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			/**
			* Copyright (©) 2022-2023 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/>.
			*/

			/* -------------------------------------------------------------------------- */

			#ifndef AKA_TENSOR_HH_
			#define AKA_TENSOR_HH_

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			/* TensorBase */
			/* -------------------------------------------------------------------------- */
			template <typename T, Int ndim> class TensorBase : public TensorTrait<ndim> {
			using RetType = TensorBase<T, ndim>;
			static_assert(ndim > 2, "TensorBase cannot by used for dimensions < 3");

			protected:
			using idx_t = Idx;

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

			public:
			using proxy = TensorBase<T, ndim>;
			using size_type = Idx;
			template <Int _ndim = ndim,
			std::enable_if_t<_ndim == 1 or _ndim == 2, int> = 0>
			TensorBase() {
			n.fill(0);
			}

			TensorBase() { n.fill(0); }

			template <typename... Args, valid_args_t<Args...> = 0>
			constexpr TensorBase(Args... args)
			: n{idx_t(args)...}, _size(detail::product_all(args...)) {}

			constexpr TensorBase(const TensorBase & other)
			: n(other.n), _size(other._size), values(other.values) {}

			constexpr TensorBase(TensorBase && other) noexcept
			: n(std::move(other.n)), _size(std::exchange(other._size, 0)),
			values(std::exchange(other.values, nullptr)) {}

			protected:
			template <typename Array, idx_t... I>
			constexpr auto check_indices(
			const Array & idx,
			std::integer_sequence<idx_t, I...> /* for_template_deduction */) const {
			bool result = true;
			(void)std::initializer_list<int>{(result &= idx[I] < n[I], 0)...};
			return result;
			}

			template <typename... Args> constexpr auto compute_index(Args... args) const {
			std::array<idx_t, sizeof...(Args)> idx{idx_t(args)...};
			assert(check_indices(
			idx, std::make_integer_sequence<idx_t, sizeof...(Args)>{}) &&
			"The indexes are out of bound");
			idx_t index = 0, i = (sizeof...(Args)) - 1;
			for (; i > 0; i--) {
			index += idx[i];
			if (i > 0) {
			index *= n[i - 1];
			}
			}
			return index + idx[0];
			}

			template <typename S, int... I>
			constexpr auto get_slice(idx_t s, std::index_sequence<I...>) {
			return S(this->values + s * detail::product_all(n[I]...), n[I]...);
			}

			template <typename S, std::size_t... I>
			constexpr auto get_slice(idx_t s, std::index_sequence<I...>) const {
			return S(this->values + s * detail::product_all(n[I]...), n[I]...);
			}

			public:
			template <typename... Args, valid_args_t<Args...> = 0>
			inline auto operator()(Args... args) -> T & {
			return *(this->values + compute_index(std::move(args)...));
			}

			template <typename... Args, valid_args_t<Args...> = 0>
			inline auto operator()(Args... args) const -> const T & {
			return *(this->values + compute_index(std::move(args)...));
			}

			template <
			class R = T, idx_t _ndim = ndim,
			std::enable_if_t<(_ndim > 3) and not std::is_const<R>::value> * = nullptr>
			inline auto operator()(idx_t s) {
			return get_slice<TensorProxy<T, ndim - 1>>(
			s, std::make_index_sequence<ndim - 1>());
			}

			template <idx_t _ndim = ndim, std::enable_if_t<(_ndim > 3)> * = nullptr>
			inline auto operator()(idx_t s) const {
			return get_slice<TensorProxy<T, ndim - 1>>(
			s, std::make_index_sequence<ndim - 1>());
			}

			template <class R = T, idx_t _ndim = ndim,
			std::enable_if_t<(_ndim == 3) and not std::is_const<R>::value> * =
			nullptr>
			inline auto operator()(idx_t s) {
			return get_slice<
			Eigen::Map<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>>>(
			s, std::make_index_sequence<ndim - 1>());
			}

			template <idx_t _ndim = ndim, std::enable_if_t<_ndim == 3> * = nullptr>
			inline auto operator()(idx_t s) const {
			return get_slice<Eigen::Map<const Eigen::Matrix<
			std::remove_const_t<T>, Eigen::Dynamic, Eigen::Dynamic>>>(
			s, std::make_index_sequence<ndim - 1>());
			}

			protected:
			template <class Operator> auto transform(Operator && op) -> RetType & {
			std::transform(this->values, this->values + this->_size, this->values,
			std::forward<Operator>(op));
			return (static_cast<RetType >(this));
			}

			template <class Other, class Operator>
			auto transform(Other && other, Operator && op) -> RetType & {
			AKANTU_DEBUG_ASSERT(_size == other.size(),
			"The two tensors do not have the same size "
			<< this->_size << " != " << other._size);

			std::transform(this->values, this->values + this->_size, other.values,
			this->values, std::forward<Operator>(op));
			return (static_cast<RetType >(this));
			}

			template <class Operator> auto accumulate(T init, Operator && op) -> T {
			return std::accumulate(this->values, this->values + this->_size,
			std::move(init), std::forward<Operator>(op));
			}

			template <class Other, class Init, class Accumulate, class Operator>
			auto transform_reduce(Other && other, T init, Accumulate && acc,
			Operator && op) -> T {
			return std::inner_product(
			this->values, this->values + this->_size, other.data(), std::move(init),
			std::forward<Accumulate>(acc), std::forward<Operator>(op));
			}

			// element wise arithmetic operators -----------------------------------------
			public:
			inline decltype(auto) operator+=(const TensorBase & other) {
			return transform(other, [](auto && a, auto && b) { return a + b; });
			}

			/* ------------------------------------------------------------------------ */
			inline auto operator-=(const TensorBase & other) -> TensorBase & {
			return transform(other, [](auto && a, auto && b) { return a - b; });
			}

			/* ------------------------------------------------------------------------ */
			inline auto operator+=(const T & x) -> TensorBase & {
			return transform([&x](auto && a) { return a + x; });
			}

			/* ------------------------------------------------------------------------ */
			inline auto operator-=(const T & x) -> TensorBase & {
			return transform([&x](auto && a) { return a - x; });
			}

			/* ------------------------------------------------------------------------ */
			inline auto operator*=(const T & x) -> TensorBase & {
			return transform([&x](auto && a) { return a * x; });
			}

			/* ---------------------------------------------------------------------- */
			inline auto operator/=(const T & x) -> TensorBase & {
			return transform([&x](auto && a) { return a / x; });
			}

			/// Y = \alpha X + Y
			inline auto aXplusY(const TensorBase & other, const T alpha = 1.)
			-> TensorBase & {
			return transform(other,
			[&alpha](auto && a, auto && b) { return alpha * a + b; });
			}

			/* ------------------------------------------------------------------------ */
			auto data() -> T * { return values; }
			auto data() const -> const T * { return values; }

			// clang-format off
			[[deprecated("use data instead to be stl compatible")]]
			auto storage() -> T*{
			return values;
			}

			[[deprecated("use data instead to be stl compatible")]]
			auto storage() const -> const T * {
			return values;
			}
			// clang-format on

			auto size() const { return _size; }
			auto size(idx_t i) const {
			AKANTU_DEBUG_ASSERT(i < ndim, "This tensor has only " << ndim
			<< " dimensions, not "
			<< (i + 1));
			return n[i];
			};

			inline void set(const T & t) { std::fill_n(values, _size, t); };
			inline void zero() { set(T()); };

			public:
			/// "Entrywise" norm norm<L_p> @f[ \\|\boldsymbol{T}\\|_p = \left(
			/// \sum_i^{n[0]}\sum_j^{n[1]}\sum_k^{n[2]} \|T_{ijk}\|^p \right)^{\frac{1}{p}}
			/// @f]
			template <Int norm_type,
			std::enable_if_t<norm_type == Eigen::Infinity> * = nullptr>
			auto lpNorm() const -> T {
			return accumulate(
			T(), [](auto && init, auto && a) { return init + std::abs(a); });
			}

			template <Int norm_type, std::enable_if_t<norm_type == 1> * = nullptr>
			auto lpNorm() const -> T {
			return accumulate(T(), [](auto && init, auto && a) {
			return std::max(init, std::abs(a));
			});
			}

			template <Int norm_type, std::enable_if_t<norm_type == 2> * = nullptr>
			auto norm() const -> T {
			return std::sqrt(
			accumulate(T(), [](auto && init, auto && a) { return init + a * a; }));
			}

			template <Int norm_type, std::enable_if_t<(norm_type > 2)> * = nullptr>
			auto norm() const -> T {
			return std::pow(accumulate(T(),
			[](auto && init, auto && a) {
			return init + std::pow(a, norm_type);
			}),
			1. / norm_type);
			}

			auto norm() const -> T { return lpNorm<2>(); }

			protected:
			template <Int N, typename... Args,
			std::enable_if_t<(sizeof...(Args) == ndim), int> = 0>
			void serialize(std::ostream & stream, Args... args) const {
			stream << this->operator()(std::move(args)...);
			}

			template <Int N, typename... Args,
			std::enable_if_t<(sizeof...(Args) < ndim), int> = 0>
			void serialize(std::ostream & stream, Args... args) const {
			stream << "[";
			for (idx_t i = 0; i < n[N]; ++i) {
			if (i != 0) {
			stream << ",";
			}
			serialize<N + 1>(stream, std::move(args)..., i);
			}
			stream << "]";
			}

			public:
			void printself(std::ostream & stream) const { serialize<0>(stream); };

			protected:
			template <std::size_t... I>
			constexpr decltype(auto) begin(std::index_sequence<I...>) {
			return view_iterator<ViewIteratorHelper_t<sizeof...(I), T>>(values,
			n[I]...);
			}

			template <std::size_t... I>
			constexpr decltype(auto) end(std::index_sequence<I...>) {
			return view_iterator<ViewIteratorHelper_t<sizeof...(I), T>>(values + _size,
			n[I]...);
			}

			template <std::size_t... I>
			constexpr decltype(auto) begin(std::index_sequence<I...>) const {
			return const_view_iterator<ViewIteratorHelper_t<sizeof...(I), T>>(values,
			n[I]...);
			}

			template <std::size_t... I>
			constexpr decltype(auto) end(std::index_sequence<I...>) const {
			return const_view_iterator<ViewIteratorHelper_t<sizeof...(I), T>>(
			values + _size, n[I]...);
			}

			public:
			decltype(auto) begin() { return begin(std::make_index_sequence<ndim - 1>{}); }
			decltype(auto) end() { return end(std::make_index_sequence<ndim - 1>{}); }

			decltype(auto) begin() const {
			return begin(std::make_index_sequence<ndim - 1>{});
			}
			decltype(auto) end() const {
			return end(std::make_index_sequence<ndim - 1>{});
			}

			protected:
			// size per dimension
			std::array<idx_t, ndim> n;

			// total storage size
			idx_t _size{0};

			// actual data location
			T * values{nullptr};
			};

			/* -------------------------------------------------------------------------- */
			/* TensorProxy */
			/* -------------------------------------------------------------------------- */
			template <typename T, Int ndim> class TensorProxy : public TensorBase<T, ndim> {
			private:
			using parent = TensorBase<T, ndim>;

			public:
			// proxy constructor
			template <typename... Args>
			constexpr TensorProxy(T * data = reinterpret_cast<T *>(0xdeadbeef),
			Args... args)
			: parent(args...) {
			this->values = data;
			}

			constexpr TensorProxy(const TensorProxy<T, ndim> & other) : parent(other) {
			this->values = other.values;
			}

			constexpr TensorProxy(const Tensor<T, ndim> & other) : parent(other) {
			this->values = other.values;
			}

			// move constructors ---------------------------------------------------------
			// proxy -> proxy
			TensorProxy(TensorProxy && other) noexcept : parent(other) {}

			auto operator=(const TensorBase<T, ndim> & other) -> TensorProxy & {
			AKANTU_DEBUG_ASSERT(
			other.size() == this->size(),
			"You are trying to copy too a tensors proxy with the wrong size "
			<< this->_size << " != " << other._size);

			static_assert(std::is_trivially_copyable<T>{},
			"Cannot copy a tensor on non trivial types");

			std::copy(other.values, other.values + this->_size, this->values);
			return *this;
			}
			};

			/* -------------------------------------------------------------------------- */
			/* Tensor */
			/* -------------------------------------------------------------------------- */
			template <typename T, Int ndim> class Tensor : public TensorBase<T, ndim> {
			private:
			using parent = TensorBase<T, ndim>;

			public:
			template <typename... Args> constexpr Tensor(Args... args) : parent(args...) {
			static_assert(
			std::is_trivially_constructible<T>{},
			"Cannot create a tensor on non trivially constructible types");
			this->values = new T[this->_size];
			}

			/* ------------------------------------------------------------------------ */
			virtual ~Tensor() { delete[] this->values; }

			// copy constructors ---------------------------------------------------------
			constexpr Tensor(const Tensor & other) : parent(other) {
			this->values = new T[this->_size];
			std::copy(other.values, other.values + this->_size, this->values);
			}

			constexpr explicit Tensor(const TensorProxy<T, ndim> & other)
			: parent(other) {
			// static_assert(false, "Copying data are you sure");
			this->values = new T[this->_size];
			std::copy(other.values, other.values + this->_size, this->values);
			}

			// move constructors ---------------------------------------------------------
			// proxy -> proxy, non proxy -> non proxy
			Tensor(Tensor && other) noexcept : parent(other) {}

			// copy operator -------------------------------------------------------------
			/// operator= copy-and-swap
			auto operator=(const TensorBase<T, ndim> & other) -> Tensor & {
			if (&other == this)
			return *this;

			std::cout << "Warning: operator= delete data" << std::endl;
			delete[] this->values;
			this->n = other.n;
			this->_size = other._size;

			static_assert(
			std::is_trivially_constructible<T>{},
			"Cannot create a tensor on non trivially constructible types");

			this->values = new T[this->_size];

			static_assert(std::is_trivially_copyable<T>{},
			"Cannot copy a tensor on non trivial types");

			std::copy(other.values, other.values + this->_size, this->values);

			return *this;
			}
			};

			/* -------------------------------------------------------------------------- */
			template <typename T> using Tensor3 = Tensor<T, 3>;
			template <typename T> using Tensor3Proxy = TensorProxy<T, 3>;
			template <typename T> using Tensor3Base = TensorBase<T, 3>;

			} // namespace akantu

			#endif // AKA_TENSOR_HH_

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aka_tensor.hh
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