Extract hypercube blocks from a numpy array with an unknown number of dimensions

Question

I have some python code that is currently tightly coupled to two-dimensional arrays as follows:

import numpy as np
data = np.random.rand(5, 5)
width = 3

for y in range(0, data.shape[1] - W + 1):
    for x in range(0, data.shape[0] - W + 1):
        block = data[x:x+W, y:y+W]
        # Do something with this block

Now this is hard-coded for a 2-dimensional array, and I would like to expand it to 3D and 4D arrays. I could, of course, write more functions for other dimensions, but I was wondering if there is a python / numpy trick to create these subunits without having to replicate this function for multidimensional data.

Answer 1

. - " " . , 4x4x4 5x5x5 (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,1), 4.

, .

import numpy as np
from itertools import product

def iterslice(data_shape, width):
    # check for invalid width
    assert(all(sh>=width for sh in data_shape), 
           'all axes lengths must be at least equal to width')

    # gather all allowed starting indices for the data shape
    start_indices = [range(sh-width+1) for sh in data_shape]

    # create tuples of all allowed starting indices
    start_coords = product(*start_indices)

    # iterate over tuples of slice objects that have the same dimension
    # as data_shape, to be passed to the vector
    for start_coord in start_coords:
        yield tuple(slice(coord, coord+width) for coord in start_coord)

# create 5x5x5 array
arr = np.arange(0,5**3).reshape(5,5,5)

# create the data slice tuple iterator for 3x3x3 sub-arrays
data_slices = iterslice(arr.shape, 3)

# the sub-arrays are a list of 3x3x3 arrays, in this case
sub_arrays = [arr[ds] for ds in data_slices]