Operators and functions

Arithmetic operators

xtensor provides overloads of traditional arithmetic operators for xexpression objects:

  • unary operator+
  • unary operator-
  • operator+
  • operator-
  • operator*
  • operator/

All these operators are element-wise operators and apply the lazy broadcasting rules explained in a previous section.

#incude "xtensor/xarray.hpp"

xt::xarray<int> a = {{1, 2}, {3, 4}};
xt::xarray<int> b = {1, 2};

xt::xarray<int> res = 2 * (a + b);
// => res = {{4, 8}, {8, 12}}

Logical operators

xtensor also provides overloads of the logical operators:

  • operator!
  • operator||
  • operator&&

Like arithmetic operators, these logical operators are element-wise operators and apply the lazy broadcasting rules. In addition to these element-wise logical operators, xtensor provides two reducing boolean functions:

  • any(E&& e) returns true if any of e elements is truthy, false otherwise.
  • all(E&& e) returns true if all alements of e are truthy, false otherwise.

and an element-wise ternary function (similar to the : ? ternary operator):

  • where(E&& b, E1&& e&, E2&& e2) returns an xexpression whose elements are those of e1 when corresponding elements of b are thruthy, and those of e2 otherwise.
#include "xtensor/xarray.hpp"

xt::xarray<bool> b = { false, true, true, false };
xt::xarray<int> a1 = { 1,   2,  3,  4 };
xt::xarray<int> a2 = { 11, 12, 13, 14 };

xt::xarray<int> res = xt::where(b, a1, a2);
// => res = { 11, 2, 3, 14 }

Unlike in numpy.where, xt::where takes full advantage of the lazyness of xtensor.

Comparison operators

xtensor provides overloads of the inequality operators:

  • operator<
  • operator<=
  • operator>
  • operator>=

These overloads of inequality operators are quite different from the standard C++ inequality operators: they are element-wise operators returning boolean xexpression:

#include "xtensor/xarray.hpp"

xt::xarray<int> a1 = {  1, 12,  3, 14 };
xt::xarray<int> a2 = { 11,  2, 13, 4  };
xt::xarray<bool> comp = a1 < a2;
// => comp = { true, false, true, false }

However, equality operators are similar to the traditional ones in C++:

  • operator==(const E1& e1, const E2& e2) returns true if e1 and e2 hold the same elements.
  • operator!=(const E1& e1, const E2& e2) returns true if e1 and e2 don’t hold the same elements.

Element-wise equality comparison can be achieved through the xt::equal function.

#include "xtensor/xarray.hpp"

xt::xarray<int> a1 = {  1,  2, 3, 4};
xt::xarray<int> a2 = { 11, 12, 3, 4};

bool res = (a1 == a2);
// => res = false

xt::xarray<bool> re = xt::equal(a1, a2);
// => re = { false, false, true, true }

Mathematical functions

xtensor provides overloads for many of the standard mathematical functions:

  • basic functions: abs, remainder, fma, ...
  • exponential functions: exp, expm1, log, log1p, ...
  • power functions: pow, sqrt, cbrt, ...
  • trigonometric functions: sin, cos, tan, ...
  • hyperbolic functions: sinh, cosh, tanh, ...
  • Error and gamma functions: erf, erfc, tgamma, lgamma, ....
  • Nearest integer floating point operations: ceil, floor, trunc, ...

See the API reference for a comprehensive list of available functions. Like operators, the mathematical functions are element-wise functions and apply the lazy broadcasting rules.

Reducers

xtensor provides reducers, that is, means for accumulating values of tensor expressions over prescribed axes. The return value of a reducer is an xexpression with the same shape as the input expression, with the specified axes removed.

#include "xtensor/xarray.hpp"
#include "xtensor/xmath.hpp"

xt::xarray<double> a = ones<double>({3, 2, 4, 6, 5 });
xt::xarray<double> res = xt::sum(a, {1, 3});
// => res.shape() = { 3, 4, 5 };
// => res(0, 0, 0) = 12

You can also call the reduce generator with your own reducing function:

#include "xtensor/xarray.hpp"
#include "xtensor/xreducer.hpp"

xt::xarray<double> a = some_init_function({3, 2, 4, 6, 5});
xt::xarray<double> res = reduce([](double a, double b) { return a*a + b*b; },
                                a,
                                {1, 3});

Universal functions and vectorization

xtensor provides utilities to vectorize any scalar function (taking multiple scalar arguments) into a function that will perform on xexpression s, applying the lazy broadcasting rules which we described in a previous section. These functions are called xfunction s. They are xtensor‘s counterpart to numpy’s universal functions.

Actually, all arithmetic and logical operators, inequality operator and mathematical functions we described before are xfunction s.

The following snippet shows how to vectorize a scalar function taking two arguments:

#include "xtensor/xarray.hpp"
#include "xtensor/xvectorize.hpp"

int f(int a, int b)
{
    return a + 2 * b;
}

auto vecf = xt::vectorize(f);
xt::xarray<int> a = { 11, 12, 13 };
xt::xarray<int> b = {  1,  2,  3 };
xt::xarray<int> res = vecf(a, b);
// => res = { 13, 16, 19 }