Given two large numpy arrays, how to efficiently compute a matrix of a-b for any all (a,b) pair of the two arrays?

Question

I have two large numpy arrays A, B. How can I efficiently (e.g. using numpy vectorization) compute a matrix C of shape len(A) * len(B) such that C[i,j]=A[i]- C[j].

For example, A is

a
b
c

B is

d
e 
f
g

Then expected C is

a-d a-e a-f a-g
b-d b-e b-f b-g
c-d c-e c-f c-g

Answer 1

import numpy as np

a = np.array([1,2,3])
b = np.array([4,5,6])

A = np.tile(a.reshape(3,1),(1,3))
B = np.tile(b,(3,1))
C = A - B

print(A)
print(B)
print(C)

Yields:

[[1 1 1]
 [2 2 2]
 [3 3 3]]
[[4 5 6]
 [4 5 6]
 [4 5 6]]
[[-3 -4 -5]
 [-2 -3 -4]
 [-1 -2 -3]]

Try it online!