multiply every element in numpy.array a with every element in numpy.array b

Question

Given two numpy.arrays a and b,

c = numpy.outer(a, b)

returns an two-dimensional array where c[i, j] == a[i] * b[j]. Now, imagine a having k dimensions.

• Which operation returns an array c of dimension k+1 where c[..., j] == a * b[j]?

Additionally, let b have l dimensions.

• Which operation returns an array c of dimension k+1 where c[..., i1, i2, i3] == a * b[i1, i2, i3]?

Answer 1

The outer method of NumPy ufuncs treats multidimensional input the way you want, so you could do

np.multiply.outer(a, b)

rather than using numpy.outer.

All solutions suggested here are equally fast; for small arrays, multiply.outer has a slight edge

Code for generating the image:

import numpy as np
import perfplot


def multiply_outer(a, b):
    return np.multiply.outer(a, b)


def outer_reshape(a, b):
    return np.outer(a, b).reshape((a.shape + b.shape))


def tensor_dot(a, b):
    return np.tensordot(a, b, 0)


b = perfplot.bench(
    setup=lambda n: (np.random.rand(n, n), np.random.rand(n, n)),
    kernels=[multiply_outer, outer_reshape, tensor_dot],
    n_range=[2 ** k for k in range(7)],
)
b.save("out.png")

Answer 2

One approach would be using np.outer and then reshape -

np.outer(a,b).reshape((a.shape + b.shape))