aka_view_iterators.hh
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	/**
	* Copyright (©) 2018-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* This file is part of Akantu
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*/

	/* -------------------------------------------------------------------------- */
	#include "aka_common.hh"
	/* -------------------------------------------------------------------------- */
	#include <memory>
	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_AKA_VIEW_ITERATORS_HH__
	#define __AKANTU_AKA_VIEW_ITERATORS_HH__

	namespace akantu {
	template <typename T, Int ndim> class TensorBase;
	}

	namespace akantu {
	/* -------------------------------------------------------------------------- */
	/* Iterators */
	/* -------------------------------------------------------------------------- */
	namespace detail {
	template <typename... V> constexpr auto product_all(V &&... v) {
	std::common_type_t<int, V...> result = 1;
	(void)std::initializer_list<int>{(result *= v, 0)...};
	return result;
	}

	template <class R> struct IteratorHelper { static constexpr Int dim = 0; };

	template <class Derived> struct IteratorHelper<Eigen::MatrixBase<Derived>> {
	private:
	using T = typename Derived::Scalar;
	static constexpr Int m = Derived::RowsAtCompileTime;
	static constexpr Int n = Derived::ColsAtCompileTime;

	public:
	static constexpr Int dim =
	Eigen::MatrixBase<Derived>::IsVectorAtCompileTime ? 1 : 2;
	using pointer = T *;
	using proxy = Eigen::Map<Eigen::Matrix<T, m, n>>;
	using const_proxy = Eigen::Map<const Eigen::Matrix<T, m, n>>;
	};

	template <class Derived> struct IteratorHelper<Eigen::Map<Derived>> {
	private:
	using T = typename Derived::Scalar;
	static constexpr Int m = Derived::RowsAtCompileTime;
	static constexpr Int n = Derived::ColsAtCompileTime;

	public:
	static constexpr Int dim =
	Derived::IsVectorAtCompileTime and m != 1 ? 1 : 2;
	using pointer =
	std::conditional_t<std::is_const_v<Derived>, const T , T >;
	using proxy = Eigen::Map<Derived>;
	using const_proxy = Eigen::Map<const Derived>;
	};

	template <typename T, Int _dim> struct IteratorHelper<TensorBase<T, _dim>> {
	static constexpr Int dim = _dim;
	using pointer = T *;
	using proxy = TensorProxy<T, _dim>;
	using const_proxy = TensorProxy<const T, _dim>;
	};

	template <typename T, Int _dim> struct IteratorHelper<TensorProxy<T, _dim>> {
	static constexpr Int dim = _dim;
	using pointer = T *;
	using proxy = TensorProxy<T, _dim>;
	using const_proxy = TensorProxy<const T, _dim>;
	};

	/* ------------------------------------------------------------------------ */
	template <class R, class daughter, class IR = R,
	Int dim = IteratorHelper<std::decay_t<R>>::dim>
	class internal_view_iterator {
	protected:
	using helper = IteratorHelper<std::decay_t<R>>;
	using internal_value_type = IR;
	using internal_pointer = IR *;
	using scalar_pointer = typename helper::pointer;
	using proxy_t = typename helper::proxy;
	static constexpr int dim_ = dim;

	public:
	using pointer = proxy_t *;
	using value_type = proxy_t;
	using reference = proxy_t &;
	using difference_type = Int;
	using iterator_category = std::random_access_iterator_tag;

	private:
	template <class ProxyType, std::size_t... I>
	constexpr auto get_new_proxy(scalar_pointer data,
	std::index_sequence<I...>) const {
	return ProxyType(data, dims[I]...);
	}

	constexpr auto get_new_proxy(scalar_pointer data) {
	return this->template get_new_proxy<proxy_t>(
	data, std::make_index_sequence<dim>());
	}

	constexpr auto get_new_proxy(scalar_pointer data) const {
	return this->template get_new_proxy<proxy_t>(
	data, std::make_index_sequence<dim>());
	}

	template <std::size_t... I>
	constexpr void reset_proxy(std::index_sequence<I...>) {
	new (&proxy) proxy_t(ret_ptr, dims[I]...);
	}

	constexpr auto reset_proxy() {
	return reset_proxy(std::make_index_sequence<dim>());
	}

	protected:
	template <typename OR, typename OD, typename OIR,
	std::enable_if_t<std::is_convertible<
	decltype(std::declval<OIR>().data()),
	decltype(std::declval<IR>().data())>::value> * = nullptr>
	explicit internal_view_iterator(
	internal_view_iterator<OR, OD, OIR, dim> & it)
	: dims(it.dims), _offset(it._offset), initial(it.initial),
	ret_ptr(it.ret_ptr), proxy(get_new_proxy(it.ret_ptr)) {}

	template <typename OR, typename OD, typename OIR, Int _dim>
	friend class internal_view_iterator;

	template <typename... Args>
	using valid_args_t = std::enable_if_t<
	aka::conjunction<aka::disjunction<std::is_integral<Args>,
	std::is_enum<Args>>...>::value and
	dim == sizeof...(Args),
	int>;

	public:
	/// Generic constructor dor any tensor dimension
	template <typename... Ns, valid_args_t<Ns...> = 0>
	internal_view_iterator(scalar_pointer data, Ns... ns)
	: dims({Int(ns)...}),
	_offset(detail::product_all(std::forward<Ns>(ns)...)), initial(data),
	ret_ptr(data), proxy(data, ns...) {}

	// Specific constructor for Vector of static size 1
	template <typename RD = std::decay_t<R>,
	std::enable_if_t<aka::is_eigen_map<RD>::value and
	RD::RowsAtCompileTime == 1 and
	RD::ColsAtCompileTime == 1> * = nullptr>
	constexpr internal_view_iterator(scalar_pointer data, Idx rows)
	: dims({rows, 1}), _offset(rows), initial(data), ret_ptr(data),
	proxy(data, rows, 1) {
	assert(rows == 1 && "1x1 Matrix");
	}

	/// Specific constructor for Eigen::Map<Matrix> that look like
	/// Eigen::Map<Vector>
	template <typename RD = std::decay_t<R>,
	std::enable_if_t<(RD::RowsAtCompileTime != 1) and
	RD::ColsAtCompileTime == 1> * = nullptr>
	constexpr internal_view_iterator(scalar_pointer data, Idx rows,
	[[gnu::unused]] Idx cols)
	: dims({rows}), _offset(rows), initial(data), ret_ptr(data),
	proxy(data, rows, 1) {
	assert(cols == 1 && "nx1 Matrix");
	}

	/// Default constructor for Eigen::Map<Vector>
	template <Int _dim = dim, typename RD = std::decay_t<R>,
	std::enable_if_t<_dim == 1> * = nullptr>
	internal_view_iterator()
	: proxy(reinterpret_cast<scalar_pointer>(0xdeadbeaf),
	RD::RowsAtCompileTime == Eigen::Dynamic
	? 1
	: RD::RowsAtCompileTime) {
	// initialized to a fake pointer to pass the static_assert in Eigen
	// this proxy should not be returned
	}

	/// Default constructor for Eigen::Map<Matrix>
	template <Int _dim = dim, typename RD = std::decay_t<R>,
	std::enable_if_t<_dim == 2> * = nullptr>
	internal_view_iterator()
	: proxy(reinterpret_cast<scalar_pointer>(0xdeadbeaf),
	RD::RowsAtCompileTime == Eigen::Dynamic ? 1
	: RD::RowsAtCompileTime,
	RD::ColsAtCompileTime == Eigen::Dynamic
	? 1
	: RD::ColsAtCompileTime) {
	// initialized to a fake pointer to pass the `static_assert` in `Eigen
	// this proxy should not be returned
	}

	template <Int _dim = dim, typename RD = std::decay_t<R>,
	std::enable_if_t<(_dim > 2)> * = nullptr>
	internal_view_iterator() {}

	internal_view_iterator(const internal_view_iterator & it)
	: dims(it.dims), _offset(it._offset), initial(it.initial),
	ret_ptr(it.ret_ptr), proxy(get_new_proxy(it.ret_ptr)) {}

	internal_view_iterator &
	operator=(internal_view_iterator && it) noexcept = default;
	internal_view_iterator(internal_view_iterator && it) noexcept = default;

	virtual ~internal_view_iterator() = default;

	template <typename OR, typename OD, typename OIR,
	std::enable_if_t<std::is_convertible<
	decltype(std::declval<OIR>().data()),
	decltype(std::declval<IR>().data())>::value> * = nullptr>
	inline internal_view_iterator &
	operator=(const internal_view_iterator<OR, OD, OIR, dim> & it) {
	this->dims = it.dims;
	this->_offset = it._offset;
	this->initial = it.initial;
	this->ret_ptr = it.ret_ptr;
	reset_proxy();
	return *this;
	}

	inline internal_view_iterator &
	operator=(const internal_view_iterator & it) {
	if (this != &it) {
	this->dims = it.dims;
	this->_offset = it._offset;
	this->initial = it.initial;
	this->ret_ptr = it.ret_ptr;
	reset_proxy();
	}
	return *this;
	}

	public:
	Idx getCurrentIndex() {
	return (this->ret_ptr - this->initial) / this->_offset;
	}

	inline reference operator*() {
	this->reset_proxy();
	return proxy;
	}

	inline reference operator*() const {
	this->reset_proxy();
	return proxy;
	}


	inline pointer operator->() {
	reset_proxy();
	return &proxy;
	}

	inline daughter & operator++() {
	ret_ptr += _offset;
	return static_cast<daughter &>(*this);
	}

	inline daughter & operator--() {
	ret_ptr -= _offset;
	return static_cast<daughter &>(*this);
	}

	inline daughter & operator+=(Idx n) {
	ret_ptr += _offset * n;
	return static_cast<daughter &>(*this);
	}

	inline daughter & operator-=(Idx n) {
	ret_ptr -= _offset * n;
	return static_cast<daughter &>(*this);
	}

	inline auto operator[](Idx n) {
	return get_new_proxy(ret_ptr + n * _offset);
	}

	inline auto operator[](Idx n) const {
	return get_new_proxy(ret_ptr + n * _offset);
	}

	inline bool operator==(const internal_view_iterator & other) const {
	return this->ret_ptr == other.ret_ptr;
	}

	inline bool operator!=(const internal_view_iterator & other) const {
	return this->ret_ptr != other.ret_ptr;
	}

	inline bool operator<(const internal_view_iterator & other) const {
	return this->ret_ptr < other.ret_ptr;
	}

	inline bool operator<=(const internal_view_iterator & other) const {
	return this->ret_ptr <= other.ret_ptr;
	}

	inline bool operator>(const internal_view_iterator & other) const {
	return this->ret_ptr > other.ret_ptr;
	}

	inline bool operator>=(const internal_view_iterator & other) const {
	return this->ret_ptr >= other.ret_ptr;
	}

	inline auto operator+(difference_type n) const {
	daughter tmp(static_cast<const daughter &>(*this));
	tmp += n;
	return tmp;
	}

	inline auto operator-(difference_type n) const {
	daughter tmp(static_cast<const daughter &>(*this));
	tmp -= n;
	return tmp;
	}

	inline difference_type operator-(const internal_view_iterator & b) const {
	return (this->ret_ptr - b.ret_ptr) / _offset;
	}

	inline scalar_pointer data() const { return ret_ptr; }
	inline difference_type offset() const { return _offset; }
	inline decltype(auto) getDims() const { return dims; }

	protected:
	std::array<Int, dim> dims;
	difference_type _offset{0};
	scalar_pointer initial{nullptr};
	scalar_pointer ret_ptr{nullptr};
	proxy_t proxy;
	};

	/* ------------------------------------------------------------------------ */
	/**
	* Specialization for scalar types
	*/
	template <class R, class daughter, class IR>
	class internal_view_iterator<R, daughter, IR, 0> {
	public:
	using value_type = R;
	using pointer = R *;
	using reference = R &;
	using const_reference = const R &;
	using difference_type = Idx; // std::ptrdiff_t;
	using iterator_category = std::random_access_iterator_tag;
	static constexpr int dim_ = 0;

	protected:
	using internal_value_type = IR;
	using internal_pointer = IR *;

	public:
	internal_view_iterator(pointer data = nullptr) : ret(data), initial(data){};
	internal_view_iterator(const internal_view_iterator & it) = default;
	internal_view_iterator(internal_view_iterator && it) = default;

	virtual ~internal_view_iterator() = default;

	inline internal_view_iterator &
	operator=(const internal_view_iterator & it) = default;

	Idx getCurrentIndex() { return (this->ret - this->initial); };

	inline reference operator() { return ret; }
	inline reference operator() const { return ret; }

	inline pointer operator->() { return ret; };

	inline daughter & operator++() {
	++ret;
	return static_cast<daughter &>(*this);
	}
	inline daughter & operator--() {
	--ret;
	return static_cast<daughter &>(*this);
	}

	inline daughter & operator+=(const Idx n) {
	ret += n;
	return static_cast<daughter &>(*this);
	}
	inline daughter & operator-=(const Idx n) {
	ret -= n;
	return static_cast<daughter &>(*this);
	}

	inline reference operator[](const Idx n) { return ret[n]; }

	inline bool operator==(const internal_view_iterator & other) const {
	return ret == other.ret;
	}
	inline bool operator!=(const internal_view_iterator & other) const {
	return ret != other.ret;
	}
	inline bool operator<(const internal_view_iterator & other) const {
	return ret < other.ret;
	}
	inline bool operator<=(const internal_view_iterator & other) const {
	return ret <= other.ret;
	}
	inline bool operator>(const internal_view_iterator & other) const {
	return ret > other.ret;
	}
	inline bool operator>=(const internal_view_iterator & other) const {
	return ret >= other.ret;
	}

	inline daughter operator-(difference_type n) const {
	return daughter(ret - n);
	}
	inline daughter operator+(difference_type n) const {
	return daughter(ret + n);
	}

	inline difference_type operator-(const internal_view_iterator & b) const {
	return ret - b.ret;
	}

	inline pointer data() const { return ret; }
	inline decltype(auto) getDims() const { return dims; }

	protected:
	std::array<int, 0> dims;
	pointer ret{nullptr};
	pointer initial{nullptr};
	};
	} // namespace detail

	/* -------------------------------------------------------------------------- */
	template <typename R> class view_iterator;

	template <typename R>
	class const_view_iterator
	: public detail::internal_view_iterator<const R, const_view_iterator<R>,
	R> {
	public:
	using parent =
	detail::internal_view_iterator<const R, const_view_iterator, R>;
	using value_type = typename parent::value_type;
	using pointer = typename parent::pointer;
	using reference = typename parent::reference;
	using difference_type = typename parent::difference_type;
	using iterator_category = typename parent::iterator_category;

	protected:
	template <typename Iterator, std::size_t... I>
	static inline auto convert_helper(const Iterator & it,
	std::index_sequence<I...>) {
	return const_view_iterator(it.data(), it.getDims()[I]...);
	}
	template <typename Iterator> static inline auto convert(const Iterator & it) {
	return convert_helper(it, std::make_index_sequence<parent::dim_>());
	}

	public:
	const_view_iterator() : parent(){};
	const_view_iterator(const const_view_iterator & it) = default;
	const_view_iterator(const_view_iterator && it) noexcept = default;

	template <typename P, typename... Ns>
	const_view_iterator(P * data, Ns... ns) : parent(data, ns...) {}

	const_view_iterator & operator=(const const_view_iterator & it) = default;

	template <typename OR,
	std::enable_if_t<not std::is_same<R, OR>::value> * = nullptr>
	const_view_iterator(const const_view_iterator<OR> & it)
	: parent(convert(it)) {}

	template <typename OR,
	std::enable_if_t<std::is_convertible<R, OR>::value> * = nullptr>
	const_view_iterator(const view_iterator<OR> & it) : parent(convert(it)) {}

	template <typename OR,
	std::enable_if_t<not std::is_same<R, OR>::value and
	std::is_convertible<R, OR>::value> * = nullptr>
	const_view_iterator & operator=(const const_view_iterator<OR> & it) {
	return dynamic_cast<const_view_iterator &>(parent::operator=(it));
	}

	template <typename OR,
	std::enable_if_t<std::is_convertible<R, OR>::value> * = nullptr>
	const_view_iterator operator=(const view_iterator<OR> & it) {
	return convert(it);
	}
	};

	template <class R, bool is_tensor_ = aka::is_tensor<R>::value>
	struct ConstConverterIteratorHelper {
	protected:
	template <std::size_t... I>
	static inline auto convert_helper(const view_iterator<R> & it,
	std::index_sequence<I...>) {
	return const_view_iterator<R>(it.data(), it.getDims()[I]...);
	}

	public:
	static inline auto convert(const view_iterator<R> & it) {
	return convert_helper(
	it, std::make_index_sequence<
	std::tuple_size<decltype(it.getDims())>::value>());
	}
	};

	template <class R> struct ConstConverterIteratorHelper<R, false> {
	static inline auto convert(const view_iterator<R> & it) {
	return const_view_iterator<R>(it.data());
	}
	};

	template <typename R>
	class view_iterator
	: public detail::internal_view_iterator<R, view_iterator<R>> {
	public:
	using parent = detail::internal_view_iterator<R, view_iterator>;
	using value_type = typename parent::value_type;
	using pointer = typename parent::pointer;
	using reference = typename parent::reference;
	using difference_type = typename parent::difference_type;
	using iterator_category = typename parent::iterator_category;

	public:
	view_iterator() : parent(){};
	view_iterator(const view_iterator & it) = default;
	view_iterator(view_iterator && it) = default;

	template <typename P, typename... Ns>
	view_iterator(P * data, Ns... ns) : parent(data, ns...) {}

	view_iterator & operator=(const view_iterator & it) = default;

	operator const_view_iterator<R>() {
	return ConstConverterIteratorHelper<R>::convert(*this);
	}
	};

	namespace {
	template <std::size_t dim, typename T> struct ViewIteratorHelper {
	using type = TensorProxy<T, dim>;
	};

	template <typename T> struct ViewIteratorHelper<0, T> { using type = T; };
	template <typename T> struct ViewIteratorHelper<1, T> {
	using type = Eigen::Map<Eigen::Matrix<T, Eigen::Dynamic, 1>>;
	};
	template <typename T> struct ViewIteratorHelper<1, const T> {
	using type = Eigen::Map<const Eigen::Matrix<T, Eigen::Dynamic, 1>>;
	};

	template <typename T> struct ViewIteratorHelper<2, T> {
	using type = Eigen::Map<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>;
	};

	template <typename T> struct ViewIteratorHelper<2, const T> {
	using type =
	Eigen::Map<const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>;
	};

	template <std::size_t dim, typename T>
	using ViewIteratorHelper_t = typename ViewIteratorHelper<dim, T>::type;
	} // namespace

	} // namespace akantu

	#include <iterator>

	namespace std {

	template <typename R> struct iterator_traits<::akantu::const_view_iterator<R>> {
	protected:
	using iterator = ::akantu::const_view_iterator<R>;

	public:
	using iterator_category = typename iterator::iterator_category;
	using value_type = typename iterator::value_type;
	using difference_type = typename iterator::difference_type;
	using pointer = typename iterator::pointer;
	using reference = typename iterator::reference;
	};

	template <typename R> struct iterator_traits<::akantu::view_iterator<R>> {
	protected:
	using iterator = ::akantu::view_iterator<R>;

	public:
	using iterator_category = typename iterator::iterator_category;
	using value_type = typename iterator::value_type;
	using difference_type = typename iterator::difference_type;
	using pointer = typename iterator::pointer;
	using reference = typename iterator::reference;
	};

	} // namespace std

	#endif /* !__AKANTU_AKA_VIEW_ITERATORS_HH__ */

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