python - Separable filter on numpy array -

say have numpy array a, , want create new array, b such b[i, j] function of, say:

a[i-1, j-1], a[i-1, j  ], a[i-1, j+1], a[i  , j-1], a[i  , j  ], a[i  , j+1], a[i+1, j-1], a[i+1, j  ], a[i+1, j+1] 

what fastest way this?

as separable filter, there way run in multiple threads? (not processes, because have copy data back)

or writing c code bypass gil mandatory?

partial solutions (like assuming function linear) welcome too.

an idealized numpy way of working sliding window construct 4d array

c.shape = (n,m,3,3) 

where

c[i,j,:,:] = np.array([a[i-1, j-1], a[i-1, j  ], a[i-1, j+1],                        a[i  , j-1], a[i  , j  ], a[i  , j+1],                        a[i+1, j-1], a[i+1, j  ], a[i+1, j+1]]) 

and write function sort of reduction on last 2 dimensions. sum or mean typical, e.g.

b = c.sum(axis=(2,3)) 

other questions show how use np.lib.stride_tricks.as_strided construct such array. 3x3 subarray, might fast like

c = np.zeros((n,m,3,3)) c[:,:,0,0] = a[:-1,:-1] etc. 

(or use hstack , vstack same effect).

but nice thing (or maybe not nice) strided approach doesn't involve copy data of a - view.

as splitting job pieces, can imagine using slices of c (on 1st 2 dimensions), e.g.

 c[0:100,0:100,:,:].sum(axis=(2,3))