What is the more efficient way to create a pairwise 2D array for a 1D numpy array?

Given 2 numPy arrays of length N, I would like to create a pairwise 2D array (N x N) based on a custom function.

    import numpy as np
    import pandas as pd
    
    A = np.array(A) # size N
    B = np.array(B) # size N
    Fij = f(A[i], B[i], A[j], B[j])
    
    # f is a pairwise function of Ai, Bi and Aj, Bj

I would like to create an array C of size NxN. such that

    C = Fij # with i, j in range(N)

Example:

    A = [1,2,3,4]
    B = ['a', 'b', 'c', 'd']
    
    def f(i,j):
        return str(A[i]+A[j])+B[i]+B[j]
    # f(0,1) = 3ab

I would like to create

C = [[2aa, 3ab, 4ac, 5ad],
     [3ba, 4bb, 5bc, 6bd], 
     [4ca, 5cb, 6cc, 7cd], 
     [5da, 6db, 7dc, 8dd]]

I know I can do this by nested loop:

C=np.empty([N, N])
for i in range(N):
    for j in range(N):
        C[i, j] = f(i,j)

but looking for a neat and more efficient solution.

Answer

In numpy you can make a nice solution by using + to both add the integers and concatenate the characters.

A = np.array([1,2,3,4])
B = np.char.array(['a', 'b', 'c', 'd']) # char array so can use "+" instead of "add"

A0 = A[:,None] + A[None,:]  # add the integers
B0 = B[:,None] + B[None,:]  # concatenate the characters
C = A0.astype('<U1') + B0

Or as a single line:

C = (A[:,None] + A[None,:]).astype('<U1') + B[:,None] + B[None,:]

Printing out each line in the above, gives:

A0
[[2 3 4 5]
 [3 4 5 6]
 [4 5 6 7]
 [5 6 7 8]]

B0
[['aa' 'ab' 'ac' 'ad']
 ['ba' 'bb' 'bc' 'bd']
 ['ca' 'cb' 'cc' 'cd']
 ['da' 'db' 'dc' 'dd']]

C
[['2aa' '3ab' '4ac' '5ad']
 ['3ba' '4bb' '5bc' '6bd']
 ['4ca' '5cb' '6cc' '7cd']
 ['5da' '6db' '7dc' '8dd']]