Implementation classes


An implementation class in xtensor is a final class that models a specific kind of expression. It must inherit (either directly or indirectly) from xt::xexpression and define (or inherit from classes that define) the following types:

container types


iterator types


template <class S, layout_type L>
broadcast_iterator<S, L>;
template <class S, layout_type L>
const_broadcast_iterator<S, L>;
template <class S, layout_type L>
reverse_broadcast_iterator<S, L>;
template <class S, layout_type L>
const_reverse_broadcast_iterator<S, L>;


layout data

static layout_type static_layout;
static bool contiguous_layout;

It must also provide the following methods, either by defining them itself, or by inheriting from classes that define them, partially or totally:

shape methods

size_type size() const noexcept;
size_type dimension() const noexcept;
const inner_shape_type& shape() const noexcept;

broadcasting methods

template <class S>
bool broadcast_shape(const S& shape) const;

data access methods

template <class... Args>
const_reference operator()(Args... args) const;

template <class... Args>
const_reference at(Args... args) const;

template <class... Args>
const_reference unchecked(Args... args) const;

template <class S>
disable_integral_t<S, const_reference> operator[](const S& index) const;

template <class I>
const_reference operator[](std::initializer_list<I> index) const;

template <class It>
const_reference element(It first, It last) const;

const storage_type& storage() const;

iteration methods

These methods are usually provided by inheriting from xconst_iterable or xiterable. See Iterating over expressions for more details.

If the expression is mutable, it must also define the non-const counterparts of the data access methods, and inherits from a semantic class to provide assignment operators.

List of available expression classes

xtensor provides the following expression classes:


  • xarray_container : N-dimensional array with dynamic shape

  • xarray_adaptor : N-dimensional array adaptor for STL-like containers or C arrays

  • xtensor_container: N-dimensional array with static number of dimensions

  • xtensor_adaptor : N-dimensional tensor adaptor for STL-like containers or C arrays

  • xfixed_container : N-dimensional array with static shape

  • xfixed_adaptor : N-dimensoinal fixed tensor adaptor for STL-like containers or C arrays

Most of the methods of these classes are implemented in the base class xcontainer, the inheriting classes only provide constructors and assignment operators for the value semantic.

The container classes are generally used through type aliases which set many of the template arguments:

The classes for adaptors can be instantiated through the many overloads of xt::adapt function, so that their templates parameters are deduced.


xtensor provides the xscalar class to adapt scalar values and give them the required API.

Optional containers

  • xoptional_assembly : N-dimensional array holding optional values.

  • xoptional_assembly_adaptor: N-dimensional adaptor holding optional values.

Most of the mehtods of these classes are defined in their base class xoptional_assembly_base.


  • xt::xview: N-dimensional view with static number of slices, supporting all kind of slices

  • xstrided_view: N-dimensional view with dynamic number of slices, supporting strided slices only (see below)

  • xdynamic_view: N-dimensional view with dynamic number of slices, supporting all kind of slices

  • xfunctor_view: N-dimensional view applying a functor to its underlying elements (e.g. imag, real)

  • xindex_view : Flat (1D) view yielding the values at the indices of its index array

  • xmasked_view : View on optional expression hiding values depending on a mask

When the index of an element in the underlying expression of a view can be computed thanks to a strided scheme, the slice used in this view is said to be a strided slice. xtensor provides the following strided slices:

  • xrange

  • xstepped_range

  • xall

  • xnewaxis

The following slices are not strided, and thus incompatible with xstrided_view:

  • xkeep_slice

  • xdrop_slice

Functional expressions

Contrary to containers and views, the functional expressions are immutable.

  • xbroadcast: Broadcasts an expression to a specific shape

  • xfunction : N-dimensional function operating on tensor expressions

  • xgenerator: N-dimensional function operating on indices

  • xreducer : Reducing function operating over specified axes

xarray and xtensor

Although they represent different concepts, xt::xarray and xt::xtensor have really similar implementations so only xt::xarray will be covered.

xt::xarray is a strided array expression that can be assigned to. Everything xt::xarray needs is already defined in classes modeling Concepts, so xt::xarray only has to inherit from these classes and define constructors and assignment operators:


Besides implementing the methods that define value semantic, xt::xarray and xt::xtensor hold the data container. Since the xcontainer base class implements all the logic for accessing the data, it must me able to access the data container. This is achieved by requiring that every class inheriting from xcontainer provides the following methods:

storage_type& storage_impl() noexcept;
const storage_type& storage_impl() const noexcept;

These are the implementation methods of the storage() interface methods defined in xcontainer, and thus are defined in the private section of xt::xarray and xt::xtensor. In order to grant access to xcontainer, this last one is declared as friend:

template <class EC, layout_type L, class SC, class Tag>
class xarray : public xstrided_container<xarray<EC, L, SC, Tag>,
               public xcontainer_semantic<xarray<EC, L, SC, Tag>>

    // ....


    storage_type m_storage;
    storage_type& storage() noexcept;
    const storage_type& storage() const noexcept;

    friend class xcontainer<xarray<EC, L, SC, Tag>>;

This pattern is similar to the template method pattern used in hierarchy of classes with entity semantic (see virtuality).

Inner types definition

Although the base classes use the types defined in the Requirement section, they cannot define them; first because different base classes may need the same types and we want to avoid duplication of type definitions. The second reason is that most of the types may rely on other types specific to the implementation classes. For instance, value_type, reference, etc, of xt::xarray are simply the types defined in the container type hold by xt::xarray:

using value_type = typename storage_type::value_type;
using reference = typename storage_type::reference;
using const_reference = typename storage_type::const_reference;

Moreover, CRTP base classes cannot access inner types defined in CRTP leaf classes, because a CRTP leaf class is only declared, not defined, when the CRTP base class is being defined.

The solution is to define those types in an external structure that is specialized for each CRTP leaf class:

// Declaration only, no generic definition
template <class C>
struct xcontainer_inner_types;

In xarray.hpp

template <class EC, layout_type L, class SC, class Tag>
struct xcontainer_inner_types<xarray<EC, L,SC, Tag>>
    // Definition of types required by CRTP bases

In order to avoid a lot of boilerplate, the CRTP base classes expect only a few types to be defined in this structure, and then compute the other types, based on these former definitions. The requirements on types definition regarding the base classes is detailed below.


The semantic classes only expect the following type: temporary_type.


xcontainer and xstrided_container expect the following types to be defined:



Since many expressions are not containers, the definition of types required by the iterable concept is done in a dedicated structure following the same pattern as xcontainer_inner_types, i.e. a sturcture declared and specialized for each final class:

template <class C>
struct xiterable_inner_types;

The following types must be defined in each specialization:


More detail about the stepper types is given in Iterating over expressions.