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* Copyright (c) 2016, Johan Mabille, Sylvain Corlay and Wolf Vollprecht *
* *
* Distributed under the terms of the BSD 3-Clause License. *
* *
* The full license is in the file LICENSE, distributed with this software. *
****************************************************************************/
#ifndef XREDUCER_HPP
#define XREDUCER_HPP
#include <algorithm>
#include <cstddef>
#include <initializer_list>
#include <iterator>
#include <stdexcept>
#include <type_traits>
#include <utility>
#ifdef X_OLD_CLANG
#include <vector>
#endif
#include "xbuilder.hpp"
#include "xexpression.hpp"
#include "xgenerator.hpp"
#include "xiterable.hpp"
#include "xreducer.hpp"
#include "xutils.hpp"
namespace xt
{
/**********
* reduce *
**********/
template <class F, class E, class X>
auto reduce(F&& f, E&& e, X&& axes) noexcept;
template <class F, class E>
auto reduce(F&& f, E&& e) noexcept;
#ifdef X_OLD_CLANG
template <class F, class E, class I>
auto reduce(F&& f, E&& e, std::initializer_list<I> axes) noexcept;
#else
template <class F, class E, class I, std::size_t N>
auto reduce(F&& f, E&& e, const I (&axes)[N]) noexcept;
#endif
/*************
* xreducer *
*************/
template <class ST, class X>
struct xreducer_shape_type;
template <class F, class CT, class X>
class xreducer;
template <class F, class CT, class X>
class xreducer_stepper;
template <class F, class CT, class X>
struct xiterable_inner_types<xreducer<F, CT, X>>
{
using xexpression_type = std::decay_t<CT>;
using inner_shape_type = typename xreducer_shape_type<typename xexpression_type::shape_type, X>::type;
using const_stepper = xreducer_stepper<F, CT, X>;
using stepper = const_stepper;
using const_iterator = xiterator<const_stepper, inner_shape_type*, DEFAULT_LAYOUT>;
using iterator = const_iterator;
using const_reverse_iterator = std::reverse_iterator<const_iterator>;
using reverse_iterator = std::reverse_iterator<iterator>;
};
/**
* @class xreducer
* @brief Reducing function operating over specified axes.
*
* The xreducer class implements an \ref xexpression applying
* a reducing function to an \ref xexpression over the specified
* axes.
*
* @tparam F the function type
* @tparam CT the closure type of the \ref xexpression to reduce
* @tparam X the list of axes
*
* @sa reduce
*/
template <class F, class CT, class X>
class xreducer : public xexpression<xreducer<F, CT, X>>,
public xexpression_const_iterable<xreducer<F, CT, X>>
{
public:
using self_type = xreducer<F, CT, X>;
using functor_type = typename std::remove_reference<F>::type;
using xexpression_type = std::decay_t<CT>;
using axes_type = X;
using value_type = typename xexpression_type::value_type;
using reference = value_type;
using const_reference = value_type;
using pointer = value_type*;
using const_pointer = const value_type*;
using size_type = typename xexpression_type::size_type;
using difference_type = typename xexpression_type::difference_type;
using iterable_base = xexpression_const_iterable<self_type>;
using inner_shape_type = typename iterable_base::inner_shape_type;
using shape_type = inner_shape_type;
using stepper = typename iterable_base::stepper;
using const_stepper = typename iterable_base::const_stepper;
static constexpr layout_type static_layout = layout_type::dynamic;
static constexpr bool contiguous_layout = false;
template <class Func, class CTA, class AX>
xreducer(Func&& func, CTA&& e, AX&& axes);
size_type size() const noexcept;
size_type dimension() const noexcept;
const inner_shape_type& shape() const noexcept;
layout_type layout() const noexcept;
template <class... Args>
const_reference operator()(Args... args) const;
const_reference operator[](const xindex& index) const;
const_reference operator[](size_type i) const;
template <class It>
const_reference element(It first, It last) const;
template <class S>
bool broadcast_shape(S& shape) const;
template <class S>
bool is_trivial_broadcast(const S& strides) const noexcept;
template <class S>
const_stepper stepper_begin(const S& shape) const noexcept;
template <class S>
const_stepper stepper_end(const S& shape, layout_type) const noexcept;
private:
CT m_e;
functor_type m_f;
axes_type m_axes;
inner_shape_type m_shape;
shape_type m_dim_mapping;
friend class xreducer_stepper<F, CT, X>;
};
/*************************
* reduce implementation *
*************************/
/**
* @brief Returns an \ref xexpression applying the speficied reducing
* function to an expresssion over the given axes.
*
* @param f the reducing function to apply.
* @param e the \ref xexpression to reduce.
* @param axes the list of axes.
*
* The returned expression either hold a const reference to \p e or a copy
* depending on whether \p e is an lvalue or an rvalue.
*/
template <class F, class E, class X>
inline auto reduce(F&& f, E&& e, X&& axes) noexcept
{
using reducer_type = xreducer<F, const_xclosure_t<E>, const_closure_t<X>>;
return reducer_type(std::forward<F>(f), std::forward<E>(e), std::forward<X>(axes));
}
template <class F, class E>
inline auto reduce(F&& f, E&& e) noexcept
{
auto ar = arange(e.dimension());
using AR = decltype(ar);
using reducer_type = xreducer<F, const_xclosure_t<E>, AR>;
return reducer_type(std::forward<F>(f), std::forward<E>(e), std::move(ar));
}
#ifdef X_OLD_CLANG
template <class F, class E, class I>
inline auto reduce(F&& f, E&& e, std::initializer_list<I> axes) noexcept
{
using axes_type = std::vector<typename std::decay_t<E>::size_type>;
using reducer_type = xreducer<F, const_xclosure_t<E>, axes_type>;
return reducer_type(std::forward<F>(f), std::forward<E>(e), forward_sequence<axes_type>(axes));
}
#else
template <class F, class E, class I, std::size_t N>
inline auto reduce(F&& f, E&& e, const I (&axes)[N]) noexcept
{
using axes_type = std::array<typename std::decay_t<E>::size_type, N>;
using reducer_type = xreducer<F, const_xclosure_t<E>, axes_type>;
return reducer_type(std::forward<F>(f), std::forward<E>(e), forward_sequence<axes_type>(axes));
}
#endif
/********************
* xreducer_stepper *
********************/
template <class F, class CT, class X>
class xreducer_stepper
{
public:
using self_type = xreducer_stepper<F, CT, X>;
using xreducer_type = xreducer<F, CT, X>;
using value_type = typename xreducer_type::value_type;
using reference = typename xreducer_type::value_type;
using pointer = typename xreducer_type::const_pointer;
using size_type = typename xreducer_type::size_type;
using difference_type = typename xreducer_type::difference_type;
using xexpression_type = typename xreducer_type::xexpression_type;
using substepper_type = typename xexpression_type::const_stepper;
using shape_type = typename xreducer_type::shape_type;
xreducer_stepper(const xreducer_type& red, size_type offset, bool end = false, layout_type l = layout_type::row_major);
reference operator*() const;
void step(size_type dim, size_type n = 1);
void step_back(size_type dim, size_type n = 1);
void reset(size_type dim);
void reset_back(size_type dim);
void to_begin();
void to_end(layout_type l);
bool equal(const self_type& rhs) const;
private:
reference aggregate(size_type dim) const;
substepper_type get_substepper_begin() const;
size_type get_dim(size_type dim) const noexcept;
size_type shape(size_type i) const noexcept;
size_type axis(size_type i) const noexcept;
const xreducer_type& m_reducer;
size_type m_offset;
mutable substepper_type m_stepper;
};
template <class F, class CT, class X>
bool operator==(const xreducer_stepper<F, CT, X>& lhs,
const xreducer_stepper<F, CT, X>& rhs);
template <class F, class CT, class X>
bool operator!=(const xreducer_stepper<F, CT, X>& lhs,
const xreducer_stepper<F, CT, X>& rhs);
/******************
* xreducer utils *
******************/
// meta-function returning the shape type for an xreducer
template <class ST, class X>
struct xreducer_shape_type
{
using type = promote_shape_t<ST, std::decay_t<X>>;
};
template <class I1, std::size_t N1, class I2, std::size_t N2>
struct xreducer_shape_type<std::array<I1, N1>, std::array<I2, N2>>
{
using type = std::array<I2, N1 - N2>;
};
namespace detail
{
template <class InputIt, class ExcludeIt, class OutputIt>
inline void excluding_copy(InputIt first, InputIt last,
ExcludeIt e_first, ExcludeIt e_last,
OutputIt d_first, OutputIt map_first)
{
using difference_type = typename std::iterator_traits<InputIt>::difference_type;
InputIt iter = first;
while (iter != last && e_first != e_last)
{
auto diff = std::distance(first, iter);
if (diff != difference_type(*e_first))
{
*d_first++ = *iter++;
*map_first++ = diff;
}
else
{
++iter;
++e_first;
}
}
auto diff = std::distance(first, iter);
auto end = std::distance(iter, last);
std::iota(map_first, map_first + end, diff);
std::copy(iter, last, d_first);
}
}
/***************************
* xreducer implementation *
***************************/
/**
* @name Constructor
*/
//@{
/**
* Constructs an xreducer expression applying the specified
* function to the given expression over the given axes.
*
* @param func the function to apply
* @param e the expression to reduce
* @param axes the axes along which the reduction is performed
*/
template <class F, class CT, class X>
template <class Func, class CTA, class AX>
inline xreducer<F, CT, X>::xreducer(Func&& func, CTA&& e, AX&& axes)
: m_e(std::forward<CTA>(e)), m_f(std::forward<Func>(func)), m_axes(std::forward<AX>(axes)),
m_shape(make_sequence<shape_type>(m_e.dimension() - m_axes.size(), 0)),
m_dim_mapping(make_sequence<shape_type>(m_e.dimension() - m_axes.size(), 0))
{
if (!std::is_sorted(m_axes.cbegin(), m_axes.cend()))
{
throw std::runtime_error("Reducing axes should be sorted");
}
detail::excluding_copy(m_e.shape().begin(), m_e.shape().end(),
m_axes.begin(), m_axes.end(),
m_shape.begin(), m_dim_mapping.begin());
}
//@}
/**
* @name Size and shape
*/
/**
* Returns the size of the expression.
*/
template <class F, class CT, class X>
inline auto xreducer<F, CT, X>::size() const noexcept -> size_type
{
return compute_size(shape());
}
/**
* Returns the number of dimensions of the expression.
*/
template <class F, class CT, class X>
inline auto xreducer<F, CT, X>::dimension() const noexcept -> size_type
{
return m_shape.size();
}
/**
* Returns the shape of the expression.
*/
template <class F, class CT, class X>
inline auto xreducer<F, CT, X>::shape() const noexcept -> const inner_shape_type&
{
return m_shape;
}
/**
* Returns the shape of the expression.
*/
template <class F, class CT, class X>
inline layout_type xreducer<F, CT, X>::layout() const noexcept
{
return static_layout;
}
//@}
/**
* @name Data
*/
/**
* Returns a constant reference to the element at the specified position in the reducer.
* @param args a list of indices specifying the position in the reducer. Indices
* must be unsigned integers, the number of indices should be equal or greater than
* the number of dimensions of the reducer.
*/
template <class F, class CT, class X>
template <class... Args>
inline auto xreducer<F, CT, X>::operator()(Args... args) const -> const_reference
{
std::array<std::size_t, sizeof...(Args)> arg_array = {{static_cast<std::size_t>(args)...}};
return element(arg_array.cbegin(), arg_array.cend());
}
/**
* Returns a constant reference to the element at the specified position in the reducer.
* @param index a sequence of indices specifying the position in the reducer. Indices
* must be unsigned integers, the number of indices in the sequence should be equal or greater
* than the number of dimensions of the reducer.
*/
template <class F, class CT, class X>
inline auto xreducer<F, CT, X>::operator[](const xindex& index) const -> const_reference
{
return element(index.cbegin(), index.cend());
}
template <class F, class CT, class X>
inline auto xreducer<F, CT, X>::operator[](size_type i) const -> const_reference
{
return operator()(i);
}
/**
* Returns a constant reference to the element at the specified position in the reducer.
* @param first iterator starting the sequence of indices
* @param last iterator ending the sequence of indices
* The number of indices in the sequence should be equal to or greater
* than the number of dimensions of the reducer.
*/
template <class F, class CT, class X>
template <class It>
inline auto xreducer<F, CT, X>::element(It first, It last) const -> const_reference
{
auto stepper = const_stepper(*this, 0);
size_type dim = 0;
while (first != last)
{
stepper.step(dim++, *first++);
}
return *stepper;
}
//@}
/**
* @name Broadcasting
*/
//@{
/**
* Broadcast the shape of the reducer to the specified parameter.
* @param shape the result shape
* @return a boolean indicating whether the broadcasting is trivial
*/
template <class F, class CT, class X>
template <class S>
inline bool xreducer<F, CT, X>::broadcast_shape(S& shape) const
{
return xt::broadcast_shape(m_shape, shape);
}
/**
* Compares the specified strides with those of the container to see whether
* the broadcasting is trivial.
* @return a boolean indicating whether the broadcasting is trivial
*/
template <class F, class CT, class X>
template <class S>
inline bool xreducer<F, CT, X>::is_trivial_broadcast(const S& /*strides*/) const noexcept
{
return false;
}
//@}
template <class F, class CT, class X>
template <class S>
inline auto xreducer<F, CT, X>::stepper_begin(const S& shape) const noexcept -> const_stepper
{
size_type offset = shape.size() - dimension();
return const_stepper(*this, offset);
}
template <class F, class CT, class X>
template <class S>
inline auto xreducer<F, CT, X>::stepper_end(const S& shape, layout_type l) const noexcept -> const_stepper
{
size_type offset = shape.size() - dimension();
return const_stepper(*this, offset, true, l);
}
/***********************************
* xreducer_stepper implementation *
***********************************/
template <class F, class CT, class X>
inline xreducer_stepper<F, CT, X>::xreducer_stepper(const xreducer_type& red, size_type offset, bool end, layout_type l)
: m_reducer(red), m_offset(offset),
m_stepper(get_substepper_begin())
{
if (end)
{
to_end(l);
}
}
template <class F, class CT, class X>
inline auto xreducer_stepper<F, CT, X>::operator*() const -> reference
{
reference r = aggregate(0);
return r;
}
template <class F, class CT, class X>
inline void xreducer_stepper<F, CT, X>::step(size_type dim, size_type n)
{
if (dim >= m_offset)
m_stepper.step(get_dim(dim), n);
}
template <class F, class CT, class X>
inline void xreducer_stepper<F, CT, X>::step_back(size_type dim, size_type n)
{
if (dim >= m_offset)
m_stepper.step_back(get_dim(dim), n);
}
template <class F, class CT, class X>
inline void xreducer_stepper<F, CT, X>::reset(size_type dim)
{
if (dim >= m_offset)
m_stepper.reset(get_dim(dim));
}
template <class F, class CT, class X>
inline void xreducer_stepper<F, CT, X>::reset_back(size_type dim)
{
if (dim >= m_offset)
m_stepper.reset_back(get_dim(dim));
}
template <class F, class CT, class X>
inline void xreducer_stepper<F, CT, X>::to_begin()
{
m_stepper.to_begin();
}
template <class F, class CT, class X>
inline void xreducer_stepper<F, CT, X>::to_end(layout_type l)
{
m_stepper.to_end(l);
}
template <class F, class CT, class X>
inline bool xreducer_stepper<F, CT, X>::equal(const self_type& rhs) const
{
return &m_reducer == &(rhs.m_reducer) && m_stepper.equal(rhs.m_stepper);
}
template <class F, class CT, class X>
inline auto xreducer_stepper<F, CT, X>::aggregate(size_type dim) const -> reference
{
size_type index = axis(dim);
size_type size = shape(index);
reference res;
if (dim != m_reducer.m_axes.size() - 1)
{
res = aggregate(dim + 1);
for (size_type i = 1; i != size; ++i)
{
m_stepper.step(index);
res = m_reducer.m_f(res, aggregate(dim + 1));
}
}
else
{
res = *m_stepper;
for (size_type i = 1; i != size; ++i)
{
m_stepper.step(index);
res = m_reducer.m_f(res, *m_stepper);
}
}
m_stepper.reset(index);
return res;
}
template <class F, class CT, class X>
inline auto xreducer_stepper<F, CT, X>::get_substepper_begin() const -> substepper_type
{
return m_reducer.m_e.stepper_begin(m_reducer.m_e.shape());
}
template <class F, class CT, class X>
inline auto xreducer_stepper<F, CT, X>::get_dim(size_type dim) const noexcept -> size_type
{
return m_reducer.m_dim_mapping[dim];
}
template <class F, class CT, class X>
inline auto xreducer_stepper<F, CT, X>::shape(size_type i) const noexcept -> size_type
{
return m_reducer.m_e.shape()[i];
}
template <class F, class CT, class X>
inline auto xreducer_stepper<F, CT, X>::axis(size_type i) const noexcept -> size_type
{
return m_reducer.m_axes[i];
}
template <class F, class CT, class X>
inline bool operator==(const xreducer_stepper<F, CT, X>& lhs,
const xreducer_stepper<F, CT, X>& rhs)
{
return lhs.equal(rhs);
}
template <class F, class CT, class X>
inline bool operator!=(const xreducer_stepper<F, CT, X>& lhs,
const xreducer_stepper<F, CT, X>& rhs)
{
return !lhs.equal(rhs);
}
}
#endif
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