Notable differences with numpy


xtensor and numpy are very different libraries in their internal semantics. While xtensor is a lazy expression system, numpy manipulates in-memory containers, however, similarities in APIs are obvious. See e.g. the numpy to xtensor cheat sheet.

And this page tracks the subtle differences of behavior between NumPy and xtensor.

Zero-dimensional arrays

With NumPy, 0-D arrays are nearly indistinguishable from scalars. This led to some issues w.r.t. universal functions returning scalars with 0-D array inputs instead of actual arrays…

In xtensor, 0-D expressions are not implicitly convertible to scalar values. Values held by 0-D expressions can be accessed in the same way as values of higher dimensional arrays, that is with operator[], operator() and element.

Accumulators (cumsum, cumprod) throw an exception if an axis argument is passed and the array argument is a 0-D argument:

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

xt::xarray<double> x = 1;
std::cout << xt::cumsum(x, 0) << std::endl;
// Outputs:
// Standard Exception: Axis larger than expression dimension in accumulator.

std::cout << xt::cumsum(x) << std::endl;
// 1


numpy.meshgrid supports two modes: the ‘xy’ indexing and the ‘ij’ indexing.

The following code

import numpy as np

x1, x2, x3, x4 = [1], [10, 20], [100, 200, 300], [1000, 2000, 3000, 4000]

ij = np.meshgrid(x1, x2, x3, x4, indexing='ij')
xy = np.meshgrid(x1, x2, x3, x4, indexing='xy')

print 'ij:', [m.shape for m in ij]
print 'xy:', [m.shape for m in xy]

would return

ij: [(1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4)]
xy: [(2, 1, 3, 4), (2, 1, 3, 4), (2, 1, 3, 4), (2, 1, 3, 4)]

In other words, the ‘xy’ indexing, which is the default only reverses the first two dimensions compared to the ‘ij’ indexing.

xtensor’s version of meshgrid corresponds to the ‘ij’ indexing.

The random module

Like most functions of xtensor, functions of the random module return expressions that don’t hold any value.

Every time an element is accessed, a new random value is generated. To fix the values of a generator, it should be assigned to a container such as xarray or xtensor.

Missing values

Support of missing values in NumPy can be emulated with the masked array module, which provides a means to handle arrays that have missing or invalid data.

Support of missing values in xtensor is done through a notion of optional values, implemented in xoptional<T, B>, which serves both as a value type for container and as a reference proxy for optimized storage types. See the section of the documentation on Missing values.


Strided containers of xtensor and NumPy having the same exact memory layout may have different strides when accessing them through the strides attribute. The reason is an optimization in xtensor, which is to set the strides to 0 in dimensions of length 1, which simplifies the implementation of broadcasting of universal functions.


Use the free function xt::strides to switch between representations.

xt::strides(a); // strides of ``a`` corresponding to storage
xt::strides(a, xt::stride_type::normal); // same

xt::strides(a, xt::stride_type::internal); // ``== a.strides()``

xt::strides(a, xt::stride_type::bytes) // strides in bytes, as in NumPy

Array indices

Array indices are in xtensor stored as a std::vector of array indices, whereby each entry corresponds to the array indices of one item. This results in a slightly different usage of xt::ravel_indices than of numpy.ravel_multi_index.