Using numpy arithmetic based on position in numpy array

Question

I am not quite sure how to describe my question, but I will try.

I want to know if numpy has the functionality to do this:

Lets say I have a 2D array called grid:

grid = [ [0,0],
         [0,0] ]

I also have a second 2D array called aList:

aList = [ [1,2],
          [3,4] ]

I want to apply math to the first array based on the index of the first array.

So the math done at each iteration would look like this:

grid[i][j] = [(i - aList[k][0]) + (j - aList[k][1])] 

Currently doing this in python with for loops is way to expensive so I need an alternative.

EDIT: more clarification, if I were not to use numpy I would write something like this:

for i in range(2):
    for j in range(2):
        num = 0 
        for k in range(2):
            num += (i-aList[k][0]) + (j-aList[k][1])
        grid[i][j] = num

This is however way to slow in python for the amount of data I have.

Answer 1

Your code can be reproduced and substantially sped up as follows:

i_s = np.arange(2)
j_s = np.arange(2)

fast_grid = (i_s + j_s[:, None])*len(aList) - aList.sum()