efficient addition of (m, 2), (n, 2) arrays

Question

I have two numpy arrays, x of shape (m, 2) and y of shape (n, 2) . I would like compute the (m, n, 2) array where at position (i, j) one finds the sum of x[i] and y[j] at out[i, j] . List comprehension works

import numpy

x = numpy.random.rand(13, 2)
y = numpy.random.rand(5, 2)

xy = numpy.array([
    [xx + yy for yy in y]
    for xx in x
])

but I was wondering if there is a more efficient solution via numpy.add.outer or something along those lines.

Answer 1

You can use numpys broadcasting rules to cast the first array to the shape (13, 1, 2) and the second to the shape (1, 5, 2) :

numpy.all(x[:, None, :] + y[None, :, :] == xy)
# True

The array is repeated across the dimension where None is added (since it has length 1).

Therefore the shape of the output becomes (13, 5, 2) .

Answer 2

xy = x[:, None]+y

应该做的伎俩。