Views

Views are used to adapt the shape of an xexpression without changing it, nor copying it. xtensor provides two kinds of views.

Sliced views

Sliced views consist of the combination of the xexpression to adapt, and a list of slice s 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 an interval
  • range(min, max, step), a slice representing a stepped interval
  • all(), a slice representing all the elements of a dimension
  • newaxis(), a slice representing an additional dimension of length one
#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)

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

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/xindexview.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}}

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/xindexview.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/xindexview.hpp"

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

Broadcasting views

Another type of view provided by xtensor is broadcasting view. Such a view broadcast 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 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}};