Generate a 'closeness to center' matrix in numpy

Question

I think this should be easy, but I'm not sure of an efficient way to do it.

I'd like to build a matrix in numpy that has the cityblock / manhattan closeness to the center of the matrix, in numpy, for any odd size.

For a size of 5, the output would be:

array([[0, 1, 2, 1, 0],
 [1, 2, 3, 2, 1],
 [2, 3, 4, 3, 2],
 [1, 2, 3, 2, 1],
 [0, 1, 2, 1, 0]])

What's the best way of doing this? Thanks

• Maximilian: I just made an edit. I actually think it makes most sense only for odd sizes. Thanks
• Divakar: Also, seems relevant : stackoverflow.com/questions/40126853

Answer 1

Easy and efficient with broadcasting -

def closeness_manhattan(N):
 r = np.arange(N)
 a = np.minimum(r,r[::-1])
 return a[:,None] + a

Sample runs -

In [14]: closeness_manhattan(4)
Out[14]: 
array([[0, 1, 1, 0],
 [1, 2, 2, 1],
 [1, 2, 2, 1],
 [0, 1, 1, 0]])
In [15]: closeness_manhattan(5)
Out[15]: 
array([[0, 1, 2, 1, 0],
 [1, 2, 3, 2, 1],
 [2, 3, 4, 3, 2],
 [1, 2, 3, 2, 1],
 [0, 1, 2, 1, 0]])