Views¶

Views are used to adapt the shape of an 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 xexpression to adapt, and a list of slice that specify how the shape must be adapted. Sliced views are implemented by the xview class. Objects of this type should not be instantiated directly, but though the view helper function.

Slices can be specified in the following ways:

selection in a dimension by specifying an index (unsigned integer)
range(min, max), a slice representing the interval [min, max)
range(min, max, step), a slice representing the stepped interval [min, max)
all(), a slice representing all the elements of a dimension
newaxis(), a slice representing an additional dimension of length one
keep(i0, i1, i2, ...) a slice selecting non-contiguous indices to keep on the underlying expression
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));

xview does not perform a copy of the underlying expression. This means if you modify an element of the 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 row and 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 keep and 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 xstrided_view is very efficient on contigous memory (e.g. xtensor or xarray) but less efficient on xexpressions.

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 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, ravel and 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 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 xstrided_view.

Dynamic views¶

The dynamic view is like the strided view, but with support of the slices returned by the keep and 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 xexpression, containing the elements whose positions are specified by a list of indices. Like for sliced views, the elements of the underlying xexpression are not copied. Index views should be built with the 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 xexpression that verify a given condition. Like for other views, the elements of the underlying xexpression are not copied. Filters should be built with the 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 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 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 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 xexpression corresponding to the real and imaginary parts of the complex numbers. Like for other views, the elements of the underlying 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 real(a) is the same as that of a. Hence, if a is a non-const lvalue, 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 imag(a). The constness and value category of imag(a) is the same as that of a.
If a has real values, imag(a) returns 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 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.}}