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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.
c of dimension k+1 where c[..., j] == a * b[j]?Additionally, let b have l dimensions.
c of dimension k+1 where c[..., i1, i2, i3] == a * b[i1, i2, i3]?
311
You can use np. multiply to multiply two same-sized arrays together. This computes something called the Hadamard product. In the Hadamard product, the two inputs have the same shape, and the output contains the element-wise product of each of the input values.
If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred. If either a or b is 0-D (scalar), it is equivalent to multiply and using numpy.multiply(a, b) or a * b is preferred. If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.
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")
One approach would be using np.outer and then reshape -
np.outer(a,b).reshape((a.shape + b.shape))
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