basic_array_view.hpp

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// Copyright (c) 2019-2023 Simons Foundation
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0.txt
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Authors: Miguel Morales, Olivier Parcollet, Nils Wentzell
 
/**
 * @file
 * @brief Provides the generic class for views.
 */
 
#pragma once
 
#include "./basic_functions.hpp"
#include "./clef.hpp"
#include "./concepts.hpp"
#include "./declarations.hpp"
#include "./exceptions.hpp"
#include "./iterators.hpp"
#include "./layout/for_each.hpp"
#include "./layout/idx_map.hpp"
#include "./layout/permutation.hpp"
#include "./layout/range.hpp"
#include "./macros.hpp"
#include "./mem/address_space.hpp"
#include "./mem/memcpy.hpp"
#include "./mem/policies.hpp"
#include "./traits.hpp"
 
#include <itertools/itertools.hpp>
 
#include <algorithm>
#include <array>
#include <cstring>
#include <memory>
#include <ranges>
#include <type_traits>
#include <utility>
 
#ifdef NDA_ENFORCE_BOUNDCHECK
#include <exception>
#include <iostream>
#endif // NDA_ENFORCE_BOUNDCHECK
 
namespace std {
 
  /**
   * @brief std::swap is deleted for nda::basic_array_view.
   * @warning The std::swap is WRONG for an nda::basic_array_view because of its copy/move semantics. Use nda::swap
   * instead (the correct one, found by ADL).
   */
  template <typename V1, int R1, typename LP1, char A1, typename AP1, typename OP1, typename V2, int R2, typename LP2, char A2, typename AP2,
            typename OP2>
  void swap(nda::basic_array_view<V1, R1, LP1, A1, AP1, OP1> &a, nda::basic_array_view<V2, R2, LP2, A2, AP2, OP2> &b) = delete;
 
} // namespace std
 
namespace nda {
 
  /**
   * @ingroup arrays_views
   * @brief A generic view of a multi-dimensional array.
   *
   * @details Together with nda::basic_array, this class forms the backbone of the nda library. It is templated with
   * the following parameters:
   *
   * - `ValueType`: This is the type of the elements in the view. Depending on how the view was constructed and on the
   * underlying array, this can be a const or non-const type.
   * - `Rank`: Integer specifying the number of dimensions of the view. This is a compile-time constant.
   * - `LayoutPolicy`: The layout policy specifies how the view accesses its elements. It provides a mapping from
   * multi-dimensional to linear indices and vice versa (see @ref layout_pols).
   * - `Algebra`: The algebra specifies how the view behaves when it is used in an expression. Possible values are 'A'
   * (array), 'M' (matrix) and 'V' (vector) (see nda::get_algebra).
   * - `AccessorPolicy`: The accessor policy specifies how the view accesses the data pointer. This can be useful for
   * optimizations.
   * - `OwningPolicy`: The owning policy specifies the ownership of the data pointer and who is responsible for
   * handling the memory resources (see @ref mem_handles).
   *
   * In contrast to regular arrays (see nda::basic_array), views do not own the data they point to. They are a fast and
   * efficient way to access and manipulate already existing data:
   *
   * @code{.cpp}
   * // create a regular 3x3 array of ones
   * auto arr = nda::ones<int>(3, 3);
   * std::cout << arr << std::endl;
   *
   * // zero out the first column
   * arr(nda::range::all, 0) = 0;
   * std::cout << arr << std::endl;
   * @endcode
   *
   * Output:
   *
   * @code{bash}
   *
   * [[1,1,1]
   *  [1,1,1]
   *  [1,1,1]]
   *
   * [[0,1,1]
   *  [0,1,1]
   *  [0,1,1]]
   * @endcode
   *
   * Views are usually created by taking a slice of a regular nda::basic_array or another view. In the example above,
   * `arr(nda::range::all, 0)` creates a view of the first column of the regular array `arr`, which is then set to zero.
   * A view of the full array can be created with `arr()`.
   *
   * @tparam ValueType Type stored in the array.
   * @tparam Rank Number of dimensions of the view.
   * @tparam LayoutPolicy Policy determining the memory layout.
   * @tparam Algebra Algebra of the view.
   * @tparam AccessorPolicy Policy determining how the data pointer is accessed.
   * @tparam OwningPolicy Policy determining the ownership of the data.
   */
  template <typename ValueType, int Rank, typename LayoutPolicy, char Algebra, typename AccessorPolicy, typename OwningPolicy>
  class basic_array_view {
    // Compile-time checks.
    static_assert((Algebra != 'N'), "Internal error in nda::basic_array_view: Algebra 'N' not supported");
    static_assert((Algebra != 'M') or (Rank == 2), "Internal error in nda::basic_array_view: Algebra 'M' requires a rank 2 view");
    static_assert((Algebra != 'V') or (Rank == 1), "Internal error in nda::basic_array_view: Algebra 'V' requires a rank 1 view");
 
    public:
    /// Type of the values in the view (might be const).
    using value_type = ValueType;
 
    /// Type of the memory layout policy (see @ref layout_pols).
    using layout_policy_t = LayoutPolicy;
 
    /// Type of the memory layout (an nda::idx_map).
    using layout_t = typename LayoutPolicy::template mapping<Rank>;
 
    /// Type of the accessor policy (see e.g. nda::default_accessor).
    using accessor_policy_t = AccessorPolicy;
 
    /// Type of the owning policy (see @ref mem_pols).
    using owning_policy_t = OwningPolicy;
 
    /// Type of the memory handle (see @ref mem_handles).
    using storage_t = typename OwningPolicy::template handle<ValueType>;
 
    /// The associated regular (nda::basic_array) type.
    using regular_type = basic_array<std::remove_const_t<ValueType>, Rank, C_layout, Algebra, heap<mem::get_addr_space<storage_t>>>;
 
    /// Number of dimensions of the view.
    static constexpr int rank = Rank;
 
    private:
    // Type of the view itself.
    using self_t = basic_array_view;
 
    // Constexpr variable that is true if the view is a view (always for basic_array_view).
    static constexpr bool is_view = true;
 
    // Constexpr variable that is true if the value_type is const.
    static constexpr bool is_const = std::is_const_v<ValueType>;
 
    // Memory layout of the view, i.e. the nda::idx_map.
    layout_t lay;
 
    // Memory handle of the view.
    storage_t sto;
 
    // Declare any nda::basic_array as a friend.
    template <typename T, int R, typename L, char A, typename CP>
    friend class basic_array;
 
    // Declare any other nda::basic_array_view as a friend.
    template <typename T, int R, typename L, char A, typename AP, typename OP>
    friend class basic_array_view;
 
    // Check the layout compatibility of this view with another layout.
    template <typename L>
    static constexpr bool requires_runtime_check = not layout_property_compatible(L::template mapping<Rank>::layout_prop, layout_t::layout_prop);
 
    public:
    // FIXME : TRIQS PORTING
    // private constructor for the previous friend
    /**
     * @brief Construct a view from a given layout and memory handle.
     *
     * @warning This should not be used directly. Use one of the other constructors instead.
     *
     * @param idxm Layout of the view.
     * @param st Memory handle of the view.
     */
    basic_array_view(layout_t const &idxm, storage_t st) : lay(idxm), sto(std::move(st)) {}
 
    public:
    // backward : FIXME : temporary to be removed
    /// @deprecated Convert the current view to a view with an 'A' (array) algebra.
    [[deprecated]] auto as_array_view() { return basic_array_view<ValueType, Rank, LayoutPolicy, 'A', AccessorPolicy, OwningPolicy>{*this}; };
 
    /// @deprecated Convert the current view to a view with an 'A' (array) algebra.
    [[deprecated]] auto as_array_view() const {
      return basic_array_view<const ValueType, Rank, LayoutPolicy, 'A', AccessorPolicy, OwningPolicy>{*this};
    };
 
    /// Default constructor constructs an empty view with a default constructed memory handle and layout.
    basic_array_view() = default;
 
    /// Default move constructor moves the memory handle and layout.
    basic_array_view(basic_array_view &&) = default;
 
    /// Default copy constructor copies the memory handle and layout.
    basic_array_view(basic_array_view const &) = default;
 
    /**
     * @brief Generic constructor from any nda::MemoryArray type.
     *
     * @details It simply copies the memory layout and initializes the memory handle with the handle of the given
     * nda::MemoryArray object.
     *
     * @tparam A nda::MemoryArray type of the same rank as the view.
     * @param a nda::MemoryArray object.
     */
    template <MemoryArrayOfRank<Rank> A>
      requires((get_layout_info<A>.stride_order == layout_t::stride_order_encoded)
               and (std::is_same_v<std::remove_const_t<ValueType>, get_value_t<A>>)
               and (std::is_const_v<ValueType> or !std::is_const_v<typename std::decay_t<A>::value_type>))
    explicit(requires_runtime_check<typename std::decay_t<A>::layout_policy_t>)
       basic_array_view(A &&a) noexcept // NOLINT (should we forward the reference?)
       : lay(a.indexmap()), sto(a.storage()) {}
 
    /**
     * @brief Construct a view from a bare pointer to some contiguous data and a shape.
     *
     * @note We do not have any control over the specified dimensions. The caller has to ensure their correctness and
     * their compatibility with the given data pointer.
     *
     * @param shape Shape of the view.
     * @param p Pointer to the data.
     */
    basic_array_view(std::array<long, Rank> const &shape, ValueType *p) noexcept : basic_array_view(layout_t{shape}, p) {}
 
    /**
     * @brief Construct a view from a bare pointer to some contiguous data and a memory layout.
     *
     * @note We do not have any control over the given layout. The caller has to ensure its correctness and its
     * compatibility with the given data pointer.
     *
     * @param idxm Layout of the view.
     * @param p Pointer to the data.
     */
    basic_array_view(layout_t const &idxm, ValueType *p) noexcept : lay(idxm), sto{p} {}
 
    /**
     * @brief Construct a 1-dimensional view of a std::array.
     *
     * @tparam N Size of the std::array.
     * @param a Reference to a std::array object.
     */
    template <size_t N>
      requires(Rank == 1)
    explicit basic_array_view(std::array<ValueType, N> &a) noexcept : basic_array_view{{long(N)}, a.data()} {}
 
    /**
     * @brief Construct a 1-dimensional view of a std::array.
     *
     * @tparam N Size of the std::array.
     * @param a Const reference to a std::array object.
     */
    template <size_t N>
      requires(Rank == 1 and std::is_const_v<ValueType>)
    explicit basic_array_view(std::array<std::remove_const_t<ValueType>, N> const &a) noexcept : basic_array_view{{long(N)}, a.data()} {}
 
    /**
     * @brief Construct a 1-dimensional view of a general contiguous range.
     *
     * @tparam R Type of the range.
     * @param rg Range object.
     */
    template <std::ranges::contiguous_range R>
      requires(Rank == 1 and not MemoryArray<R>
               and (std::is_same_v<std::ranges::range_value_t<R>, ValueType> or std::is_same_v<const std::ranges::range_value_t<R>, ValueType>))
    explicit basic_array_view(R &rg) noexcept : basic_array_view{{long(std::ranges::size(rg))}, std::to_address(std::begin(rg))} {}
 
    /**
     * @brief Copy assignment operator makes a deep copy of the contents of the view.
     *
     * @details The dimension of the right hand side must be large enough or the behaviour is undefined. If
     * `NDA_ENFORCE_BOUNDCHECK` is defined, bounds checking is enabled.
     *
     * @param rhs Right hand side of the assignment operation.
     */
    basic_array_view &operator=(basic_array_view const &rhs) noexcept {
      assign_from_ndarray(rhs);
      return *this;
    }
 
    /**
     * @brief Assignment operator makes a deep copy of the contents of an nda::ArrayOfRank object.
     *
     * @details The dimension of the right hand side must be large enough or the behaviour is undefined. If
     * `NDA_ENFORCE_BOUNDCHECK` is defined, bounds checking is enabled.
     *
     * @tparam RHS nda::ArrayOfRank type with the same rank as the view.
     * @param rhs Right hand side of the assignment operation.
     */
    template <ArrayOfRank<Rank> RHS>
    basic_array_view &operator=(RHS const &rhs) noexcept {
      static_assert(!is_const, "Cannot assign to an nda::basic_array_view with const value_type");
      assign_from_ndarray(rhs);
      return *this;
    }
 
    /**
     * @brief Assignment operator assigns a scalar to the view.
     *
     * @details The behavior depends on the algebra of the view:
     * - 'A' (array) and 'V' (vector): The scalar is assigned to all elements of the view.
     * - 'M' (matrix): The scalar is assigned to the diagonal elements of the shorter dimension.
     *
     * @tparam RHS Type of the scalar.
     * @param rhs Right hand side of the assignment operation.
     */
    template <typename RHS>
    basic_array_view &operator=(RHS const &rhs) noexcept
      requires(is_scalar_for_v<RHS, basic_array_view>)
    {
      static_assert(!is_const, "Cannot assign to an nda::basic_array_view with const value_type");
      assign_from_scalar(rhs);
      return *this;
    }
 
    /**
     * @brief Assignment operator uses an nda::ArrayInitializer to assign to the view.
     *
     * @details The shape of the view is expected to be the same as the shape of the initializer.
     *
     * @tparam Initializer nda::ArrayInitializer type.
     * @param initializer Initializer object.
     */
    template <ArrayInitializer<basic_array_view> Initializer>
    basic_array_view &operator=(Initializer const &initializer) noexcept {
      EXPECTS(shape() == initializer.shape());
      initializer.invoke(*this);
      return *this;
    }
 
    /**
     * @brief Rebind the current view to another view.
     *
     * @details It simply copies the layout and memory handle of the other view.
     *
     * @tparam T Value type of the other view.
     * @tparam R Rank of the other view.
     * @tparam LP Layout policy of the other view.
     * @tparam A Algebra of the other view.
     * @tparam AP Accessor policy of the other view.
     * @tparam OP Owning policy of the other view.
     *
     * @param v Other view.
     */
    template <typename T, int R, typename LP, char A, typename AP, typename OP>
    void rebind(basic_array_view<T, R, LP, A, AP, OP> v) noexcept {
      static_assert(R == Rank, "Cannot rebind a view to another view of a different rank");
      static_assert(std::is_same_v<std::remove_const_t<T>, std::remove_const_t<ValueType>>,
                    "Cannot rebind a view to another view with a different value_type (except for const)");
      static constexpr bool same_type = std::is_same_v<T, ValueType>;
      static_assert(same_type or is_const, "Cannot rebind a view with non-const value_type to another view with const value_type");
      if constexpr (same_type) {
        // FIXME Error message in layout error !
        lay = v.lay;
        sto = v.sto;
      } else if constexpr (is_const) {
        // the last if is always trivially true but in case of an error in the static_assert above,
        // it improves the error message by not compiling the = afterwards
        lay = layout_t{v.indexmap()};
        sto = storage_t{v.storage()};
      }
    }
 
    /**
     * @brief Swap two views by swapping their memory handles and layouts.
     *
     * @details This does not modify the data the views point to.
     *
     * @param a First view.
     * @param b Second view.
     */
    friend void swap(basic_array_view &a, basic_array_view &b) noexcept {
      std::swap(a.lay, b.lay);
      std::swap(a.sto, b.sto);
    }
 
    /**
     * @brief Swap two views by swapping their data.
     *
     * @details This modifies the data the views point to.
     *
     * @param a First view.
     * @param b Second view.
     */
    friend void deep_swap(basic_array_view a, basic_array_view b) noexcept {
      auto tmp = make_regular(a);
      a        = b;
      b        = tmp;
    }
 
// include common functionality of arrays and views
// Copyright (c) 2019-2024 Simons Foundation
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0.txt
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Authors: Thomas Hahn, Miguel Morales, Olivier Parcollet, Nils Wentzell
 
/**
 * @brief Get the memory layout of the view/array.
 * @return nda::idx_map specifying the layout of the view/array.
 */
[[nodiscard]] constexpr auto const &indexmap() const noexcept { return lay; }
 
/**
 * @brief Get the data storage of the view/array.
 * @return A const reference to the memory handle of the view/array.
 */
[[nodiscard]] storage_t const &storage() const & noexcept { return sto; }
 
/**
 * @brief Get the data storage of the view/array.
 * @return A reference to the memory handle of the view/array.
 */
[[nodiscard]] storage_t &storage() & noexcept { return sto; }
 
/**
 * @brief Get the data storage of the view/array.
 * @return A copy of the memory handle of the view/array.
 */
[[nodiscard]] storage_t storage() && noexcept { return std::move(sto); }
 
/**
 * @brief Get the stride order of the memory layout of the view/array (see nda::idx_map for more details on how we
 * define stride orders).
 *
 * @return `std::array<int, Rank>` object specifying the stride order.
 */
[[nodiscard]] constexpr auto stride_order() const noexcept { return lay.stride_order; }
 
/**
 * @brief Get a pointer to the actual data (in general this is not the beginning of the memory block for a view).
 * @return Const pointer to the first element of the view/array.
 */
[[nodiscard]] ValueType const *data() const noexcept { return sto.data(); }
 
/**
 * @brief Get a pointer to the actual data (in general this is not the beginning of thr memory block for a view).
 * @return Pointer to the first element of the view/array.
 */
[[nodiscard]] ValueType *data() noexcept { return sto.data(); }
 
/**
 * @brief Get the shape of the view/array.
 * @return `std::array<long, Rank>` object specifying the shape of the view/array.
 */
[[nodiscard]] auto const &shape() const noexcept { return lay.lengths(); }
 
/**
 * @brief Get the strides of the view/array (see nda::idx_map for more details on how we define strides).
 * @return `std::array<long, Rank>` object specifying the strides of the view/array.
 */
[[nodiscard]] auto const &strides() const noexcept { return lay.strides(); }
 
/**
 * @brief Get the total size of the view/array.
 * @return Number of elements contained in the view/array.
 */
[[nodiscard]] long size() const noexcept { return lay.size(); }
 
/**
 * @brief Is the memory layout of the view/array contiguous?
 * @return True if the nda::idx_map is contiguous, false otherwise.
 */
[[nodiscard]] long is_contiguous() const noexcept { return lay.is_contiguous(); }
 
/**
 * @brief Is the view/array empty?
 * @return True if the view/array does not contain any elements.
 */
[[nodiscard]] bool empty() const { return sto.is_null(); }
 
/// @deprecated Use empty() instead.
[[nodiscard]] bool is_empty() const noexcept { return sto.is_null(); }
 
/**
 * @brief Get the extent of the i<sup>th</sup> dimension.
 * @return Number of elements along the i<sup>th</sup> dimension.
 */
[[nodiscard]] long extent(int i) const noexcept {
#ifdef NDA_ENFORCE_BOUNDCHECK
  if (i < 0 || i >= rank) {
    std::cerr << "Error in extent: Dimension " << i << " is incompatible with array of rank " << rank << std::endl;
    std::terminate();
  }
#endif
  return lay.lengths()[i];
}
 
/// @deprecated Use `extent(i)` or `shape()[i]` instead.
[[nodiscard]] long shape(int i) const noexcept { return extent(i); }
 
/**
 * @brief Get a range that generates all valid index tuples.
 * @return An `itertools::multiplied` range that can be used to iterate over all valid index tuples.
 */
[[nodiscard]] auto indices() const noexcept { return itertools::product_range(shape()); }
 
/**
 * @brief Is the stride order of the view/array in C-order?
 * @return True if the stride order of the nda::idx_map is C-order, false otherwise.
 */
static constexpr bool is_stride_order_C() noexcept { return layout_t::is_stride_order_C(); }
 
/**
 * @brief Is the stride order of the view/array in Fortran-order?
 * @return True if the stride order of the nda::idx_map is Fortran-order, false otherwise.
 */
static constexpr bool is_stride_order_Fortran() noexcept { return layout_t::is_stride_order_Fortran(); }
 
/**
 * @brief Access the element of the view/array at the given nda::_linear_index_t.
 *
 * @details The linear index specifies the position of the element in the view/array and not the position of the
 * element w.r.t. to the data pointer (i.e. any possible strides should not be taken into account).
 *
 * @param idx nda::_linear_index_t object.
 * @return Const reference to the element at the given linear index.
 */
decltype(auto) operator()(_linear_index_t idx) const noexcept {
  if constexpr (layout_t::layout_prop == layout_prop_e::strided_1d)
    return sto[idx.value * lay.min_stride()];
  else if constexpr (layout_t::layout_prop == layout_prop_e::contiguous)
    return sto[idx.value];
  else
    static_assert(always_false<layout_t>, "Internal error in array/view: Calling this type with a _linear_index_t is not allowed");
}
 
/// Non-const overload of @ref nda::basic_array_view::operator()(_linear_index_t) const.
decltype(auto) operator()(_linear_index_t idx) noexcept {
  if constexpr (layout_t::layout_prop == layout_prop_e::strided_1d)
    return sto[idx.value * lay.min_stride()];
  else if constexpr (layout_t::layout_prop == layout_prop_e::contiguous)
    return sto[idx.value];
  else
    static_assert(always_false<layout_t>, "Internal error in array/view: Calling this type with a _linear_index_t is not allowed");
}
 
private:
// Constexpr variable that is true if bounds checking is disabled.
#ifdef NDA_ENFORCE_BOUNDCHECK
static constexpr bool has_no_boundcheck = false;
#else
static constexpr bool has_no_boundcheck = true;
#endif
 
public:
/**
 * @brief Implementation of the function call operator.
 *
 * @details This function is an implementation detail an should be private. Since the Green's function library in
 * TRIQS uses this function, it is kept public (for now).
 *
 * @tparam ResultAlgebra Algebra of the resulting view/array.
 * @tparam SelfIsRvalue True if the view/array is an rvalue.
 * @tparam Self Type of the calling view/array.
 * @tparam T Types of the arguments.
 *
 * @param self Calling view.
 * @param idxs Multi-dimensional index consisting of `long`, `nda::range`, `nda::range::all_t`, nda::ellipsis or lazy
 * arguments.
 * @return Result of the function call depending on the given arguments and type of the view/array.
 */
template <char ResultAlgebra, bool SelfIsRvalue, typename Self, typename... Ts>
FORCEINLINE static decltype(auto) call(Self &&self, Ts const &...idxs) noexcept(has_no_boundcheck) {
  // resulting value type
  using r_v_t = std::conditional_t<std::is_const_v<std::remove_reference_t<Self>>, ValueType const, ValueType>;
 
  // behavior depends on the given arguments
  if constexpr (clef::is_any_lazy<Ts...>) {
    // if there are lazy arguments, e.g. as in A(i_) << i_, a lazy expression is returned
    return clef::make_expr_call(std::forward<Self>(self), idxs...);
  } else if constexpr (sizeof...(Ts) == 0) {
    // if no arguments are given, a full view is returned
    return basic_array_view<r_v_t, Rank, LayoutPolicy, Algebra, AccessorPolicy, OwningPolicy>{self.lay, self.sto};
  } else {
    // otherwise we check the arguments and either access a single element or make a slice
    static_assert(((layout_t::template argument_is_allowed_for_call_or_slice<Ts> + ...) > 0),
                  "Error in array/view: Slice arguments must be convertible to range, ellipsis, or long (or string if the layout permits it)");
 
    // number of arguments convertible to long
    static constexpr int n_args_long = (layout_t::template argument_is_allowed_for_call<Ts> + ...);
 
    if constexpr (n_args_long == rank) {
      // access a single element
      long offset = self.lay(idxs...);
      if constexpr (is_view or not SelfIsRvalue) {
        // if the calling object is a view or an lvalue, we return a reference
        return AccessorPolicy::template accessor<ValueType>::access(self.sto.data(), offset);
      } else {
        // otherwise, we return a copy of the value
        return ValueType{self.sto[offset]};
      }
    } else {
      // access a slice of the view/array
      auto const [offset, idxm]      = self.lay.slice(idxs...);
      static constexpr auto res_rank = decltype(idxm)::rank();
      // resulting algebra
      static constexpr char newAlgebra = (ResultAlgebra == 'M' and (res_rank == 1) ? 'V' : ResultAlgebra);
      // resulting layout policy
      using r_layout_p = typename detail::layout_to_policy<std::decay_t<decltype(idxm)>>::type;
      return basic_array_view<ValueType, res_rank, r_layout_p, newAlgebra, AccessorPolicy, OwningPolicy>{std::move(idxm), {self.sto, offset}};
    }
  }
}
 
public:
/**
 * @brief Function call operator to access the view/array.
 *
 * @details Depending on the type of the calling object and the given arguments, this function call does the following:
 * - If any of the arguments is lazy, an nda::clef::expr with the nda::clef::tags::function tag is returned.
 * - If no arguments are given, a full view of the calling object is returned:
 *   - If the calling object itself or its value type is const, a view with a const value type is returned.
 *   - Otherwise, a view with a non-const value type is returned.
 * - If the number of arguments is equal to the rank of the calling object and all arguments are convertible to `long`,
 * a single element is accessed:
 *   - If the calling object is a view or an lvalue, a (const) reference to the element is returned.
 *   - Otherwise, a copy of the element is returned.
 * - Otherwise a slice of the calling object is returned with the same value type and accessor and owning policies as
 * the calling object. The algebra of the slice is the same as well, except if a 1-dimensional slice of a matrix is
 * taken. In this case, the algebra is changed to 'V'.
 *
 * @tparam Ts Types of the function arguments.
 * @param idxs Multi-dimensional index consisting of `long`, `nda::range`, `nda::range::all_t`, nda::ellipsis or lazy
 * arguments.
 * @return Result of the function call depending on the given arguments and type of the view/array.
 */
template <typename... Ts>
FORCEINLINE decltype(auto) operator()(Ts const &...idxs) const & noexcept(has_no_boundcheck) {
  static_assert((rank == -1) or (sizeof...(Ts) == rank) or (sizeof...(Ts) == 0) or (ellipsis_is_present<Ts...> and (sizeof...(Ts) <= rank + 1)),
                "Error in array/view: Incorrect number of parameters in call operator");
  return call<Algebra, false>(*this, idxs...);
}
 
/// Non-const overload of `nda::basic_array_view::operator()(Ts const &...) const &`.
template <typename... Ts>
FORCEINLINE decltype(auto) operator()(Ts const &...idxs) & noexcept(has_no_boundcheck) {
  static_assert((rank == -1) or (sizeof...(Ts) == rank) or (sizeof...(Ts) == 0) or (ellipsis_is_present<Ts...> and (sizeof...(Ts) <= rank + 1)),
                "Error in array/view: Incorrect number of parameters in call operator");
  return call<Algebra, false>(*this, idxs...);
}
 
/// Rvalue overload of `nda::basic_array_view::operator()(Ts const &...) const &`.
template <typename... Ts>
FORCEINLINE decltype(auto) operator()(Ts const &...idxs) && noexcept(has_no_boundcheck) {
  static_assert((rank == -1) or (sizeof...(Ts) == rank) or (sizeof...(Ts) == 0) or (ellipsis_is_present<Ts...> and (sizeof...(Ts) <= rank + 1)),
                "Error in array/view: Incorrect number of parameters in call operator");
  return call<Algebra, true>(*this, idxs...);
}
 
/**
 * @brief Subscript operator to access the 1-dimensional view/array.
 *
 * @details Depending on the type of the calling object and the given argument, this subscript operation does the
 * following:
 * - If the argument is lazy, an nda::clef::expr with the nda::clef::tags::function tag is returned.
 * - If the argument is convertible to `long`, a single element is accessed:
 *   - If the calling object is a view or an lvalue, a (const) reference to the element is returned.
 *   - Otherwise, a copy of the element is returned.
 * - Otherwise a slice of the calling object is returned with the same value type, algebra and accessor and owning
 * policies as the calling object.
 *
 * @tparam T Type of the argument.
 * @param idx 1-dimensional index that is either a `long`, `nda::range`, `nda::range::all_t`, nda::ellipsis or a lazy
 * argument.
 * @return Result of the subscript operation depending on the given argument and type of the view/array.
 */
template <typename T>
decltype(auto) operator[](T const &idx) const & noexcept(has_no_boundcheck) {
  static_assert((rank == 1), "Error in array/view: Subscript operator is only available for rank 1 views/arrays in C++17/20");
  return call<Algebra, false>(*this, idx);
}
 
/// Non-const overload of `nda::basic_array_view::operator[](T const &) const &`.
template <typename T>
decltype(auto) operator[](T const &x) & noexcept(has_no_boundcheck) {
  static_assert((rank == 1), "Error in array/view: Subscript operator is only available for rank 1 views/arrays in C++17/20");
  return call<Algebra, false>(*this, x);
}
 
/// Rvalue overload of `nda::basic_array_view::operator[](T const &) const &`.
template <typename T>
decltype(auto) operator[](T const &x) && noexcept(has_no_boundcheck) {
  static_assert((rank == 1), "Error in array/view: Subscript operator is only available for rank 1 views/arrays in C++17/20");
  return call<Algebra, true>(*this, x);
}
 
/// Rank of the nda::array_iterator for the view/array.
static constexpr int iterator_rank = (has_strided_1d(layout_t::layout_prop) ? 1 : Rank);
 
/// Const iterator type of the view/array.
using const_iterator = array_iterator<iterator_rank, ValueType const, typename AccessorPolicy::template accessor<ValueType>::pointer>;
 
/// Iterator type of the view/array.
using iterator = array_iterator<iterator_rank, ValueType, typename AccessorPolicy::template accessor<ValueType>::pointer>;
 
private:
// Make an iterator for the view/array depending on its type.
template <typename Iterator>
[[nodiscard]] auto make_iterator(bool at_end) const noexcept {
  if constexpr (iterator_rank == Rank) {
    // multi-dimensional iterator
    if constexpr (layout_t::is_stride_order_C()) {
      // C-order case (array_iterator already traverses the data in C-order)
      return Iterator{indexmap().lengths(), indexmap().strides(), sto.data(), at_end};
    } else {
      // general case (we need to permute the shape and the strides according to the stride order of the layout)
      return Iterator{nda::permutations::apply(layout_t::stride_order, indexmap().lengths()),
                      nda::permutations::apply(layout_t::stride_order, indexmap().strides()), sto.data(), at_end};
    }
  } else {
    // 1-dimensional iterator
    return Iterator{std::array<long, 1>{size()}, std::array<long, 1>{indexmap().min_stride()}, sto.data(), at_end};
  }
}
 
public:
/// Get a const iterator to the beginning of the view/array.
[[nodiscard]] const_iterator begin() const noexcept { return make_iterator<const_iterator>(false); }
 
/// Get a const iterator to the beginning of the view/array.
[[nodiscard]] const_iterator cbegin() const noexcept { return make_iterator<const_iterator>(false); }
 
/// Get an iterator to the beginning of the view/array.
iterator begin() noexcept { return make_iterator<iterator>(false); }
 
/// Get a const iterator to the end of the view/array.
[[nodiscard]] const_iterator end() const noexcept { return make_iterator<const_iterator>(true); }
 
/// Get a const iterator to the end of the view/array.
[[nodiscard]] const_iterator cend() const noexcept { return make_iterator<const_iterator>(true); }
 
/// Get an iterator to the end of the view/array.
iterator end() noexcept { return make_iterator<iterator>(true); }
 
/**
 * @brief Addition assignment operator.
 *
 * @details It first performs the (lazy) addition with the right hand side operand and then assigns the result to the
 * left hand side view/array.
 *
 * See nda::operator+(L &&, R &&) and nda::operator+(A &&, S &&) for more details.
 *
 * @tparam RHS nda::Scalar or nda::Array type.
 * @param rhs Right hand side operand of the addition assignment operation.
 * @return Reference to this object.
 */
template <typename RHS>
auto &operator+=(RHS const &rhs) noexcept {
  static_assert(not is_const, "Error in array/view: Can not assign to a const view");
  return operator=(*this + rhs);
}
 
/**
 * @brief Subtraction assignment operator.
 *
 * @details It first performs the (lazy) subtraction with the right hand side operand and then assigns the result to
 * the left hand side view/array.
 *
 * See nda::operator-(L &&, R &&) and nda::operator-(A &&, S &&) for more details.
 *
 * @tparam RHS nda::Scalar or nda::Array type.
 * @param rhs Right hand side operand of the subtraction assignment operation.
 * @return Reference to this object.
 */
template <typename RHS>
auto &operator-=(RHS const &rhs) noexcept {
  static_assert(not is_const, "Error in array/view: Can not assign to a const view");
  return operator=(*this - rhs);
}
 
/**
 * @brief Multiplication assignment operator.
 *
 * @details It first performs the (lazy) multiplication with the right hand side operand and then assigns the result
 * to the left hand side view/array.
 *
 * See nda::operator*(L &&, R &&) and nda::operator*(A &&, S &&) for more details.
 *
 * @tparam RHS nda::Scalar or nda::Array type.
 * @param rhs Right hand side operand of the multiplication assignment operation.
 * @return Reference to this object.
 */
template <typename RHS>
auto &operator*=(RHS const &rhs) noexcept {
  static_assert(not is_const, "Error in array/view: Can not assign to a const view");
  return operator=((*this) * rhs);
}
 
/**
 * @brief Division assignment operator.
 *
 * @details It first performs the (lazy) division with the right hand side operand and then assigns the result to the
 * left hand side view/array.
 *
 * See nda::operator/(L &&, R &&) and nda::operator/(A &&, S &&) for more details.
 *
 * @tparam RHS nda::Scalar or nda::Array type.
 * @param rhs Right hand side operand of the division assignment operation.
 * @return Reference to this object.
 */
template <typename RHS>
auto &operator/=(RHS const &rhs) noexcept {
  static_assert(not is_const, "Error in array/view: Can not assign to a const view");
  return operator=(*this / rhs);
}
 
/**
 * @brief Assignment operator makes a deep copy of a general contiguous range and assigns it to the 1-dimensional
 * view/array.
 *
 * @tparam R Range type.
 * @param rhs Right hand side range object.
 * @return Reference to this object.
 */
template <std::ranges::contiguous_range R>
auto &operator=(R const &rhs) noexcept
  requires(Rank == 1 and not MemoryArray<R>)
{
  *this = basic_array_view{rhs};
  return *this;
}
 
private:
// Implementation of the assignment from an n-dimensional array type.
template <typename RHS>
void assign_from_ndarray(RHS const &rhs) { // FIXME noexcept {
#ifdef NDA_ENFORCE_BOUNDCHECK
  if (this->shape() != rhs.shape())
    NDA_RUNTIME_ERROR << "Error in assign_from_ndarray: Size mismatch:"
                      << "\n LHS.shape() = " << this->shape() << "\n RHS.shape() = " << rhs.shape();
#endif
  // compile-time check if assignment is possible
  static_assert(std::is_assignable_v<value_type &, get_value_t<RHS>>, "Error in assign_from_ndarray: Incompatible value types");
 
  // are both operands nda::MemoryArray types?
  static constexpr bool both_in_memory = MemoryArray<self_t> and MemoryArray<RHS>;
 
  // do both operands have the same stride order?
  static constexpr bool same_stride_order = get_layout_info<self_t>.stride_order == get_layout_info<RHS>.stride_order;
 
  // prefer optimized options if possible
  if constexpr (both_in_memory and same_stride_order) {
    if (rhs.empty()) return;
    // are both operands strided in 1d?
    static constexpr bool both_1d_strided = has_layout_strided_1d<self_t> and has_layout_strided_1d<RHS>;
    if constexpr (mem::on_host<self_t, RHS> and both_1d_strided) {
      // vectorizable copy on host
      for (long i = 0; i < size(); ++i) (*this)(_linear_index_t{i}) = rhs(_linear_index_t{i});
      return;
    } else if constexpr (!mem::on_host<self_t, RHS> and have_same_value_type_v<self_t, RHS>) {
      // check for block-layout and use mem::memcpy2D if possible
      auto bl_layout_dst = get_block_layout(*this);
      auto bl_layout_src = get_block_layout(rhs);
      if (bl_layout_dst && bl_layout_src) {
        auto [n_bl_dst, bl_size_dst, bl_str_dst] = *bl_layout_dst;
        auto [n_bl_src, bl_size_src, bl_str_src] = *bl_layout_src;
        // check that the total memory size is the same
        if (n_bl_dst * bl_size_dst != n_bl_src * bl_size_src) NDA_RUNTIME_ERROR << "Error in assign_from_ndarray: Incompatible block sizes";
        // if either destination or source consists of a single block, we can chunk it up to make the layouts compatible
        if (n_bl_dst == 1 && n_bl_src > 1) {
          n_bl_dst = n_bl_src;
          bl_size_dst /= n_bl_src;
          bl_str_dst = bl_size_dst;
        }
        if (n_bl_src == 1 && n_bl_dst > 1) {
          n_bl_src = n_bl_dst;
          bl_size_src /= n_bl_dst;
          bl_str_src = bl_size_src;
        }
        // copy only if block-layouts are compatible, otherwise continue to fallback
        if (n_bl_dst == n_bl_src && bl_size_dst == bl_size_src) {
          mem::memcpy2D<mem::get_addr_space<self_t>, mem::get_addr_space<RHS>>((void *)data(), bl_str_dst * sizeof(value_type), (void *)rhs.data(),
                                                                               bl_str_src * sizeof(value_type), bl_size_src * sizeof(value_type),
                                                                               n_bl_src);
          return;
        }
      }
    }
  }
  // otherwise fallback to elementwise assignment
  if constexpr (mem::on_device<self_t> || mem::on_device<RHS>) {
    NDA_RUNTIME_ERROR << "Error in assign_from_ndarray: Fallback to elementwise assignment not implemented for arrays/views on the GPU";
  }
  nda::for_each(shape(), [this, &rhs](auto const &...args) { (*this)(args...) = rhs(args...); });
}
 
// Implementation to fill a view/array with a constant scalar value.
template <typename Scalar>
void fill_with_scalar(Scalar const &scalar) noexcept {
  // we make a special implementation if the array is strided in 1d or contiguous
  if constexpr (has_layout_strided_1d<self_t>) {
    const long L             = size();
    auto *__restrict const p = data(); // no alias possible here!
    if constexpr (has_contiguous_layout<self_t>) {
      for (long i = 0; i < L; ++i) p[i] = scalar;
    } else {
      const long stri  = indexmap().min_stride();
      const long Lstri = L * stri;
      for (long i = 0; i < Lstri; i += stri) p[i] = scalar;
    }
  } else {
    // no compile-time memory layout guarantees
    for (auto &x : *this) x = scalar;
  }
}
 
// Implementation of the assignment from a scalar value.
template <typename Scalar>
void assign_from_scalar(Scalar const &scalar) noexcept {
  static_assert(!is_const, "Error in assign_from_ndarray: Cannot assign to a const view");
  if constexpr (Algebra != 'M') {
    // element-wise assignment for non-matrix algebras
    fill_with_scalar(scalar);
  } else {
    // a scalar has to be interpreted as a unit matrix for matrix algebras (the scalar in the shortest diagonal)
    // FIXME : A priori faster to put 0 everywhere and then change the diag to avoid the if.
    // FIXME : Benchmark and confirm.
    if constexpr (is_scalar_or_convertible_v<Scalar>)
      fill_with_scalar(0);
    else
      fill_with_scalar(Scalar{0 * scalar}); // FIXME : improve this
    const long imax = std::min(extent(0), extent(1));
    for (long i = 0; i < imax; ++i) operator()(i, i) = scalar;
  }
}
  };
 
  // Class template argument deduction guides.
  template <MemoryArray A>
  basic_array_view(A &&a)
     -> basic_array_view<std::conditional_t<std::is_const_v<std::remove_reference_t<A>>, const typename std::decay_t<A>::value_type,
                                            typename std::decay_t<A>::value_type>,
                         get_rank<A>, typename std::decay_t<A>::layout_policy_t, get_algebra<A>, default_accessor, borrowed<mem::get_addr_space<A>>>;
 
  template <typename V, size_t R>
  basic_array_view(std::array<V, R> &a)
     -> basic_array_view<V, 1, nda::basic_layout<nda::static_extents(R), nda::C_stride_order<1>, nda::layout_prop_e::contiguous>, 'V',
                         default_accessor, borrowed<>>;
 
  template <typename V, size_t R>
  basic_array_view(std::array<V, R> const &a)
     -> basic_array_view<const V, 1, nda::basic_layout<nda::static_extents(R), nda::C_stride_order<1>, nda::layout_prop_e::contiguous>, 'V',
                         default_accessor, borrowed<>>;
 
  template <std::ranges::contiguous_range R>
  basic_array_view(R &r) -> basic_array_view<std::conditional_t<std::is_const_v<R>, const typename R::value_type, typename R::value_type>, 1,
                                             C_layout, 'V', default_accessor, borrowed<>>;
 
} // namespace nda