# Views

Views are used to adapt the shape of an `xt::xexpression` without changing it, nor copying it. Views are convenient tools for assigning parts of an expression: since they do not copy the underlying expression, assigning to the view actually assigns to the underlying expression. xtensor provides many kinds of views.

## Sliced views

Sliced views consist of the combination of the `xt::xexpression` to adapt, and a list of `slice` that specify how the shape must be adapted. Sliced views are implemented by the `xt::xview` class. Objects of this type should not be instantiated directly, but though the `xt::view()` helper function.

Slices can be specified in the following ways:

- selection in a dimension by specifying an index (unsigned integer)

- `xt::range(min, max)`, a slice representing the interval [min, max)

- `xt::range(min, max, step)`, a slice representing the stepped interval [min, max)

- `xt::all()`, a slice representing all the elements of a dimension

- `xt::newaxis()`, a slice representing an additional dimension of length one

- `xt::keep(i0, i1, i2, ...)` a slice selecting non-contiguous indices to keep on the underlying expression

- `xt::drop(i0, i1, i2, ...)` a slice selecting non-contiguous indices to drop on the underlying expression

    #include <vector>
    #include <xtensor/xarray.hpp>
    #include <xtensor/xview.hpp>

    std::vector<size_t> shape = {3, 2, 4};
    xt::xarray<int> a(shape);

    // View with same number of dimensions
    auto v1 = xt::view(a, xt::range(1, 3), xt::all(), xt::range(1, 3));
    // => v1.shape() = { 2, 2, 2 }
    // => v1(0, 0, 0) = a(1, 0, 1)
    // => v1(1, 1, 1) = a(2, 1, 2)

    // View reducing the number of dimensions
    auto v2 = xt::view(a, 1, xt::all(), xt::range(0, 4, 2));
    // => v2.shape() = { 2, 2 }
    // => v2(0, 0) = a(1, 0, 0)
    // => v2(1, 1) = a(1, 1, 2)

    // View increasing the number of dimensions
    auto v3 = xt::view(a, xt::all(), xt::all(), xt::newaxis(), xt::all());
    // => v3.shape() = { 3, 2, 1, 4 }
    // => v3(0, 0, 0, 0) = a(0, 0, 0)

    // View with non contiguous slices
    auto v4 = xt::view(a, xt::drop(0), xt::all(), xt::keep(0, 3));
    // => v4.shape() = { 2, 2, 2 }
    // => v4(0, 0, 0) = a(1, 0, 0)
    // => v4(1, 1, 1) = a(2, 1, 3)

    // View built with negative index
    auto v5 = xt::view(a, -2, xt::all(), xt::range(0, 4, 2));
    // => v5 == v2

The range function supports the placeholder `_` syntax:

    #include <xtensor/xarray.hpp>
    #include <xtensor/xview.hpp>

    using namespace xt::placeholders;  // required for ``_`` to work

    auto a = xt::xarray<int>::from_shape({3, 2, 4});
    auto v1 = xt::view(a, xt::range(_, 2), xt::all(), xt::range(1, _));
    // The previous line is equivalent to
    auto v2 = xt::view(a, xt::range(0, 2), xt::all(), xt::range(1, 4));

`xt::xview` does not perform a copy of the underlying expression. This means if you modify an element of the `xt::xview`, you are actually also altering the underlying expression.

    #include <vector>
    #include <xtensor/xarray.hpp>
    #include <xtensor/xview.hpp>

    std::vector<size_t> shape = {3, 2, 4};
    xt::xarray<int> a(shape, 0);

    auto v1 = xt::view(a, 1, xt::all(), xt::range(1, 3));
    v1(0, 0) = 1;
    // => a(1, 0, 1) = 1

The convenient methods `xt::row()` and `xt::col()` are available for 2-D expressions:

    #include <vector>
    #include <xtensor/xtensor.hpp>
    #include <xtensor/xview.hpp>

    xt::xtensor<double, 2> a = {{1, 2}, {3, 4}};
    auto r = xt::row(a, 0);
    // => r = {1, 2}
    auto c = xt::col(a, -1);
    // => c = { 2, 4 }

## Strided views

While the `xt::view()` is a compile-time static expression, xtensor also contains a dynamic strided view in `xstrided_view.hpp`. The strided view and the slice vector allow to dynamically push_back slices, so when the dimension is unknown at compile time, the slice vector can be built dynamically at runtime. Note that the slice vector is actually a type-alias for a `std::vector` of a `variant` for all the slice types. The strided view does not support the slices returned by the `xt::keep()` and `xt::drop()` functions.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xstrided_view.hpp>

    auto a = xt::xarray<int>::from_shape({3, 2, 3, 4, 5});

    xt::xstrided_slice_vector sv({xt::range(0, 1), xt::newaxis()});
    sv.push_back(1);
    sv.push_back(xt::all());

    auto v1 = xt::strided_view(a, sv);
    // v1 has the same behavior as the static view

    // Equivalent but shorter
    auto v2 = xt::strided_view(a, { xt::range(0, 1), xt::newaxis(), 1, xt::all() });
    // v2 == v1

    // ILLEGAL:
    auto v2 = xt::strided_view(a, { xt::all(), xt::all(), xt::all(), xt::keep(0, 3), xt::drop(1, 4) });
    // xt::drop and xt::keep are not supported with strided views

Since `xtensor 0.16.3`, a new range syntax can be used with strided views:

    #include <xtensor/xarray.hpp>
    #include <xtensor/xstrided_view.hpp>

    using namespace xt::placeholders;

    auto a = xt::xarray<int>::from_shape({3, 2, 3, 4, 5});
    auto v1 = xt::strided_view(a, {_r|0|1, 1, _r|_|2, _r|_|_|-1});
    // The previous line is equivalent to
    auto v2 = xt::strided_view(a, {xt::range(0, 1), 1, xt::range(_, 2), xt::range(_, _, -1)});

The `xt::xstrided_view` is very efficient on contigous memory (e.g. `xt::xtensor` or `xt::xarray`) but less efficient on:cpp:type:`xt::xexpression`s.

## Transposed views

xtensor provides a lazy transposed view on any expression, whose layout is either row-major order or column major order. Trying to build a transposed view on a expression with a dynamic layout throws an exception.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xstrided_view.hpp>

    xt::xarray<int> a = { {0, 1, 2}, {3, 4, 5} };
    auto tr = xt::transpose(a);
    // tr == { {0, 3}, {1, 4}, {2, 5} }

    xt::xarray<int, layout_type::dynamic> b = { {0, 1, 2}, {3, 4, 5} };
    auto tr2 = xt::transpose(b);
    // => throw transpose_error

Like the strided view, the transposed view is built upon the `xt::xstrided_view`.

## Flatten views

It is sometimes useful to have a one-dimensional view of all the elements of an expression. xtensor provides two functions for that, `xt::ravel()` and `xt::flatten()`. The former one lets you specify the order used to read the elements while the latter one uses the layout of the expression.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xstrided_view.hpp>

    xt::xarray<int> a = { {0, 1, 2}, {3, 4, 5} };
    auto flc = xt::ravel<layout_type::column_major>(a);
    std::cout << flc << std::endl;
    // => prints { 0, 3, 1, 4, 2, 5 }

    auto fl = xt::flatten(a);
    std::cout << fl << std::endl;
    // => prints { 0, 1, 2, 3, 4, 5 }

Like the strided view and the transposed view, the flatten view is built upon the `xt::xstrided_view`.

## Reshape views

The reshape view allows to handle an expression as if it was given a new shape, however no additional memory allocation occurs, the original expression keeps its shape. Like any view, the underlying expression is not copied, thus assigning a value through the view modifies the underlying expression.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xstrided_view.hpp>

    auto a = xt::xarray<int>::from_shape({3, 2, 4});
    auto v = xt::reshape_view(a, { 4, 2, 3 });
    // a(0, 0, 3) == v(0, 1, 0)
    // a(0, 1, 0) == v(0, 1, 1)

    v(0, 2, 0) = 4;
    // a(0, 1, 2) == 4

Like the strided view and the transposed view, the reshape view is built upon the `xt::xstrided_view`.

## Dynamic views

The dynamic view is like the strided view, but with support of the slices returned by the `xt::keep()` and `xt::drop()` functions. However, this support has a cost and the dynamic view is slower than the strided view, even when no keeping or dropping of a slice is involved.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xdynamic_view.hp>

    auto a = xt::xarray<int>::from_shape({3, 2, 3, 4, 5});
    xt::xdynamic_slice_vector sv({xt::range(0, 1), xt::newaxis()});
    sv.push_back(1);
    sv.push_back(xt::all());
    sv.push_back(xt::keep(0, 2, 3));
    sv.push_back(xt::drop(1, 2, 4));

    auto v1 = xt::dynamic_view(a, sv});

    // Equivalent but shorter
    auto v2 = xt::dynamic_view(a, { xt::range(0, 1), xt::newaxis(), 1, xt::all(), xt::keep(0, 2, 3), xt::drop(1, 2, 4) });
    // v2 == v1

## Index views

Index views are one-dimensional views of an `xt::xexpression`, containing the elements whose positions are specified by a list of indices. Like for sliced views, the elements of the underlying `xt::xexpression` are not copied. Index views should be built with the `xt::index_view()` helper function.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xindex_view.hpp>

    xt::xarray<double> a = {{1, 5, 3}, {4, 5, 6}};
    auto b = xt::index_view(a, {{0,0}, {1, 0}, {0, 1}});
    // => b = { 1, 4, 5 }
    b += 100;
    // => a = {{101, 5, 3}, {104, 105, 6}}

The type used for representing indices can be any 1-D container providing an `std::vector`-like API. The same stands for the type of the list of indices:

    #include <xtensor/xarray.hpp>
    #include <xtensor/xindex_view.hpp>

    xt::xarray<double> a = {{1, 5, 3}, {4, 5, 6}};
    using index_type = std::array<std::size_t, 2>;
    std::vector<index_type> indices = {{0, 0}, {1, 0}, {0, 1}};
    auto b = xt::index_view(a, indices);
    // => b = { 1, 4, 5 }
    b += 100;
    // => a = {{101, 5, 3}, {104, 105, 6}}

## Filter views

Filters are one-dimensional views holding elements of an `xt::xexpression` that verify a given condition. Like for other views, the elements of the underlying `xt::xexpression` are not copied. Filters should be built with the `xt::filter()` helper function.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xindex_view.hpp>

    xt::xarray<double> a = {{1, 5, 3}, {4, 5, 6}};
    auto v = xt::filter(a, a >= 5);
    // => v = { 5, 5, 6 }
    v += 100;
    // => a = {{1, 105, 3}, {4, 105, 106}}

## Filtration

Sometimes, the only thing you want to do with a filter is to assign it a scalar. Though this can be done as shown in the previous section, this is not the optimal way to do it. xtensor provides a specially optimized mechanism for that, called filtration. A filtration IS NOT an `xt::xexpression`, the only methods it provides are scalar and computed scalar assignments.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xindex_view.hpp>

    xt::xarray<double> a = {{1, 5, 3}, {4, 5, 6}};
    filtration(a, a >= 5) += 100;
    // => a = {{1, 105, 3}, {4, 105, 106}}

## Masked view

Masked views are multidimensional views that apply a mask on an `xt::xexpression`.

    #include <xtensor/xarray.hpp>
    #include <xtensor/xmasked_view.hpp>

    xt::xarray<double> a = {{1, 5, 3}, {4, 5, 6}};
    xt::xarray<bool> mask = {{true, false, false}, {false, true, false}};

    auto m = xt::masked_view(a, mask);
    // => m = {{1, masked, masked}, {masked, 5, masked}}

    m += 100;
    // => a = {{101, 5, 3}, {4, 105, 6}}

## Broadcasting views

Another type of view provided by xtensor is broadcasting view. Such a view broadcasts an expression to the specified shape. As long as the view is not assigned to an array, no memory allocation or copy occurs. Broadcasting views should be built with the `xt::broadcast()` helper function.

    #include <vector>
    #include <xtensor/xarray.hpp>
    #include <xtensor/xbroadcast.hpp>

    std::vector<size_t> s1 = { 2, 3 };
    std::vector<size_t> s2 = { 3, 2, 3 };

    xt::xarray<int> a1(s1);
    auto bv = xt::broadcast(a1, s2);
    // => bv(0, 0, 0) = bv(1, 0, 0) = bv(2, 0, 0) = a(0, 0)

## Complex views

In the case of a tensor containing complex numbers, xtensor provides views returning `xt::xexpression` corresponding to the real and imaginary parts of the complex numbers. Like for other views, the elements of the underlying `xt::xexpression` are not copied.

Functions `xt::real()` and `xt::imag()` respectively return views on the real and imaginary part of a complex expression. The returned value is an expression holding a closure on the passed argument.

- The constness and value category (rvalue / lvalue) of `xt::real(a)` is the same as that of `a`. Hence, if `a` is a non-const lvalue, `xt::real(a)` is an non-const lvalue reference, to which one can assign a real expression.

- If `a` has complex values, the same holds for `xt::imag(a)`. The constness and value category of `xt::imag(a)` is the same as that of `a`.

- If `a` has real values, `xt::imag(a)` returns `xt::zeros(a.shape())`.

    #include <complex>
    #include <xtensor/xarray.hpp>
    #include <xtensor/xcomplex.hpp>

    using namespace std::complex_literals;

    xarray<std::complex<double>> e =
        {{1.0       , 1.0 + 1.0i},
         {1.0 - 1.0i, 1.0       }};

    real(e) = zeros<double>({2, 2});
    // => e = {{0.0, 0.0 + 1.0i}, {0.0 - 1.0i, 0.0}};

## Assigning to a view

When assigning an expression `rhs` to a container such as `xt::xarray`, the container is resized so its shape is the same as the one of `rhs`. However, since views cannot be resized, when assigning an expression to a view, broadcasting rules are applied:

    #include <xtensor/xarray.hpp>
    #include <xtensor/xview.hpp>

    xarray<double> a = {{0., 1., 2.}, {3., 4., 5.}};
    double b = 1.2;
    auto tr = view(a, 0, all());
    tr = b;
    // => a = {{1.2, 1.2, 1.2}, {3., 4., 5.}}