numpy vectorise approach to creating array results computed from indices

Question

What is an efficient numpy way of achieving an array of results based on a pair of index datasets?

So, lets say there are 2 arrays these are the row and column headers in the table underneath:

a = [1,3,4,6]
b = [2,7,8,10,15]

The resultant matrix I am looking for is a function based on a and b: f(a,b) So assuming the function is simply a+b thus:

  a ||  1 |  3 |  4 |  6
=========================
b 2 ||  3 |  5 |  6 |  8 <-- ie 2+1=3, 2+3=5 etc 
  7 ||  8 | 10 | 11 | 13
  8 ||  9 | 11 | 12 | 14
 10 || 11 | 13 | 14 | 16
 15 || 16 | 18 | 19 | 21

Obviously I could loop through each array and update the results of say a np.zeros() but I am assuming there should be a more efficient way of achieving this? TIA

colonel · Accepted Answer · 2025-10-30 17:35:40Z

6

You can do this efficiently and vectorized in NumPy using broadcasting.

import numpy as np
a = np.array([1, 3, 4, 6])
b = np.array([2, 7, 8, 10, 15])
result = b[:, None] + a
print(result)

answered Oct 30 at 17:35

colonel

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PaulS · Accepted Answer · 2025-10-30 20:11:02Z

4

Another possible solution:

np.add.outer(b, a)

The np.add function performs element-wise addition, and the outer method applies that operation to every possible combination of one element from each input array. We can use other function beyond add.

Output:

array([[ 3,  5,  6,  8],
       [ 8, 10, 11, 13],
       [ 9, 11, 12, 14],
       [11, 13, 14, 16],
       [16, 18, 19, 21]])

edited Oct 30 at 20:11

answered Oct 30 at 20:04

PaulS

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1 Comment

juanpa.arrivillaga Oct 30 at 21:25

One of the advantages of this approach is that you can provide the dtype or out parameter to .outer

leofun01 · Accepted Answer · 2025-11-01 11:16:34Z

0

I did not understand why numpy was mentioned. Regular Python iterables will be enough for your goal.

a = [1,3,4,6]
b = [2,7,8,10,15]

def f(a, b): return a + b
# or
# f = lambda a, b: a + b

[[f(a, b) for a in a] for b in b]

[[ 3,  5,  6,  8],
 [ 8, 10, 11, 13],
 [ 9, 11, 12, 14],
 [11, 13, 14, 16],
 [16, 18, 19, 21]]

answered Nov 1 at 11:16

leofun01

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