPLEX_HPP_EAN_01_17_2006
#define BOOST_NUMERIC_FUNCTIONAL_COMPLEX_HPP_EAN_01_17_2006
#ifdef BOOST_NUMERIC_FUNCTIONAL_HPP_INCLUDED
# error Include this file before boost/accumulators/numeric/functional.hpp
#endif
#include <complex>
#include <boost/mpl/or.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/typeof/std/complex.hpp>
#include <boost/accumulators/numeric/functional_fwd.hpp>
namespace boost { namespace numeric { namespace operators
{
// So that the stats compile when Sample type is std::complex
template<typename T, typename U>
typename
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)
{
// BUGBUG promote result to typeof(T()*u) ?
return ri *= static_cast<T>(u);
}
template<typename T, typename U>
typename
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)
{
// BUGBUG promote result to typeof(T()*u) ?
return ri /= static_cast<T>(u);
}
}}} // namespace boost::numeric::operators
namespace boost { namespace numeric
{
namespace detail
{
template<typename T>
struct one_complex
{
static std::complex<T> const value;
};
template<typename T>
std::complex<T> const one_complex<T>::value
= std::complex<T>(numeric::one<T>::value, numeric::one<T>::value);
}
/// INTERNAL ONLY
///
template<typename T>
struct one<std::complex<T> >
: detail::one_complex<T>
{
typedef one type;
typedef std::complex<T> value_type;
operator value_type const & () const
{
return detail::one_complex<T>::value;
}
};
}} // namespace boost::numeric
#endif

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///////////////////////////////////////////////////////////////////////////////
/// \file valarray.hpp
///
// Copyright 2005 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_NUMERIC_FUNCTIONAL_VALARRAY_HPP_EAN_12_12_2005
#define BOOST_NUMERIC_FUNCTIONAL_VALARRAY_HPP_EAN_12_12_2005
#ifdef BOOST_NUMERIC_FUNCTIONAL_HPP_INCLUDED
# error Include this file before boost/accumulators/numeric/functional.hpp
#endif
#include <valarray>
#include <functional>
#include <boost/assert.hpp>
#include <boost/mpl/and.hpp>
#include <boost/mpl/not.hpp>
#include <boost/mpl/assert.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/is_scalar.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/typeof/std/valarray.hpp>
#include <boost/accumulators/numeric/functional_fwd.hpp>
namespace boost { namespace numeric
{
namespace operators
{
namespace acc_detail
{
template<typename Fun>
struct make_valarray
{
typedef std::valarray<typename Fun::result_type> type;
};
}
///////////////////////////////////////////////////////////////////////////////
// Handle valarray<Left> / Right where Right is a scalar and Right != Left.
template<typename Left, typename Right>
typename lazy_enable_if<
mpl::and_<is_scalar<Right>, mpl::not_<is_same<Left, Right> > >
, acc_detail::make_valarray<functional::divides<Left, Right> >
>::type
operator /(std::valarray<Left> const &left, Right const &right)
{
typedef typename functional::divides<Left, Right>::result_type value_type;
std::valarray<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::divides(left[i], right);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle valarray<Left> * Right where Right is a scalar and Right != Left.
template<typename Left, typename Right>
typename lazy_enable_if<
mpl::and_<is_scalar<Right>, mpl::not_<is_same<Left, Right> > >
, acc_detail::make_valarray<functional::multiplies<Left, Right> >
>::type
operator *(std::valarray<Left> const &left, Right const &right)
{
typedef typename functional::multiplies<Left, Right>::result_type value_type;
std::valarray<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::multiplies(left[i], right);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle valarray<Left> + valarray<Right> where Right != Left.
template<typename Left, typename Right>
typename lazy_disable_if<
is_same<Left, Right>
, acc_detail::make_valarray<functional::plus<Left, Right> >
>::type
operator +(std::valarray<Left> const &left, std::valarray<Right> const &right)
{
typedef typename functional::plus<Left, Right>::result_type value_type;
std::valarray<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::plus(left[i], right[i]);
}
return result;
}
}
namespace functional
{
struct std_valarray_tag;
template<typename T>
struct tag<std::valarray<T> >
{
typedef std_valarray_tag type;
};
#ifdef __GLIBCXX__
template<typename T, typename U>
struct tag<std::_Expr<T, U> >
{
typedef std_valarray_tag type;
};
#endif
/// INTERNAL ONLY
///
// This is necessary because the GCC stdlib uses expression templates, and
// typeof(som-valarray-expression) is not an instance of std::valarray
#define BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP(Name, Op) \
template<typename Left, typename Right> \
struct Name<Left, Right, std_valarray_tag, std_valarray_tag> \
{ \
typedef Left first_argument_type; \
typedef Right second_argument_type; \
typedef typename Left::value_type left_value_type; \
typedef typename Right::value_type right_value_type; \
typedef \
std::valarray< \
typename Name<left_value_type, right_value_type>::result_type \
> \
result_type; \
result_type \
operator ()(Left &left, Right &right) const \
{ \
return numeric::promote<std::valarray<left_value_type> >(left) \
Op numeric::promote<std::valarray<right_value_type> >(right); \
} \
}; \
template<typename Left, typename Right> \
struct Name<Left, Right, std_valarray_tag, void> \
{ \
typedef Left first_argument_type; \
typedef Right second_argument_type; \
typedef typename Left::value_type left_value_type; \
typedef \
std::valarray< \
typename Name<left_value_type, Right>::result_type \
> \
result_type; \
result_type \
operator ()(Left &left, Right &right) const \
{ \
return numeric::promote<std::valarray<left_value_type> >(left) Op right;\
} \
}; \
template<typename Left, typename Right> \
struct Name<Left, Right, void, std_valarray_tag> \
{ \
typedef Left first_argument_type; \
typedef Right second_argument_type; \
typedef typename Right::value_type right_value_type; \
typedef \
std::valarray< \
typename Name<Left, right_value_type>::result_type \
> \
result_type; \
result_type \
operator ()(Left &left, Right &right) const \
{ \
return left Op numeric::promote<std::valarray<right_value_type> >(right);\
} \
};
BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP(plus, +)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP(minus, -)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP(multiplies, *)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP(divides, /)
BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP(modulus, %)
#undef BOOST_NUMERIC_FUNCTIONAL_DEFINE_VALARRAY_BIN_OP
///////////////////////////////////////////////////////////////////////////////
// element-wise min of std::valarray
template<typename Left, typename Right>
struct min_assign<Left, Right, std_valarray_tag, std_valarray_tag>
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef void result_type;
void operator ()(Left &left, Right &right) const
{
BOOST_ASSERT(left.size() == right.size());
for(std::size_t i = 0, size = left.size(); i != size; ++i)
{
if(numeric::less(right[i], left[i]))
{
left[i] = right[i];
}
}
}
};
///////////////////////////////////////////////////////////////////////////////
// element-wise max of std::valarray
template<typename Left, typename Right>
struct max_assign<Left, Right, std_valarray_tag, std_valarray_tag>
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef void result_type;
void operator ()(Left &left, Right &right) const
{
BOOST_ASSERT(left.size() == right.size());
for(std::size_t i = 0, size = left.size(); i != size; ++i)
{
if(numeric::greater(right[i], left[i]))
{
left[i] = right[i];
}
}
}
};
// partial specialization of numeric::fdiv<> for std::valarray.
template<typename Left, typename Right, typename RightTag>
struct fdiv<Left, Right, std_valarray_tag, RightTag>
: mpl::if_<
are_integral<typename Left::value_type, Right>
, divides<Left, double const>
, divides<Left, Right>
>::type
{};
// promote
template<typename To, typename From>
struct promote<To, From, std_valarray_tag, std_valarray_tag>
{
typedef From argument_type;
typedef To result_type;
To operator ()(From &arr) const
{
typename remove_const<To>::type res(arr.size());
for(std::size_t i = 0, size = arr.size(); i != size; ++i)
{
res[i] = numeric::promote<typename To::value_type>(arr[i]);
}
return res;
}
};
template<typename ToFrom>
struct promote<ToFrom, ToFrom, std_valarray_tag, std_valarray_tag>
{
typedef ToFrom argument_type;
typedef ToFrom result_type;
ToFrom &operator ()(ToFrom &tofrom) const
{
return tofrom;
}
};
// for "promoting" a std::valarray<bool> to a bool, useful for
// comparing 2 valarrays for equality:
// if(numeric::promote<bool>(a == b))
template<typename From>
struct promote<bool, From, void, std_valarray_tag>
{
typedef From argument_type;
typedef bool result_type;
bool operator ()(From &arr) const
{
BOOST_MPL_ASSERT((is_same<bool, typename From::value_type>));
for(std::size_t i = 0, size = arr.size(); i != size; ++i)
{
if(!arr[i])
{
return false;
}
}
return true;
}
};
template<typename From>
struct promote<bool const, From, void, std_valarray_tag>
: promote<bool, From, void, std_valarray_tag>
{};
///////////////////////////////////////////////////////////////////////////////
// functional::as_min
template<typename T>
struct as_min<T, std_valarray_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(numeric::as_min(arr[0]), arr.size());
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_max
template<typename T>
struct as_max<T, std_valarray_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(numeric::as_max(arr[0]), arr.size());
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_zero
template<typename T>
struct as_zero<T, std_valarray_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(numeric::as_zero(arr[0]), arr.size());
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_one
template<typename T>
struct as_one<T, std_valarray_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(numeric::as_one(arr[0]), arr.size());
}
};
} // namespace functional
}} // namespace boost::numeric
#endif

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///////////////////////////////////////////////////////////////////////////////
/// \file vector.hpp
///
// Copyright 2005 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_NUMERIC_FUNCTIONAL_VECTOR_HPP_EAN_12_12_2005
#define BOOST_NUMERIC_FUNCTIONAL_VECTOR_HPP_EAN_12_12_2005
#ifdef BOOST_NUMERIC_FUNCTIONAL_HPP_INCLUDED
# error Include this file before boost/accumulators/numeric/functional.hpp
#endif
#include <vector>
#include <functional>
#include <boost/assert.hpp>
#include <boost/mpl/and.hpp>
#include <boost/mpl/not.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/is_scalar.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/typeof/std/vector.hpp>
#include <boost/accumulators/numeric/functional_fwd.hpp>
namespace boost { namespace numeric
{
namespace operators
{
namespace acc_detail
{
template<typename Fun>
struct make_vector
{
typedef std::vector<typename Fun::result_type> type;
};
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> / Right where Right is a scalar.
template<typename Left, typename Right>
typename lazy_enable_if<
is_scalar<Right>
, acc_detail::make_vector<functional::divides<Left, Right> >
>::type
operator /(std::vector<Left> const &left, Right const &right)
{
typedef typename functional::divides<Left, Right>::result_type value_type;
std::vector<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::divides(left[i], right);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> / vector<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)
{
typedef typename functional::divides<Left, Right>::result_type value_type;
std::vector<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::divides(left[i], right[i]);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> * Right where Right is a scalar.
template<typename Left, typename Right>
typename lazy_enable_if<
is_scalar<Right>
, acc_detail::make_vector<functional::multiplies<Left, Right> >
>::type
operator *(std::vector<Left> const &left, Right const &right)
{
typedef typename functional::multiplies<Left, Right>::result_type value_type;
std::vector<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::multiplies(left[i], right);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle Left * vector<Right> where Left is a scalar.
template<typename Left, typename Right>
typename lazy_enable_if<
is_scalar<Left>
, acc_detail::make_vector<functional::multiplies<Left, Right> >
>::type
operator *(Left const &left, std::vector<Right> const &right)
{
typedef typename functional::multiplies<Left, Right>::result_type value_type;
std::vector<value_type> result(right.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::multiplies(left, right[i]);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> * vector<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)
{
typedef typename functional::multiplies<Left, Right>::result_type value_type;
std::vector<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::multiplies(left[i], right[i]);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> + vector<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)
{
typedef typename functional::plus<Left, Right>::result_type value_type;
std::vector<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::plus(left[i], right[i]);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> - vector<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)
{
typedef typename functional::minus<Left, Right>::result_type value_type;
std::vector<value_type> result(left.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::minus(left[i], right[i]);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////
// Handle vector<Left> += vector<Left>
template<typename Left>
std::vector<Left> &
operator +=(std::vector<Left> &left, std::vector<Left> const &right)
{
BOOST_ASSERT(left.size() == right.size());
for(std::size_t i = 0, size = left.size(); i != size; ++i)
{
numeric::plus_assign(left[i], right[i]);
}
return left;
}
///////////////////////////////////////////////////////////////////////////////
// Handle -vector<Arg>
template<typename Arg>
std::vector<typename functional::unary_minus<Arg>::result_type>
operator -(std::vector<Arg> const &arg)
{
typedef typename functional::unary_minus<Arg>::result_type value_type;
std::vector<value_type> result(arg.size());
for(std::size_t i = 0, size = result.size(); i != size; ++i)
{
result[i] = numeric::unary_minus(arg[i]);
}
return result;
}
}
namespace functional
{
struct std_vector_tag;
template<typename T, typename Al>
struct tag<std::vector<T, Al> >
{
typedef std_vector_tag type;
};
///////////////////////////////////////////////////////////////////////////////
// element-wise min of std::vector
template<typename Left, typename Right>
struct min_assign<Left, Right, std_vector_tag, std_vector_tag>
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef void result_type;
void operator ()(Left &left, Right &right) const
{
BOOST_ASSERT(left.size() == right.size());
for(std::size_t i = 0, size = left.size(); i != size; ++i)
{
if(numeric::less(right[i], left[i]))
{
left[i] = right[i];
}
}
}
};
///////////////////////////////////////////////////////////////////////////////
// element-wise max of std::vector
template<typename Left, typename Right>
struct max_assign<Left, Right, std_vector_tag, std_vector_tag>
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef void result_type;
void operator ()(Left &left, Right &right) const
{
BOOST_ASSERT(left.size() == right.size());
for(std::size_t i = 0, size = left.size(); i != size; ++i)
{
if(numeric::greater(right[i], left[i]))
{
left[i] = right[i];
}
}
}
};
// partial specialization for std::vector.
template<typename Left, typename Right>
struct fdiv<Left, Right, std_vector_tag, void>
: mpl::if_<
are_integral<typename Left::value_type, Right>
, divides<Left, double const>
, divides<Left, Right>
>::type
{};
// promote
template<typename To, typename From>
struct promote<To, From, std_vector_tag, std_vector_tag>
{
typedef From argument_type;
typedef To result_type;
To operator ()(From &arr) const
{
typename remove_const<To>::type res(arr.size());
for(std::size_t i = 0, size = arr.size(); i != size; ++i)
{
res[i] = numeric::promote<typename To::value_type>(arr[i]);
}
return res;
}
};
template<typename ToFrom>
struct promote<ToFrom, ToFrom, std_vector_tag, std_vector_tag>
{
typedef ToFrom argument_type;
typedef ToFrom result_type;
ToFrom &operator ()(ToFrom &tofrom) const
{
return tofrom;
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_min
template<typename T>
struct as_min<T, std_vector_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(arr.size(), numeric::as_min(arr[0]));
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_max
template<typename T>
struct as_max<T, std_vector_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(arr.size(), numeric::as_max(arr[0]));
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_zero
template<typename T>
struct as_zero<T, std_vector_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(arr.size(), numeric::as_zero(arr[0]));
}
};
///////////////////////////////////////////////////////////////////////////////
// functional::as_one
template<typename T>
struct as_one<T, std_vector_tag>
{
typedef T argument_type;
typedef typename remove_const<T>::type result_type;
typename remove_const<T>::type operator ()(T &arr) const
{
return 0 == arr.size()
? T()
: T(arr.size(), numeric::as_one(arr[0]));
}
};
} // namespace functional
}} // namespace boost::numeric
#endif

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///////////////////////////////////////////////////////////////////////////////
/// \file functional_fwd.hpp
///
// Copyright 2005 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_NUMERIC_FUNCTIONAL_FWD_HPP_EAN_08_12_2005
#define BOOST_NUMERIC_FUNCTIONAL_FWD_HPP_EAN_08_12_2005
#include <boost/mpl/if.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/is_const.hpp>
namespace boost { namespace numeric
{
// For using directives -- this namespace may be re-opened elsewhere
namespace operators
{}
namespace op
{
using mpl::_;
using mpl::_1;
using mpl::_2;
}
namespace functional
{
using namespace operators;
template<typename T>
struct tag
{
typedef void type;
};
template<typename T>
struct tag<T const>
: tag<T>
{};
template<typename T>
struct tag<T volatile>
: tag<T>
{};
template<typename T>
struct tag<T const volatile>
: tag<T>
{};
template<typename T>
struct static_;
template<typename A0, typename A1>
struct are_integral;
}
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_DECLARE_UNARY_OP(Name, Op) \
namespace functional \
{ \
template<typename Arg, typename EnableIf = void> \
struct Name ## _base; \
template<typename Arg, typename ArgTag = typename tag<Arg>::type> \
struct Name; \
} \
namespace op \
{ \
struct Name; \
} \
namespace \
{ \
extern op::Name const &Name; \
}
/// INTERNAL ONLY
///
#define BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(Name) \
namespace functional \
{ \
template<typename Left, typename Right, typename EnableIf = void> \
struct result_of_ ## Name; \
template<typename Left, typename Right, typename EnableIf = void> \
struct Name ## _base; \
template< \
typename Left \
, typename Right \
, typename LeftTag = typename tag<Left>::type \
, typename RightTag = typename tag<Right>::type \
> \
struct Name; \
} \
namespace op \
{ \
struct Name; \
} \
namespace \
{ \
extern op::Name const &Name; \
}
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(plus)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(minus)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(multiplies)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(divides)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(modulus)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(greater)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(greater_equal)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(less)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(less_equal)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(equal_to)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(not_equal_to)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(assign)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(plus_assign)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(minus_assign)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(multiplies_assign)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(divides_assign)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP(modulus_assign)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_UNARY_OP(unary_plus, +)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_UNARY_OP(unary_minus, -)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_UNARY_OP(complement, ~)
BOOST_NUMERIC_FUNCTIONAL_DECLARE_UNARY_OP(logical_not, !)
#undef BOOST_NUMERIC_FUNCTIONAL_DECLARE_UNARY_OP
#undef BOOST_NUMERIC_FUNCTIONAL_DECLARE_BINARY_OP
namespace functional
{
template<typename To, typename From, typename EnableIf = void>
struct promote_base;
template<typename Left, typename Right, typename EnableIf = void>
struct min_assign_base;
template<typename Left, typename Right, typename EnableIf = void>
struct max_assign_base;
template<typename Left, typename Right, typename EnableIf = void>
struct fdiv_base;
template<typename Arg, typename EnableIf = void>
struct as_min_base;
template<typename Arg, typename EnableIf = void>
struct as_max_base;
template<typename Arg, typename EnableIf = void>
struct as_zero_base;
template<typename Arg, typename EnableIf = void>
struct as_one_base;
template<typename To, typename From, typename ToTag = typename tag<To>::type, typename FromTag = typename tag<From>::type>
struct promote;
template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
struct min_assign;
template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
struct max_assign;
template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
struct fdiv;
template<typename Arg, typename Tag = typename tag<Arg>::type>
struct as_min;
template<typename Arg, typename Tag = typename tag<Arg>::type>
struct as_max;
template<typename Arg, typename Tag = typename tag<Arg>::type>
struct as_zero;
template<typename Arg, typename Tag = typename tag<Arg>::type>
struct as_one;
}
namespace op
{
template<typename To>
struct promote;
struct min_assign;
struct max_assign;
struct fdiv;
struct as_min;
struct as_max;
struct as_zero;
struct as_one;
}
namespace
{
extern op::min_assign const &min_assign;
extern op::max_assign const &max_assign;
extern op::fdiv const &fdiv;
extern op::as_min const &as_min;
extern op::as_max const &as_max;
extern op::as_zero const &as_zero;
extern op::as_one const &as_one;
}
template<typename To, typename From>
typename lazy_disable_if<is_const<From>, mpl::if_<is_same<To, From>, To &, To> >::type
promote(From &from);
template<typename To, typename From>
typename mpl::if_<is_same<To const, From const>, To const &, To const>::type
promote(From const &from);
template<typename T>
struct default_;
template<typename T>
struct one;
template<typename T>
struct zero;
template<typename T>
struct one_or_default;
template<typename T>
struct zero_or_default;
}} // namespace boost::numeric
#endif

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///////////////////////////////////////////////////////////////////////////////
/// \file statistics.hpp
/// Includes all of the Statistical Accumulators Library
//
// Copyright 2005 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_HPP_EAN_01_17_2006
#define BOOST_ACCUMULATORS_STATISTICS_HPP_EAN_01_17_2006
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/covariance.hpp>
#include <boost/accumulators/statistics/density.hpp>
#include <boost/accumulators/statistics/error_of.hpp>
#include <boost/accumulators/statistics/error_of_mean.hpp>
#include <boost/accumulators/statistics/extended_p_square.hpp>
#include <boost/accumulators/statistics/extended_p_square_quantile.hpp>
#include <boost/accumulators/statistics/kurtosis.hpp>
#include <boost/accumulators/statistics/max.hpp>
#include <boost/accumulators/statistics/mean.hpp>
#include <boost/accumulators/statistics/median.hpp>
#include <boost/accumulators/statistics/min.hpp>
#include <boost/accumulators/statistics/moment.hpp>
#include <boost/accumulators/statistics/peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/pot_tail_mean.hpp>
#include <boost/accumulators/statistics/pot_quantile.hpp>
#include <boost/accumulators/statistics/p_square_cumul_dist.hpp>
#include <boost/accumulators/statistics/p_square_quantile.hpp>
#include <boost/accumulators/statistics/skewness.hpp>
#include <boost/accumulators/statistics/stats.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/sum_kahan.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_quantile.hpp>
#include <boost/accumulators/statistics/tail_mean.hpp>
#include <boost/accumulators/statistics/tail_variate.hpp>
#include <boost/accumulators/statistics/tail_variate_means.hpp>
#include <boost/accumulators/statistics/variance.hpp>
#include <boost/accumulators/statistics/weighted_covariance.hpp>
#include <boost/accumulators/statistics/weighted_density.hpp>
#include <boost/accumulators/statistics/weighted_kurtosis.hpp>
#include <boost/accumulators/statistics/weighted_extended_p_square.hpp>
#include <boost/accumulators/statistics/weighted_mean.hpp>
#include <boost/accumulators/statistics/weighted_median.hpp>
#include <boost/accumulators/statistics/weighted_moment.hpp>
#include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp>
#include <boost/accumulators/statistics/weighted_p_square_quantile.hpp>
#include <boost/accumulators/statistics/weighted_skewness.hpp>
#include <boost/accumulators/statistics/weighted_sum.hpp>
#include <boost/accumulators/statistics/weighted_sum_kahan.hpp>
#include <boost/accumulators/statistics/weighted_tail_quantile.hpp>
#include <boost/accumulators/statistics/weighted_tail_mean.hpp>
#include <boost/accumulators/statistics/weighted_tail_variate_means.hpp>
#include <boost/accumulators/statistics/weighted_variance.hpp>
#include <boost/accumulators/statistics/with_error.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#include <boost/accumulators/statistics/variates/covariate.hpp>
#endif

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///////////////////////////////////////////////////////////////////////////////
// count.hpp
//
// Copyright 2005 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_COUNT_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_COUNT_HPP_EAN_28_10_2005
#include <boost/mpl/always.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// count_impl
struct count_impl
: accumulator_base
{
// for boost::result_of
typedef std::size_t result_type;
count_impl(dont_care)
: cnt(0)
{
}
void operator ()(dont_care)
{
++this->cnt;
}
result_type result(dont_care) const
{
return this->cnt;
}
private:
std::size_t cnt;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::count
//
namespace tag
{
struct count
: depends_on<>
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::count_impl> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::count
//
namespace extract
{
extractor<tag::count> const count = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(count)
}
using extract::count;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// covariance.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_COVARIANCE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_COVARIANCE_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <complex>
#include <boost/mpl/assert.hpp>
#include <boost/mpl/bool.hpp>
#include <boost/range.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/type_traits/is_scalar.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/mean.hpp>
namespace boost { namespace numeric
{
namespace functional
{
struct std_vector_tag;
///////////////////////////////////////////////////////////////////////////////
// functional::outer_product
template<typename Left, typename Right, typename EnableIf = void>
struct outer_product_base
: functional::multiplies<Left, Right>
{};
template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
struct outer_product
: outer_product_base<Left, Right, void>
{};
template<typename Left, typename Right>
struct outer_product<Left, Right, std_vector_tag, std_vector_tag>
{
typedef Left first_argument_type;
typedef Right second_argument_type;
typedef
ublas::matrix<
typename functional::multiplies<
typename Left::value_type
, typename Right::value_type
>::result_type
>
result_type;
result_type
operator ()(Left & left, Right & right) const
{
std::size_t left_size = left.size();
std::size_t right_size = right.size();
result_type result(left_size, right_size);
for (std::size_t i = 0; i < left_size; ++i)
for (std::size_t j = 0; j < right_size; ++j)
result(i,j) = numeric::multiplies(left[i], right[j]);
return result;
}
};
}
namespace op
{
struct outer_product
: boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > >
{};
}
namespace
{
op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance;
}
}}
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// covariance_impl
//
/**
@brief Covariance Estimator
An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
and \f$X'\f$ is a variate, is given by:
\f[
\hat{c}_n = \frac{n-1}{n} \hat{c}_{n-1} + \frac{1}{n-1}(X_n - \hat{\mu}_n)(X_n' - \hat{\mu}_n'),\quad n\ge2,\quad\hat{c}_1 = 0,
\f]
\f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates.
*/
template<typename Sample, typename VariateType, typename VariateTag>
struct covariance_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type sample_type;
typedef typename numeric::functional::fdiv<VariateType, std::size_t>::result_type variate_type;
// for boost::result_of
typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type;
template<typename Args>
covariance_impl(Args const &args)
: cov_(
numeric::outer_product(
numeric::fdiv(args[sample | Sample()], (std::size_t)1)
, numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
)
)
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
if (cnt > 1)
{
extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {};
this->cov_ = this->cov_*(cnt-1.)/cnt
+ numeric::outer_product(
some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
, mean(args) - args[sample]
) / (cnt-1.);
}
}
result_type result(dont_care) const
{
return this->cov_;
}
private:
result_type cov_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::covariance
//
namespace tag
{
template<typename VariateType, typename VariateTag>
struct covariance
: depends_on<count, mean, mean_of_variates<VariateType, VariateTag> >
{
typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl;
};
struct abstract_covariance
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::covariance
//
namespace extract
{
extractor<tag::abstract_covariance> const covariance = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance)
}
using extract::covariance;
template<typename VariateType, typename VariateTag>
struct feature_of<tag::covariance<VariateType, VariateTag> >
: feature_of<tag::abstract_covariance>
{
};
// So that covariance can be automatically substituted with
// weighted_covariance when the weight parameter is non-void.
template<typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::covariance<VariateType, VariateTag> >
{
typedef tag::weighted_covariance<VariateType, VariateTag> type;
};
template<typename VariateType, typename VariateTag>
struct feature_of<tag::weighted_covariance<VariateType, VariateTag> >
: feature_of<tag::covariance<VariateType, VariateTag> >
{};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// density.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_DENSITY_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_DENSITY_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <functional>
#include <boost/range.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/accumulators_fwd.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/max.hpp>
#include <boost/accumulators/statistics/min.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// cache_size and num_bins named parameters
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, density_cache_size, cache_size)
BOOST_PARAMETER_NESTED_KEYWORD(tag, density_num_bins, num_bins)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(density_cache_size)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(density_num_bins)
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// density_impl
// density histogram
/**
@brief Histogram density estimator
The histogram density estimator returns a histogram of the sample distribution. The positions and sizes of the bins
are determined using a specifiable number of cached samples (cache_size). The range between the minimum and the
maximum of the cached samples is subdivided into a specifiable number of bins (num_bins) of same size. Additionally,
an under- and an overflow bin is added to capture future under- and overflow samples. Once the bins are determined,
the cached samples and all subsequent samples are added to the correct bins. At the end, a range of std::pair is
return, where each pair contains the position of the bin (lower bound) and the samples count (normalized with the
total number of samples).
@param density_cache_size Number of first samples used to determine min and max.
@param density_num_bins Number of bins (two additional bins collect under- and overflow samples).
*/
template<typename Sample>
struct density_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef std::vector<float_type> array_type;
// for boost::result_of
typedef iterator_range<typename histogram_type::iterator> result_type;
template<typename Args>
density_impl(Args const &args)
: cache_size(args[density_cache_size])
, cache(cache_size)
, num_bins(args[density_num_bins])
, samples_in_bin(num_bins + 2, 0.)
, bin_positions(num_bins + 2)
, histogram(
num_bins + 2
, std::make_pair(
numeric::fdiv(args[sample | Sample()],(std::size_t)1)
, numeric::fdiv(args[sample | Sample()],(std::size_t)1)
)
)
, is_dirty(true)
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->is_dirty = true;
std::size_t cnt = count(args);
// Fill up cache with cache_size first samples
if (cnt <= this->cache_size)
{
this->cache[cnt - 1] = args[sample];
}
// Once cache_size samples have been accumulated, create num_bins bins of same size between
// the minimum and maximum of the cached samples as well as under and overflow bins.
// Store their lower bounds (bin_positions) and fill the bins with the cached samples (samples_in_bin).
if (cnt == this->cache_size)
{
float_type minimum = numeric::fdiv((min)(args), (std::size_t)1);
float_type maximum = numeric::fdiv((max)(args), (std::size_t)1);
float_type bin_size = numeric::fdiv(maximum - minimum, this->num_bins );
// determine bin positions (their lower bounds)
for (std::size_t i = 0; i < this->num_bins + 2; ++i)
{
this->bin_positions[i] = minimum + (i - 1.) * bin_size;
}
for (typename array_type::const_iterator iter = this->cache.begin(); iter != this->cache.end(); ++iter)
{
if (*iter < this->bin_positions[1])
{
++(this->samples_in_bin[0]);
}
else if (*iter >= this->bin_positions[this->num_bins + 1])
{
++(this->samples_in_bin[this->num_bins + 1]);
}
else
{
typename array_type::iterator it = std::upper_bound(
this->bin_positions.begin()
, this->bin_positions.end()
, *iter
);
std::size_t d = std::distance(this->bin_positions.begin(), it);
++(this->samples_in_bin[d - 1]);
}
}
}
// Add each subsequent sample to the correct bin
else if (cnt > this->cache_size)
{
if (args[sample] < this->bin_positions[1])
{
++(this->samples_in_bin[0]);
}
else if (args[sample] >= this->bin_positions[this->num_bins + 1])
{
++(this->samples_in_bin[this->num_bins + 1]);
}
else
{
typename array_type::iterator it = std::upper_bound(
this->bin_positions.begin()
, this->bin_positions.end()
, args[sample]
);
std::size_t d = std::distance(this->bin_positions.begin(), it);
++(this->samples_in_bin[d - 1]);
}
}
}
/**
@pre The number of samples must meet or exceed the cache size
*/
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
// creates a vector of std::pair where each pair i holds
// the values bin_positions[i] (x-axis of histogram) and
// samples_in_bin[i] / cnt (y-axis of histogram).
for (std::size_t i = 0; i < this->num_bins + 2; ++i)
{
this->histogram[i] = std::make_pair(this->bin_positions[i], numeric::fdiv(this->samples_in_bin[i], count(args)));
}
}
// returns a range of pairs
return make_iterator_range(this->histogram);
}
private:
std::size_t cache_size; // number of cached samples
array_type cache; // cache to store the first cache_size samples
std::size_t num_bins; // number of bins
array_type samples_in_bin; // number of samples in each bin
array_type bin_positions; // lower bounds of bins
mutable histogram_type histogram; // histogram
mutable bool is_dirty;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::density
//
namespace tag
{
struct density
: depends_on<count, min, max>
, density_cache_size
, density_num_bins
{
/// INTERNAL ONLY
///
typedef accumulators::impl::density_impl<mpl::_1> impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::density::cache_size named parameter
/// tag::density::num_bins named parameter
static boost::parameter::keyword<density_cache_size> const cache_size;
static boost::parameter::keyword<density_num_bins> const num_bins;
#endif
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::density
//
namespace extract
{
extractor<tag::density> const density = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(density)
}
using extract::density;
// So that density can be automatically substituted
// with weighted_density when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::density>
{
typedef tag::weighted_density type;
};
template<>
struct feature_of<tag::weighted_density>
: feature_of<tag::density>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// error_of.hpp
//
// Copyright 2005 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_ERROR_OF_HPP_EAN_29_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_ERROR_OF_HPP_EAN_29_11_2005
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
/// INTERNAL ONLY
///
template<typename Feature>
struct this_feature_has_no_error_calculation
: mpl::false_
{
};
///////////////////////////////////////////////////////////////////////////////
// error_of_impl
/// INTERNAL ONLY
///
template<typename Sample, typename Feature>
struct error_of_impl
: accumulator_base
{
// TODO: specialize this on the specific features that have errors we're
// interested in.
BOOST_MPL_ASSERT((this_feature_has_no_error_calculation<Feature>));
// for boost::result_of
typedef int result_type;
error_of_impl(dont_care)
{
}
result_type result(dont_care) const
{
return 0;
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::error_of
//
namespace tag
{
template<typename Feature>
struct error_of
: depends_on<Feature>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::error_of_impl<mpl::_1, Feature> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::error_of
//
namespace extract
{
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, error_of, (typename))
}
using extract::error_of;
// make tag::error_of<tag::feature(modifier)> work
template<typename Feature>
struct as_feature<tag::error_of<Feature> >
{
typedef tag::error_of<typename as_feature<Feature>::type> type;
};
// make error_of<tag::mean> work with non-void weights (should become
// error_of<tag::weighted_mean>
template<typename Feature>
struct as_weighted_feature<tag::error_of<Feature> >
{
typedef tag::error_of<typename as_weighted_feature<Feature>::type> type;
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// error_of.hpp
//
// Copyright 2005 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_ERROR_OF_MEAN_HPP_EAN_27_03_2006
#define BOOST_ACCUMULATORS_STATISTICS_ERROR_OF_MEAN_HPP_EAN_27_03_2006
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/error_of.hpp>
#include <boost/accumulators/statistics/variance.hpp>
#include <boost/accumulators/statistics/count.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// error_of_mean_impl
template<typename Sample, typename Variance>
struct error_of_mean_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
error_of_mean_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
using namespace std;
extractor<Variance> const variance = {};
return sqrt(numeric::fdiv(variance(args), count(args) - 1));
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::error_of
//
namespace tag
{
template<>
struct error_of<mean>
: depends_on<lazy_variance, count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::error_of_mean_impl<mpl::_1, lazy_variance> impl;
};
template<>
struct error_of<immediate_mean>
: depends_on<variance, count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::error_of_mean_impl<mpl::_1, variance> impl;
};
}
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// extended_p_square.hpp
//
// Copyright 2005 Daniel Egloff. 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_EXTENDED_SINGLE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_HPP_DE_01_01_2006
#include <vector>
#include <functional>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/accumulators_fwd.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/times2_iterator.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// probabilities named parameter
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, extended_p_square_probabilities, probabilities)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_probabilities)
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// extended_p_square_impl
// multiple quantile estimation
/**
@brief Multiple quantile estimation with the extended \f$P^2\f$ algorithm
Extended \f$P^2\f$ algorithm for estimation of several quantiles without storing samples.
Assume that \f$m\f$ quantiles \f$\xi_{p_1}, \ldots, \xi_{p_m}\f$ are to be estimated.
Instead of storing the whole sample cumulative distribution, the algorithm maintains only
\f$m+2\f$ principal markers and \f$m+1\f$ middle markers, whose positions are updated
with each sample and whose heights are adjusted (if necessary) using a piecewise-parablic
formula. The heights of these central markers are the current estimates of the quantiles
and returned as an iterator range.
For further details, see
K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49,
Number 4 (October), 1986, p. 159-164.
The extended \f$ P^2 \f$ algorithm generalizes the \f$ P^2 \f$ algorithm of
R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
histograms without storing observations, Communications of the ACM,
Volume 28 (October), Number 10, 1985, p. 1076-1085.
@param extended_p_square_probabilities A vector of quantile probabilities.
*/
template<typename Sample>
struct extended_p_square_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<float_type> array_type;
// for boost::result_of
typedef iterator_range<
detail::lvalue_index_iterator<
permutation_iterator<
typename array_type::const_iterator
, detail::times2_iterator
>
>
> result_type;
template<typename Args>
extended_p_square_impl(Args const &args)
: probabilities(
boost::begin(args[extended_p_square_probabilities])
, boost::end(args[extended_p_square_probabilities])
)
, heights(2 * probabilities.size() + 3)
, actual_positions(heights.size())
, desired_positions(heights.size())
, positions_increments(heights.size())
{
std::size_t num_quantiles = this->probabilities.size();
std::size_t num_markers = this->heights.size();
for(std::size_t i = 0; i < num_markers; ++i)
{
this->actual_positions[i] = i + 1;
}
this->positions_increments[0] = 0.;
this->positions_increments[num_markers - 1] = 1.;
for(std::size_t i = 0; i < num_quantiles; ++i)
{
this->positions_increments[2 * i + 2] = probabilities[i];
}
for(std::size_t i = 0; i <= num_quantiles; ++i)
{
this->positions_increments[2 * i + 1] =
0.5 * (this->positions_increments[2 * i] + this->positions_increments[2 * i + 2]);
}
for(std::size_t i = 0; i < num_markers; ++i)
{
this->desired_positions[i] = 1. + 2. * (num_quantiles + 1.) * this->positions_increments[i];
}
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
// m+2 principal markers and m+1 middle markers
std::size_t num_markers = 2 * this->probabilities.size() + 3;
// first accumulate num_markers samples
if(cnt <= num_markers)
{
this->heights[cnt - 1] = args[sample];
// complete the initialization of heights by sorting
if(cnt == num_markers)
{
std::sort(this->heights.begin(), this->heights.end());
}
}
else
{
std::size_t sample_cell = 1;
// find cell k = sample_cell such that heights[k-1] <= sample < heights[k]
if(args[sample] < this->heights[0])
{
this->heights[0] = args[sample];
sample_cell = 1;
}
else if(args[sample] >= this->heights[num_markers - 1])
{
this->heights[num_markers - 1] = args[sample];
sample_cell = num_markers - 1;
}
else
{
typedef typename array_type::iterator iterator;
iterator it = std::upper_bound(
this->heights.begin()
, this->heights.end()
, args[sample]
);
sample_cell = std::distance(this->heights.begin(), it);
}
// update actual positions of all markers above sample_cell index
for(std::size_t i = sample_cell; i < num_markers; ++i)
{
++this->actual_positions[i];
}
// update desired positions of all markers
for(std::size_t i = 0; i < num_markers; ++i)
{
this->desired_positions[i] += this->positions_increments[i];
}
// adjust heights and actual positions of markers 1 to num_markers-2 if necessary
for(std::size_t i = 1; i <= num_markers - 2; ++i)
{
// offset to desired position
float_type d = this->desired_positions[i] - this->actual_positions[i];
// offset to next position
float_type dp = this->actual_positions[i+1] - this->actual_positions[i];
// offset to previous position
float_type dm = this->actual_positions[i-1] - this->actual_positions[i];
// height ds
float_type hp = (this->heights[i+1] - this->heights[i]) / dp;
float_type hm = (this->heights[i-1] - this->heights[i]) / dm;
if((d >= 1 && dp > 1) || (d <= -1 && dm < -1))
{
short sign_d = static_cast<short>(d / std::abs(d));
float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm)*hp
+ (dp - sign_d) * hm);
// try adjusting heights[i] using p-squared formula
if(this->heights[i - 1] < h && h < this->heights[i + 1])
{
this->heights[i] = h;
}
else
{
// use linear formula
if(d > 0)
{
this->heights[i] += hp;
}
if(d < 0)
{
this->heights[i] -= hm;
}
}
this->actual_positions[i] += sign_d;
}
}
}
}
result_type result(dont_care) const
{
// for i in [1,probabilities.size()], return heights[i * 2]
detail::times2_iterator idx_begin = detail::make_times2_iterator(1);
detail::times2_iterator idx_end = detail::make_times2_iterator(this->probabilities.size() + 1);
return result_type(
make_permutation_iterator(this->heights.begin(), idx_begin)
, make_permutation_iterator(this->heights.begin(), idx_end)
);
}
private:
array_type probabilities; // the quantile probabilities
array_type heights; // q_i
array_type actual_positions; // n_i
array_type desired_positions; // d_i
array_type positions_increments; // f_i
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::extended_p_square
//
namespace tag
{
struct extended_p_square
: depends_on<count>
, extended_p_square_probabilities
{
typedef accumulators::impl::extended_p_square_impl<mpl::_1> impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::extended_p_square::probabilities named parameter
static boost::parameter::keyword<tag::probabilities> const probabilities;
#endif
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::extended_p_square
//
namespace extract
{
extractor<tag::extended_p_square> const extended_p_square = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square)
}
using extract::extended_p_square;
// So that extended_p_square can be automatically substituted with
// weighted_extended_p_square when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::extended_p_square>
{
typedef tag::weighted_extended_p_square type;
};
template<>
struct feature_of<tag::weighted_extended_p_square>
: feature_of<tag::extended_p_square>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// extended_p_square_quantile.hpp
//
// Copyright 2005 Daniel Egloff. 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_EXTENDED_SINGLE_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_QUANTILE_HPP_DE_01_01_2006
#include <vector>
#include <functional>
#include <boost/throw_exception.hpp>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.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/parameters/quantile_probability.hpp>
#include <boost/accumulators/statistics/extended_p_square.hpp>
#include <boost/accumulators/statistics/weighted_extended_p_square.hpp>
#include <boost/accumulators/statistics/times2_iterator.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// extended_p_square_quantile_impl
// single quantile estimation
/**
@brief Quantile estimation using the extended \f$P^2\f$ algorithm for weighted and unweighted samples
Uses the quantile estimates calculated by the extended \f$P^2\f$ algorithm to compute
intermediate quantile estimates by means of quadratic interpolation.
@param quantile_probability The probability of the quantile to be estimated.
*/
template<typename Sample, typename Impl1, typename Impl2> // Impl1: weighted/unweighted // Impl2: linear/quadratic
struct extended_p_square_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<float_type> array_type;
typedef iterator_range<
detail::lvalue_index_iterator<
permutation_iterator<
typename array_type::const_iterator
, detail::times2_iterator
>
>
> range_type;
// for boost::result_of
typedef float_type result_type;
template<typename Args>
extended_p_square_quantile_impl(Args const &args)
: probabilities(
boost::begin(args[extended_p_square_probabilities])
, boost::end(args[extended_p_square_probabilities])
)
{
}
template<typename Args>
result_type result(Args const &args) const
{
typedef
typename mpl::if_<
is_same<Impl1, weighted>
, tag::weighted_extended_p_square
, tag::extended_p_square
>::type
extended_p_square_tag;
extractor<extended_p_square_tag> const some_extended_p_square = {};
array_type heights(some_extended_p_square(args).size());
std::copy(some_extended_p_square(args).begin(), some_extended_p_square(args).end(), heights.begin());
this->probability = args[quantile_probability];
typename array_type::const_iterator iter_probs = std::lower_bound(this->probabilities.begin(), this->probabilities.end(), this->probability);
std::size_t dist = std::distance(this->probabilities.begin(), iter_probs);
typename array_type::const_iterator iter_heights = heights.begin() + dist;
// If this->probability is not in a valid range return NaN or throw exception
if (this->probability < *this->probabilities.begin() || this->probability > *(this->probabilities.end() - 1))
{
if (std::numeric_limits<result_type>::has_quiet_NaN)
{
return std::numeric_limits<result_type>::quiet_NaN();
}
else
{
std::ostringstream msg;
msg << "probability = " << this->probability << " is not in valid range (";
msg << *this->probabilities.begin() << ", " << *(this->probabilities.end() - 1) << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return Sample(0);
}
}
if (*iter_probs == this->probability)
{
return heights[dist];
}
else
{
result_type res;
if (is_same<Impl2, linear>::value)
{
/////////////////////////////////////////////////////////////////////////////////
// LINEAR INTERPOLATION
//
float_type p1 = *iter_probs;
float_type p0 = *(iter_probs - 1);
float_type h1 = *iter_heights;
float_type h0 = *(iter_heights - 1);
float_type a = numeric::fdiv(h1 - h0, p1 - p0);
float_type b = h1 - p1 * a;
res = a * this->probability + b;
}
else
{
/////////////////////////////////////////////////////////////////////////////////
// QUADRATIC INTERPOLATION
//
float_type p0, p1, p2;
float_type h0, h1, h2;
if ( (dist == 1 || *iter_probs - this->probability <= this->probability - *(iter_probs - 1) ) && dist != this->probabilities.size() - 1 )
{
p0 = *(iter_probs - 1);
p1 = *iter_probs;
p2 = *(iter_probs + 1);
h0 = *(iter_heights - 1);
h1 = *iter_heights;
h2 = *(iter_heights + 1);
}
else
{
p0 = *(iter_probs - 2);
p1 = *(iter_probs - 1);
p2 = *iter_probs;
h0 = *(iter_heights - 2);
h1 = *(iter_heights - 1);
h2 = *iter_heights;
}
float_type hp21 = numeric::fdiv(h2 - h1, p2 - p1);
float_type hp10 = numeric::fdiv(h1 - h0, p1 - p0);
float_type p21 = numeric::fdiv(p2 * p2 - p1 * p1, p2 - p1);
float_type p10 = numeric::fdiv(p1 * p1 - p0 * p0, p1 - p0);
float_type a = numeric::fdiv(hp21 - hp10, p21 - p10);
float_type b = hp21 - a * p21;
float_type c = h2 - a * p2 * p2 - b * p2;
res = a * this->probability * this-> probability + b * this->probability + c;
}
return res;
}
}
private:
array_type probabilities;
mutable float_type probability;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::extended_p_square_quantile
//
namespace tag
{
struct extended_p_square_quantile
: depends_on<extended_p_square>
{
typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, unweighted, linear> impl;
};
struct extended_p_square_quantile_quadratic
: depends_on<extended_p_square>
{
typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, unweighted, quadratic> impl;
};
struct weighted_extended_p_square_quantile
: depends_on<weighted_extended_p_square>
{
typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, weighted, linear> impl;
};
struct weighted_extended_p_square_quantile_quadratic
: depends_on<weighted_extended_p_square>
{
typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, weighted, quadratic> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::extended_p_square_quantile
// extract::weighted_extended_p_square_quantile
//
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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_quantile)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_quantile_quadratic)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square_quantile)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square_quantile_quadratic)
}
using extract::extended_p_square_quantile;
using extract::extended_p_square_quantile_quadratic;
using extract::weighted_extended_p_square_quantile;
using extract::weighted_extended_p_square_quantile_quadratic;
// extended_p_square_quantile(linear) -> extended_p_square_quantile
template<>
struct as_feature<tag::extended_p_square_quantile(linear)>
{
typedef tag::extended_p_square_quantile type;
};
// extended_p_square_quantile(quadratic) -> extended_p_square_quantile_quadratic
template<>
struct as_feature<tag::extended_p_square_quantile(quadratic)>
{
typedef tag::extended_p_square_quantile_quadratic type;
};
// weighted_extended_p_square_quantile(linear) -> weighted_extended_p_square_quantile
template<>
struct as_feature<tag::weighted_extended_p_square_quantile(linear)>
{
typedef tag::weighted_extended_p_square_quantile type;
};
// weighted_extended_p_square_quantile(quadratic) -> weighted_extended_p_square_quantile_quadratic
template<>
struct as_feature<tag::weighted_extended_p_square_quantile(quadratic)>
{
typedef tag::weighted_extended_p_square_quantile_quadratic type;
};
// for the purposes of feature-based dependency resolution,
// extended_p_square_quantile and weighted_extended_p_square_quantile
// provide the same feature as quantile
template<>
struct feature_of<tag::extended_p_square_quantile>
: feature_of<tag::quantile>
{
};
template<>
struct feature_of<tag::extended_p_square_quantile_quadratic>
: feature_of<tag::quantile>
{
};
// So that extended_p_square_quantile can be automatically substituted with
// weighted_extended_p_square_quantile when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::extended_p_square_quantile>
{
typedef tag::weighted_extended_p_square_quantile type;
};
template<>
struct feature_of<tag::weighted_extended_p_square_quantile>
: feature_of<tag::extended_p_square_quantile>
{
};
// So that extended_p_square_quantile_quadratic can be automatically substituted with
// weighted_extended_p_square_quantile_quadratic when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::extended_p_square_quantile_quadratic>
{
typedef tag::weighted_extended_p_square_quantile_quadratic type;
};
template<>
struct feature_of<tag::weighted_extended_p_square_quantile_quadratic>
: feature_of<tag::extended_p_square_quantile_quadratic>
{
};
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// kurtosis.hpp
//
// Copyright 2006 Olivier Gygi, Daniel Egloff. 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_KURTOSIS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005
#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics/mean.hpp>
#include <boost/accumulators/statistics/moment.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// kurtosis_impl
/**
@brief Kurtosis estimation
The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central
moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution
has zero kurtosis. The kurtosis can also be expressed by the simple moments:
\f[
\hat{g}_2 =
\frac
{\widehat{m}_n^{(4)}-4\widehat{m}_n^{(3)}\hat{\mu}_n+6\widehat{m}_n^{(2)}\hat{\mu}_n^2-3\hat{\mu}_n^4}
{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3,
\f]
where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
\f$ n \f$ samples.
*/
template<typename Sample>
struct kurtosis_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type;
kurtosis_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::moment<4>(args)
- 4. * accumulators::moment<3>(args) * mean(args)
+ 6. * accumulators::moment<2>(args) * mean(args) * mean(args)
- 3. * mean(args) * mean(args) * mean(args) * mean(args)
, ( accumulators::moment<2>(args) - mean(args) * mean(args) )
* ( accumulators::moment<2>(args) - mean(args) * mean(args) )
) - 3.;
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::kurtosis
//
namespace tag
{
struct kurtosis
: depends_on<mean, moment<2>, moment<3>, moment<4> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::kurtosis_impl<mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::kurtosis
//
namespace extract
{
extractor<tag::kurtosis> const kurtosis = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis)
}
using extract::kurtosis;
// So that kurtosis can be automatically substituted with
// weighted_kurtosis when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::kurtosis>
{
typedef tag::weighted_kurtosis type;
};
template<>
struct feature_of<tag::weighted_kurtosis>
: feature_of<tag::kurtosis>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// max.hpp
//
// Copyright 2005 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_MAX_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_MAX_HPP_EAN_28_10_2005
#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// max_impl
template<typename Sample>
struct max_impl
: accumulator_base
{
// for boost::result_of
typedef Sample result_type;
template<typename Args>
max_impl(Args const &args)
: max_(numeric::as_min(args[sample | Sample()]))
{
}
template<typename Args>
void operator ()(Args const &args)
{
numeric::max_assign(this->max_, args[sample]);
}
result_type result(dont_care) const
{
return this->max_;
}
private:
Sample max_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::max
//
namespace tag
{
struct max
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::max_impl<mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::max
//
namespace extract
{
extractor<tag::max> const max = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(max)
}
using extract::max;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// mean.hpp
//
// Copyright 2005 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_MEAN_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_MEAN_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>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// mean_impl
// lazy, by default
template<typename Sample, typename SumFeature>
struct mean_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
mean_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
extractor<SumFeature> sum;
return numeric::fdiv(sum(args), count(args));
}
};
template<typename Sample, typename Tag>
struct immediate_mean_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
template<typename Args>
immediate_mean_impl(Args const &args)
: mean(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
this->mean = numeric::fdiv(
(this->mean * (cnt - 1)) + args[parameter::keyword<Tag>::get()]
, cnt
);
}
result_type result(dont_care) const
{
return this->mean;
}
private:
result_type mean;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::mean
// tag::immediate_mean
// tag::mean_of_weights
// tag::immediate_mean_of_weights
// tag::mean_of_variates
// tag::immediate_mean_of_variates
//
namespace tag
{
struct mean
: depends_on<count, sum>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::mean_impl<mpl::_1, sum> impl;
};
struct immediate_mean
: depends_on<count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::immediate_mean_impl<mpl::_1, tag::sample> impl;
};
struct mean_of_weights
: depends_on<count, sum_of_weights>
{
typedef mpl::true_ is_weight_accumulator;
/// INTERNAL ONLY
///
typedef accumulators::impl::mean_impl<mpl::_2, sum_of_weights> impl;
};
struct immediate_mean_of_weights
: depends_on<count>
{
typedef mpl::true_ is_weight_accumulator;
/// INTERNAL ONLY
///
typedef accumulators::impl::immediate_mean_impl<mpl::_2, tag::weight> impl;
};
template<typename VariateType, typename VariateTag>
struct mean_of_variates
: depends_on<count, sum_of_variates<VariateType, VariateTag> >
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::mean_impl<VariateType, sum_of_variates<VariateType, VariateTag> > > impl;
};
template<typename VariateType, typename VariateTag>
struct immediate_mean_of_variates
: depends_on<count>
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::immediate_mean_impl<VariateType, VariateTag> > impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::mean
// extract::mean_of_weights
// extract::mean_of_variates
//
namespace extract
{
extractor<tag::mean> const mean = {};
extractor<tag::mean_of_weights> const mean_of_weights = {};
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, mean_of_variates, (typename)(typename))
BOOST_ACCUMULATORS_IGNORE_GLOBAL(mean)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(mean_of_weights)
}
using extract::mean;
using extract::mean_of_weights;
using extract::mean_of_variates;
// mean(lazy) -> mean
template<>
struct as_feature<tag::mean(lazy)>
{
typedef tag::mean type;
};
// mean(immediate) -> immediate_mean
template<>
struct as_feature<tag::mean(immediate)>
{
typedef tag::immediate_mean type;
};
// mean_of_weights(lazy) -> mean_of_weights
template<>
struct as_feature<tag::mean_of_weights(lazy)>
{
typedef tag::mean_of_weights type;
};
// mean_of_weights(immediate) -> immediate_mean_of_weights
template<>
struct as_feature<tag::mean_of_weights(immediate)>
{
typedef tag::immediate_mean_of_weights type;
};
// mean_of_variates<VariateType, VariateTag>(lazy) -> mean_of_variates<VariateType, VariateTag>
template<typename VariateType, typename VariateTag>
struct as_feature<tag::mean_of_variates<VariateType, VariateTag>(lazy)>
{
typedef tag::mean_of_variates<VariateType, VariateTag> type;
};
// mean_of_variates<VariateType, VariateTag>(immediate) -> immediate_mean_of_variates<VariateType, VariateTag>
template<typename VariateType, typename VariateTag>
struct as_feature<tag::mean_of_variates<VariateType, VariateTag>(immediate)>
{
typedef tag::immediate_mean_of_variates<VariateType, VariateTag> type;
};
// for the purposes of feature-based dependency resolution,
// immediate_mean provides the same feature as mean
template<>
struct feature_of<tag::immediate_mean>
: feature_of<tag::mean>
{
};
// for the purposes of feature-based dependency resolution,
// immediate_mean provides the same feature as mean
template<>
struct feature_of<tag::immediate_mean_of_weights>
: feature_of<tag::mean_of_weights>
{
};
// for the purposes of feature-based dependency resolution,
// immediate_mean provides the same feature as mean
template<typename VariateType, typename VariateTag>
struct feature_of<tag::immediate_mean_of_variates<VariateType, VariateTag> >
: feature_of<tag::mean_of_variates<VariateType, VariateTag> >
{
};
// So that mean can be automatically substituted with
// weighted_mean when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::mean>
{
typedef tag::weighted_mean type;
};
template<>
struct feature_of<tag::weighted_mean>
: feature_of<tag::mean>
{};
// So that immediate_mean can be automatically substituted with
// immediate_weighted_mean when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::immediate_mean>
{
typedef tag::immediate_weighted_mean type;
};
template<>
struct feature_of<tag::immediate_weighted_mean>
: feature_of<tag::immediate_mean>
{};
// So that mean_of_weights<> can be automatically substituted with
// weighted_mean_of_variates<> when the weight parameter is non-void.
template<typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::mean_of_variates<VariateType, VariateTag> >
{
typedef tag::weighted_mean_of_variates<VariateType, VariateTag> type;
};
template<typename VariateType, typename VariateTag>
struct feature_of<tag::weighted_mean_of_variates<VariateType, VariateTag> >
: feature_of<tag::mean_of_variates<VariateType, VariateTag> >
{
};
// So that immediate_mean_of_weights<> can be automatically substituted with
// immediate_weighted_mean_of_variates<> when the weight parameter is non-void.
template<typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::immediate_mean_of_variates<VariateType, VariateTag> >
{
typedef tag::immediate_weighted_mean_of_variates<VariateType, VariateTag> type;
};
template<typename VariateType, typename VariateTag>
struct feature_of<tag::immediate_weighted_mean_of_variates<VariateType, VariateTag> >
: feature_of<tag::immediate_mean_of_variates<VariateType, VariateTag> >
{
};
////////////////////////////////////////////////////////////////////////////
//// droppable_accumulator<mean_impl>
//// need to specialize droppable lazy mean to cache the result at the
//// point the accumulator is dropped.
///// INTERNAL ONLY
/////
//template<typename Sample, typename SumFeature>
//struct droppable_accumulator<impl::mean_impl<Sample, SumFeature> >
// : droppable_accumulator_base<
// with_cached_result<impl::mean_impl<Sample, SumFeature> >
// >
//{
// template<typename Args>
// droppable_accumulator(Args const &args)
// : droppable_accumulator::base(args)
// {
// }
//};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// median.hpp
//
// Copyright 2006 Eric Niebler, Olivier Gygi. 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_MEDIAN_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_MEDIAN_HPP_EAN_28_10_2005
#include <boost/mpl/placeholders.hpp>
#include <boost/range/iterator_range.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/p_square_quantile.hpp>
#include <boost/accumulators/statistics/density.hpp>
#include <boost/accumulators/statistics/p_square_cumul_dist.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// median_impl
//
/**
@brief Median estimation based on the \f$P^2\f$ quantile estimator
The \f$P^2\f$ algorithm is invoked with a quantile probability of 0.5.
*/
template<typename Sample>
struct median_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
median_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
return p_square_quantile_for_median(args);
}
};
///////////////////////////////////////////////////////////////////////////////
// with_density_median_impl
//
/**
@brief Median estimation based on the density estimator
The algorithm determines the bin in which the \f$0.5*cnt\f$-th sample lies, \f$cnt\f$ being
the total number of samples. It returns the approximate horizontal position of this sample,
based on a linear interpolation inside the bin.
*/
template<typename Sample>
struct with_density_median_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef iterator_range<typename histogram_type::iterator> range_type;
// for boost::result_of
typedef float_type result_type;
template<typename Args>
with_density_median_impl(Args const &args)
: sum(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, is_dirty(true)
{
}
void operator ()(dont_care)
{
this->is_dirty = true;
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
std::size_t cnt = count(args);
range_type histogram = density(args);
typename range_type::iterator it = histogram.begin();
while (this->sum < 0.5 * cnt)
{
this->sum += it->second * cnt;
++it;
}
--it;
float_type over = numeric::fdiv(this->sum - 0.5 * cnt, it->second * cnt);
this->median = it->first * over + (it + 1)->first * (1. - over);
}
return this->median;
}
private:
mutable float_type sum;
mutable bool is_dirty;
mutable float_type median;
};
///////////////////////////////////////////////////////////////////////////////
// with_p_square_cumulative_distribution_median_impl
//
/**
@brief Median estimation based on the \f$P^2\f$ cumulative distribution estimator
The algorithm determines the first (leftmost) bin with a height exceeding 0.5. It
returns the approximate horizontal position of where the cumulative distribution
equals 0.5, based on a linear interpolation inside the bin.
*/
template<typename Sample>
struct with_p_square_cumulative_distribution_median_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef iterator_range<typename histogram_type::iterator> range_type;
// for boost::result_of
typedef float_type result_type;
with_p_square_cumulative_distribution_median_impl(dont_care)
: is_dirty(true)
{
}
void operator ()(dont_care)
{
this->is_dirty = true;
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
range_type histogram = p_square_cumulative_distribution(args);
typename range_type::iterator it = histogram.begin();
while (it->second < 0.5)
{
++it;
}
float_type over = numeric::fdiv(it->second - 0.5, it->second - (it - 1)->second);
this->median = it->first * over + (it + 1)->first * ( 1. - over );
}
return this->median;
}
private:
mutable bool is_dirty;
mutable float_type median;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::median
// tag::with_densisty_median
// tag::with_p_square_cumulative_distribution_median
//
namespace tag
{
struct median
: depends_on<p_square_quantile_for_median>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::median_impl<mpl::_1> impl;
};
struct with_density_median
: depends_on<count, density>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::with_density_median_impl<mpl::_1> impl;
};
struct with_p_square_cumulative_distribution_median
: depends_on<p_square_cumulative_distribution>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::with_p_square_cumulative_distribution_median_impl<mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::median
// extract::with_density_median
// extract::with_p_square_cumulative_distribution_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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(median)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(with_density_median)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(with_p_square_cumulative_distribution_median)
}
using extract::median;
using extract::with_density_median;
using extract::with_p_square_cumulative_distribution_median;
// median(with_p_square_quantile) -> median
template<>
struct as_feature<tag::median(with_p_square_quantile)>
{
typedef tag::median type;
};
// median(with_density) -> with_density_median
template<>
struct as_feature<tag::median(with_density)>
{
typedef tag::with_density_median type;
};
// median(with_p_square_cumulative_distribution) -> with_p_square_cumulative_distribution_median
template<>
struct as_feature<tag::median(with_p_square_cumulative_distribution)>
{
typedef tag::with_p_square_cumulative_distribution_median type;
};
// for the purposes of feature-based dependency resolution,
// with_density_median and with_p_square_cumulative_distribution_median
// provide the same feature as median
template<>
struct feature_of<tag::with_density_median>
: feature_of<tag::median>
{
};
template<>
struct feature_of<tag::with_p_square_cumulative_distribution_median>
: feature_of<tag::median>
{
};
// So that median can be automatically substituted with
// weighted_median when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::median>
{
typedef tag::weighted_median type;
};
template<>
struct feature_of<tag::weighted_median>
: feature_of<tag::median>
{
};
// So that with_density_median can be automatically substituted with
// with_density_weighted_median when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::with_density_median>
{
typedef tag::with_density_weighted_median type;
};
template<>
struct feature_of<tag::with_density_weighted_median>
: feature_of<tag::with_density_median>
{
};
// So that with_p_square_cumulative_distribution_median can be automatically substituted with
// with_p_square_cumulative_distribution_weighted_median when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::with_p_square_cumulative_distribution_median>
{
typedef tag::with_p_square_cumulative_distribution_weighted_median type;
};
template<>
struct feature_of<tag::with_p_square_cumulative_distribution_weighted_median>
: feature_of<tag::with_p_square_cumulative_distribution_median>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// min.hpp
//
// Copyright 2005 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_MIN_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_MIN_HPP_EAN_28_10_2005
#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// min_impl
template<typename Sample>
struct min_impl
: accumulator_base
{
// for boost::result_of
typedef Sample result_type;
template<typename Args>
min_impl(Args const &args)
: min_(numeric::as_max(args[sample | Sample()]))
{
}
template<typename Args>
void operator ()(Args const &args)
{
numeric::min_assign(this->min_, args[sample]);
}
result_type result(dont_care) const
{
return this->min_;
}
private:
Sample min_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::min
//
namespace tag
{
struct min
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::min_impl<mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::min
//
namespace extract
{
extractor<tag::min> const min = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(min)
}
using extract::min;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// moment.hpp
//
// Copyright 2005 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_MOMENT_HPP_EAN_15_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_MOMENT_HPP_EAN_15_11_2005
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/assert.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/count.hpp>
namespace boost { namespace numeric
{
/// INTERNAL ONLY
///
template<typename T>
T const &pow(T const &x, mpl::int_<1>)
{
return x;
}
/// INTERNAL ONLY
///
template<typename T, int N>
T pow(T const &x, mpl::int_<N>)
{
using namespace operators;
T y = numeric::pow(x, mpl::int_<N/2>());
T z = y * y;
return (N % 2) ? (z * x) : z;
}
}}
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// moment_impl
template<typename N, typename Sample>
struct moment_impl
: accumulator_base // TODO: also depends_on sum of powers
{
BOOST_MPL_ASSERT_RELATION(N::value, >, 0);
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
template<typename Args>
moment_impl(Args const &args)
: sum(args[sample | Sample()])
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->sum += numeric::pow(args[sample], N());
}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(this->sum, count(args));
}
private:
Sample sum;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::moment
//
namespace tag
{
template<int N>
struct moment
: depends_on<count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::moment_impl<mpl::int_<N>, mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::moment
//
namespace extract
{
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, moment, (int))
}
using extract::moment;
// So that moment<N> can be automatically substituted with
// weighted_moment<N> when the weight parameter is non-void
template<int N>
struct as_weighted_feature<tag::moment<N> >
{
typedef tag::weighted_moment<N> type;
};
template<int N>
struct feature_of<tag::weighted_moment<N> >
: feature_of<tag::moment<N> >
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// p_square_cumulative_distribution.hpp
//
// Copyright 2005 Daniel Egloff, Olivier Gygi. 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_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006
#include <vector>
#include <functional>
#include <boost/parameter/keyword.hpp>
#include <boost/range.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/accumulators_fwd.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// num_cells named parameter
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, p_square_cumulative_distribution_num_cells, num_cells)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_cumulative_distribution_num_cells)
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// p_square_cumulative_distribution_impl
// cumulative_distribution calculation (as histogram)
/**
@brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm
A histogram of the sample cumulative distribution is computed dynamically without storing samples
based on the \f$ P^2 \f$ algorithm. The returned histogram has a specifiable amount (num_cells)
equiprobable (and not equal-sized) cells.
For further details, see
R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
histograms without storing observations, Communications of the ACM,
Volume 28 (October), Number 10, 1985, p. 1076-1085.
@param p_square_cumulative_distribution_num_cells.
*/
template<typename Sample>
struct p_square_cumulative_distribution_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<float_type> array_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
// for boost::result_of
typedef iterator_range<typename histogram_type::iterator> result_type;
template<typename Args>
p_square_cumulative_distribution_impl(Args const &args)
: num_cells(args[p_square_cumulative_distribution_num_cells])
, heights(num_cells + 1)
, actual_positions(num_cells + 1)
, desired_positions(num_cells + 1)
, positions_increments(num_cells + 1)
, histogram(num_cells + 1)
, is_dirty(true)
{
std::size_t b = this->num_cells;
for (std::size_t i = 0; i < b + 1; ++i)
{
this->actual_positions[i] = i + 1.;
this->desired_positions[i] = i + 1.;
this->positions_increments[i] = numeric::fdiv(i, b);
}
}
template<typename Args>
void operator ()(Args const &args)
{
this->is_dirty = true;
std::size_t cnt = count(args);
std::size_t sample_cell = 1; // k
std::size_t b = this->num_cells;
// accumulate num_cells + 1 first samples
if (cnt <= b + 1)
{
this->heights[cnt - 1] = args[sample];
// complete the initialization of heights by sorting
if (cnt == b + 1)
{
std::sort(this->heights.begin(), this->heights.end());
}
}
else
{
// find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
if (args[sample] < this->heights[0])
{
this->heights[0] = args[sample];
sample_cell = 1;
}
else if (this->heights[b] <= args[sample])
{
this->heights[b] = args[sample];
sample_cell = b;
}
else
{
typename array_type::iterator it;
it = std::upper_bound(
this->heights.begin()
, this->heights.end()
, args[sample]
);
sample_cell = std::distance(this->heights.begin(), it);
}
// increment positions of markers above sample_cell
for (std::size_t i = sample_cell; i < b + 1; ++i)
{
++this->actual_positions[i];
}
// update desired position of markers 2 to num_cells + 1
// (desired position of first marker is always 1)
for (std::size_t i = 1; i < b + 1; ++i)
{
this->desired_positions[i] += this->positions_increments[i];
}
// adjust heights of markers 2 to num_cells if necessary
for (std::size_t i = 1; i < b; ++i)
{
// offset to desire position
float_type d = this->desired_positions[i] - this->actual_positions[i];
// offset to next position
float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
// offset to previous position
float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
// height ds
float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) )
{
short sign_d = static_cast<short>(d / std::abs(d));
// try adjusting heights[i] using p-squared formula
float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm );
if ( this->heights[i - 1] < h && h < this->heights[i + 1] )
{
this->heights[i] = h;
}
else
{
// use linear formula
if (d>0)
{
this->heights[i] += hp;
}
if (d<0)
{
this->heights[i] -= hm;
}
}
this->actual_positions[i] += sign_d;
}
}
}
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
// creates a vector of std::pair where each pair i holds
// the values heights[i] (x-axis of histogram) and
// actual_positions[i] / cnt (y-axis of histogram)
std::size_t cnt = count(args);
for (std::size_t i = 0; i < this->histogram.size(); ++i)
{
this->histogram[i] = std::make_pair(this->heights[i], numeric::fdiv(this->actual_positions[i], cnt));
}
}
//return histogram;
return make_iterator_range(this->histogram);
}
private:
std::size_t num_cells; // number of cells b
array_type heights; // q_i
array_type actual_positions; // n_i
array_type desired_positions; // n'_i
array_type positions_increments; // dn'_i
mutable histogram_type histogram; // histogram
mutable bool is_dirty;
};
} // namespace detail
///////////////////////////////////////////////////////////////////////////////
// tag::p_square_cumulative_distribution
//
namespace tag
{
struct p_square_cumulative_distribution
: depends_on<count>
, p_square_cumulative_distribution_num_cells
{
/// INTERNAL ONLY
///
typedef accumulators::impl::p_square_cumulative_distribution_impl<mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::p_square_cumulative_distribution
//
namespace extract
{
extractor<tag::p_square_cumulative_distribution> const p_square_cumulative_distribution = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_cumulative_distribution)
}
using extract::p_square_cumulative_distribution;
// So that p_square_cumulative_distribution can be automatically substituted with
// weighted_p_square_cumulative_distribution when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::p_square_cumulative_distribution>
{
typedef tag::weighted_p_square_cumulative_distribution type;
};
template<>
struct feature_of<tag::weighted_p_square_cumulative_distribution>
: feature_of<tag::p_square_cumulative_distribution>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// p_square_cumulative_distribution.hpp
//
// Copyright 2012 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_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_03_19_2012
#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_03_19_2012
#if defined(_MSC_VER) || defined(__BORLANDC__) || defined(__DMC__)
# pragma message ("Warning: This header is deprecated. Please use: boost/accumulators/statistics/p_square_cumul_dist.hpp")
#elif defined(__GNUC__) || defined(__HP_aCC) || defined(__SUNPRO_CC) || defined(__IBMCPP__)
# warning "This header is deprecated. Please use: boost/accumulators/statistics/p_square_cumul_dist.hpp"
#endif
#include <boost/accumulators/statistics/p_square_cumul_dist.hpp>
#endif

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///////////////////////////////////////////////////////////////////////////////
// p_square_quantile.hpp
//
// Copyright 2005 Daniel Egloff. 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_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
#include <cmath>
#include <functional>
#include <boost/array.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/parameter/keyword.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/parameters/quantile_probability.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// p_square_quantile_impl
// single quantile estimation
/**
@brief Single quantile estimation with the \f$P^2\f$ algorithm
The \f$P^2\f$ algorithm estimates a quantile dynamically without storing samples. Instead of
storing the whole sample cumulative distribution, only five points (markers) are stored. The heights
of these markers are the minimum and the maximum of the samples and the current estimates of the
\f$(p/2)\f$-, \f$p\f$- and \f$(1+p)/2\f$-quantiles. Their positions are equal to the number
of samples that are smaller or equal to the markers. Each time a new samples is recorded, the
positions of the markers are updated and if necessary their heights are adjusted using a piecewise-
parabolic formula.
For further details, see
R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
histograms without storing observations, Communications of the ACM,
Volume 28 (October), Number 10, 1985, p. 1076-1085.
@param quantile_probability
*/
template<typename Sample, typename Impl>
struct p_square_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef array<float_type, 5> array_type;
// for boost::result_of
typedef float_type result_type;
template<typename Args>
p_square_quantile_impl(Args const &args)
: p(is_same<Impl, for_median>::value ? 0.5 : args[quantile_probability | 0.5])
, heights()
, actual_positions()
, desired_positions()
, positions_increments()
{
for(std::size_t i = 0; i < 5; ++i)
{
this->actual_positions[i] = i + 1.;
}
this->desired_positions[0] = 1.;
this->desired_positions[1] = 1. + 2. * this->p;
this->desired_positions[2] = 1. + 4. * this->p;
this->desired_positions[3] = 3. + 2. * this->p;
this->desired_positions[4] = 5.;
this->positions_increments[0] = 0.;
this->positions_increments[1] = this->p / 2.;
this->positions_increments[2] = this->p;
this->positions_increments[3] = (1. + this->p) / 2.;
this->positions_increments[4] = 1.;
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
// accumulate 5 first samples
if(cnt <= 5)
{
this->heights[cnt - 1] = args[sample];
// complete the initialization of heights by sorting
if(cnt == 5)
{
std::sort(this->heights.begin(), this->heights.end());
}
}
else
{
std::size_t sample_cell = 1; // k
// find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
if (args[sample] < this->heights[0])
{
this->heights[0] = args[sample];
sample_cell = 1;
}
else if (this->heights[4] <= args[sample])
{
this->heights[4] = args[sample];
sample_cell = 4;
}
else
{
typedef typename array_type::iterator iterator;
iterator it = std::upper_bound(
this->heights.begin()
, this->heights.end()
, args[sample]
);
sample_cell = std::distance(this->heights.begin(), it);
}
// update positions of markers above sample_cell
for(std::size_t i = sample_cell; i < 5; ++i)
{
++this->actual_positions[i];
}
// update desired positions of all markers
for(std::size_t i = 0; i < 5; ++i)
{
this->desired_positions[i] += this->positions_increments[i];
}
// adjust heights and actual positions of markers 1 to 3 if necessary
for(std::size_t i = 1; i <= 3; ++i)
{
// offset to desired positions
float_type d = this->desired_positions[i] - this->actual_positions[i];
// offset to next position
float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
// offset to previous position
float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
// height ds
float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
if((d >= 1. && dp > 1.) || (d <= -1. && dm < -1.))
{
short sign_d = static_cast<short>(d / std::abs(d));
// try adjusting heights[i] using p-squared formula
float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm) * hp
+ (dp - sign_d) * hm);
if(this->heights[i - 1] < h && h < this->heights[i + 1])
{
this->heights[i] = h;
}
else
{
// use linear formula
if(d > 0)
{
this->heights[i] += hp;
}
if(d < 0)
{
this->heights[i] -= hm;
}
}
this->actual_positions[i] += sign_d;
}
}
}
}
result_type result(dont_care) const
{
return this->heights[2];
}
private:
float_type p; // the quantile probability p
array_type heights; // q_i
array_type actual_positions; // n_i
array_type desired_positions; // n'_i
array_type positions_increments; // dn'_i
};
} // namespace detail
///////////////////////////////////////////////////////////////////////////////
// tag::p_square_quantile
//
namespace tag
{
struct p_square_quantile
: depends_on<count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::p_square_quantile_impl<mpl::_1, regular> impl;
};
struct p_square_quantile_for_median
: depends_on<count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::p_square_quantile_impl<mpl::_1, for_median> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::p_square_quantile
// extract::p_square_quantile_for_median
//
namespace extract
{
extractor<tag::p_square_quantile> const p_square_quantile = {};
extractor<tag::p_square_quantile_for_median> const p_square_quantile_for_median = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile_for_median)
}
using extract::p_square_quantile;
using extract::p_square_quantile_for_median;
// So that p_square_quantile can be automatically substituted with
// weighted_p_square_quantile when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::p_square_quantile>
{
typedef tag::weighted_p_square_quantile type;
};
template<>
struct feature_of<tag::weighted_p_square_quantile>
: feature_of<tag::p_square_quantile>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// quantile_probability.hpp
//
// Copyright 2005 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_PARAMETERS_QUANTILE_PROBABILITY_HPP_EAN_03_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_PARAMETERS_QUANTILE_PROBABILITY_HPP_EAN_03_11_2005
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
BOOST_PARAMETER_KEYWORD(tag, quantile_probability)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(quantile_probability)
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// peaks_over_threshold.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <boost/config/no_tr1/cmath.hpp> // pow
#include <sstream> // stringstream
#include <stdexcept> // runtime_error
#include <boost/throw_exception.hpp>
#include <boost/range.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/accumulators/accumulators_fwd.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/parameters/quantile_probability.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// threshold_probability and threshold named parameters
//
BOOST_PARAMETER_NESTED_KEYWORD(tag, pot_threshold_value, threshold_value)
BOOST_PARAMETER_NESTED_KEYWORD(tag, pot_threshold_probability, threshold_probability)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(pot_threshold_value)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(pot_threshold_probability)
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// peaks_over_threshold_impl
// works with an explicit threshold value and does not depend on order statistics
/**
@brief Peaks over Threshold Method for Quantile and Tail Mean Estimation
According to the theorem of Pickands-Balkema-de Haan, the distribution function \f$F_u(x)\f$ of
the excesses \f$x\f$ over some sufficiently high threshold \f$u\f$ of a distribution function \f$F(x)\f$
may be approximated by a generalized Pareto distribution
\f[
G_{\xi,\beta}(x) =
\left\{
\begin{array}{ll}
\beta^{-1}\left(1+\frac{\xi x}{\beta}\right)^{-1/\xi-1} & \textrm{if }\xi\neq0\\
\beta^{-1}\exp\left(-\frac{x}{\beta}\right) & \textrm{if }\xi=0,
\end{array}
\right.
\f]
with suitable parameters \f$\xi\f$ and \f$\beta\f$ that can be estimated, e.g., with the method of moments, cf.
Hosking and Wallis (1987),
\f[
\begin{array}{lll}
\hat{\xi} & = & \frac{1}{2}\left[1-\frac{(\hat{\mu}-u)^2}{\hat{\sigma}^2}\right]\\
\hat{\beta} & = & \frac{\hat{\mu}-u}{2}\left[\frac{(\hat{\mu}-u)^2}{\hat{\sigma}^2}+1\right],
\end{array}
\f]
\f$\hat{\mu}\f$ and \f$\hat{\sigma}^2\f$ being the empirical mean and variance of the samples over
the threshold \f$u\f$. Equivalently, the distribution function
\f$F_u(x-u)\f$ of the exceedances \f$x-u\f$ can be approximated by
\f$G_{\xi,\beta}(x-u)=G_{\xi,\beta,u}(x)\f$. Since for \f$x\geq u\f$ the distribution function \f$F(x)\f$
can be written as
\f[
F(x) = [1 - \P(X \leq u)]F_u(x - u) + \P(X \leq u)
\f]
and the probability \f$\P(X \leq u)\f$ can be approximated by the empirical distribution function
\f$F_n(u)\f$ evaluated at \f$u\f$, an estimator of \f$F(x)\f$ is given by
\f[
\widehat{F}(x) = [1 - F_n(u)]G_{\xi,\beta,u}(x) + F_n(u).
\f]
It can be shown that \f$\widehat{F}(x)\f$ is a generalized
Pareto distribution \f$G_{\xi,\bar{\beta},\bar{u}}(x)\f$ with \f$\bar{\beta}=\beta[1-F_n(u)]^{\xi}\f$
and \f$\bar{u}=u-\bar{\beta}\left\{[1-F_n(u)]^{-\xi}-1\right\}/\xi\f$. By inverting \f$\widehat{F}(x)\f$,
one obtains an estimator for the \f$\alpha\f$-quantile,
\f[
\hat{q}_{\alpha} = \bar{u} + \frac{\bar{\beta}}{\xi}\left[(1-\alpha)^{-\xi}-1\right],
\f]
and similarly an estimator for the (coherent) tail mean,
\f[
\widehat{CTM}_{\alpha} = \hat{q}_{\alpha} - \frac{\bar{\beta}}{\xi-1}(1-\alpha)^{-\xi},
\f]
cf. McNeil and Frey (2000).
Note that in case extreme values of the left tail are fitted, the distribution is mirrored with respect to the
\f$y\f$ axis such that the left tail can be treated as a right tail. The computed fit parameters thus define
the Pareto distribution that fits the mirrored left tail. When quantities like a quantile or a tail mean are
computed using the fit parameters obtained from the mirrored data, the result is mirrored back, yielding the
correct result.
For further details, see
J. R. M. Hosking and J. R. Wallis, Parameter and quantile estimation for the generalized Pareto distribution,
Technometrics, Volume 29, 1987, p. 339-349
A. J. McNeil and R. Frey, Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series:
an Extreme Value Approach, Journal of Empirical Finance, Volume 7, 2000, p. 271-300
@param quantile_probability
@param pot_threshold_value
*/
template<typename Sample, typename LeftRight>
struct peaks_over_threshold_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef boost::tuple<float_type, float_type, float_type> result_type;
// for left tail fitting, mirror the extreme values
typedef mpl::int_<is_same<LeftRight, left>::value ? -1 : 1> sign;
template<typename Args>
peaks_over_threshold_impl(Args const &args)
: Nu_(0)
, mu_(sign::value * numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, sigma2_(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, threshold_(sign::value * args[pot_threshold_value])
, fit_parameters_(boost::make_tuple(0., 0., 0.))
, is_dirty_(true)
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->is_dirty_ = true;
if (sign::value * args[sample] > this->threshold_)
{
this->mu_ += args[sample];
this->sigma2_ += args[sample] * args[sample];
++this->Nu_;
}
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty_)
{
this->is_dirty_ = false;
std::size_t cnt = count(args);
this->mu_ = sign::value * numeric::fdiv(this->mu_, this->Nu_);
this->sigma2_ = numeric::fdiv(this->sigma2_, this->Nu_);
this->sigma2_ -= this->mu_ * this->mu_;
float_type threshold_probability = numeric::fdiv(cnt - this->Nu_, cnt);
float_type tmp = numeric::fdiv(( this->mu_ - this->threshold_ )*( this->mu_ - this->threshold_ ), this->sigma2_);
float_type xi_hat = 0.5 * ( 1. - tmp );
float_type beta_hat = 0.5 * ( this->mu_ - this->threshold_ ) * ( 1. + tmp );
float_type beta_bar = beta_hat * std::pow(1. - threshold_probability, xi_hat);
float_type u_bar = this->threshold_ - beta_bar * ( std::pow(1. - threshold_probability, -xi_hat) - 1.)/xi_hat;
this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
}
return this->fit_parameters_;
}
private:
std::size_t Nu_; // number of samples larger than threshold
mutable float_type mu_; // mean of Nu_ largest samples
mutable float_type sigma2_; // variance of Nu_ largest samples
float_type threshold_;
mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
mutable bool is_dirty_;
};
///////////////////////////////////////////////////////////////////////////////
// peaks_over_threshold_prob_impl
// determines threshold from a given threshold probability using order statistics
/**
@brief Peaks over Threshold Method for Quantile and Tail Mean Estimation
@sa peaks_over_threshold_impl
@param quantile_probability
@param pot_threshold_probability
*/
template<typename Sample, typename LeftRight>
struct peaks_over_threshold_prob_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef boost::tuple<float_type, float_type, float_type> result_type;
// for left tail fitting, mirror the extreme values
typedef mpl::int_<is_same<LeftRight, left>::value ? -1 : 1> sign;
template<typename Args>
peaks_over_threshold_prob_impl(Args const &args)
: mu_(sign::value * numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, sigma2_(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, threshold_probability_(args[pot_threshold_probability])
, fit_parameters_(boost::make_tuple(0., 0., 0.))
, is_dirty_(true)
{
}
void operator ()(dont_care)
{
this->is_dirty_ = true;
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty_)
{
this->is_dirty_ = false;
std::size_t cnt = count(args);
// the n'th cached sample provides an approximate threshold value u
std::size_t n = static_cast<std::size_t>(
std::ceil(
cnt * ( ( is_same<LeftRight, left>::value ) ? this->threshold_probability_ : 1. - this->threshold_probability_ )
)
);
// If n is in a valid range, return result, otherwise return NaN or throw exception
if ( n >= static_cast<std::size_t>(tail(args).size()))
{
if (std::numeric_limits<float_type>::has_quiet_NaN)
{
return boost::make_tuple(
std::numeric_limits<float_type>::quiet_NaN()
, std::numeric_limits<float_type>::quiet_NaN()
, std::numeric_limits<float_type>::quiet_NaN()
);
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return boost::make_tuple(Sample(0), Sample(0), Sample(0));
}
}
else
{
float_type u = *(tail(args).begin() + n - 1) * sign::value;
// compute mean and variance of samples above/under threshold value u
for (std::size_t i = 0; i < n; ++i)
{
mu_ += *(tail(args).begin() + i);
sigma2_ += *(tail(args).begin() + i) * (*(tail(args).begin() + i));
}
this->mu_ = sign::value * numeric::fdiv(this->mu_, n);
this->sigma2_ = numeric::fdiv(this->sigma2_, n);
this->sigma2_ -= this->mu_ * this->mu_;
if (is_same<LeftRight, left>::value)
this->threshold_probability_ = 1. - this->threshold_probability_;
float_type tmp = numeric::fdiv(( this->mu_ - u )*( this->mu_ - u ), this->sigma2_);
float_type xi_hat = 0.5 * ( 1. - tmp );
float_type beta_hat = 0.5 * ( this->mu_ - u ) * ( 1. + tmp );
float_type beta_bar = beta_hat * std::pow(1. - threshold_probability_, xi_hat);
float_type u_bar = u - beta_bar * ( std::pow(1. - threshold_probability_, -xi_hat) - 1.)/xi_hat;
this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
}
}
return this->fit_parameters_;
}
private:
mutable float_type mu_; // mean of samples above threshold u
mutable float_type sigma2_; // variance of samples above threshold u
mutable float_type threshold_probability_;
mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
mutable bool is_dirty_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::peaks_over_threshold
//
namespace tag
{
template<typename LeftRight>
struct peaks_over_threshold
: depends_on<count>
, pot_threshold_value
{
/// INTERNAL ONLY
///
typedef accumulators::impl::peaks_over_threshold_impl<mpl::_1, LeftRight> impl;
};
template<typename LeftRight>
struct peaks_over_threshold_prob
: depends_on<count, tail<LeftRight> >
, pot_threshold_probability
{
/// INTERNAL ONLY
///
typedef accumulators::impl::peaks_over_threshold_prob_impl<mpl::_1, LeftRight> impl;
};
struct abstract_peaks_over_threshold
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::peaks_over_threshold
//
namespace extract
{
extractor<tag::abstract_peaks_over_threshold> const peaks_over_threshold = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(peaks_over_threshold)
}
using extract::peaks_over_threshold;
// peaks_over_threshold<LeftRight>(with_threshold_value) -> peaks_over_threshold<LeftRight>
template<typename LeftRight>
struct as_feature<tag::peaks_over_threshold<LeftRight>(with_threshold_value)>
{
typedef tag::peaks_over_threshold<LeftRight> type;
};
// peaks_over_threshold<LeftRight>(with_threshold_probability) -> peaks_over_threshold_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::peaks_over_threshold<LeftRight>(with_threshold_probability)>
{
typedef tag::peaks_over_threshold_prob<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::peaks_over_threshold<LeftRight> >
: feature_of<tag::abstract_peaks_over_threshold>
{
};
template<typename LeftRight>
struct feature_of<tag::peaks_over_threshold_prob<LeftRight> >
: feature_of<tag::abstract_peaks_over_threshold>
{
};
// So that peaks_over_threshold can be automatically substituted
// with weighted_peaks_over_threshold when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::peaks_over_threshold<LeftRight> >
{
typedef tag::weighted_peaks_over_threshold<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_peaks_over_threshold<LeftRight> >
: feature_of<tag::peaks_over_threshold<LeftRight> >
{};
// So that peaks_over_threshold_prob can be automatically substituted
// with weighted_peaks_over_threshold_prob when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::peaks_over_threshold_prob<LeftRight> >
{
typedef tag::weighted_peaks_over_threshold_prob<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_peaks_over_threshold_prob<LeftRight> >
: feature_of<tag::peaks_over_threshold_prob<LeftRight> >
{};
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// pot_quantile.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_POT_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_POT_QUANTILE_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <boost/parameter/keyword.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/mpl/if.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// pot_quantile_impl
//
/**
@brief Quantile Estimation based on Peaks over Threshold Method (for both left and right tails)
Computes an estimate
\f[
\hat{q}_{\alpha} = \bar{u} + \frac{\bar{\beta}}{\xi}\left[(1-\alpha)^{-\xi}-1\right]
\f]
for a right or left extreme quantile, \f$\bar[u]\f$, \f$\bar{\beta}\f$ and \f$\xi\f$ being the parameters of the
generalized Pareto distribution that approximates the right tail of the distribution (or the mirrored left tail,
in case the left tail is used). In the latter case, the result is mirrored back, yielding the correct result.
*/
template<typename Sample, typename Impl, typename LeftRight>
struct pot_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef float_type result_type;
pot_quantile_impl(dont_care)
: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
{
}
template<typename Args>
result_type result(Args const &args) const
{
typedef
typename mpl::if_<
is_same<Impl, weighted>
, tag::weighted_peaks_over_threshold<LeftRight>
, tag::peaks_over_threshold<LeftRight>
>::type
peaks_over_threshold_tag;
extractor<peaks_over_threshold_tag> const some_peaks_over_threshold = {};
float_type u_bar = some_peaks_over_threshold(args).template get<0>();
float_type beta_bar = some_peaks_over_threshold(args).template get<1>();
float_type xi_hat = some_peaks_over_threshold(args).template get<2>();
return this->sign_ * (u_bar + beta_bar/xi_hat * ( std::pow(
is_same<LeftRight, left>::value ? args[quantile_probability] : 1. - args[quantile_probability]
, -xi_hat
) - 1.));
}
private:
short sign_; // if the fit parameters from the mirrored left tail extreme values are used, mirror back the result
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::pot_quantile<>
// tag::pot_quantile_prob<>
// tag::weighted_pot_quantile<>
// tag::weighted_pot_quantile_prob<>
//
namespace tag
{
template<typename LeftRight>
struct pot_quantile
: depends_on<peaks_over_threshold<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_quantile_impl<mpl::_1, unweighted, LeftRight> impl;
};
template<typename LeftRight>
struct pot_quantile_prob
: depends_on<peaks_over_threshold_prob<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_quantile_impl<mpl::_1, unweighted, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_pot_quantile
: depends_on<weighted_peaks_over_threshold<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_quantile_impl<mpl::_1, weighted, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_pot_quantile_prob
: depends_on<weighted_peaks_over_threshold_prob<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_quantile_impl<mpl::_1, weighted, LeftRight> impl;
};
}
// pot_quantile<LeftRight>(with_threshold_value) -> pot_quantile<LeftRight>
template<typename LeftRight>
struct as_feature<tag::pot_quantile<LeftRight>(with_threshold_value)>
{
typedef tag::pot_quantile<LeftRight> type;
};
// pot_quantile<LeftRight>(with_threshold_probability) -> pot_quantile_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::pot_quantile<LeftRight>(with_threshold_probability)>
{
typedef tag::pot_quantile_prob<LeftRight> type;
};
// weighted_pot_quantile<LeftRight>(with_threshold_value) -> weighted_pot_quantile<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_pot_quantile<LeftRight>(with_threshold_value)>
{
typedef tag::weighted_pot_quantile<LeftRight> type;
};
// weighted_pot_quantile<LeftRight>(with_threshold_probability) -> weighted_pot_quantile_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_pot_quantile<LeftRight>(with_threshold_probability)>
{
typedef tag::weighted_pot_quantile_prob<LeftRight> type;
};
// for the purposes of feature-based dependency resolution,
// pot_quantile<LeftRight> and pot_quantile_prob<LeftRight> provide
// the same feature as quantile
template<typename LeftRight>
struct feature_of<tag::pot_quantile<LeftRight> >
: feature_of<tag::quantile>
{
};
template<typename LeftRight>
struct feature_of<tag::pot_quantile_prob<LeftRight> >
: feature_of<tag::quantile>
{
};
// So that pot_quantile can be automatically substituted
// with weighted_pot_quantile when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::pot_quantile<LeftRight> >
{
typedef tag::weighted_pot_quantile<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_pot_quantile<LeftRight> >
: feature_of<tag::pot_quantile<LeftRight> >
{
};
// So that pot_quantile_prob can be automatically substituted
// with weighted_pot_quantile_prob when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::pot_quantile_prob<LeftRight> >
{
typedef tag::weighted_pot_quantile_prob<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_pot_quantile_prob<LeftRight> >
: feature_of<tag::pot_quantile_prob<LeftRight> >
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// pot_tail_mean.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_POT_TAIL_MEAN_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <boost/range.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp>
#include <boost/accumulators/statistics/pot_quantile.hpp>
#include <boost/accumulators/statistics/tail_mean.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// pot_tail_mean_impl
//
/**
@brief Estimation of the (coherent) tail mean based on the peaks over threshold method (for both left and right tails)
Computes an estimate for the (coherent) tail mean
\f[
\widehat{CTM}_{\alpha} = \hat{q}_{\alpha} - \frac{\bar{\beta}}{\xi-1}(1-\alpha)^{-\xi},
\f]
where \f$\bar[u]\f$, \f$\bar{\beta}\f$ and \f$\xi\f$ are the parameters of the
generalized Pareto distribution that approximates the right tail of the distribution (or the
mirrored left tail, in case the left tail is used). In the latter case, the result is mirrored
back, yielding the correct result.
*/
template<typename Sample, typename Impl, typename LeftRight>
struct pot_tail_mean_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef float_type result_type;
pot_tail_mean_impl(dont_care)
: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
{
}
template<typename Args>
result_type result(Args const &args) const
{
typedef
typename mpl::if_<
is_same<Impl, weighted>
, tag::weighted_peaks_over_threshold<LeftRight>
, tag::peaks_over_threshold<LeftRight>
>::type
peaks_over_threshold_tag;
typedef
typename mpl::if_<
is_same<Impl, weighted>
, tag::weighted_pot_quantile<LeftRight>
, tag::pot_quantile<LeftRight>
>::type
pot_quantile_tag;
extractor<peaks_over_threshold_tag> const some_peaks_over_threshold = {};
extractor<pot_quantile_tag> const some_pot_quantile = {};
float_type beta_bar = some_peaks_over_threshold(args).template get<1>();
float_type xi_hat = some_peaks_over_threshold(args).template get<2>();
return some_pot_quantile(args) - this->sign_ * beta_bar/( xi_hat - 1. ) * std::pow(
is_same<LeftRight, left>::value ? args[quantile_probability] : 1. - args[quantile_probability]
, -xi_hat);
}
private:
short sign_; // if the fit parameters from the mirrored left tail extreme values are used, mirror back the result
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::pot_tail_mean
// tag::pot_tail_mean_prob
//
namespace tag
{
template<typename LeftRight>
struct pot_tail_mean
: depends_on<peaks_over_threshold<LeftRight>, pot_quantile<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl;
};
template<typename LeftRight>
struct pot_tail_mean_prob
: depends_on<peaks_over_threshold_prob<LeftRight>, pot_quantile_prob<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_pot_tail_mean
: depends_on<weighted_peaks_over_threshold<LeftRight>, weighted_pot_quantile<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_pot_tail_mean_prob
: depends_on<weighted_peaks_over_threshold_prob<LeftRight>, weighted_pot_quantile_prob<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl;
};
}
// pot_tail_mean<LeftRight>(with_threshold_value) -> pot_tail_mean<LeftRight>
template<typename LeftRight>
struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_value)>
{
typedef tag::pot_tail_mean<LeftRight> type;
};
// pot_tail_mean<LeftRight>(with_threshold_probability) -> pot_tail_mean_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_probability)>
{
typedef tag::pot_tail_mean_prob<LeftRight> type;
};
// weighted_pot_tail_mean<LeftRight>(with_threshold_value) -> weighted_pot_tail_mean<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_value)>
{
typedef tag::weighted_pot_tail_mean<LeftRight> type;
};
// weighted_pot_tail_mean<LeftRight>(with_threshold_probability) -> weighted_pot_tail_mean_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_probability)>
{
typedef tag::weighted_pot_tail_mean_prob<LeftRight> type;
};
// for the purposes of feature-based dependency resolution,
// pot_tail_mean<LeftRight> and pot_tail_mean_prob<LeftRight> provide
// the same feature as tail_mean
template<typename LeftRight>
struct feature_of<tag::pot_tail_mean<LeftRight> >
: feature_of<tag::tail_mean>
{
};
template<typename LeftRight>
struct feature_of<tag::pot_tail_mean_prob<LeftRight> >
: feature_of<tag::tail_mean>
{
};
// So that pot_tail_mean can be automatically substituted
// with weighted_pot_tail_mean when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::pot_tail_mean<LeftRight> >
{
typedef tag::weighted_pot_tail_mean<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_pot_tail_mean<LeftRight> >
: feature_of<tag::pot_tail_mean<LeftRight> >
{
};
// So that pot_tail_mean_prob can be automatically substituted
// with weighted_pot_tail_mean_prob when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::pot_tail_mean_prob<LeftRight> >
{
typedef tag::weighted_pot_tail_mean_prob<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_pot_tail_mean_prob<LeftRight> >
: feature_of<tag::pot_tail_mean_prob<LeftRight> >
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// rolling_count.hpp
//
// Copyright 2008 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_ROLLING_COUNT_HPP_EAN_26_12_2008
#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_COUNT_HPP_EAN_26_12_2008
#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_window.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// rolling_count_impl
// returns the count of elements in the rolling window
template<typename Sample>
struct rolling_count_impl
: accumulator_base
{
typedef std::size_t result_type;
rolling_count_impl(dont_care)
{}
template<typename Args>
result_type result(Args const &args) const
{
return static_cast<std::size_t>(rolling_window_plus1(args).size()) - is_rolling_window_plus1_full(args);
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::rolling_count
//
namespace tag
{
struct rolling_count
: depends_on< rolling_window_plus1 >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::rolling_count_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
};
} // namespace tag
///////////////////////////////////////////////////////////////////////////////
// extract::rolling_count
//
namespace extract
{
extractor<tag::rolling_count> const rolling_count = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_count)
}
using extract::rolling_count;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// rolling_mean.hpp
// Copyright (C) 2008 Eric Niebler.
// Copyright (C) 2012 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_MEAN_HPP_EAN_26_12_2008
#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_MEAN_HPP_EAN_26_12_2008
#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_sum.hpp>
#include <boost/accumulators/statistics/rolling_count.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// lazy_rolling_mean_impl
// returns the mean over the rolling window and is calculated only
// when the result is requested
template<typename Sample>
struct lazy_rolling_mean_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t, void, void>::result_type result_type;
lazy_rolling_mean_impl(dont_care)
{
}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(rolling_sum(args), rolling_count(args));
}
};
///////////////////////////////////////////////////////////////////////////////
// immediate_rolling_mean_impl
// The non-lazy version computes the rolling mean recursively when a new
// sample is added
template<typename Sample>
struct immediate_rolling_mean_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_mean_impl(Args const &args)
: mean_(numeric::fdiv(args[sample | Sample()],numeric::one<std::size_t>::value))
{
}
template<typename Args>
void operator()(Args const &args)
{
if(is_rolling_window_plus1_full(args))
{
mean_ += numeric::fdiv(args[sample]-rolling_window_plus1(args).front(),rolling_count(args));
}
else
{
result_type prev_mean = mean_;
mean_ += numeric::fdiv(args[sample]-prev_mean,rolling_count(args));
}
}
template<typename Args>
result_type result(Args const &) const
{
return mean_;
}
private:
result_type mean_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::lazy_rolling_mean
// tag::immediate_rolling_mean
// tag::rolling_mean
//
namespace tag
{
struct lazy_rolling_mean
: depends_on< rolling_sum, rolling_count >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::lazy_rolling_mean_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_mean
: depends_on< rolling_window_plus1, rolling_count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::immediate_rolling_mean_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_mean the default implementation
struct rolling_mean : immediate_rolling_mean {};
} // namespace tag
///////////////////////////////////////////////////////////////////////////////
// extract::lazy_rolling_mean
// extract::immediate_rolling_mean
// extract::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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_rolling_mean)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(immediate_rolling_mean)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_mean)
}
using extract::lazy_rolling_mean;
using extract::immediate_rolling_mean;
using extract::rolling_mean;
// rolling_mean(lazy) -> lazy_rolling_mean
template<>
struct as_feature<tag::rolling_mean(lazy)>
{
typedef tag::lazy_rolling_mean type;
};
// rolling_mean(immediate) -> immediate_rolling_mean
template<>
struct as_feature<tag::rolling_mean(immediate)>
{
typedef tag::immediate_rolling_mean type;
};
// for the purposes of feature-based dependency resolution,
// immediate_rolling_mean provides the same feature as rolling_mean
template<>
struct feature_of<tag::immediate_rolling_mean>
: feature_of<tag::rolling_mean>
{
};
// for the purposes of feature-based dependency resolution,
// lazy_rolling_mean provides the same feature as rolling_mean
template<>
struct feature_of<tag::lazy_rolling_mean>
: feature_of<tag::rolling_mean>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// rolling_moment.hpp
// Copyright 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_MOMENT_HPP_EAN_27_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_MOMENT_HPP_EAN_27_11_2005
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/assert.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/moment.hpp>
#include <boost/accumulators/statistics/rolling_count.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// rolling_moment_impl
template<typename N, typename Sample>
struct rolling_moment_impl
: accumulator_base
{
BOOST_MPL_ASSERT_RELATION(N::value, >, 0);
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t,void,void>::result_type result_type;
template<typename Args>
rolling_moment_impl(Args const &args)
: sum_(args[sample | Sample()])
{
}
template<typename Args>
void operator ()(Args const &args)
{
if(is_rolling_window_plus1_full(args))
{
this->sum_ -= numeric::pow(rolling_window_plus1(args).front(), N());
}
this->sum_ += numeric::pow(args[sample], N());
}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(this->sum_, rolling_count(args));
}
private:
result_type sum_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::rolling_moment
//
namespace tag
{
template<int N>
struct rolling_moment
: depends_on< rolling_window_plus1, rolling_count>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::rolling_moment_impl<mpl::int_<N>, 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
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::rolling_moment
//
namespace extract
{
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, rolling_moment, (int))
}
using extract::rolling_moment;
// There is no weighted_rolling_moment (yet)...
//
//// So that rolling_moment<N> can be automatically substituted with
//// weighted_rolling_moment<N> when the weight parameter is non-void
//template<int N>
//struct as_weighted_feature<tag::rolling_moment<N> >
//{
// typedef tag::weighted_rolling_moment<N> type;
//};
//
//template<int N>
//struct feature_of<tag::weighted_rolling_moment<N> >
// : feature_of<tag::rolling_moment<N> >
//{
//};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// rolling_sum.hpp
//
// Copyright 2008 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_ROLLING_SUM_HPP_EAN_26_12_2008
#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_SUM_HPP_EAN_26_12_2008
#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_window.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// rolling_sum_impl
// returns the sum of the samples in the rolling window
template<typename Sample>
struct rolling_sum_impl
: accumulator_base
{
typedef Sample result_type;
template<typename Args>
rolling_sum_impl(Args const &args)
: sum_(args[sample | Sample()])
{}
template<typename Args>
void operator ()(Args const &args)
{
if(is_rolling_window_plus1_full(args))
{
this->sum_ -= rolling_window_plus1(args).front();
}
this->sum_ += args[sample];
}
template<typename Args>
result_type result(Args const & /*args*/) const
{
return this->sum_;
}
private:
Sample sum_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::rolling_sum
//
namespace tag
{
struct rolling_sum
: depends_on< rolling_window_plus1 >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::rolling_sum_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
};
} // namespace tag
///////////////////////////////////////////////////////////////////////////////
// extract::rolling_sum
//
namespace extract
{
extractor<tag::rolling_sum> const rolling_sum = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_sum)
}
using extract::rolling_sum;
}} // namespace boost::accumulators
#endif

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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

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///////////////////////////////////////////////////////////////////////////////
// rolling_window.hpp
//
// Copyright 2008 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_ROLLING_WINDOW_HPP_EAN_26_12_2008
#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_WINDOW_HPP_EAN_26_12_2008
#include <cstddef>
#include <boost/version.hpp>
#include <boost/assert.hpp>
#include <boost/circular_buffer.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/framework/parameters/accumulator.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// tag::rolling_window::size named parameter
BOOST_PARAMETER_NESTED_KEYWORD(tag, rolling_window_size, window_size)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_window_size)
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// rolling_window_plus1_impl
// stores the latest N+1 samples, where N is specified at construction time
// with the rolling_window_size named parameter
template<typename Sample>
struct rolling_window_plus1_impl
: accumulator_base
{
typedef typename circular_buffer<Sample>::const_iterator const_iterator;
typedef iterator_range<const_iterator> result_type;
template<typename Args>
rolling_window_plus1_impl(Args const & args)
: buffer_(args[rolling_window_size] + 1)
{}
#if BOOST_VERSION < 103600
// Before Boost 1.36, copying a circular buffer didn't copy
// it's capacity, and we need that behavior.
rolling_window_plus1_impl(rolling_window_plus1_impl const &that)
: buffer_(that.buffer_)
{
this->buffer_.set_capacity(that.buffer_.capacity());
}
rolling_window_plus1_impl &operator =(rolling_window_plus1_impl const &that)
{
this->buffer_ = that.buffer_;
this->buffer_.set_capacity(that.buffer_.capacity());
}
#endif
template<typename Args>
void operator ()(Args const &args)
{
this->buffer_.push_back(args[sample]);
}
bool full() const
{
return this->buffer_.full();
}
// The result of a shifted rolling window is the range including
// everything except the most recently added element.
result_type result(dont_care) const
{
return result_type(this->buffer_.begin(), this->buffer_.end());
}
private:
circular_buffer<Sample> buffer_;
};
template<typename Args>
bool is_rolling_window_plus1_full(Args const &args)
{
return find_accumulator<tag::rolling_window_plus1>(args[accumulator]).full();
}
///////////////////////////////////////////////////////////////////////////////
// rolling_window_impl
// stores the latest N samples, where N is specified at construction type
// with the rolling_window_size named parameter
template<typename Sample>
struct rolling_window_impl
: accumulator_base
{
typedef typename circular_buffer<Sample>::const_iterator const_iterator;
typedef iterator_range<const_iterator> result_type;
rolling_window_impl(dont_care)
{}
template<typename Args>
result_type result(Args const &args) const
{
return rolling_window_plus1(args).advance_begin(is_rolling_window_plus1_full(args));
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::rolling_window_plus1
// tag::rolling_window
//
namespace tag
{
struct rolling_window_plus1
: depends_on<>
, tag::rolling_window_size
{
/// INTERNAL ONLY
///
typedef accumulators::impl::rolling_window_plus1_impl< mpl::_1 > impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::rolling_window::size named parameter
static boost::parameter::keyword<tag::rolling_window_size> const window_size;
#endif
};
struct rolling_window
: depends_on< rolling_window_plus1 >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::rolling_window_impl< mpl::_1 > impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::rolling_window::size named parameter
static boost::parameter::keyword<tag::rolling_window_size> const window_size;
#endif
};
} // namespace tag
///////////////////////////////////////////////////////////////////////////////
// extract::rolling_window_plus1
// extract::rolling_window
//
namespace extract
{
extractor<tag::rolling_window_plus1> const rolling_window_plus1 = {};
extractor<tag::rolling_window> const rolling_window = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_window_plus1)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_window)
}
using extract::rolling_window_plus1;
using extract::rolling_window;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// skewness.hpp
//
// Copyright 2006 Olivier Gygi, Daniel Egloff. 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_SKEWNESS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_HPP_EAN_28_10_2005
#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/moment.hpp>
#include <boost/accumulators/statistics/mean.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// skewness_impl
/**
@brief Skewness estimation
The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power
of the 2nd central moment (the variance) of the samples 3. The skewness can also be expressed by the simple moments:
\f[
\hat{g}_1 =
\frac
{\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3}
{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}}
\f]
where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
\f$ n \f$ samples.
*/
template<typename Sample>
struct skewness_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type;
skewness_impl(dont_care)
{
}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::moment<3>(args)
- 3. * accumulators::moment<2>(args) * mean(args)
+ 2. * mean(args) * mean(args) * mean(args)
, ( accumulators::moment<2>(args) - mean(args) * mean(args) )
* std::sqrt( accumulators::moment<2>(args) - mean(args) * mean(args) )
);
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::skewness
//
namespace tag
{
struct skewness
: depends_on<mean, moment<2>, moment<3> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::skewness_impl<mpl::_1> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::skewness
//
namespace extract
{
extractor<tag::skewness> const skewness = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness)
}
using extract::skewness;
// So that skewness can be automatically substituted with
// weighted_skewness when the weight parameter is non-void
template<>
struct as_weighted_feature<tag::skewness>
{
typedef tag::weighted_skewness type;
};
template<>
struct feature_of<tag::weighted_skewness>
: feature_of<tag::skewness>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
/// \file stats.hpp
/// Contains the stats<> template.
///
// Copyright 2005 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_STATS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_STATS_HPP_EAN_28_10_2005
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/mpl/vector.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
/// An MPL sequence of statistics.
template<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, typename Stat)>
struct stats
: mpl::vector<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, Stat)>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// sum.hpp
//
// Copyright 2005 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_SUM_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_SUM_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/parameters/weight.hpp>
#include <boost/accumulators/framework/accumulators/external_accumulator.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// sum_impl
template<typename Sample, typename Tag>
struct sum_impl
: accumulator_base
{
// for boost::result_of
typedef Sample result_type;
template<typename Args>
sum_impl(Args const &args)
: sum(args[parameter::keyword<Tag>::get() | Sample()])
{
}
template<typename Args>
void operator ()(Args const &args)
{
// what about overflow?
this->sum += args[parameter::keyword<Tag>::get()];
}
result_type result(dont_care) const
{
return this->sum;
}
private:
Sample sum;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::sum
// tag::sum_of_weights
// tag::sum_of_variates
//
namespace tag
{
struct sum
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::sum_impl<mpl::_1, tag::sample> impl;
};
struct sum_of_weights
: depends_on<>
{
typedef mpl::true_ is_weight_accumulator;
/// INTERNAL ONLY
///
typedef accumulators::impl::sum_impl<mpl::_2, tag::weight> impl;
};
template<typename VariateType, typename VariateTag>
struct sum_of_variates
: depends_on<>
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::sum_impl<VariateType, VariateTag> > impl;
};
struct abstract_sum_of_variates
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::sum
// extract::sum_of_weights
// extract::sum_of_variates
//
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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sum)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sum_of_weights)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sum_of_variates)
}
using extract::sum;
using extract::sum_of_weights;
using extract::sum_of_variates;
// So that mean can be automatically substituted with
// weighted_mean when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::sum>
{
typedef tag::weighted_sum type;
};
template<>
struct feature_of<tag::weighted_sum>
: feature_of<tag::sum>
{};
template<typename VariateType, typename VariateTag>
struct feature_of<tag::sum_of_variates<VariateType, VariateTag> >
: feature_of<tag::abstract_sum_of_variates>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// sum_kahan.hpp
//
// Copyright 2010 Gaetano Mendola, 2011 Simon West. 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_SUM_KAHAN_HPP_EAN_26_07_2010
#define BOOST_ACCUMULATORS_STATISTICS_SUM_KAHAN_HPP_EAN_26_07_2010
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/weighted_sum_kahan.hpp>
#include <boost/numeric/conversion/cast.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
#if _MSC_VER > 1400
# pragma float_control(push)
# pragma float_control(precise, on)
#endif
template<typename Sample, typename Tag>
struct sum_kahan_impl
: accumulator_base
{
typedef Sample result_type;
////////////////////////////////////////////////////////////////////////////
// sum_kahan_impl
/**
@brief Kahan summation algorithm
The Kahan summation algorithm reduces the numerical error obtained with standard
sequential sum.
*/
template<typename Args>
sum_kahan_impl(Args const & args)
: sum(args[parameter::keyword<Tag>::get() | Sample()]),
compensation(boost::numeric_cast<Sample>(0.0))
{
}
template<typename Args>
void
#if BOOST_ACCUMULATORS_GCC_VERSION > 40305
__attribute__((__optimize__("no-associative-math")))
#endif
operator ()(Args const & args)
{
const Sample myTmp1 = args[parameter::keyword<Tag>::get()] - this->compensation;
const Sample myTmp2 = this->sum + myTmp1;
this->compensation = (myTmp2 - this->sum) - myTmp1;
this->sum = myTmp2;
}
result_type result(dont_care) const
{
return this->sum;
}
private:
Sample sum;
Sample compensation;
};
#if _MSC_VER > 1400
# pragma float_control(pop)
#endif
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::sum_kahan
// tag::sum_of_weights_kahan
// tag::sum_of_variates_kahan
//
namespace tag
{
struct sum_kahan
: depends_on<>
{
/// INTERNAL ONLY
///
typedef impl::sum_kahan_impl< mpl::_1, tag::sample > impl;
};
struct sum_of_weights_kahan
: depends_on<>
{
typedef mpl::true_ is_weight_accumulator;
/// INTERNAL ONLY
///
typedef accumulators::impl::sum_kahan_impl<mpl::_2, tag::weight> impl;
};
template<typename VariateType, typename VariateTag>
struct sum_of_variates_kahan
: depends_on<>
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::sum_kahan_impl<VariateType, VariateTag> > impl;
};
} // namespace tag
///////////////////////////////////////////////////////////////////////////////
// extract::sum_kahan
// extract::sum_of_weights_kahan
// extract::sum_of_variates_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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sum_kahan)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sum_of_weights_kahan)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(sum_of_variates_kahan)
} // namespace extract
using extract::sum_kahan;
using extract::sum_of_weights_kahan;
using extract::sum_of_variates_kahan;
// sum(kahan) -> sum_kahan
template<>
struct as_feature<tag::sum(kahan)>
{
typedef tag::sum_kahan type;
};
// sum_of_weights(kahan) -> sum_of_weights_kahan
template<>
struct as_feature<tag::sum_of_weights(kahan)>
{
typedef tag::sum_of_weights_kahan type;
};
// So that sum_kahan can be automatically substituted with
// weighted_sum_kahan when the weight parameter is non-void.
template<>
struct as_weighted_feature<tag::sum_kahan>
{
typedef tag::weighted_sum_kahan type;
};
template<>
struct feature_of<tag::weighted_sum_kahan>
: feature_of<tag::sum>
{};
// for the purposes of feature-based dependency resolution,
// sum_kahan provides the same feature as sum
template<>
struct feature_of<tag::sum_kahan>
: feature_of<tag::sum>
{
};
// for the purposes of feature-based dependency resolution,
// sum_of_weights_kahan provides the same feature as sum_of_weights
template<>
struct feature_of<tag::sum_of_weights_kahan>
: feature_of<tag::sum_of_weights>
{
};
template<typename VariateType, typename VariateTag>
struct feature_of<tag::sum_of_variates_kahan<VariateType, VariateTag> >
: feature_of<tag::abstract_sum_of_variates>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// tail.hpp
//
// Copyright 2005 Eric Niebler, Michael Gauckler. 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_TAIL_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_TAIL_HPP_EAN_28_10_2005
#include <vector>
#include <functional>
#include <boost/assert.hpp>
#include <boost/range.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/or.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/iterator/reverse_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
#include <boost/accumulators/accumulators_fwd.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>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// cache_size named parameters
BOOST_PARAMETER_NESTED_KEYWORD(tag, right_tail_cache_size, cache_size)
BOOST_PARAMETER_NESTED_KEYWORD(tag, left_tail_cache_size, cache_size)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(right_tail_cache_size)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(left_tail_cache_size)
namespace detail
{
///////////////////////////////////////////////////////////////////////////////
// tail_range
/// INTERNAL ONLY
///
template<typename ElementIterator, typename IndexIterator>
struct tail_range
{
typedef boost::iterator_range<
boost::reverse_iterator<boost::permutation_iterator<ElementIterator, IndexIterator> >
> type;
};
///////////////////////////////////////////////////////////////////////////////
// make_tail_range
/// INTERNAL ONLY
///
template<typename ElementIterator, typename IndexIterator>
typename tail_range<ElementIterator, IndexIterator>::type
make_tail_range(ElementIterator elem_begin, IndexIterator index_begin, IndexIterator index_end)
{
return boost::make_iterator_range(
boost::make_reverse_iterator(
boost::make_permutation_iterator(elem_begin, index_end)
)
, boost::make_reverse_iterator(
boost::make_permutation_iterator(elem_begin, index_begin)
)
);
}
///////////////////////////////////////////////////////////////////////////////
// stat_assign_visitor
/// INTERNAL ONLY
///
template<typename Args>
struct stat_assign_visitor
{
stat_assign_visitor(Args const &a, std::size_t i)
: args(a)
, index(i)
{
}
template<typename Stat>
void operator ()(Stat &stat) const
{
stat.assign(this->args, this->index);
}
private:
stat_assign_visitor &operator =(stat_assign_visitor const &);
Args const &args;
std::size_t index;
};
///////////////////////////////////////////////////////////////////////////////
// stat_assign
/// INTERNAL ONLY
///
template<typename Args>
inline stat_assign_visitor<Args> const stat_assign(Args const &args, std::size_t index)
{
return stat_assign_visitor<Args>(args, index);
}
///////////////////////////////////////////////////////////////////////////////
// is_tail_variate_feature
/// INTERNAL ONLY
///
template<typename Stat, typename LeftRight>
struct is_tail_variate_feature
: mpl::false_
{
};
/// INTERNAL ONLY
///
template<typename VariateType, typename VariateTag, typename LeftRight>
struct is_tail_variate_feature<tag::tail_variate<VariateType, VariateTag, LeftRight>, LeftRight>
: mpl::true_
{
};
/// INTERNAL ONLY
///
template<typename LeftRight>
struct is_tail_variate_feature<tag::tail_weights<LeftRight>, LeftRight>
: mpl::true_
{
};
} // namespace detail
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// tail_impl
template<typename Sample, typename LeftRight>
struct tail_impl
: accumulator_base
{
// LeftRight must be either right or left
BOOST_MPL_ASSERT((
mpl::or_<is_same<LeftRight, right>, is_same<LeftRight, left> >
));
typedef
typename mpl::if_<
is_same<LeftRight, right>
, numeric::functional::greater<Sample const, Sample const>
, numeric::functional::less<Sample const, Sample const>
>::type
predicate_type;
// for boost::result_of
typedef typename detail::tail_range<
typename std::vector<Sample>::const_iterator
, std::vector<std::size_t>::iterator
>::type result_type;
template<typename Args>
tail_impl(Args const &args)
: is_sorted(false)
, indices()
, samples(args[tag::tail<LeftRight>::cache_size], args[sample | Sample()])
{
this->indices.reserve(this->samples.size());
}
tail_impl(tail_impl const &that)
: is_sorted(that.is_sorted)
, indices(that.indices)
, samples(that.samples)
{
this->indices.reserve(this->samples.size());
}
// This just stores the heap and the samples.
// In operator()() below, if we are adding a new sample
// to the sample cache, we force all the
// tail_variates to update also. (It's not
// good enough to wait for the accumulator_set to do it
// for us because then information about whether a sample
// was stored and where is lost, and would need to be
// queried at runtime, which would be slow.) This is
// implemented as a filtered visitation over the stats,
// which we can access because args[accumulator] gives us
// all the stats.
template<typename Args>
void operator ()(Args const &args)
{
if(this->indices.size() < this->samples.size())
{
this->indices.push_back(this->indices.size());
this->assign(args, this->indices.back());
}
else if(predicate_type()(args[sample], this->samples[this->indices[0]]))
{
std::pop_heap(this->indices.begin(), this->indices.end(), indirect_cmp(this->samples));
this->assign(args, this->indices.back());
}
}
result_type result(dont_care) const
{
if(!this->is_sorted)
{
// Must use the same predicate here as in push_heap/pop_heap above.
std::sort_heap(this->indices.begin(), this->indices.end(), indirect_cmp(this->samples));
// sort_heap puts elements in reverse order. Calling std::reverse
// turns the sorted sequence back into a valid heap.
std::reverse(this->indices.begin(), this->indices.end());
this->is_sorted = true;
}
return detail::make_tail_range(
this->samples.begin()
, this->indices.begin()
, this->indices.end()
);
}
private:
struct is_tail_variate
{
template<typename T>
struct apply
: detail::is_tail_variate_feature<
typename detail::feature_tag<T>::type
, LeftRight
>
{};
};
template<typename Args>
void assign(Args const &args, std::size_t index)
{
BOOST_ASSERT(index < this->samples.size());
this->samples[index] = args[sample];
std::push_heap(this->indices.begin(), this->indices.end(), indirect_cmp(this->samples));
this->is_sorted = false;
// Tell the tail variates to store their values also
args[accumulator].template visit_if<is_tail_variate>(detail::stat_assign(args, index));
}
///////////////////////////////////////////////////////////////////////////////
//
struct indirect_cmp
{
typedef std::size_t first_argument_type;
typedef std::size_t second_argument_type;
typedef bool result_type;
indirect_cmp(std::vector<Sample> const &s)
: samples(s)
{
}
bool operator ()(std::size_t left, std::size_t right) const
{
return predicate_type()(this->samples[left], this->samples[right]);
}
private:
indirect_cmp &operator =(indirect_cmp const &);
std::vector<Sample> const &samples;
};
mutable bool is_sorted;
mutable std::vector<std::size_t> indices;
std::vector<Sample> samples;
};
} // namespace impl
// TODO The templatized tag::tail below should inherit from the correct named parameter.
// The following lines provide a workaround, but there must be a better way of doing this.
template<typename T>
struct tail_cache_size_named_arg
{
};
template<>
struct tail_cache_size_named_arg<left>
: tag::left_tail_cache_size
{
};
template<>
struct tail_cache_size_named_arg<right>
: tag::right_tail_cache_size
{
};
///////////////////////////////////////////////////////////////////////////////
// tag::tail<>
//
namespace tag
{
template<typename LeftRight>
struct tail
: depends_on<>
, tail_cache_size_named_arg<LeftRight>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::tail_impl<mpl::_1, LeftRight> impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::tail<LeftRight>::cache_size named parameter
static boost::parameter::keyword<tail_cache_size_named_arg<LeftRight> > const cache_size;
#endif
};
struct abstract_tail
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::tail
//
namespace extract
{
extractor<tag::abstract_tail> const tail = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail)
}
using extract::tail;
template<typename LeftRight>
struct feature_of<tag::tail<LeftRight> >
: feature_of<tag::abstract_tail>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// tail_mean.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_TAIL_MEAN_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_HPP_DE_01_01_2006
#include <numeric>
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_quantile.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// coherent_tail_mean_impl
//
/**
@brief Estimation of the coherent tail mean based on order statistics (for both left and right tails)
The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$
plus a correction term that ensures coherence in case of non-continuous distributions.
\f[
\widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) +
\frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right)
\f]
\f[
\widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) +
\frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right)
\f]
*/
template<typename Sample, typename LeftRight>
struct coherent_tail_mean_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef float_type result_type;
coherent_tail_mean_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
std::size_t cnt = count(args);
std::size_t n = static_cast<std::size_t>(
std::ceil(
cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
)
);
extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {};
return some_non_coherent_tail_mean(args)
+ numeric::fdiv(quantile(args), n)
* (
( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability]
- numeric::fdiv(n, count(args))
);
}
};
///////////////////////////////////////////////////////////////////////////////
// non_coherent_tail_mean_impl
//
/**
@brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails)
An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the
\f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the \f$\lceil n(1-\alpha)\rceil\f$
largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level:
\f[
\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n}
\f]
\f[
\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n}
\f]
It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$
largest samples.
@param quantile_probability
*/
template<typename Sample, typename LeftRight>
struct non_coherent_tail_mean_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef float_type result_type;
non_coherent_tail_mean_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
std::size_t cnt = count(args);
std::size_t n = static_cast<std::size_t>(
std::ceil(
cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
)
);
// If n is in a valid range, return result, otherwise return NaN or throw exception
if (n <= static_cast<std::size_t>(tail(args).size()))
return numeric::fdiv(
std::accumulate(
tail(args).begin()
, tail(args).begin() + n
, Sample(0)
)
, n
);
else
{
if (std::numeric_limits<result_type>::has_quiet_NaN)
{
return std::numeric_limits<result_type>::quiet_NaN();
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return Sample(0);
}
}
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::coherent_tail_mean<>
// tag::non_coherent_tail_mean<>
//
namespace tag
{
template<typename LeftRight>
struct coherent_tail_mean
: depends_on<count, quantile, non_coherent_tail_mean<LeftRight> >
{
typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
};
template<typename LeftRight>
struct non_coherent_tail_mean
: depends_on<count, tail<LeftRight> >
{
typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
};
struct abstract_non_coherent_tail_mean
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::non_coherent_tail_mean;
// extract::coherent_tail_mean;
//
namespace extract
{
extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {};
extractor<tag::tail_mean> const coherent_tail_mean = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean)
}
using extract::non_coherent_tail_mean;
using extract::coherent_tail_mean;
// for the purposes of feature-based dependency resolution,
// coherent_tail_mean<LeftRight> provides the same feature as tail_mean
template<typename LeftRight>
struct feature_of<tag::coherent_tail_mean<LeftRight> >
: feature_of<tag::tail_mean>
{
};
template<typename LeftRight>
struct feature_of<tag::non_coherent_tail_mean<LeftRight> >
: feature_of<tag::abstract_non_coherent_tail_mean>
{
};
// So that non_coherent_tail_mean can be automatically substituted
// with weighted_non_coherent_tail_mean when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> >
{
typedef tag::non_coherent_weighted_tail_mean<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> >
: feature_of<tag::non_coherent_tail_mean<LeftRight> >
{};
// NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean,
// which is the base feature for coherent tail means, since (at least for
// non-continuous distributions) non_coherent_tail_mean is a different measure!
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// tail_quantile.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_TAIL_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_TAIL_QUANTILE_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/config/no_tr1/cmath.hpp> // For ceil
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/mpl/if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/framework/depends_on.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// tail_quantile_impl
// Tail quantile estimation based on order statistics
/**
@brief Tail quantile estimation based on order statistics (for both left and right tails)
The estimation of a tail quantile \f$\hat{q}\f$ with level \f$\alpha\f$ based on order statistics requires the
caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$ largest samples,
\f$n\f$ being the total number of samples. The largest of the \f$\lceil n\alpha\rceil\f$ smallest samples or the
smallest of the \f$\lceil n(1-\alpha)\rceil\f$ largest samples provides an estimate for the quantile:
\f[
\hat{q}_{n,\alpha} = X_{\lceil \alpha n \rceil:n}
\f]
@param quantile_probability
*/
template<typename Sample, typename LeftRight>
struct tail_quantile_impl
: accumulator_base
{
// for boost::result_of
typedef Sample result_type;
tail_quantile_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
std::size_t cnt = count(args);
std::size_t n = static_cast<std::size_t>(
std::ceil(
cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
)
);
// If n is in a valid range, return result, otherwise return NaN or throw exception
if ( n < static_cast<std::size_t>(tail(args).size()))
{
// Note that the cached samples of the left are sorted in ascending order,
// whereas the samples of the right tail are sorted in descending order
return *(boost::begin(tail(args)) + n - 1);
}
else
{
if (std::numeric_limits<result_type>::has_quiet_NaN)
{
return std::numeric_limits<result_type>::quiet_NaN();
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return Sample(0);
}
}
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::tail_quantile<>
//
namespace tag
{
template<typename LeftRight>
struct tail_quantile
: depends_on<count, tail<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::tail_quantile_impl<mpl::_1, LeftRight> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::tail_quantile
//
namespace extract
{
extractor<tag::quantile> const tail_quantile = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_quantile)
}
using extract::tail_quantile;
// for the purposes of feature-based dependency resolution,
// tail_quantile<LeftRight> provide the same feature as quantile
template<typename LeftRight>
struct feature_of<tag::tail_quantile<LeftRight> >
: feature_of<tag::quantile>
{
};
// So that tail_quantile can be automatically substituted with
// weighted_tail_quantile when the weight parameter is non-void.
template<typename LeftRight>
struct as_weighted_feature<tag::tail_quantile<LeftRight> >
{
typedef tag::weighted_tail_quantile<LeftRight> type;
};
template<typename LeftRight>
struct feature_of<tag::weighted_tail_quantile<LeftRight> >
: feature_of<tag::tail_quantile<LeftRight> >
{};
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// tail_variate.hpp
//
// Copyright 2005 Eric Niebler, Michael Gauckler. 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_STAT_STATISTICS_TAIL_VARIATE_HPP_EAN_28_10_2005
#define BOOST_STAT_STATISTICS_TAIL_VARIATE_HPP_EAN_28_10_2005
#include <boost/range.hpp>
#include <boost/mpl/always.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/iterator/reverse_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// tail_variate_impl
template<typename VariateType, typename VariateTag, typename LeftRight>
struct tail_variate_impl
: accumulator_base
{
// for boost::result_of
typedef
typename detail::tail_range<
typename std::vector<VariateType>::const_iterator
, std::vector<std::size_t>::iterator
>::type
result_type;
template<typename Args>
tail_variate_impl(Args const &args)
: variates(args[tag::tail<LeftRight>::cache_size], args[parameter::keyword<VariateTag>::get() | VariateType()])
{
}
template<typename Args>
void assign(Args const &args, std::size_t index)
{
this->variates[index] = args[parameter::keyword<VariateTag>::get()];
}
template<typename Args>
result_type result(Args const &args) const
{
// getting the order result causes the indices vector to be sorted.
extractor<tag::tail<LeftRight> > const some_tail = {};
return this->do_result(some_tail(args));
}
private:
template<typename TailRng>
result_type do_result(TailRng const &rng) const
{
return detail::make_tail_range(
this->variates.begin()
, rng.end().base().base() // the index iterator
, rng.begin().base().base() // (begin and end reversed because these are reverse iterators)
);
}
std::vector<VariateType> variates;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::tail_variate<>
//
namespace tag
{
template<typename VariateType, typename VariateTag, typename LeftRight>
struct tail_variate
: depends_on<tail<LeftRight> >
{
/// INTERNAL ONLY
///
typedef mpl::always<accumulators::impl::tail_variate_impl<VariateType, VariateTag, LeftRight> > impl;
};
struct abstract_tail_variate
: depends_on<>
{
};
template<typename LeftRight>
struct tail_weights
: depends_on<tail<LeftRight> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::tail_variate_impl<mpl::_2, tag::weight, LeftRight> impl;
};
struct abstract_tail_weights
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::tail_variate
// extract::tail_weights
//
namespace extract
{
extractor<tag::abstract_tail_variate> const tail_variate = {};
extractor<tag::abstract_tail_weights> const tail_weights = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_weights)
}
using extract::tail_variate;
using extract::tail_weights;
template<typename VariateType, typename VariateTag, typename LeftRight>
struct feature_of<tag::tail_variate<VariateType, VariateTag, LeftRight> >
: feature_of<tag::abstract_tail_variate>
{
};
template<typename LeftRight>
struct feature_of<tag::tail_weights<LeftRight> >
{
typedef tag::abstract_tail_weights type;
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// tail_variate_means.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
#include <numeric>
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_variate.hpp>
#include <boost/accumulators/statistics/tail_mean.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
/**
@brief Estimation of the absolute and relative tail variate means (for both left and right tails)
For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the
\f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means
\f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively,
the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute
tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
\f[
\widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
\frac{1}{\lceil n(1-\alpha) \rceil}
\sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i}
\f]
\f[
\widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
\frac{1}{\lceil n\alpha \rceil}
\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}
\f]
\f[
\widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
\frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}}
{\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
\f]
\f[
\widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
\frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}}
{\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
\f]
*/
///////////////////////////////////////////////////////////////////////////////
// tail_variate_means_impl
// by default: absolute tail_variate_means
template<typename Sample, typename Impl, typename LeftRight, typename VariateTag>
struct tail_variate_means_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<float_type> array_type;
// for boost::result_of
typedef iterator_range<typename array_type::iterator> result_type;
tail_variate_means_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
std::size_t cnt = count(args);
std::size_t n = static_cast<std::size_t>(
std::ceil(
cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
)
);
std::size_t num_variates = tail_variate(args).begin()->size();
this->tail_means_.clear();
this->tail_means_.resize(num_variates, Sample(0));
// If n is in a valid range, return result, otherwise return NaN or throw exception
if (n < static_cast<std::size_t>(tail(args).size()))
{
this->tail_means_ = std::accumulate(
tail_variate(args).begin()
, tail_variate(args).begin() + n
, this->tail_means_
, numeric::plus
);
float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. );
std::transform(
this->tail_means_.begin()
, this->tail_means_.end()
, this->tail_means_.begin()
#ifdef BOOST_NO_CXX98_BINDERS
, std::bind(std::divides<float_type>(), std::placeholders::_1, factor)
#else
, std::bind2nd(std::divides<float_type>(), factor)
#endif
);
}
else
{
if (std::numeric_limits<float_type>::has_quiet_NaN)
{
std::fill(
this->tail_means_.begin()
, this->tail_means_.end()
, std::numeric_limits<float_type>::quiet_NaN()
);
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
}
}
return make_iterator_range(this->tail_means_);
}
private:
mutable array_type tail_means_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::absolute_tail_variate_means
// tag::relative_tail_variate_means
//
namespace tag
{
template<typename LeftRight, typename VariateType, typename VariateTag>
struct absolute_tail_variate_means
: depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
{
typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl;
};
template<typename LeftRight, typename VariateType, typename VariateTag>
struct relative_tail_variate_means
: depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
{
typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl;
};
struct abstract_absolute_tail_variate_means
: depends_on<>
{
};
struct abstract_relative_tail_variate_means
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::tail_variate_means
// extract::relative_tail_variate_means
//
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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means)
}
using extract::tail_variate_means;
using extract::relative_tail_variate_means;
// tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
{
typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};
// tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
{
typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};
// Provides non-templatized extractor
template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
: feature_of<tag::abstract_absolute_tail_variate_means>
{
};
// Provides non-templatized extractor
template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
: feature_of<tag::abstract_relative_tail_variate_means>
{
};
// So that absolute_tail_means can be automatically substituted
// with absolute_weighted_tail_means when the weight parameter is non-void.
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};
template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
: feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
};
// So that relative_tail_means can be automatically substituted
// with relative_weighted_tail_means when the weight parameter is non-void.
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};
template<typename LeftRight, typename VariateType, typename VariateTag>
struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
: feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
{
};
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// times2_iterator.hpp
//
// Copyright 2006 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_TIMES2_ITERATOR_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_TIMES2_ITERATOR_HPP_DE_01_01_2006
#include <functional>
#include <boost/detail/workaround.hpp>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
namespace boost { namespace accumulators
{
namespace detail
{
typedef transform_iterator<
#ifdef BOOST_NO_CXX98_BINDERS
decltype(std::bind(std::multiplies<std::size_t>(), 2, std::placeholders::_1))
#else
std::binder1st<std::multiplies<std::size_t> >
#endif
, counting_iterator<std::size_t>
> times2_iterator;
inline times2_iterator make_times2_iterator(std::size_t i)
{
return make_transform_iterator(
make_counting_iterator(i)
#ifdef BOOST_NO_CXX98_BINDERS
, std::bind(std::multiplies<std::size_t>(), 2, std::placeholders::_1)
#else
, std::bind1st(std::multiplies<std::size_t>(), 2)
#endif
);
}
///////////////////////////////////////////////////////////////////////////////
// lvalue_index_iterator
template<typename Base>
struct lvalue_index_iterator
: Base
{
lvalue_index_iterator()
: Base()
{}
lvalue_index_iterator(Base base)
: Base(base)
{
}
typename Base::reference operator [](typename Base::difference_type n) const
{
return *(*this + n);
}
};
} // namespace detail
}}
#endif

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///////////////////////////////////////////////////////////////////////////////
// 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::fdiv<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 accumulators::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::fdiv<Sample, std::size_t>::result_type result_type;
template<typename Args>
variance_impl(Args const &args)
: variance(numeric::fdiv(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::fdiv(this->variance * (cnt - 1), cnt)
+ numeric::fdiv(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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_variance)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(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

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///////////////////////////////////////////////////////////////////////////////
// weight.hpp
//
// Copyright 2005 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_VARIATES_COVARIATE_HPP_EAN_03_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_VARIATES_COVARIATE_HPP_EAN_03_11_2005
#include <boost/parameter/keyword.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
namespace boost { namespace accumulators
{
BOOST_PARAMETER_KEYWORD(tag, covariate1)
BOOST_PARAMETER_KEYWORD(tag, covariate2)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariate1)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariate2)
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_covariance.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <complex>
#include <boost/mpl/assert.hpp>
#include <boost/mpl/bool.hpp>
#include <boost/range.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/type_traits/is_scalar.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/covariance.hpp> // for numeric::outer_product() and type traits
#include <boost/accumulators/statistics/weighted_mean.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_covariance_impl
//
/**
@brief Weighted Covariance Estimator
An iterative Monte Carlo estimator for the weighted covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
and \f$X'\f$ a variate, is given by:
\f[
\hat{c}_n = \frac{\bar{w}_n-w_n}{\bar{w}_n} \hat{c}_{n-1} + \frac{w_n}{\bar{w}_n-w_n}(X_n - \hat{\mu}_n)(X_n' - \hat{\mu}_n'),
\quad n\ge2,\quad\hat{c}_1 = 0,
\f]
\f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the weighted means of the samples and variates and
\f$\bar{w}_n\f$ the sum of the \f$n\f$ first weights \f$w_i\f$.
*/
template<typename Sample, typename Weight, typename VariateType, typename VariateTag>
struct weighted_covariance_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<Sample, std::size_t>::result_type>::result_type weighted_sample_type;
typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<VariateType, std::size_t>::result_type>::result_type weighted_variate_type;
// for boost::result_of
typedef typename numeric::functional::outer_product<weighted_sample_type, weighted_variate_type>::result_type result_type;
template<typename Args>
weighted_covariance_impl(Args const &args)
: cov_(
numeric::outer_product(
numeric::fdiv(args[sample | Sample()], (std::size_t)1)
* numeric::one<Weight>::value
, numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
* numeric::one<Weight>::value
)
)
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
if (cnt > 1)
{
extractor<tag::weighted_mean_of_variates<VariateType, VariateTag> > const some_weighted_mean_of_variates = {};
this->cov_ = this->cov_ * (sum_of_weights(args) - args[weight]) / sum_of_weights(args)
+ numeric::outer_product(
some_weighted_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
, weighted_mean(args) - args[sample]
) * args[weight] / (sum_of_weights(args) - args[weight]);
}
}
result_type result(dont_care) const
{
return this->cov_;
}
private:
result_type cov_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_covariance
//
namespace tag
{
template<typename VariateType, typename VariateTag>
struct weighted_covariance
: depends_on<count, sum_of_weights, weighted_mean, weighted_mean_of_variates<VariateType, VariateTag> >
{
typedef accumulators::impl::weighted_covariance_impl<mpl::_1, mpl::_2, VariateType, VariateTag> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_covariance
//
namespace extract
{
extractor<tag::abstract_covariance> const weighted_covariance = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance)
}
using extract::weighted_covariance;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_density.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_DENSITY_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_DENSITY_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <functional>
#include <boost/range.hpp>
#include <boost/parameter/keyword.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/max.hpp>
#include <boost/accumulators/statistics/min.hpp>
#include <boost/accumulators/statistics/density.hpp> // for named parameters density_cache_size and density_num_bins
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_density_impl
// density histogram for weighted samples
/**
@brief Histogram density estimator for weighted samples
The histogram density estimator returns a histogram of the sample distribution. The positions and sizes of the bins
are determined using a specifiable number of cached samples (cache_size). The range between the minimum and the
maximum of the cached samples is subdivided into a specifiable number of bins (num_bins) of same size. Additionally,
an under- and an overflow bin is added to capture future under- and overflow samples. Once the bins are determined,
the cached samples and all subsequent samples are added to the correct bins. At the end, a range of std::pair is
returned, where each pair contains the position of the bin (lower bound) and the sum of the weights (normalized with the
sum of all weights).
@param density_cache_size Number of first samples used to determine min and max.
@param density_num_bins Number of bins (two additional bins collect under- and overflow samples).
*/
template<typename Sample, typename Weight>
struct weighted_density_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef std::vector<float_type> array_type;
// for boost::result_of
typedef iterator_range<typename histogram_type::iterator> result_type;
template<typename Args>
weighted_density_impl(Args const &args)
: cache_size(args[density_cache_size])
, cache(cache_size)
, num_bins(args[density_num_bins])
, samples_in_bin(num_bins + 2, 0.)
, bin_positions(num_bins + 2)
, histogram(
num_bins + 2
, std::make_pair(
numeric::fdiv(args[sample | Sample()],(std::size_t)1)
, numeric::fdiv(args[sample | Sample()],(std::size_t)1)
)
)
, is_dirty(true)
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->is_dirty = true;
std::size_t cnt = count(args);
// Fill up cache with cache_size first samples
if (cnt <= this->cache_size)
{
this->cache[cnt - 1] = std::make_pair(args[sample], args[weight]);
}
// Once cache_size samples have been accumulated, create num_bins bins of same size between
// the minimum and maximum of the cached samples as well as an under- and an overflow bin.
// Store their lower bounds (bin_positions) and fill the bins with the cached samples (samples_in_bin).
if (cnt == this->cache_size)
{
float_type minimum = numeric::fdiv((min)(args),(std::size_t)1);
float_type maximum = numeric::fdiv((max)(args),(std::size_t)1);
float_type bin_size = numeric::fdiv(maximum - minimum, this->num_bins);
// determine bin positions (their lower bounds)
for (std::size_t i = 0; i < this->num_bins + 2; ++i)
{
this->bin_positions[i] = minimum + (i - 1.) * bin_size;
}
for (typename histogram_type::const_iterator iter = this->cache.begin(); iter != this->cache.end(); ++iter)
{
if (iter->first < this->bin_positions[1])
{
this->samples_in_bin[0] += iter->second;
}
else if (iter->first >= this->bin_positions[this->num_bins + 1])
{
this->samples_in_bin[this->num_bins + 1] += iter->second;
}
else
{
typename array_type::iterator it = std::upper_bound(
this->bin_positions.begin()
, this->bin_positions.end()
, iter->first
);
std::size_t d = std::distance(this->bin_positions.begin(), it);
this->samples_in_bin[d - 1] += iter->second;
}
}
}
// Add each subsequent sample to the correct bin
else if (cnt > this->cache_size)
{
if (args[sample] < this->bin_positions[1])
{
this->samples_in_bin[0] += args[weight];
}
else if (args[sample] >= this->bin_positions[this->num_bins + 1])
{
this->samples_in_bin[this->num_bins + 1] += args[weight];
}
else
{
typename array_type::iterator it = std::upper_bound(
this->bin_positions.begin()
, this->bin_positions.end()
, args[sample]
);
std::size_t d = std::distance(this->bin_positions.begin(), it);
this->samples_in_bin[d - 1] += args[weight];
}
}
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
// creates a vector of std::pair where each pair i holds
// the values bin_positions[i] (x-axis of histogram) and
// samples_in_bin[i] / cnt (y-axis of histogram).
for (std::size_t i = 0; i < this->num_bins + 2; ++i)
{
this->histogram[i] = std::make_pair(this->bin_positions[i], numeric::fdiv(this->samples_in_bin[i], sum_of_weights(args)));
}
}
// returns a range of pairs
return make_iterator_range(this->histogram);
}
private:
std::size_t cache_size; // number of cached samples
histogram_type cache; // cache to store the first cache_size samples with their weights as std::pair
std::size_t num_bins; // number of bins
array_type samples_in_bin; // number of samples in each bin
array_type bin_positions; // lower bounds of bins
mutable histogram_type histogram; // histogram
mutable bool is_dirty;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_density
//
namespace tag
{
struct weighted_density
: depends_on<count, sum_of_weights, min, max>
, density_cache_size
, density_num_bins
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_density_impl<mpl::_1, mpl::_2> impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
static boost::parameter::keyword<density_cache_size> const cache_size;
static boost::parameter::keyword<density_num_bins> const num_bins;
#endif
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_density
//
namespace extract
{
extractor<tag::density> const weighted_density = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_density)
}
using extract::weighted_density;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_extended_p_square.hpp
//
// Copyright 2005 Daniel Egloff. 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_WEIGHTED_EXTENDED_P_SQUARE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_EXTENDED_P_SQUARE_HPP_DE_01_01_2006
#include <vector>
#include <functional>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/range/iterator_range.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/permutation_iterator.hpp>
#include <boost/parameter/keyword.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/count.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/times2_iterator.hpp>
#include <boost/accumulators/statistics/extended_p_square.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_extended_p_square_impl
// multiple quantile estimation with weighted samples
/**
@brief Multiple quantile estimation with the extended \f$P^2\f$ algorithm for weighted samples
This version of the extended \f$P^2\f$ algorithm extends the extended \f$P^2\f$ algorithm to
support weighted samples. The extended \f$P^2\f$ algorithm dynamically estimates several
quantiles without storing samples. Assume that \f$m\f$ quantiles
\f$\xi_{p_1}, \ldots, \xi_{p_m}\f$ are to be estimated. Instead of storing the whole sample
cumulative distribution, the algorithm maintains only \f$m+2\f$ principal markers and
\f$m+1\f$ middle markers, whose positions are updated with each sample and whose heights
are adjusted (if necessary) using a piecewise-parablic formula. The heights of the principal
markers are the current estimates of the quantiles and are returned as an iterator range.
For further details, see
K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49,
Number 4 (October), 1986, p. 159-164.
The extended \f$ P^2 \f$ algorithm generalizes the \f$ P^2 \f$ algorithm of
R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
histograms without storing observations, Communications of the ACM,
Volume 28 (October), Number 10, 1985, p. 1076-1085.
@param extended_p_square_probabilities A vector of quantile probabilities.
*/
template<typename Sample, typename Weight>
struct weighted_extended_p_square_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
typedef std::vector<float_type> array_type;
// for boost::result_of
typedef iterator_range<
detail::lvalue_index_iterator<
permutation_iterator<
typename array_type::const_iterator
, detail::times2_iterator
>
>
> result_type;
template<typename Args>
weighted_extended_p_square_impl(Args const &args)
: probabilities(
boost::begin(args[extended_p_square_probabilities])
, boost::end(args[extended_p_square_probabilities])
)
, heights(2 * probabilities.size() + 3)
, actual_positions(heights.size())
, desired_positions(heights.size())
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
std::size_t sample_cell = 1; // k
std::size_t num_quantiles = this->probabilities.size();
// m+2 principal markers and m+1 middle markers
std::size_t num_markers = 2 * num_quantiles + 3;
// first accumulate num_markers samples
if(cnt <= num_markers)
{
this->heights[cnt - 1] = args[sample];
this->actual_positions[cnt - 1] = args[weight];
// complete the initialization of heights (and actual_positions) by sorting
if(cnt == num_markers)
{
// TODO: we need to sort the initial samples (in heights) in ascending order and
// sort their weights (in actual_positions) the same way. The following lines do
// it, but there must be a better and more efficient way of doing this.
typename array_type::iterator it_begin, it_end, it_min;
it_begin = this->heights.begin();
it_end = this->heights.end();
std::size_t pos = 0;
while (it_begin != it_end)
{
it_min = std::min_element(it_begin, it_end);
std::size_t d = std::distance(it_begin, it_min);
std::swap(*it_begin, *it_min);
std::swap(this->actual_positions[pos], this->actual_positions[pos + d]);
++it_begin;
++pos;
}
// calculate correct initial actual positions
for (std::size_t i = 1; i < num_markers; ++i)
{
actual_positions[i] += actual_positions[i - 1];
}
}
}
else
{
if(args[sample] < this->heights[0])
{
this->heights[0] = args[sample];
this->actual_positions[0] = args[weight];
sample_cell = 1;
}
else if(args[sample] >= this->heights[num_markers - 1])
{
this->heights[num_markers - 1] = args[sample];
sample_cell = num_markers - 1;
}
else
{
// find cell k = sample_cell such that heights[k-1] <= sample < heights[k]
typedef typename array_type::iterator iterator;
iterator it = std::upper_bound(
this->heights.begin()
, this->heights.end()
, args[sample]
);
sample_cell = std::distance(this->heights.begin(), it);
}
// update actual position of all markers above sample_cell
for(std::size_t i = sample_cell; i < num_markers; ++i)
{
this->actual_positions[i] += args[weight];
}
// compute desired positions
{
this->desired_positions[0] = this->actual_positions[0];
this->desired_positions[num_markers - 1] = sum_of_weights(args);
this->desired_positions[1] = (sum_of_weights(args) - this->actual_positions[0]) * probabilities[0]
/ 2. + this->actual_positions[0];
this->desired_positions[num_markers - 2] = (sum_of_weights(args) - this->actual_positions[0])
* (probabilities[num_quantiles - 1] + 1.)
/ 2. + this->actual_positions[0];
for (std::size_t i = 0; i < num_quantiles; ++i)
{
this->desired_positions[2 * i + 2] = (sum_of_weights(args) - this->actual_positions[0])
* probabilities[i] + this->actual_positions[0];
}
for (std::size_t i = 1; i < num_quantiles; ++i)
{
this->desired_positions[2 * i + 1] = (sum_of_weights(args) - this->actual_positions[0])
* (probabilities[i - 1] + probabilities[i])
/ 2. + this->actual_positions[0];
}
}
// adjust heights and actual_positions of markers 1 to num_markers - 2 if necessary
for (std::size_t i = 1; i <= num_markers - 2; ++i)
{
// offset to desired position
float_type d = this->desired_positions[i] - this->actual_positions[i];
// offset to next position
float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
// offset to previous position
float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
// height ds
float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
if((d >= 1 && dp > 1) || (d <= -1 && dm < -1))
{
short sign_d = static_cast<short>(d / std::abs(d));
float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm)*hp + (dp - sign_d) * hm);
// try adjusting heights[i] using p-squared formula
if(this->heights[i - 1] < h && h < this->heights[i + 1])
{
this->heights[i] = h;
}
else
{
// use linear formula
if(d > 0)
{
this->heights[i] += hp;
}
if(d < 0)
{
this->heights[i] -= hm;
}
}
this->actual_positions[i] += sign_d;
}
}
}
}
result_type result(dont_care) const
{
// for i in [1,probabilities.size()], return heights[i * 2]
detail::times2_iterator idx_begin = detail::make_times2_iterator(1);
detail::times2_iterator idx_end = detail::make_times2_iterator(this->probabilities.size() + 1);
return result_type(
make_permutation_iterator(this->heights.begin(), idx_begin)
, make_permutation_iterator(this->heights.begin(), idx_end)
);
}
private:
array_type probabilities; // the quantile probabilities
array_type heights; // q_i
array_type actual_positions; // n_i
array_type desired_positions; // d_i
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_extended_p_square
//
namespace tag
{
struct weighted_extended_p_square
: depends_on<count, sum_of_weights>
, extended_p_square_probabilities
{
typedef accumulators::impl::weighted_extended_p_square_impl<mpl::_1, mpl::_2> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_extended_p_square
//
namespace extract
{
extractor<tag::weighted_extended_p_square> const weighted_extended_p_square = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square)
}
using extract::weighted_extended_p_square;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_kurtosis.hpp
//
// Copyright 2006 Olivier Gygi, Daniel Egloff. 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_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005
#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/weighted_moment.hpp>
#include <boost/accumulators/statistics/weighted_mean.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_kurtosis_impl
/**
@brief Kurtosis estimation for weighted samples
The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central
moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution
has zero kurtosis. The kurtosis can also be expressed by the simple moments:
\f[
\hat{g}_2 =
\frac
{\widehat{m}_n^{(4)}-4\widehat{m}_n^{(3)}\hat{\mu}_n+6\widehat{m}_n^{(2)}\hat{\mu}_n^2-3\hat{\mu}_n^4}
{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3,
\f]
where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
\f$ n \f$ samples.
The kurtosis estimator for weighted samples is formally identical to the estimator for unweighted samples, except that
the weighted counterparts of all measures it depends on are to be taken.
*/
template<typename Sample, typename Weight>
struct weighted_kurtosis_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, weighted_sample>::result_type result_type;
weighted_kurtosis_impl(dont_care)
{
}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::weighted_moment<4>(args)
- 4. * accumulators::weighted_moment<3>(args) * weighted_mean(args)
+ 6. * accumulators::weighted_moment<2>(args) * weighted_mean(args) * weighted_mean(args)
- 3. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
, ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
* ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
) - 3.;
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_kurtosis
//
namespace tag
{
struct weighted_kurtosis
: depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3>, weighted_moment<4> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_kurtosis_impl<mpl::_1, mpl::_2> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_kurtosis
//
namespace extract
{
extractor<tag::weighted_kurtosis> const weighted_kurtosis = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_kurtosis)
}
using extract::weighted_kurtosis;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_mean.hpp
//
// Copyright 2006 Eric Niebler, Olivier Gygi. 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_WEIGHTED_MEAN_HPP_EAN_03_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_MEAN_HPP_EAN_03_11_2005
#include <boost/mpl/assert.hpp>
#include <boost/mpl/eval_if.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.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/weights.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/mean.hpp>
#include <boost/accumulators/statistics/weighted_sum.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_mean_impl
// lazy, by default
template<typename Sample, typename Weight, typename Tag>
struct weighted_mean_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
weighted_mean_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
typedef
typename mpl::if_<
is_same<Tag, tag::sample>
, tag::weighted_sum
, tag::weighted_sum_of_variates<Sample, Tag>
>::type
weighted_sum_tag;
extractor<weighted_sum_tag> const some_weighted_sum = {};
return numeric::fdiv(some_weighted_sum(args), sum_of_weights(args));
}
};
///////////////////////////////////////////////////////////////////////////////
// immediate_weighted_mean_impl
// immediate
template<typename Sample, typename Weight, typename Tag>
struct immediate_weighted_mean_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
template<typename Args>
immediate_weighted_mean_impl(Args const &args)
: mean(
numeric::fdiv(
args[parameter::keyword<Tag>::get() | Sample()]
* numeric::one<Weight>::value
, numeric::one<Weight>::value
)
)
{
}
template<typename Args>
void operator ()(Args const &args)
{
// Matthias:
// need to pass the argument pack since the weight might be an external
// accumulator set passed as a named parameter
Weight w_sum = sum_of_weights(args);
Weight w = args[weight];
weighted_sample const &s = args[parameter::keyword<Tag>::get()] * w;
this->mean = numeric::fdiv(this->mean * (w_sum - w) + s, w_sum);
}
result_type result(dont_care) const
{
return this->mean;
}
private:
result_type mean;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_mean
// tag::immediate_weighted_mean
//
namespace tag
{
struct weighted_mean
: depends_on<sum_of_weights, weighted_sum>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_mean_impl<mpl::_1, mpl::_2, tag::sample> impl;
};
struct immediate_weighted_mean
: depends_on<sum_of_weights>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::immediate_weighted_mean_impl<mpl::_1, mpl::_2, tag::sample> impl;
};
template<typename VariateType, typename VariateTag>
struct weighted_mean_of_variates
: depends_on<sum_of_weights, weighted_sum_of_variates<VariateType, VariateTag> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_mean_impl<VariateType, mpl::_2, VariateTag> impl;
};
template<typename VariateType, typename VariateTag>
struct immediate_weighted_mean_of_variates
: depends_on<sum_of_weights>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::immediate_weighted_mean_impl<VariateType, mpl::_2, VariateTag> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_mean
// extract::weighted_mean_of_variates
//
namespace extract
{
extractor<tag::mean> const weighted_mean = {};
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, weighted_mean_of_variates, (typename)(typename))
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_mean)
}
using extract::weighted_mean;
using extract::weighted_mean_of_variates;
// weighted_mean(lazy) -> weighted_mean
template<>
struct as_feature<tag::weighted_mean(lazy)>
{
typedef tag::weighted_mean type;
};
// weighted_mean(immediate) -> immediate_weighted_mean
template<>
struct as_feature<tag::weighted_mean(immediate)>
{
typedef tag::immediate_weighted_mean type;
};
// weighted_mean_of_variates<VariateType, VariateTag>(lazy) -> weighted_mean_of_variates<VariateType, VariateTag>
template<typename VariateType, typename VariateTag>
struct as_feature<tag::weighted_mean_of_variates<VariateType, VariateTag>(lazy)>
{
typedef tag::weighted_mean_of_variates<VariateType, VariateTag> type;
};
// weighted_mean_of_variates<VariateType, VariateTag>(immediate) -> immediate_weighted_mean_of_variates<VariateType, VariateTag>
template<typename VariateType, typename VariateTag>
struct as_feature<tag::weighted_mean_of_variates<VariateType, VariateTag>(immediate)>
{
typedef tag::immediate_weighted_mean_of_variates<VariateType, VariateTag> type;
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_median.hpp
//
// Copyright 2006 Eric Niebler, Olivier Gygi. 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_WEIGHTED_MEDIAN_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_MEDIAN_HPP_EAN_28_10_2005
#include <boost/mpl/placeholders.hpp>
#include <boost/range/iterator_range.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/median.hpp>
#include <boost/accumulators/statistics/weighted_p_square_quantile.hpp>
#include <boost/accumulators/statistics/weighted_density.hpp>
#include <boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_median_impl
//
/**
@brief Median estimation for weighted samples based on the \f$P^2\f$ quantile estimator
The \f$P^2\f$ algorithm for weighted samples is invoked with a quantile probability of 0.5.
*/
template<typename Sample>
struct weighted_median_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
weighted_median_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
return weighted_p_square_quantile_for_median(args);
}
};
///////////////////////////////////////////////////////////////////////////////
// with_density_weighted_median_impl
//
/**
@brief Median estimation for weighted samples based on the density estimator
The algorithm determines the bin in which the \f$0.5*cnt\f$-th sample lies, \f$cnt\f$ being
the total number of samples. It returns the approximate horizontal position of this sample,
based on a linear interpolation inside the bin.
*/
template<typename Sample>
struct with_density_weighted_median_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef iterator_range<typename histogram_type::iterator> range_type;
// for boost::result_of
typedef float_type result_type;
template<typename Args>
with_density_weighted_median_impl(Args const &args)
: sum(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, is_dirty(true)
{
}
void operator ()(dont_care)
{
this->is_dirty = true;
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
std::size_t cnt = count(args);
range_type histogram = weighted_density(args);
typename range_type::iterator it = histogram.begin();
while (this->sum < 0.5 * cnt)
{
this->sum += it->second * cnt;
++it;
}
--it;
float_type over = numeric::fdiv(this->sum - 0.5 * cnt, it->second * cnt);
this->median = it->first * over + (it + 1)->first * ( 1. - over );
}
return this->median;
}
private:
mutable float_type sum;
mutable bool is_dirty;
mutable float_type median;
};
///////////////////////////////////////////////////////////////////////////////
// with_p_square_cumulative_distribution_weighted_median_impl
//
/**
@brief Median estimation for weighted samples based on the \f$P^2\f$ cumulative distribution estimator
The algorithm determines the first (leftmost) bin with a height exceeding 0.5. It
returns the approximate horizontal position of where the cumulative distribution
equals 0.5, based on a linear interpolation inside the bin.
*/
template<typename Sample, typename Weight>
struct with_p_square_cumulative_distribution_weighted_median_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef iterator_range<typename histogram_type::iterator> range_type;
// for boost::result_of
typedef float_type result_type;
with_p_square_cumulative_distribution_weighted_median_impl(dont_care)
: is_dirty(true)
{
}
void operator ()(dont_care)
{
this->is_dirty = true;
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
range_type histogram = weighted_p_square_cumulative_distribution(args);
typename range_type::iterator it = histogram.begin();
while (it->second < 0.5)
{
++it;
}
float_type over = numeric::fdiv(it->second - 0.5, it->second - (it - 1)->second);
this->median = it->first * over + (it + 1)->first * ( 1. - over );
}
return this->median;
}
private:
mutable bool is_dirty;
mutable float_type median;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_median
// tag::with_density_weighted_median
// tag::with_p_square_cumulative_distribution_weighted_median
//
namespace tag
{
struct weighted_median
: depends_on<weighted_p_square_quantile_for_median>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_median_impl<mpl::_1> impl;
};
struct with_density_weighted_median
: depends_on<count, weighted_density>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::with_density_weighted_median_impl<mpl::_1> impl;
};
struct with_p_square_cumulative_distribution_weighted_median
: depends_on<weighted_p_square_cumulative_distribution>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::with_p_square_cumulative_distribution_weighted_median_impl<mpl::_1, mpl::_2> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_median
//
namespace extract
{
extractor<tag::median> const weighted_median = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_median)
}
using extract::weighted_median;
// weighted_median(with_p_square_quantile) -> weighted_median
template<>
struct as_feature<tag::weighted_median(with_p_square_quantile)>
{
typedef tag::weighted_median type;
};
// weighted_median(with_density) -> with_density_weighted_median
template<>
struct as_feature<tag::weighted_median(with_density)>
{
typedef tag::with_density_weighted_median type;
};
// weighted_median(with_p_square_cumulative_distribution) -> with_p_square_cumulative_distribution_weighted_median
template<>
struct as_feature<tag::weighted_median(with_p_square_cumulative_distribution)>
{
typedef tag::with_p_square_cumulative_distribution_weighted_median type;
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_moment.hpp
//
// Copyright 2006, Eric Niebler, Olivier Gygi. 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_WEIGHTED_MOMENT_HPP_EAN_15_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_MOMENT_HPP_EAN_15_11_2005
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/assert.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/preprocessor/arithmetic/inc.hpp>
#include <boost/preprocessor/repetition/repeat_from_to.hpp>
#include <boost/preprocessor/repetition/enum_trailing_params.hpp>
#include <boost/preprocessor/repetition/enum_trailing_binary_params.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/moment.hpp> // for pow()
#include <boost/accumulators/statistics/sum.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_moment_impl
template<typename N, typename Sample, typename Weight>
struct weighted_moment_impl
: accumulator_base // TODO: also depends_on sum of powers
{
BOOST_MPL_ASSERT_RELATION(N::value, >, 0);
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
template<typename Args>
weighted_moment_impl(Args const &args)
: sum(args[sample | Sample()] * numeric::one<Weight>::value)
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->sum += args[weight] * numeric::pow(args[sample], N());
}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(this->sum, sum_of_weights(args));
}
private:
weighted_sample sum;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_moment
//
namespace tag
{
template<int N>
struct weighted_moment
: depends_on<count, sum_of_weights>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_moment_impl<mpl::int_<N>, mpl::_1, mpl::_2> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_moment
//
namespace extract
{
BOOST_ACCUMULATORS_DEFINE_EXTRACTOR(tag, weighted_moment, (int))
}
using extract::weighted_moment;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_p_square_cumul_dist.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006
#include <vector>
#include <functional>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/range.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/p_square_cumul_dist.hpp> // for named parameter p_square_cumulative_distribution_num_cells
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_p_square_cumulative_distribution_impl
// cumulative distribution calculation (as histogram)
/**
@brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm for weighted samples
A histogram of the sample cumulative distribution is computed dynamically without storing samples
based on the \f$ P^2 \f$ algorithm for weighted samples. The returned histogram has a specifiable
amount (num_cells) equiprobable (and not equal-sized) cells.
Note that applying importance sampling results in regions to be more and other regions to be less
accurately estimated than without importance sampling, i.e., with unweighted samples.
For further details, see
R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
histograms without storing observations, Communications of the ACM,
Volume 28 (October), Number 10, 1985, p. 1076-1085.
@param p_square_cumulative_distribution_num_cells
*/
template<typename Sample, typename Weight>
struct weighted_p_square_cumulative_distribution_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
typedef std::vector<std::pair<float_type, float_type> > histogram_type;
typedef std::vector<float_type> array_type;
// for boost::result_of
typedef iterator_range<typename histogram_type::iterator> result_type;
template<typename Args>
weighted_p_square_cumulative_distribution_impl(Args const &args)
: num_cells(args[p_square_cumulative_distribution_num_cells])
, heights(num_cells + 1)
, actual_positions(num_cells + 1)
, desired_positions(num_cells + 1)
, histogram(num_cells + 1)
, is_dirty(true)
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->is_dirty = true;
std::size_t cnt = count(args);
std::size_t sample_cell = 1; // k
std::size_t b = this->num_cells;
// accumulate num_cells + 1 first samples
if (cnt <= b + 1)
{
this->heights[cnt - 1] = args[sample];
this->actual_positions[cnt - 1] = args[weight];
// complete the initialization of heights by sorting
if (cnt == b + 1)
{
//std::sort(this->heights.begin(), this->heights.end());
// TODO: we need to sort the initial samples (in heights) in ascending order and
// sort their weights (in actual_positions) the same way. The following lines do
// it, but there must be a better and more efficient way of doing this.
typename array_type::iterator it_begin, it_end, it_min;
it_begin = this->heights.begin();
it_end = this->heights.end();
std::size_t pos = 0;
while (it_begin != it_end)
{
it_min = std::min_element(it_begin, it_end);
std::size_t d = std::distance(it_begin, it_min);
std::swap(*it_begin, *it_min);
std::swap(this->actual_positions[pos], this->actual_positions[pos + d]);
++it_begin;
++pos;
}
// calculate correct initial actual positions
for (std::size_t i = 1; i < b; ++i)
{
this->actual_positions[i] += this->actual_positions[i - 1];
}
}
}
else
{
// find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
if (args[sample] < this->heights[0])
{
this->heights[0] = args[sample];
this->actual_positions[0] = args[weight];
sample_cell = 1;
}
else if (this->heights[b] <= args[sample])
{
this->heights[b] = args[sample];
sample_cell = b;
}
else
{
typename array_type::iterator it;
it = std::upper_bound(
this->heights.begin()
, this->heights.end()
, args[sample]
);
sample_cell = std::distance(this->heights.begin(), it);
}
// increment positions of markers above sample_cell
for (std::size_t i = sample_cell; i < b + 1; ++i)
{
this->actual_positions[i] += args[weight];
}
// determine desired marker positions
for (std::size_t i = 1; i < b + 1; ++i)
{
this->desired_positions[i] = this->actual_positions[0]
+ numeric::fdiv((i-1) * (sum_of_weights(args) - this->actual_positions[0]), b);
}
// adjust heights of markers 2 to num_cells if necessary
for (std::size_t i = 1; i < b; ++i)
{
// offset to desire position
float_type d = this->desired_positions[i] - this->actual_positions[i];
// offset to next position
float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
// offset to previous position
float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
// height ds
float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) )
{
short sign_d = static_cast<short>(d / std::abs(d));
// try adjusting heights[i] using p-squared formula
float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm );
if ( this->heights[i - 1] < h && h < this->heights[i + 1] )
{
this->heights[i] = h;
}
else
{
// use linear formula
if (d>0)
{
this->heights[i] += hp;
}
if (d<0)
{
this->heights[i] -= hm;
}
}
this->actual_positions[i] += sign_d;
}
}
}
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
// creates a vector of std::pair where each pair i holds
// the values heights[i] (x-axis of histogram) and
// actual_positions[i] / sum_of_weights (y-axis of histogram)
for (std::size_t i = 0; i < this->histogram.size(); ++i)
{
this->histogram[i] = std::make_pair(this->heights[i], numeric::fdiv(this->actual_positions[i], sum_of_weights(args)));
}
}
return make_iterator_range(this->histogram);
}
private:
std::size_t num_cells; // number of cells b
array_type heights; // q_i
array_type actual_positions; // n_i
array_type desired_positions; // n'_i
mutable histogram_type histogram; // histogram
mutable bool is_dirty;
};
} // namespace detail
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_p_square_cumulative_distribution
//
namespace tag
{
struct weighted_p_square_cumulative_distribution
: depends_on<count, sum_of_weights>
, p_square_cumulative_distribution_num_cells
{
typedef accumulators::impl::weighted_p_square_cumulative_distribution_impl<mpl::_1, mpl::_2> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_p_square_cumulative_distribution
//
namespace extract
{
extractor<tag::weighted_p_square_cumulative_distribution> const weighted_p_square_cumulative_distribution = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_cumulative_distribution)
}
using extract::weighted_p_square_cumulative_distribution;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_p_square_cumulative_distribution.hpp
//
// Copyright 2012 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_WEIGHTED_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_03_19_2012
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_P_SQUARE_CUMULATIVE_DISTRIBUTION_HPP_03_19_2012
#if defined(_MSC_VER) || defined(__BORLANDC__) || defined(__DMC__)
# pragma message ("Warning: This header is deprecated. Please use: boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp")
#elif defined(__GNUC__) || defined(__HP_aCC) || defined(__SUNPRO_CC) || defined(__IBMCPP__)
# warning "This header is deprecated. Please use: boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp"
#endif
#include <boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp>
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_p_square_quantile.hpp
//
// Copyright 2005 Daniel Egloff. 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_WEIGHTED_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
#include <cmath>
#include <functional>
#include <boost/array.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.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/statistics_fwd.hpp>
#include <boost/accumulators/statistics/count.hpp>
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
namespace boost { namespace accumulators
{
namespace impl {
///////////////////////////////////////////////////////////////////////////////
// weighted_p_square_quantile_impl
// single quantile estimation with weighted samples
/**
@brief Single quantile estimation with the \f$P^2\f$ algorithm for weighted samples
This version of the \f$P^2\f$ algorithm extends the \f$P^2\f$ algorithm to support weighted samples.
The \f$P^2\f$ algorithm estimates a quantile dynamically without storing samples. Instead of
storing the whole sample cumulative distribution, only five points (markers) are stored. The heights
of these markers are the minimum and the maximum of the samples and the current estimates of the
\f$(p/2)\f$-, \f$p\f$ - and \f$(1+p)/2\f$ -quantiles. Their positions are equal to the number
of samples that are smaller or equal to the markers. Each time a new sample is added, the
positions of the markers are updated and if necessary their heights are adjusted using a piecewise-
parabolic formula.
For further details, see
R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
histograms without storing observations, Communications of the ACM,
Volume 28 (October), Number 10, 1985, p. 1076-1085.
@param quantile_probability
*/
template<typename Sample, typename Weight, typename Impl>
struct weighted_p_square_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
typedef array<float_type, 5> array_type;
// for boost::result_of
typedef float_type result_type;
template<typename Args>
weighted_p_square_quantile_impl(Args const &args)
: p(is_same<Impl, for_median>::value ? 0.5 : args[quantile_probability | 0.5])
, heights()
, actual_positions()
, desired_positions()
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
// accumulate 5 first samples
if (cnt <= 5)
{
this->heights[cnt - 1] = args[sample];
// In this initialization phase, actual_positions stores the weights of the
// initial samples that are needed at the end of the initialization phase to
// compute the correct initial positions of the markers.
this->actual_positions[cnt - 1] = args[weight];
// complete the initialization of heights and actual_positions by sorting
if (cnt == 5)
{
// TODO: we need to sort the initial samples (in heights) in ascending order and
// sort their weights (in actual_positions) the same way. The following lines do
// it, but there must be a better and more efficient way of doing this.
typename array_type::iterator it_begin, it_end, it_min;
it_begin = this->heights.begin();
it_end = this->heights.end();
std::size_t pos = 0;
while (it_begin != it_end)
{
it_min = std::min_element(it_begin, it_end);
std::size_t d = std::distance(it_begin, it_min);
std::swap(*it_begin, *it_min);
std::swap(this->actual_positions[pos], this->actual_positions[pos + d]);
++it_begin;
++pos;
}
// calculate correct initial actual positions
for (std::size_t i = 1; i < 5; ++i)
{
this->actual_positions[i] += this->actual_positions[i - 1];
}
}
}
else
{
std::size_t sample_cell = 1; // k
// find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
if (args[sample] < this->heights[0])
{
this->heights[0] = args[sample];
this->actual_positions[0] = args[weight];
sample_cell = 1;
}
else if (this->heights[4] <= args[sample])
{
this->heights[4] = args[sample];
sample_cell = 4;
}
else
{
typedef typename array_type::iterator iterator;
iterator it = std::upper_bound(
this->heights.begin()
, this->heights.end()
, args[sample]
);
sample_cell = std::distance(this->heights.begin(), it);
}
// increment positions of markers above sample_cell
for (std::size_t i = sample_cell; i < 5; ++i)
{
this->actual_positions[i] += args[weight];
}
// update desired positions for all markers
this->desired_positions[0] = this->actual_positions[0];
this->desired_positions[1] = (sum_of_weights(args) - this->actual_positions[0])
* this->p/2. + this->actual_positions[0];
this->desired_positions[2] = (sum_of_weights(args) - this->actual_positions[0])
* this->p + this->actual_positions[0];
this->desired_positions[3] = (sum_of_weights(args) - this->actual_positions[0])
* (1. + this->p)/2. + this->actual_positions[0];
this->desired_positions[4] = sum_of_weights(args);
// adjust height and actual positions of markers 1 to 3 if necessary
for (std::size_t i = 1; i <= 3; ++i)
{
// offset to desired positions
float_type d = this->desired_positions[i] - this->actual_positions[i];
// offset to next position
float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
// offset to previous position
float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
// height ds
float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) )
{
short sign_d = static_cast<short>(d / std::abs(d));
// try adjusting heights[i] using p-squared formula
float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm );
if ( this->heights[i - 1] < h && h < this->heights[i + 1] )
{
this->heights[i] = h;
}
else
{
// use linear formula
if (d>0)
{
this->heights[i] += hp;
}
if (d<0)
{
this->heights[i] -= hm;
}
}
this->actual_positions[i] += sign_d;
}
}
}
}
result_type result(dont_care) const
{
return this->heights[2];
}
private:
float_type p; // the quantile probability p
array_type heights; // q_i
array_type actual_positions; // n_i
array_type desired_positions; // n'_i
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_p_square_quantile
//
namespace tag
{
struct weighted_p_square_quantile
: depends_on<count, sum_of_weights>
{
typedef accumulators::impl::weighted_p_square_quantile_impl<mpl::_1, mpl::_2, regular> impl;
};
struct weighted_p_square_quantile_for_median
: depends_on<count, sum_of_weights>
{
typedef accumulators::impl::weighted_p_square_quantile_impl<mpl::_1, mpl::_2, for_median> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_p_square_quantile
// extract::weighted_p_square_quantile_for_median
//
namespace extract
{
extractor<tag::weighted_p_square_quantile> const weighted_p_square_quantile = {};
extractor<tag::weighted_p_square_quantile_for_median> const weighted_p_square_quantile_for_median = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_quantile)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_quantile_for_median)
}
using extract::weighted_p_square_quantile;
using extract::weighted_p_square_quantile_for_median;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_peaks_over_threshold.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <numeric>
#include <functional>
#include <boost/throw_exception.hpp>
#include <boost/range.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.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/parameters/quantile_probability.hpp>
#include <boost/accumulators/statistics/peaks_over_threshold.hpp> // for named parameters pot_threshold_value and pot_threshold_probability
#include <boost/accumulators/statistics/sum.hpp>
#include <boost/accumulators/statistics/tail_variate.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_peaks_over_threshold_impl
// works with an explicit threshold value and does not depend on order statistics of weighted samples
/**
@brief Weighted Peaks over Threshold Method for Weighted Quantile and Weighted Tail Mean Estimation
@sa peaks_over_threshold_impl
@param quantile_probability
@param pot_threshold_value
*/
template<typename Sample, typename Weight, typename LeftRight>
struct weighted_peaks_over_threshold_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef boost::tuple<float_type, float_type, float_type> result_type;
template<typename Args>
weighted_peaks_over_threshold_impl(Args const &args)
: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
, mu_(sign_ * numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, sigma2_(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, w_sum_(numeric::fdiv(args[weight | Weight()], (std::size_t)1))
, threshold_(sign_ * args[pot_threshold_value])
, fit_parameters_(boost::make_tuple(0., 0., 0.))
, is_dirty_(true)
{
}
template<typename Args>
void operator ()(Args const &args)
{
this->is_dirty_ = true;
if (this->sign_ * args[sample] > this->threshold_)
{
this->mu_ += args[weight] * args[sample];
this->sigma2_ += args[weight] * args[sample] * args[sample];
this->w_sum_ += args[weight];
}
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty_)
{
this->is_dirty_ = false;
this->mu_ = this->sign_ * numeric::fdiv(this->mu_, this->w_sum_);
this->sigma2_ = numeric::fdiv(this->sigma2_, this->w_sum_);
this->sigma2_ -= this->mu_ * this->mu_;
float_type threshold_probability = numeric::fdiv(sum_of_weights(args) - this->w_sum_, sum_of_weights(args));
float_type tmp = numeric::fdiv(( this->mu_ - this->threshold_ )*( this->mu_ - this->threshold_ ), this->sigma2_);
float_type xi_hat = 0.5 * ( 1. - tmp );
float_type beta_hat = 0.5 * ( this->mu_ - this->threshold_ ) * ( 1. + tmp );
float_type beta_bar = beta_hat * std::pow(1. - threshold_probability, xi_hat);
float_type u_bar = this->threshold_ - beta_bar * ( std::pow(1. - threshold_probability, -xi_hat) - 1.)/xi_hat;
this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
}
return this->fit_parameters_;
}
private:
short sign_; // for left tail fitting, mirror the extreme values
mutable float_type mu_; // mean of samples above threshold
mutable float_type sigma2_; // variance of samples above threshold
mutable float_type w_sum_; // sum of weights of samples above threshold
float_type threshold_;
mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
mutable bool is_dirty_;
};
///////////////////////////////////////////////////////////////////////////////
// weighted_peaks_over_threshold_prob_impl
// determines threshold from a given threshold probability using order statistics
/**
@brief Peaks over Threshold Method for Quantile and Tail Mean Estimation
@sa weighted_peaks_over_threshold_impl
@param quantile_probability
@param pot_threshold_probability
*/
template<typename Sample, typename Weight, typename LeftRight>
struct weighted_peaks_over_threshold_prob_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
// for boost::result_of
typedef boost::tuple<float_type, float_type, float_type> result_type;
template<typename Args>
weighted_peaks_over_threshold_prob_impl(Args const &args)
: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
, mu_(sign_ * numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, sigma2_(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
, threshold_probability_(args[pot_threshold_probability])
, fit_parameters_(boost::make_tuple(0., 0., 0.))
, is_dirty_(true)
{
}
void operator ()(dont_care)
{
this->is_dirty_ = true;
}
template<typename Args>
result_type result(Args const &args) const
{
if (this->is_dirty_)
{
this->is_dirty_ = false;
float_type threshold = sum_of_weights(args)
* ( ( is_same<LeftRight, left>::value ) ? this->threshold_probability_ : 1. - this->threshold_probability_ );
std::size_t n = 0;
Weight sum = Weight(0);
while (sum < threshold)
{
if (n < static_cast<std::size_t>(tail_weights(args).size()))
{
mu_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n);
sigma2_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n) * (*(tail(args).begin() + n));
sum += *(tail_weights(args).begin() + n);
n++;
}
else
{
if (std::numeric_limits<float_type>::has_quiet_NaN)
{
return boost::make_tuple(
std::numeric_limits<float_type>::quiet_NaN()
, std::numeric_limits<float_type>::quiet_NaN()
, std::numeric_limits<float_type>::quiet_NaN()
);
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return boost::make_tuple(Sample(0), Sample(0), Sample(0));
}
}
}
float_type u = *(tail(args).begin() + n - 1) * this->sign_;
this->mu_ = this->sign_ * numeric::fdiv(this->mu_, sum);
this->sigma2_ = numeric::fdiv(this->sigma2_, sum);
this->sigma2_ -= this->mu_ * this->mu_;
if (is_same<LeftRight, left>::value)
this->threshold_probability_ = 1. - this->threshold_probability_;
float_type tmp = numeric::fdiv(( this->mu_ - u )*( this->mu_ - u ), this->sigma2_);
float_type xi_hat = 0.5 * ( 1. - tmp );
float_type beta_hat = 0.5 * ( this->mu_ - u ) * ( 1. + tmp );
float_type beta_bar = beta_hat * std::pow(1. - threshold_probability_, xi_hat);
float_type u_bar = u - beta_bar * ( std::pow(1. - threshold_probability_, -xi_hat) - 1.)/xi_hat;
this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
}
return this->fit_parameters_;
}
private:
short sign_; // for left tail fitting, mirror the extreme values
mutable float_type mu_; // mean of samples above threshold u
mutable float_type sigma2_; // variance of samples above threshold u
mutable float_type threshold_probability_;
mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
mutable bool is_dirty_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_peaks_over_threshold
//
namespace tag
{
template<typename LeftRight>
struct weighted_peaks_over_threshold
: depends_on<sum_of_weights>
, pot_threshold_value
{
/// INTERNAL ONLY
typedef accumulators::impl::weighted_peaks_over_threshold_impl<mpl::_1, mpl::_2, LeftRight> impl;
};
template<typename LeftRight>
struct weighted_peaks_over_threshold_prob
: depends_on<sum_of_weights, tail_weights<LeftRight> >
, pot_threshold_probability
{
/// INTERNAL ONLY
typedef accumulators::impl::weighted_peaks_over_threshold_prob_impl<mpl::_1, mpl::_2, LeftRight> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_peaks_over_threshold
//
namespace extract
{
extractor<tag::abstract_peaks_over_threshold> const weighted_peaks_over_threshold = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_peaks_over_threshold)
}
using extract::weighted_peaks_over_threshold;
// weighted_peaks_over_threshold<LeftRight>(with_threshold_value) -> weighted_peaks_over_threshold<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_value)>
{
typedef tag::weighted_peaks_over_threshold<LeftRight> type;
};
// weighted_peaks_over_threshold<LeftRight>(with_threshold_probability) -> weighted_peaks_over_threshold_prob<LeftRight>
template<typename LeftRight>
struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_probability)>
{
typedef tag::weighted_peaks_over_threshold_prob<LeftRight> type;
};
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_skewness.hpp
//
// Copyright 2006 Olivier Gygi, Daniel Egloff. 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_WEIGHTED_SKEWNESS_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_SKEWNESS_HPP_EAN_28_10_2005
#include <limits>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/weighted_moment.hpp>
#include <boost/accumulators/statistics/weighted_mean.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_skewness_impl
/**
@brief Skewness estimation for weighted samples
The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power $
of the 2nd central moment (the variance) of the samples. The skewness can also be expressed by the simple moments:
\f[
\hat{g}_1 =
\frac
{\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3}
{\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}}
\f]
where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
\f$ n \f$ samples.
The skewness estimator for weighted samples is formally identical to the estimator for unweighted samples, except that
the weighted counterparts of all measures it depends on are to be taken.
*/
template<typename Sample, typename Weight>
struct weighted_skewness_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, weighted_sample>::result_type result_type;
weighted_skewness_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
return numeric::fdiv(
accumulators::weighted_moment<3>(args)
- 3. * accumulators::weighted_moment<2>(args) * weighted_mean(args)
+ 2. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args)
, ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
* std::sqrt( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) )
);
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_skewness
//
namespace tag
{
struct weighted_skewness
: depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_skewness_impl<mpl::_1, mpl::_2> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_skewness
//
namespace extract
{
extractor<tag::weighted_skewness> const weighted_skewness = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_skewness)
}
using extract::weighted_skewness;
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_sum.hpp
//
// Copyright 2006 Eric Niebler, Olivier Gygi. 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_WEIGHTED_SUM_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_SUM_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/parameters/weight.hpp>
#include <boost/accumulators/framework/accumulators/external_accumulator.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_sum_impl
template<typename Sample, typename Weight, typename Tag>
struct weighted_sum_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef weighted_sample result_type;
template<typename Args>
weighted_sum_impl(Args const &args)
: weighted_sum_(
args[parameter::keyword<Tag>::get() | Sample()]
* numeric::one<Weight>::value
)
{
}
template<typename Args>
void operator ()(Args const &args)
{
// what about overflow?
this->weighted_sum_ += args[parameter::keyword<Tag>::get()] * args[weight];
}
result_type result(dont_care) const
{
return this->weighted_sum_;
}
private:
weighted_sample weighted_sum_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_sum
//
namespace tag
{
struct weighted_sum
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_sum_impl<mpl::_1, mpl::_2, tag::sample> impl;
};
template<typename VariateType, typename VariateTag>
struct weighted_sum_of_variates
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_sum_impl<VariateType, mpl::_2, VariateTag> impl;
};
struct abstract_weighted_sum_of_variates
: depends_on<>
{
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_sum
//
namespace extract
{
extractor<tag::weighted_sum> const weighted_sum = {};
extractor<tag::abstract_weighted_sum_of_variates> const weighted_sum_of_variates = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_sum)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_sum_of_variates)
}
using extract::weighted_sum;
using extract::weighted_sum_of_variates;
template<typename VariateType, typename VariateTag>
struct feature_of<tag::weighted_sum_of_variates<VariateType, VariateTag> >
: feature_of<tag::abstract_weighted_sum_of_variates>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_sum_kahan.hpp
//
// Copyright 2011 Simon West. 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_WEIGHTED_SUM_KAHAN_HPP_EAN_11_05_2011
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_SUM_KAHAN_HPP_EAN_11_05_2011
#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/parameters/weight.hpp>
#include <boost/accumulators/framework/accumulators/external_accumulator.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/weighted_sum.hpp>
#include <boost/numeric/conversion/cast.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
#if _MSC_VER > 1400
# pragma float_control(push)
# pragma float_control(precise, on)
#endif
///////////////////////////////////////////////////////////////////////////////
// weighted_sum_kahan_impl
template<typename Sample, typename Weight, typename Tag>
struct weighted_sum_kahan_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef weighted_sample result_type;
template<typename Args>
weighted_sum_kahan_impl(Args const &args)
: weighted_sum_(
args[parameter::keyword<Tag>::get() | Sample()] * numeric::one<Weight>::value),
compensation(boost::numeric_cast<weighted_sample>(0.0))
{
}
template<typename Args>
void
#if BOOST_ACCUMULATORS_GCC_VERSION > 40305
__attribute__((__optimize__("no-associative-math")))
#endif
operator ()(Args const &args)
{
const weighted_sample myTmp1 = args[parameter::keyword<Tag>::get()] * args[weight] - this->compensation;
const weighted_sample myTmp2 = this->weighted_sum_ + myTmp1;
this->compensation = (myTmp2 - this->weighted_sum_) - myTmp1;
this->weighted_sum_ = myTmp2;
}
result_type result(dont_care) const
{
return this->weighted_sum_;
}
private:
weighted_sample weighted_sum_;
weighted_sample compensation;
};
#if _MSC_VER > 1400
# pragma float_control(pop)
#endif
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_sum_kahan
// tag::weighted_sum_of_variates_kahan
//
namespace tag
{
struct weighted_sum_kahan
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_sum_kahan_impl<mpl::_1, mpl::_2, tag::sample> impl;
};
template<typename VariateType, typename VariateTag>
struct weighted_sum_of_variates_kahan
: depends_on<>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_sum_kahan_impl<VariateType, mpl::_2, VariateTag> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_sum_kahan
// extract::weighted_sum_of_variates_kahan
//
namespace extract
{
extractor<tag::weighted_sum_kahan> const weighted_sum_kahan = {};
extractor<tag::abstract_weighted_sum_of_variates> const weighted_sum_of_variates_kahan = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_sum_kahan)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_sum_of_variates_kahan)
}
using extract::weighted_sum_kahan;
using extract::weighted_sum_of_variates_kahan;
// weighted_sum(kahan) -> weighted_sum_kahan
template<>
struct as_feature<tag::weighted_sum(kahan)>
{
typedef tag::weighted_sum_kahan type;
};
template<typename VariateType, typename VariateTag>
struct feature_of<tag::weighted_sum_of_variates_kahan<VariateType, VariateTag> >
: feature_of<tag::abstract_weighted_sum_of_variates>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_tail_mean.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_MEAN_HPP_DE_01_01_2006
#include <numeric>
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_mean.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// coherent_weighted_tail_mean_impl
//
// TODO
///////////////////////////////////////////////////////////////////////////////
// non_coherent_weighted_tail_mean_impl
//
/**
@brief Estimation of the (non-coherent) weighted tail mean based on order statistics (for both left and right tails)
An estimation of the non-coherent, weighted tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the weighted mean
of the
\f[
\lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
\f]
smallest samples (left tail) or the weighted mean of the
\f[
n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\}
\f]
largest samples (right tail) above a quantile \f$\hat{q}_{\alpha}\f$ of level \f$\alpha\f$, \f$n\f$ being the total number of sample
and \f$\bar{w}_n\f$ the sum of all \f$n\f$ weights:
\f[
\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{\sum_{i=1}^{\lambda} w_i X_{i:n}}{\sum_{i=1}^{\lambda} w_i},
\f]
\f[
\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{\sum_{i=\rho}^n w_i X_{i:n}}{\sum_{i=\rho}^n w_i}.
\f]
@param quantile_probability
*/
template<typename Sample, typename Weight, typename LeftRight>
struct non_coherent_weighted_tail_mean_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type result_type;
non_coherent_weighted_tail_mean_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
float_type threshold = sum_of_weights(args)
* ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
std::size_t n = 0;
Weight sum = Weight(0);
while (sum < threshold)
{
if (n < static_cast<std::size_t>(tail_weights(args).size()))
{
sum += *(tail_weights(args).begin() + n);
n++;
}
else
{
if (std::numeric_limits<result_type>::has_quiet_NaN)
{
return std::numeric_limits<result_type>::quiet_NaN();
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return result_type(0);
}
}
}
return numeric::fdiv(
std::inner_product(
tail(args).begin()
, tail(args).begin() + n
, tail_weights(args).begin()
, weighted_sample(0)
)
, sum
);
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::non_coherent_weighted_tail_mean<>
//
namespace tag
{
template<typename LeftRight>
struct non_coherent_weighted_tail_mean
: depends_on<sum_of_weights, tail_weights<LeftRight> >
{
typedef accumulators::impl::non_coherent_weighted_tail_mean_impl<mpl::_1, mpl::_2, LeftRight> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::non_coherent_weighted_tail_mean;
//
namespace extract
{
extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_weighted_tail_mean = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_weighted_tail_mean)
}
using extract::non_coherent_weighted_tail_mean;
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_tail_quantile.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_QUANTILE_HPP_DE_01_01_2006
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/mpl/if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_quantile.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost { namespace accumulators
{
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// weighted_tail_quantile_impl
// Tail quantile estimation based on order statistics of weighted samples
/**
@brief Tail quantile estimation based on order statistics of weighted samples (for both left and right tails)
An estimator \f$\hat{q}\f$ of tail quantiles with level \f$\alpha\f$ based on order statistics
\f$X_{1:n} \leq X_{2:n} \leq\dots\leq X_{n:n}\f$ of weighted samples are given by \f$X_{\lambda:n}\f$ (left tail)
and \f$X_{\rho:n}\f$ (right tail), where
\f[
\lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
\f]
and
\f[
\rho = \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\},
\f]
\f$n\f$ being the number of samples and \f$\bar{w}_n\f$ the sum of all weights.
@param quantile_probability
*/
template<typename Sample, typename Weight, typename LeftRight>
struct weighted_tail_quantile_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Weight, std::size_t>::result_type float_type;
// for boost::result_of
typedef Sample result_type;
weighted_tail_quantile_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
float_type threshold = sum_of_weights(args)
* ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
std::size_t n = 0;
Weight sum = Weight(0);
while (sum < threshold)
{
if (n < static_cast<std::size_t>(tail_weights(args).size()))
{
sum += *(tail_weights(args).begin() + n);
n++;
}
else
{
if (std::numeric_limits<result_type>::has_quiet_NaN)
{
return std::numeric_limits<result_type>::quiet_NaN();
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
return Sample(0);
}
}
}
// Note that the cached samples of the left are sorted in ascending order,
// whereas the samples of the right tail are sorted in descending order
return *(boost::begin(tail(args)) + n - 1);
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_tail_quantile<>
//
namespace tag
{
template<typename LeftRight>
struct weighted_tail_quantile
: depends_on<sum_of_weights, tail_weights<LeftRight> >
{
/// INTERNAL ONLY
typedef accumulators::impl::weighted_tail_quantile_impl<mpl::_1, mpl::_2, LeftRight> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_tail_quantile
//
namespace extract
{
extractor<tag::quantile> const weighted_tail_quantile = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_quantile)
}
using extract::weighted_tail_quantile;
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_tail_variate_means.hpp
//
// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
#include <numeric>
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_variate.hpp>
#include <boost/accumulators/statistics/tail_variate_means.hpp>
#include <boost/accumulators/statistics/weighted_tail_mean.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif
namespace boost
{
// for _BinaryOperatrion2 in std::inner_product below
// multiplies two values and promotes the result to double
namespace numeric { namespace functional
{
///////////////////////////////////////////////////////////////////////////////
// numeric::functional::multiply_and_promote_to_double
template<typename T, typename U>
struct multiply_and_promote_to_double
: multiplies<T, double const>
{
};
}}
}
namespace boost { namespace accumulators
{
namespace impl
{
/**
@brief Estimation of the absolute and relative weighted tail variate means (for both left and right tails)
For all \f$j\f$-th variates associated to the
\f[
\lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
\f]
smallest samples (left tail) or the weighted mean of the
\f[
n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\}
\f]
largest samples (right tail), the absolute weighted tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$
are computed and returned as an iterator range. Alternatively, the relative weighted tail means
\f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute weighted tail means
normalized with the weighted (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
\f[
\widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
\frac{1}{\sum_{i=\rho}^n w_i}
\sum_{i=\rho}^n w_i \xi_{j,i}
\f]
\f[
\widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
\frac{1}{\sum_{i=1}^{\lambda}}
\sum_{i=1}^{\lambda} w_i \xi_{j,i}
\f]
\f[
\widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
\frac{\sum_{i=\rho}^n w_i \xi_{j,i}}
{\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
\f]
\f[
\widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
\frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}}
{\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
\f]
*/
///////////////////////////////////////////////////////////////////////////////
// weighted_tail_variate_means_impl
// by default: absolute weighted_tail_variate_means
template<typename Sample, typename Weight, typename Impl, typename LeftRight, typename VariateType>
struct weighted_tail_variate_means_impl
: accumulator_base
{
typedef typename numeric::functional::fdiv<Weight, Weight>::result_type float_type;
typedef typename numeric::functional::fdiv<typename numeric::functional::multiplies<VariateType, Weight>::result_type, Weight>::result_type array_type;
// for boost::result_of
typedef iterator_range<typename array_type::iterator> result_type;
weighted_tail_variate_means_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
float_type threshold = sum_of_weights(args)
* ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
std::size_t n = 0;
Weight sum = Weight(0);
while (sum < threshold)
{
if (n < static_cast<std::size_t>(tail_weights(args).size()))
{
sum += *(tail_weights(args).begin() + n);
n++;
}
else
{
if (std::numeric_limits<float_type>::has_quiet_NaN)
{
std::fill(
this->tail_means_.begin()
, this->tail_means_.end()
, std::numeric_limits<float_type>::quiet_NaN()
);
}
else
{
std::ostringstream msg;
msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
boost::throw_exception(std::runtime_error(msg.str()));
}
}
}
std::size_t num_variates = tail_variate(args).begin()->size();
this->tail_means_.clear();
this->tail_means_.resize(num_variates, Sample(0));
this->tail_means_ = std::inner_product(
tail_variate(args).begin()
, tail_variate(args).begin() + n
, tail_weights(args).begin()
, this->tail_means_
, numeric::functional::plus<array_type const, array_type const>()
, numeric::functional::multiply_and_promote_to_double<VariateType const, Weight const>()
);
float_type factor = sum * ( (is_same<Impl, relative>::value) ? non_coherent_weighted_tail_mean(args) : 1. );
std::transform(
this->tail_means_.begin()
, this->tail_means_.end()
, this->tail_means_.begin()
#ifdef BOOST_NO_CXX98_BINDERS
, std::bind(numeric::functional::divides<typename array_type::value_type const, float_type const>(), std::placeholders::_1, factor)
#else
, std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor)
#endif
);
return make_iterator_range(this->tail_means_);
}
private:
mutable array_type tail_means_;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::absolute_weighted_tail_variate_means
// tag::relative_weighted_tail_variate_means
//
namespace tag
{
template<typename LeftRight, typename VariateType, typename VariateTag>
struct absolute_weighted_tail_variate_means
: depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
{
typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl;
};
template<typename LeftRight, typename VariateType, typename VariateTag>
struct relative_weighted_tail_variate_means
: depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
{
typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_tail_variate_means
// extract::relative_weighted_tail_variate_means
//
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 = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_variate_means)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_weighted_tail_variate_means)
}
using extract::weighted_tail_variate_means;
using extract::relative_weighted_tail_variate_means;
// weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
{
typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};
// weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
{
typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};
}} // namespace boost::accumulators
#ifdef _MSC_VER
# pragma warning(pop)
#endif
#endif

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///////////////////////////////////////////////////////////////////////////////
// weighted_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_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/variance.hpp>
#include <boost/accumulators/statistics/weighted_sum.hpp>
#include <boost/accumulators/statistics/weighted_mean.hpp>
#include <boost/accumulators/statistics/weighted_moment.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
//! Lazy calculation of variance of weighted samples.
/*!
The default implementation of the variance of weighted samples is based on the second moment
\f$\widehat{m}_n^{(2)}\f$ (weighted_moment<2>) and the mean\f$ \hat{\mu}_n\f$ (weighted_mean):
\f[
\hat{\sigma}_n^2 = \widehat{m}_n^{(2)}-\hat{\mu}_n^2,
\f]
where \f$n\f$ is the number of samples.
*/
template<typename Sample, typename Weight, typename MeanFeature>
struct lazy_weighted_variance_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
lazy_weighted_variance_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
extractor<MeanFeature> const some_mean = {};
result_type tmp = some_mean(args);
return accumulators::weighted_moment<2>(args) - tmp * tmp;
}
};
//! Iterative calculation of variance of weighted samples.
/*!
Iterative calculation of variance of weighted samples:
\f[
\hat{\sigma}_n^2 =
\frac{\bar{w}_n - w_n}{\bar{w}_n}\hat{\sigma}_{n - 1}^2
+ \frac{w_n}{\bar{w}_n - w_n}\left(X_n - \hat{\mu}_n\right)^2
,\quad n\ge2,\quad\hat{\sigma}_0^2 = 0.
\f]
where \f$\bar{w}_n\f$ is the sum of the \f$n\f$ weights \f$w_i\f$ and \f$\hat{\mu}_n\f$
the estimate of the mean of the weighted samples. Note that the sample variance is not defined for
\f$n <= 1\f$.
*/
template<typename Sample, typename Weight, typename MeanFeature, typename Tag>
struct weighted_variance_impl
: accumulator_base
{
typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
// for boost::result_of
typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type;
template<typename Args>
weighted_variance_impl(Args const &args)
: weighted_variance(numeric::fdiv(args[sample | Sample()], numeric::one<Weight>::value))
{
}
template<typename Args>
void operator ()(Args const &args)
{
std::size_t cnt = count(args);
if(cnt > 1)
{
extractor<MeanFeature> const some_mean = {};
result_type tmp = args[parameter::keyword<Tag>::get()] - some_mean(args);
this->weighted_variance =
numeric::fdiv(this->weighted_variance * (sum_of_weights(args) - args[weight]), sum_of_weights(args))
+ numeric::fdiv(tmp * tmp * args[weight], sum_of_weights(args) - args[weight] );
}
}
result_type result(dont_care) const
{
return this->weighted_variance;
}
private:
result_type weighted_variance;
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag::weighted_variance
// tag::immediate_weighted_variance
//
namespace tag
{
struct lazy_weighted_variance
: depends_on<weighted_moment<2>, weighted_mean>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::lazy_weighted_variance_impl<mpl::_1, mpl::_2, weighted_mean> impl;
};
struct weighted_variance
: depends_on<count, immediate_weighted_mean>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::weighted_variance_impl<mpl::_1, mpl::_2, immediate_weighted_mean, sample> impl;
};
}
///////////////////////////////////////////////////////////////////////////////
// extract::weighted_variance
// extract::immediate_weighted_variance
//
namespace extract
{
extractor<tag::lazy_weighted_variance> const lazy_weighted_variance = {};
extractor<tag::weighted_variance> const weighted_variance = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_weighted_variance)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_variance)
}
using extract::lazy_weighted_variance;
using extract::weighted_variance;
// weighted_variance(lazy) -> lazy_weighted_variance
template<>
struct as_feature<tag::weighted_variance(lazy)>
{
typedef tag::lazy_weighted_variance type;
};
// weighted_variance(immediate) -> weighted_variance
template<>
struct as_feature<tag::weighted_variance(immediate)>
{
typedef tag::weighted_variance type;
};
////////////////////////////////////////////////////////////////////////////
//// droppable_accumulator<weighted_variance_impl>
//// need to specialize droppable lazy weighted_variance to cache the result at the
//// point the accumulator is dropped.
///// INTERNAL ONLY
/////
//template<typename Sample, typename Weight, typename MeanFeature>
//struct droppable_accumulator<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
// : droppable_accumulator_base<
// with_cached_result<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
// >
//{
// template<typename Args>
// droppable_accumulator(Args const &args)
// : droppable_accumulator::base(args)
// {
// }
//};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// with_error.hpp
//
// Copyright 2005 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_WITH_ERROR_HPP_EAN_01_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_WITH_ERROR_HPP_EAN_01_11_2005
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/mpl/vector.hpp>
#include <boost/mpl/transform_view.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/error_of.hpp>
namespace boost { namespace accumulators
{
namespace detail
{
template<typename Feature>
struct error_of_tag
{
typedef tag::error_of<Feature> type;
};
}
///////////////////////////////////////////////////////////////////////////////
// with_error
//
template<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature)>
struct with_error
: mpl::transform_view<
mpl::vector<BOOST_PP_ENUM_PARAMS(BOOST_ACCUMULATORS_MAX_FEATURES, Feature)>
, detail::error_of_tag<mpl::_1>
>
{
};
}} // namespace boost::accumulators
#endif

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///////////////////////////////////////////////////////////////////////////////
// statistics_fwd.hpp
//
// Copyright 2005 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_STATISTICS_FWD_HPP_EAN_23_11_2005
#define BOOST_ACCUMULATORS_STATISTICS_STATISTICS_FWD_HPP_EAN_23_11_2005
#include <boost/mpl/apply_fwd.hpp> // for mpl::na
#include <boost/mpl/print.hpp>
#include <boost/preprocessor/repetition/enum_params_with_a_default.hpp>
#include <boost/accumulators/accumulators_fwd.hpp>
#include <boost/accumulators/framework/depends_on.hpp>
#include <boost/accumulators/framework/extractor.hpp>
namespace boost { namespace accumulators
{
///////////////////////////////////////////////////////////////////////////////
// base struct and base extractor for quantiles
namespace tag
{
struct quantile
: depends_on<>
{
typedef mpl::print<class ____MISSING_SPECIFIC_QUANTILE_FEATURE_IN_ACCUMULATOR_SET____ > impl;
};
}
namespace extract
{
extractor<tag::quantile> const quantile = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(quantile)
}
using extract::quantile;
///////////////////////////////////////////////////////////////////////////////
// base struct and base extractor for *coherent* tail means
namespace tag
{
struct tail_mean
: depends_on<>
{
typedef mpl::print<class ____MISSING_SPECIFIC_TAIL_MEAN_FEATURE_IN_ACCUMULATOR_SET____ > impl;
};
}
namespace extract
{
extractor<tag::tail_mean> const tail_mean = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_mean)
}
using extract::tail_mean;
namespace tag
{
///////////////////////////////////////////////////////////////////////////////
// Variates tags
struct weights;
struct covariate1;
struct covariate2;
///////////////////////////////////////////////////////////////////////////////
// Statistic tags
struct count;
template<typename VariateType, typename VariateTag>
struct covariance;
struct density;
template<typename Feature>
struct error_of;
struct extended_p_square;
struct extended_p_square_quantile;
struct extended_p_square_quantile_quadratic;
struct kurtosis;
struct max;
struct mean;
struct immediate_mean;
struct mean_of_weights;
struct immediate_mean_of_weights;
template<typename VariateType, typename VariateTag>
struct mean_of_variates;
template<typename VariateType, typename VariateTag>
struct immediate_mean_of_variates;
struct median;
struct with_density_median;
struct with_p_square_cumulative_distribution_median;
struct min;
template<int N>
struct moment;
template<typename LeftRight>
struct peaks_over_threshold;
template<typename LeftRight>
struct peaks_over_threshold_prob;
template<typename LeftRight>
struct pot_tail_mean;
template<typename LeftRight>
struct pot_tail_mean_prob;
template<typename LeftRight>
struct pot_quantile;
template<typename LeftRight>
struct pot_quantile_prob;
struct p_square_cumulative_distribution;
struct p_square_quantile;
struct p_square_quantile_for_median;
struct skewness;
struct sum;
struct sum_of_weights;
template<typename VariateType, typename VariateTag>
struct sum_of_variates;
struct sum_kahan;
struct sum_of_weights_kahan;
template<typename VariateType, typename VariateTag>
struct sum_of_variates_kahan;
template<typename LeftRight>
struct tail;
template<typename LeftRight>
struct coherent_tail_mean;
template<typename LeftRight>
struct non_coherent_tail_mean;
template<typename LeftRight>
struct tail_quantile;
template<typename VariateType, typename VariateTag, typename LeftRight>
struct tail_variate;
template<typename LeftRight>
struct tail_weights;
template<typename VariateType, typename VariateTag, typename LeftRight>
struct right_tail_variate;
template<typename VariateType, typename VariateTag, typename LeftRight>
struct left_tail_variate;
template<typename LeftRight, typename VariateType, typename VariateTag>
struct tail_variate_means;
template<typename LeftRight, typename VariateType, typename VariateTag>
struct absolute_tail_variate_means;
template<typename LeftRight, typename VariateType, typename VariateTag>
struct relative_tail_variate_means;
struct lazy_variance;
struct variance;
template<typename VariateType, typename VariateTag>
struct weighted_covariance;
struct weighted_density;
struct weighted_kurtosis;
struct weighted_mean;
struct immediate_weighted_mean;
template<typename VariateType, typename VariateTag>
struct weighted_mean_of_variates;
template<typename VariateType, typename VariateTag>
struct immediate_weighted_mean_of_variates;
struct weighted_median;
struct with_density_weighted_median;
struct with_p_square_cumulative_distribution_weighted_median;
struct weighted_extended_p_square;
struct weighted_extended_p_square_quantile;
struct weighted_extended_p_square_quantile_quadratic;
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;
struct weighted_p_square_cumulative_distribution;
struct weighted_p_square_quantile;
struct weighted_p_square_quantile_for_median;
struct weighted_skewness;
template<typename LeftRight>
struct weighted_tail_quantile;
template<typename LeftRight>
struct non_coherent_weighted_tail_mean;
template<typename LeftRight>
struct weighted_tail_quantile;
template<typename LeftRight, typename VariateType, typename VariateTag>
struct weighted_tail_variate_means;
template<typename LeftRight, typename VariateType, typename VariateTag>
struct absolute_weighted_tail_variate_means;
template<typename LeftRight, typename VariateType, typename VariateTag>
struct relative_weighted_tail_variate_means;
struct lazy_weighted_variance;
struct weighted_variance;
struct weighted_sum;
template<typename VariateType, typename VariateTag>
struct weighted_sum_of_variates;
struct rolling_window_plus1;
struct rolling_window;
struct rolling_sum;
struct rolling_count;
struct rolling_mean;
} // namespace tag
namespace impl
{
///////////////////////////////////////////////////////////////////////////////
// Statistics impls
struct count_impl;
template<typename Sample, typename VariateType, typename VariateTag>
struct covariance_impl;
template<typename Sample>
struct density_impl;
template<typename Sample, typename Feature>
struct error_of_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>
struct kurtosis_impl;
template<typename Sample>
struct max_impl;
template<typename Sample>
struct median_impl;
template<typename Sample>
struct with_density_median_impl;
template<typename Sample>
struct with_p_square_cumulative_distribution_median_impl;
template<typename Sample>
struct min_impl;
template<typename Sample, typename SumFeature = tag::sum>
struct mean_impl;
template<typename Sample, typename Tag = tag::sample>
struct immediate_mean_impl;
template<typename N, typename Sample>
struct moment_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 p_square_cumulative_distribution_impl;
template<typename Sample, typename Impl>
struct p_square_quantile_impl;
template<typename Sample>
struct skewness_impl;
template<typename Sample, typename Tag = tag::sample>
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 coherent_tail_mean_impl;
template<typename Sample, typename LeftRight>
struct non_coherent_tail_mean_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>
struct lazy_variance_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_kurtosis_impl;
template<typename Sample>
struct weighted_median_impl;
template<typename Sample>
struct with_density_weighted_median_impl;
template<typename Sample, typename Weight>
struct with_p_square_cumulative_distribution_weighted_median_impl;
template<typename Sample, typename Weight, typename Tag>
struct weighted_mean_impl;
template<typename Sample, typename Weight, typename Tag>
struct immediate_weighted_mean_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 with_p_square_cumulative_distribution_weighted_median_impl;
template<typename Sample, typename Weight>
struct weighted_extended_p_square_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>
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 non_coherent_weighted_tail_mean_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>
struct lazy_weighted_variance_impl;
template<typename Sample, typename Weight, typename MeanFeature, typename Tag>
struct weighted_variance_impl;
template<typename Sample>
struct rolling_window_plus1_impl;
template<typename Sample>
struct rolling_window_impl;
template<typename Sample>
struct rolling_sum_impl;
template<typename Sample>
struct rolling_count_impl;
template<typename Sample>
struct rolling_mean_impl;
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// stats
// A more descriptive name for an MPL sequence of statistics.
template<BOOST_PP_ENUM_PARAMS_WITH_A_DEFAULT(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature, mpl::na)>
struct stats;
template<BOOST_PP_ENUM_PARAMS_WITH_A_DEFAULT(BOOST_ACCUMULATORS_MAX_FEATURES, typename Feature, mpl::na)>
struct with_error;
// modifiers for the mean and variance stats
struct lazy {};
struct immediate {};
// modifiers for the variance stat
// struct fast {};
// struct accurate {};
// modifiers for order
struct right {};
struct left {};
// typedef right default_order_tag_type;
// modifiers for the tail_variate_means stat
struct absolute {};
struct relative {};
// modifiers for median and weighted_median stats
struct with_density {};
struct with_p_square_cumulative_distribution {};
struct with_p_square_quantile {};
// modifiers for peaks_over_threshold stat
struct with_threshold_value {};
struct with_threshold_probability {};
// modifiers for extended_p_square_quantile and weighted_extended_p_square_quantile stats
struct weighted {};
struct unweighted {};
struct linear {};
struct quadratic {};
// modifiers for p_square_quantile
struct regular {};
struct for_median {};
// modifier for sum_kahan, sum_of_weights_kahan, sum_of_variates_kahan, weighted_sum_kahan
struct kahan {};
}} // namespace boost::accumulators
#endif

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/*
Copyright (c) Marshall Clow 2014.
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)
Revision history:
2 Dec 2014 mtc First version; power
*/
/// \file algorithm.hpp
/// \brief Misc Algorithms
/// \author Marshall Clow
///
#ifndef BOOST_ALGORITHM_HPP
#define BOOST_ALGORITHM_HPP
#include <functional> // for plus and multiplies
#include <boost/utility/enable_if.hpp> // for boost::disable_if
#include <boost/type_traits/is_integral.hpp>
namespace boost { namespace algorithm {
template <typename T>
T identity_operation ( std::multiplies<T> ) { return T(1); }
template <typename T>
T identity_operation ( std::plus<T> ) { return T(0); }
/// \fn power ( T x, Integer n )
/// \return the value "x" raised to the power "n"
///
/// \param x The value to be exponentiated
/// \param n The exponent (must be >= 0)
///
// \remark Taken from Knuth, The Art of Computer Programming, Volume 2:
// Seminumerical Algorithms, Section 4.6.3
template <typename T, typename Integer>
typename boost::enable_if<boost::is_integral<Integer>, T>::type
power (T x, Integer n) {
T y = 1; // Should be "T y{1};"
if (n == 0) return y;
while (true) {
if (n % 2 == 1) {
y = x * y;
if (n == 1)
return y;
}
n = n / 2;
x = x * x;
}
return y;
}
/// \fn power ( T x, Integer n, Operation op )
/// \return the value "x" raised to the power "n"
/// using the operation "op".
///
/// \param x The value to be exponentiated
/// \param n The exponent (must be >= 0)
/// \param op The operation used
///
// \remark Taken from Knuth, The Art of Computer Programming, Volume 2:
// Seminumerical Algorithms, Section 4.6.3
template <typename T, typename Integer, typename Operation>
typename boost::enable_if<boost::is_integral<Integer>, T>::type
power (T x, Integer n, Operation op) {
T y = identity_operation(op);
if (n == 0) return y;
while (true) {
if (n % 2 == 1) {
y = op(x, y);
if (n == 1)
return y;
}
n = n / 2;
x = op(x, x);
}
return y;
}
}}
#endif // BOOST_ALGORITHM_HPP

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/*
Copyright (c) Marshall Clow 2008-2012.
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)
Revision history:
27 June 2009 mtc First version
23 Oct 2010 mtc Added predicate version
*/
/// \file clamp.hpp
/// \brief Clamp algorithm
/// \author Marshall Clow
///
/// Suggested by olafvdspek in https://svn.boost.org/trac/boost/ticket/3215
#ifndef BOOST_ALGORITHM_CLAMP_HPP
#define BOOST_ALGORITHM_CLAMP_HPP
#include <functional> // For std::less
#include <iterator> // For std::iterator_traits
#include <cassert>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/mpl/identity.hpp> // for identity
#include <boost/utility/enable_if.hpp> // for boost::disable_if
namespace boost { namespace algorithm {
/// \fn clamp ( T const& val,
/// typename boost::mpl::identity<T>::type const & lo,
/// typename boost::mpl::identity<T>::type const & hi, Pred p )
/// \return the value "val" brought into the range [ lo, hi ]
/// using the comparison predicate p.
/// If p ( val, lo ) return lo.
/// If p ( hi, val ) return hi.
/// Otherwise, return the original value.
///
/// \param val The value to be clamped
/// \param lo The lower bound of the range to be clamped to
/// \param hi The upper bound of the range to be clamped to
/// \param p A predicate to use to compare the values.
/// p ( a, b ) returns a boolean.
///
template<typename T, typename Pred>
T const & clamp ( T const& val,
typename boost::mpl::identity<T>::type const & lo,
typename boost::mpl::identity<T>::type const & hi, Pred p )
{
// assert ( !p ( hi, lo )); // Can't assert p ( lo, hi ) b/c they might be equal
return p ( val, lo ) ? lo : p ( hi, val ) ? hi : val;
}
/// \fn clamp ( T const& val,
/// typename boost::mpl::identity<T>::type const & lo,
/// typename boost::mpl::identity<T>::type const & hi )
/// \return the value "val" brought into the range [ lo, hi ].
/// If the value is less than lo, return lo.
/// If the value is greater than "hi", return hi.
/// Otherwise, return the original value.
///
/// \param val The value to be clamped
/// \param lo The lower bound of the range to be clamped to
/// \param hi The upper bound of the range to be clamped to
///
template<typename T>
T const& clamp ( const T& val,
typename boost::mpl::identity<T>::type const & lo,
typename boost::mpl::identity<T>::type const & hi )
{
return (clamp) ( val, lo, hi, std::less<T>());
}
/// \fn clamp_range ( InputIterator first, InputIterator last, OutputIterator out,
/// std::iterator_traits<InputIterator>::value_type const & lo,
/// std::iterator_traits<InputIterator>::value_type const & hi )
/// \return clamp the sequence of values [first, last) into [ lo, hi ]
///
/// \param first The start of the range of values
/// \param last One past the end of the range of input values
/// \param out An output iterator to write the clamped values into
/// \param lo The lower bound of the range to be clamped to
/// \param hi The upper bound of the range to be clamped to
///
template<typename InputIterator, typename OutputIterator>
OutputIterator clamp_range ( InputIterator first, InputIterator last, OutputIterator out,
typename std::iterator_traits<InputIterator>::value_type const & lo,
typename std::iterator_traits<InputIterator>::value_type const & hi )
{
// this could also be written with bind and std::transform
while ( first != last )
*out++ = clamp ( *first++, lo, hi );
return out;
}
/// \fn clamp_range ( const Range &r, OutputIterator out,
/// typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & lo,
/// typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & hi )
/// \return clamp the sequence of values [first, last) into [ lo, hi ]
///
/// \param r The range of values to be clamped
/// \param out An output iterator to write the clamped values into
/// \param lo The lower bound of the range to be clamped to
/// \param hi The upper bound of the range to be clamped to
///
template<typename Range, typename OutputIterator>
typename boost::disable_if_c<boost::is_same<Range, OutputIterator>::value, OutputIterator>::type
clamp_range ( const Range &r, OutputIterator out,
typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & lo,
typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & hi )
{
return clamp_range ( boost::begin ( r ), boost::end ( r ), out, lo, hi );
}
/// \fn clamp_range ( InputIterator first, InputIterator last, OutputIterator out,
/// std::iterator_traits<InputIterator>::value_type const & lo,
/// std::iterator_traits<InputIterator>::value_type const & hi, Pred p )
/// \return clamp the sequence of values [first, last) into [ lo, hi ]
/// using the comparison predicate p.
///
/// \param first The start of the range of values
/// \param last One past the end of the range of input values
/// \param out An output iterator to write the clamped values into
/// \param lo The lower bound of the range to be clamped to
/// \param hi The upper bound of the range to be clamped to
/// \param p A predicate to use to compare the values.
/// p ( a, b ) returns a boolean.
///
template<typename InputIterator, typename OutputIterator, typename Pred>
OutputIterator clamp_range ( InputIterator first, InputIterator last, OutputIterator out,
typename std::iterator_traits<InputIterator>::value_type const & lo,
typename std::iterator_traits<InputIterator>::value_type const & hi, Pred p )
{
// this could also be written with bind and std::transform
while ( first != last )
*out++ = clamp ( *first++, lo, hi, p );
return out;
}
/// \fn clamp_range ( const Range &r, OutputIterator out,
/// typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & lo,
/// typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & hi,
/// Pred p )
/// \return clamp the sequence of values [first, last) into [ lo, hi ]
/// using the comparison predicate p.
///
/// \param r The range of values to be clamped
/// \param out An output iterator to write the clamped values into
/// \param lo The lower bound of the range to be clamped to
/// \param hi The upper bound of the range to be clamped to
/// \param p A predicate to use to compare the values.
/// p ( a, b ) returns a boolean.
//
// Disable this template if the first two parameters are the same type;
// In that case, the user will get the two iterator version.
template<typename Range, typename OutputIterator, typename Pred>
typename boost::disable_if_c<boost::is_same<Range, OutputIterator>::value, OutputIterator>::type
clamp_range ( const Range &r, OutputIterator out,
typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & lo,
typename std::iterator_traits<typename boost::range_iterator<const Range>::type>::value_type const & hi,
Pred p )
{
return clamp_range ( boost::begin ( r ), boost::end ( r ), out, lo, hi, p );
}
}}
#endif // BOOST_ALGORITHM_CLAMP_HPP

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/*
Copyright (c) Marshall Clow 2008-2012.
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)
*/
/// \file all_of.hpp
/// \brief Test ranges to see if all elements match a value or predicate.
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_ALL_OF_HPP
#define BOOST_ALGORITHM_ALL_OF_HPP
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost { namespace algorithm {
/// \fn all_of ( InputIterator first, InputIterator last, Predicate p )
/// \return true if all elements in [first, last) satisfy the predicate 'p'
/// \note returns true on an empty range
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param p A predicate for testing the elements of the sequence
///
/// \note This function is part of the C++2011 standard library.
template<typename InputIterator, typename Predicate>
bool all_of ( InputIterator first, InputIterator last, Predicate p )
{
for ( ; first != last; ++first )
if ( !p(*first))
return false;
return true;
}
/// \fn all_of ( const Range &r, Predicate p )
/// \return true if all elements in the range satisfy the predicate 'p'
/// \note returns true on an empty range
///
/// \param r The input range
/// \param p A predicate for testing the elements of the range
///
template<typename Range, typename Predicate>
bool all_of ( const Range &r, Predicate p )
{
return boost::algorithm::all_of ( boost::begin (r), boost::end (r), p );
}
/// \fn all_of_equal ( InputIterator first, InputIterator last, const T &val )
/// \return true if all elements in [first, last) are equal to 'val'
/// \note returns true on an empty range
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param val A value to compare against
///
template<typename InputIterator, typename T>
bool all_of_equal ( InputIterator first, InputIterator last, const T &val )
{
for ( ; first != last; ++first )
if ( val != *first )
return false;
return true;
}
/// \fn all_of_equal ( const Range &r, const T &val )
/// \return true if all elements in the range are equal to 'val'
/// \note returns true on an empty range
///
/// \param r The input range
/// \param val A value to compare against
///
template<typename Range, typename T>
bool all_of_equal ( const Range &r, const T &val )
{
return boost::algorithm::all_of_equal ( boost::begin (r), boost::end (r), val );
}
}} // namespace boost and algorithm
#endif // BOOST_ALGORITHM_ALL_OF_HPP

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/*
Copyright (c) Marshall Clow 2008-2012.
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)
For more information, see http://www.boost.org
*/
/// \file
/// \brief Test ranges to see if any elements match a value or predicate.
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_ANY_OF_HPP
#define BOOST_ALGORITHM_ANY_OF_HPP
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost { namespace algorithm {
/// \fn any_of ( InputIterator first, InputIterator last, Predicate p )
/// \return true if any of the elements in [first, last) satisfy the predicate
/// \note returns false on an empty range
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param p A predicate for testing the elements of the sequence
///
template<typename InputIterator, typename Predicate>
bool any_of ( InputIterator first, InputIterator last, Predicate p )
{
for ( ; first != last; ++first )
if ( p(*first))
return true;
return false;
}
/// \fn any_of ( const Range &r, Predicate p )
/// \return true if any elements in the range satisfy the predicate 'p'
/// \note returns false on an empty range
///
/// \param r The input range
/// \param p A predicate for testing the elements of the range
///
template<typename Range, typename Predicate>
bool any_of ( const Range &r, Predicate p )
{
return boost::algorithm::any_of (boost::begin (r), boost::end (r), p);
}
/// \fn any_of_equal ( InputIterator first, InputIterator last, const V &val )
/// \return true if any of the elements in [first, last) are equal to 'val'
/// \note returns false on an empty range
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param val A value to compare against
///
template<typename InputIterator, typename V>
bool any_of_equal ( InputIterator first, InputIterator last, const V &val )
{
for ( ; first != last; ++first )
if ( val == *first )
return true;
return false;
}
/// \fn any_of_equal ( const Range &r, const V &val )
/// \return true if any of the elements in the range are equal to 'val'
/// \note returns false on an empty range
///
/// \param r The input range
/// \param val A value to compare against
///
template<typename Range, typename V>
bool any_of_equal ( const Range &r, const V &val )
{
return boost::algorithm::any_of_equal (boost::begin (r), boost::end (r), val);
}
}} // namespace boost and algorithm
#endif // BOOST_ALGORITHM_ANY_OF_HPP

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/*
Copyright (c) Marshall Clow 2008-2012.
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)
*/
/// \file copy_if.hpp
/// \brief Copy a subset of a sequence to a new sequence
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_COPY_IF_HPP
#define BOOST_ALGORITHM_COPY_IF_HPP
#include <utility> // for std::pair, std::make_pair
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost { namespace algorithm {
/// \fn copy_if ( InputIterator first, InputIterator last, OutputIterator result, Predicate p )
/// \brief Copies all the elements from the input range that satisfy the
/// predicate to the output range.
/// \return The updated output iterator
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param result An output iterator to write the results into
/// \param p A predicate for testing the elements of the range
/// \note This function is part of the C++2011 standard library.
template<typename InputIterator, typename OutputIterator, typename Predicate>
OutputIterator copy_if ( InputIterator first, InputIterator last, OutputIterator result, Predicate p )
{
for ( ; first != last; ++first )
if (p(*first))
*result++ = *first;
return result;
}
/// \fn copy_if ( const Range &r, OutputIterator result, Predicate p )
/// \brief Copies all the elements from the input range that satisfy the
/// predicate to the output range.
/// \return The updated output iterator
///
/// \param r The input range
/// \param result An output iterator to write the results into
/// \param p A predicate for testing the elements of the range
///
template<typename Range, typename OutputIterator, typename Predicate>
OutputIterator copy_if ( const Range &r, OutputIterator result, Predicate p )
{
return boost::algorithm::copy_if (boost::begin (r), boost::end(r), result, p);
}
/// \fn copy_while ( InputIterator first, InputIterator last, OutputIterator result, Predicate p )
/// \brief Copies all the elements at the start of the input range that
/// satisfy the predicate to the output range.
/// \return The updated input and output iterators
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param result An output iterator to write the results into
/// \param p A predicate for testing the elements of the range
///
template<typename InputIterator, typename OutputIterator, typename Predicate>
std::pair<InputIterator, OutputIterator>
copy_while ( InputIterator first, InputIterator last, OutputIterator result, Predicate p )
{
for ( ; first != last && p(*first); ++first )
*result++ = *first;
return std::make_pair(first, result);
}
/// \fn copy_while ( const Range &r, OutputIterator result, Predicate p )
/// \brief Copies all the elements at the start of the input range that
/// satisfy the predicate to the output range.
/// \return The updated input and output iterators
///
/// \param r The input range
/// \param result An output iterator to write the results into
/// \param p A predicate for testing the elements of the range
///
template<typename Range, typename OutputIterator, typename Predicate>
std::pair<typename boost::range_iterator<const Range>::type, OutputIterator>
copy_while ( const Range &r, OutputIterator result, Predicate p )
{
return boost::algorithm::copy_while (boost::begin (r), boost::end(r), result, p);
}
/// \fn copy_until ( InputIterator first, InputIterator last, OutputIterator result, Predicate p )
/// \brief Copies all the elements at the start of the input range that do not
/// satisfy the predicate to the output range.
/// \return The updated output iterator
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param result An output iterator to write the results into
/// \param p A predicate for testing the elements of the range
///
template<typename InputIterator, typename OutputIterator, typename Predicate>
std::pair<InputIterator, OutputIterator>
copy_until ( InputIterator first, InputIterator last, OutputIterator result, Predicate p )
{
for ( ; first != last && !p(*first); ++first )
*result++ = *first;
return std::make_pair(first, result);
}
/// \fn copy_until ( const Range &r, OutputIterator result, Predicate p )
/// \brief Copies all the elements at the start of the input range that do not
/// satisfy the predicate to the output range.
/// \return The updated output iterator
///
/// \param r The input range
/// \param result An output iterator to write the results into
/// \param p A predicate for testing the elements of the range
///
template<typename Range, typename OutputIterator, typename Predicate>
std::pair<typename boost::range_iterator<const Range>::type, OutputIterator>
copy_until ( const Range &r, OutputIterator result, Predicate p )
{
return boost::algorithm::copy_until (boost::begin (r), boost::end(r), result, p);
}
}} // namespace boost and algorithm
#endif // BOOST_ALGORITHM_COPY_IF_HPP

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/*
Copyright (c) Marshall Clow 2011-2012.
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)
*/
/// \file copy_n.hpp
/// \brief Copy n items from one sequence to another
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_COPY_N_HPP
#define BOOST_ALGORITHM_COPY_N_HPP
namespace boost { namespace algorithm {
/// \fn copy_n ( InputIterator first, Size n, OutputIterator result )
/// \brief Copies exactly n (n > 0) elements from the range starting at first to
/// the range starting at result.
/// \return The updated output iterator
///
/// \param first The start of the input sequence
/// \param n The number of elements to copy
/// \param result An output iterator to write the results into
/// \note This function is part of the C++2011 standard library.
template <typename InputIterator, typename Size, typename OutputIterator>
OutputIterator copy_n ( InputIterator first, Size n, OutputIterator result )
{
for ( ; n > 0; --n, ++first, ++result )
*result = *first;
return result;
}
}} // namespace boost and algorithm
#endif // BOOST_ALGORITHM_COPY_IF_HPP

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/*
Copyright (c) Marshall Clow 2011-2012.
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)
*/
/// \file find_if_not.hpp
/// \brief Find the first element in a sequence that does not satisfy a predicate.
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_FIND_IF_NOT_HPP
#define BOOST_ALGORITHM_FIND_IF_NOT_HPP
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost { namespace algorithm {
/// \fn find_if_not(InputIterator first, InputIterator last, Predicate p)
/// \brief Finds the first element in the sequence that does not satisfy the predicate.
/// \return The iterator pointing to the desired element.
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param p A predicate for testing the elements of the range
/// \note This function is part of the C++2011 standard library.
template<typename InputIterator, typename Predicate>
InputIterator find_if_not ( InputIterator first, InputIterator last, Predicate p )
{
for ( ; first != last; ++first )
if ( !p(*first))
break;
return first;
}
/// \fn find_if_not ( const Range &r, Predicate p )
/// \brief Finds the first element in the sequence that does not satisfy the predicate.
/// \return The iterator pointing to the desired element.
///
/// \param r The input range
/// \param p A predicate for testing the elements of the range
///
template<typename Range, typename Predicate>
typename boost::range_iterator<const Range>::type find_if_not ( const Range &r, Predicate p )
{
return boost::algorithm::find_if_not (boost::begin (r), boost::end(r), p);
}
}}
#endif // BOOST_ALGORITHM_FIND_IF_NOT_HPP

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/*
Copyright (c) Marshall Clow 2008-2012.
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)
*/
/// \file iota.hpp
/// \brief Generate an increasing series
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_IOTA_HPP
#define BOOST_ALGORITHM_IOTA_HPP
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost { namespace algorithm {
/// \fn iota ( ForwardIterator first, ForwardIterator last, T value )
/// \brief Generates an increasing sequence of values, and stores them in [first, last)
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param value The initial value of the sequence to be generated
/// \note This function is part of the C++2011 standard library.
template <typename ForwardIterator, typename T>
void iota ( ForwardIterator first, ForwardIterator last, T value )
{
for ( ; first != last; ++first, ++value )
*first = value;
}
/// \fn iota ( Range &r, T value )
/// \brief Generates an increasing sequence of values, and stores them in the input Range.
///
/// \param r The input range
/// \param value The initial value of the sequence to be generated
///
template <typename Range, typename T>
void iota ( Range &r, T value )
{
boost::algorithm::iota (boost::begin(r), boost::end(r), value);
}
/// \fn iota_n ( OutputIterator out, T value, std::size_t n )
/// \brief Generates an increasing sequence of values, and stores them in the input Range.
///
/// \param out An output iterator to write the results into
/// \param value The initial value of the sequence to be generated
/// \param n The number of items to write
///
template <typename OutputIterator, typename T>
OutputIterator iota_n ( OutputIterator out, T value, std::size_t n )
{
for ( ; n > 0; --n, ++value )
*out++ = value;
return out;
}
}}
#endif // BOOST_ALGORITHM_IOTA_HPP

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/*
Copyright (c) Marshall Clow 2011-2012.
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)
*/
/// \file is_partitioned.hpp
/// \brief Tell if a sequence is partitioned
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_IS_PARTITIONED_HPP
#define BOOST_ALGORITHM_IS_PARTITIONED_HPP
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
namespace boost { namespace algorithm {
/// \fn is_partitioned ( InputIterator first, InputIterator last, UnaryPredicate p )
/// \brief Tests to see if a sequence is partitioned according to a predicate.
/// In other words, all the items in the sequence that satisfy the predicate are at the beginning of the sequence.
///
/// \param first The start of the input sequence
/// \param last One past the end of the input sequence
/// \param p The predicate to test the values with
/// \note This function is part of the C++2011 standard library.
template <typename InputIterator, typename UnaryPredicate>
bool is_partitioned ( InputIterator first, InputIterator last, UnaryPredicate p )
{
// Run through the part that satisfy the predicate
for ( ; first != last; ++first )
if ( !p (*first))
break;
// Now the part that does not satisfy the predicate
for ( ; first != last; ++first )
if ( p (*first))
return false;
return true;
}
/// \fn is_partitioned ( const Range &r, UnaryPredicate p )
/// \brief Tests to see if a sequence is partitioned according to a predicate.
/// In other words, all the items in the sequence that satisfy the predicate are at the beginning of the sequence.
///
/// \param r The input range
/// \param p The predicate to test the values with
///
template <typename Range, typename UnaryPredicate>
bool is_partitioned ( const Range &r, UnaryPredicate p )
{
return boost::algorithm::is_partitioned (boost::begin(r), boost::end(r), p);
}
}}
#endif // BOOST_ALGORITHM_IS_PARTITIONED_HPP

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/*
Copyright (c) Marshall Clow 2011-2012.
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)
*/
/// \file is_permutation.hpp
/// \brief Is a sequence a permutation of another sequence
/// \author Marshall Clow
#ifndef BOOST_ALGORITHM_IS_PERMUTATION11_HPP
#define BOOST_ALGORITHM_IS_PERMUTATION11_HPP
#include <algorithm> // for std::find_if, count_if, mismatch
#include <utility> // for std::pair
#include <functional> // for std::equal_to
#include <iterator>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/type_traits/is_same.hpp>
namespace boost { namespace algorithm {
/// \cond DOXYGEN_HIDE
namespace detail {
template <typename Predicate, typename Iterator>
struct value_predicate {
value_predicate ( Predicate p, Iterator it ) : p_ ( p ), it_ ( it ) {}
template <typename T1>
bool operator () ( const T1 &t1 ) const { return p_ ( *it_, t1 ); }
private:
Predicate p_;
Iterator it_;
};
// Preconditions:
// 1. The sequences are the same length
// 2. Any common elements on the front have been removed (not necessary for correctness, just for performance)
template< class ForwardIterator1, class ForwardIterator2, class BinaryPredicate >
bool is_permutation_inner ( ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
BinaryPredicate p ) {
// for each unique value in the sequence [first1,last1), count how many times
// it occurs, and make sure it occurs the same number of times in [first2, last2)
for ( ForwardIterator1 iter = first1; iter != last1; ++iter ) {
value_predicate<BinaryPredicate, ForwardIterator1> pred ( p, iter );
/* For each value we haven't seen yet... */
if ( std::find_if ( first1, iter, pred ) == iter ) {
std::size_t dest_count = std::count_if ( first2, last2, pred );
if ( dest_count == 0 || dest_count != (std::size_t) std::count_if ( iter, last1, pred ))
return false;
}
}
return true;
}
template< class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
bool is_permutation_tag ( ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
BinaryPredicate p,
std::forward_iterator_tag, std::forward_iterator_tag ) {
// Skip the common prefix (if any)
while ( first1 != last1 && first2 != last2 && p ( *first1, *first2 )) {
++first1;
++first2;
}
if ( first1 != last1 && first2 != last2 )
return boost::algorithm::detail::is_permutation_inner ( first1, last1, first2, last2,
std::equal_to<typename std::iterator_traits<ForwardIterator1>::value_type> ());
return first1 == last1 && first2 == last2;
}
template <class RandomAccessIterator1, class RandomAccessIterator2, class BinaryPredicate>
bool is_permutation_tag ( RandomAccessIterator1 first1, RandomAccessIterator1 last1,
RandomAccessIterator2 first2, RandomAccessIterator2 last2,
BinaryPredicate p,
std::random_access_iterator_tag, std::random_access_iterator_tag ) {
// Cheap check
if ( std::distance ( first1, last1 ) != std::distance ( first2, last2 ))
return false;
// Skip the common prefix (if any)
while ( first1 != last1 && first2 != last2 && p ( *first1, *first2 )) {
++first1;
++first2;
}
if ( first1 != last1 && first2 != last2 )
return is_permutation_inner (first1, last1, first2, last2, p);
return first1 == last1 && first2 == last2;
}
}
/// \endcond
/// \fn is_permutation ( ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 first2, BinaryPredicate p )
/// \brief Tests to see if the sequence [first,last) is a permutation of the sequence starting at first2
///
/// \param first1 The start of the input sequence
/// \param last1 One past the end of the input sequence
/// \param first2 The start of the second sequence
/// \param p The predicate to compare elements with
///
/// \note This function is part of the C++2011 standard library.
template< class ForwardIterator1, class ForwardIterator2, class BinaryPredicate >
bool is_permutation ( ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, BinaryPredicate p )
{
// Skip the common prefix (if any)
std::pair<ForwardIterator1, ForwardIterator2> eq = std::mismatch (first1, last1, first2, p);
first1 = eq.first;
first2 = eq.second;
if ( first1 != last1 ) {
// Create last2
ForwardIterator2 last2 = first2;
std::advance ( last2, std::distance (first1, last1));
return boost::algorithm::detail::is_permutation_inner ( first1, last1, first2, last2, p );
}
return true;
}
/// \fn is_permutation ( ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 first2 )
/// \brief Tests to see if the sequence [first,last) is a permutation of the sequence starting at first2
///
/// \param first1 The start of the input sequence
/// \param last2 One past the end of the input sequence
/// \param first2 The start of the second sequence
/// \note This function is part of the C++2011 standard library.
template< class ForwardIterator1, class ForwardIterator2 >
bool is_permutation ( ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2 )
{
// How should I deal with the idea that ForwardIterator1::value_type
// and ForwardIterator2::value_type could be different? Define my own comparison predicate?
// Skip the common prefix (if any)
std::pair<ForwardIterator1, ForwardIterator2> eq = std::mismatch (first1, last1, first2 );
first1 = eq.first;
first2 = eq.second;
if ( first1 != last1 ) {
// Create last2
ForwardIterator2 last2 = first2;
std::advance ( last2, std::distance (first1, last1));
return boost::algorithm::detail::is_permutation_inner ( first1, last1, first2, last2,
std::equal_to<typename std::iterator_traits<ForwardIterator1>::value_type> ());
}
return true;
}
/// \fn is_permutation ( const Range &r, ForwardIterator first2 )
/// \brief Tests to see if the sequence [first,last) is a permutation of the sequence starting at first2
///
/// \param r The input range
/// \param first2 The start of the second sequence
template <typename Range, typename ForwardIterator>
bool is_permutation ( const Range &r, ForwardIterator first2 )
{
return boost::algorithm::is_permutation (boost::begin (r), boost::end (r), first2 );
}
/// \fn is_permutation ( const Range &r, ForwardIterator first2, BinaryPredicate pred )
/// \brief Tests to see if the sequence [first,last) is a permutation of the sequence starting at first2
///
/// \param r The input range
/// \param first2 The start of the second sequence
/// \param pred The predicate to compare elements with
///
// Disable this template when the first two parameters are the same type
// That way the non-range version will be chosen.
template <typename Range, typename ForwardIterator, typename BinaryPredicate>
typename boost::disable_if_c<boost::is_same<Range, ForwardIterator>::value, bool>::type
is_permutation ( const Range &r, ForwardIterator first2, BinaryPredicate pred )
{
return boost::algorithm::is_permutation (boost::begin (r), boost::end (r), first2, pred );
}
}}
#endif // BOOST_ALGORITHM_IS_PERMUTATION11_HPP

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// Copyright (c) 2010 Nuovation System Designs, LLC
// Grant Erickson <gerickson@nuovations.com>
//
// Reworked somewhat by Marshall Clow; August 2010
//
// 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)
//
// See http://www.boost.org/ for latest version.
//
#ifndef BOOST_ALGORITHM_ORDERED_HPP
#define BOOST_ALGORITHM_ORDERED_HPP
#include <functional>
#include <iterator>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/mpl/identity.hpp>
namespace boost { namespace algorithm {
/// \fn is_sorted_until ( ForwardIterator first, ForwardIterator last, Pred p )
/// \return the point in the sequence [first, last) where the elements are unordered
/// (according to the comparison predicate 'p').
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
/// \param p A binary predicate that returns true if two elements are ordered.
///
template <typename ForwardIterator, typename Pred>
ForwardIterator is_sorted_until ( ForwardIterator first, ForwardIterator last, Pred p )
{
if ( first == last ) return last; // the empty sequence is ordered
ForwardIterator next = first;
while ( ++next != last )
{
if ( p ( *next, *first ))
return next;
first = next;
}
return last;
}
/// \fn is_sorted_until ( ForwardIterator first, ForwardIterator last )
/// \return the point in the sequence [first, last) where the elements are unordered
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
///
template <typename ForwardIterator>
ForwardIterator is_sorted_until ( ForwardIterator first, ForwardIterator last )
{
typedef typename std::iterator_traits<ForwardIterator>::value_type value_type;
return boost::algorithm::is_sorted_until ( first, last, std::less<value_type>());
}
/// \fn is_sorted ( ForwardIterator first, ForwardIterator last, Pred p )
/// \return whether or not the entire sequence is sorted
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
/// \param p A binary predicate that returns true if two elements are ordered.
///
template <typename ForwardIterator, typename Pred>
bool is_sorted ( ForwardIterator first, ForwardIterator last, Pred p )
{
return boost::algorithm::is_sorted_until (first, last, p) == last;
}
/// \fn is_sorted ( ForwardIterator first, ForwardIterator last )
/// \return whether or not the entire sequence is sorted
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
///
template <typename ForwardIterator>
bool is_sorted ( ForwardIterator first, ForwardIterator last )
{
return boost::algorithm::is_sorted_until (first, last) == last;
}
///
/// -- Range based versions of the C++11 functions
///
/// \fn is_sorted_until ( const R &range, Pred p )
/// \return the point in the range R where the elements are unordered
/// (according to the comparison predicate 'p').
///
/// \param range The range to be tested.
/// \param p A binary predicate that returns true if two elements are ordered.
///
template <typename R, typename Pred>
typename boost::lazy_disable_if_c<
boost::is_same<R, Pred>::value,
typename boost::range_iterator<const R>
>::type is_sorted_until ( const R &range, Pred p )
{
return boost::algorithm::is_sorted_until ( boost::begin ( range ), boost::end ( range ), p );
}
/// \fn is_sorted_until ( const R &range )
/// \return the point in the range R where the elements are unordered
///
/// \param range The range to be tested.
///
template <typename R>
typename boost::range_iterator<const R>::type is_sorted_until ( const R &range )
{
return boost::algorithm::is_sorted_until ( boost::begin ( range ), boost::end ( range ));
}
/// \fn is_sorted ( const R &range, Pred p )
/// \return whether or not the entire range R is sorted
/// (according to the comparison predicate 'p').
///
/// \param range The range to be tested.
/// \param p A binary predicate that returns true if two elements are ordered.
///
template <typename R, typename Pred>
typename boost::lazy_disable_if_c< boost::is_same<R, Pred>::value, boost::mpl::identity<bool> >::type
is_sorted ( const R &range, Pred p )
{
return boost::algorithm::is_sorted ( boost::begin ( range ), boost::end ( range ), p );
}
/// \fn is_sorted ( const R &range )
/// \return whether or not the entire range R is sorted
///
/// \param range The range to be tested.
///
template <typename R>
bool is_sorted ( const R &range )
{
return boost::algorithm::is_sorted ( boost::begin ( range ), boost::end ( range ));
}
///
/// -- Range based versions of the C++11 functions
///
/// \fn is_increasing ( ForwardIterator first, ForwardIterator last )
/// \return true if the entire sequence is increasing; i.e, each item is greater than or
/// equal to the previous one.
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
///
/// \note This function will return true for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_strictly_increasing instead.
template <typename ForwardIterator>
bool is_increasing ( ForwardIterator first, ForwardIterator last )
{
typedef typename std::iterator_traits<ForwardIterator>::value_type value_type;
return boost::algorithm::is_sorted (first, last, std::less<value_type>());
}
/// \fn is_increasing ( const R &range )
/// \return true if the entire sequence is increasing; i.e, each item is greater than or
/// equal to the previous one.
///
/// \param range The range to be tested.
///
/// \note This function will return true for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_strictly_increasing instead.
template <typename R>
bool is_increasing ( const R &range )
{
return is_increasing ( boost::begin ( range ), boost::end ( range ));
}
/// \fn is_decreasing ( ForwardIterator first, ForwardIterator last )
/// \return true if the entire sequence is decreasing; i.e, each item is less than
/// or equal to the previous one.
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
///
/// \note This function will return true for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_strictly_decreasing instead.
template <typename ForwardIterator>
bool is_decreasing ( ForwardIterator first, ForwardIterator last )
{
typedef typename std::iterator_traits<ForwardIterator>::value_type value_type;
return boost::algorithm::is_sorted (first, last, std::greater<value_type>());
}
/// \fn is_decreasing ( const R &range )
/// \return true if the entire sequence is decreasing; i.e, each item is less than
/// or equal to the previous one.
///
/// \param range The range to be tested.
///
/// \note This function will return true for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_strictly_decreasing instead.
template <typename R>
bool is_decreasing ( const R &range )
{
return is_decreasing ( boost::begin ( range ), boost::end ( range ));
}
/// \fn is_strictly_increasing ( ForwardIterator first, ForwardIterator last )
/// \return true if the entire sequence is strictly increasing; i.e, each item is greater
/// than the previous one
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
///
/// \note This function will return false for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_increasing instead.
template <typename ForwardIterator>
bool is_strictly_increasing ( ForwardIterator first, ForwardIterator last )
{
typedef typename std::iterator_traits<ForwardIterator>::value_type value_type;
return boost::algorithm::is_sorted (first, last, std::less_equal<value_type>());
}
/// \fn is_strictly_increasing ( const R &range )
/// \return true if the entire sequence is strictly increasing; i.e, each item is greater
/// than the previous one
///
/// \param range The range to be tested.
///
/// \note This function will return false for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_increasing instead.
template <typename R>
bool is_strictly_increasing ( const R &range )
{
return is_strictly_increasing ( boost::begin ( range ), boost::end ( range ));
}
/// \fn is_strictly_decreasing ( ForwardIterator first, ForwardIterator last )
/// \return true if the entire sequence is strictly decreasing; i.e, each item is less than
/// the previous one
///
/// \param first The start of the sequence to be tested.
/// \param last One past the end of the sequence
///
/// \note This function will return false for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_decreasing instead.
template <typename ForwardIterator>
bool is_strictly_decreasing ( ForwardIterator first, ForwardIterator last )
{
typedef typename std::iterator_traits<ForwardIterator>::value_type value_type;
return boost::algorithm::is_sorted (first, last, std::greater_equal<value_type>());
}
/// \fn is_strictly_decreasing ( const R &range )
/// \return true if the entire sequence is strictly decreasing; i.e, each item is less than
/// the previous one
///
/// \param range The range to be tested.
///
/// \note This function will return false for sequences that contain items that compare
/// equal. If that is not what you intended, you should use is_decreasing instead.
template <typename R>
bool is_strictly_decreasing ( const R &range )
{
return is_strictly_decreasing ( boost::begin ( range ), boost::end ( range ));
}
}} // namespace boost
#endif // BOOST_ALGORITHM_ORDERED_HPP

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