/////////////////////////////////////////////////////////////////////////////// | |
// 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/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::average<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::average(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::average(h2 - h1, p2 - p1); | |
float_type hp10 = numeric::average(h1 - h0, p1 - p0); | |
float_type p21 = numeric::average(p2 * p2 - p1 * p1, p2 - p1); | |
float_type p10 = numeric::average(p1 * p1 - p0 * p0, p1 - p0); | |
float_type a = numeric::average(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 |