In numpy, how to efficiently list all fixed-size submatrices?

Question

I have an arbitrary NxM matrix, for example:

1 2 3 4 5 6
7 8 9 0 1 2
3 4 5 6 7 8
9 0 1 2 3 4

I want to get a list of all 3x3 submatrices in

Answer 1

You want a windowed view:

from numpy.lib.stride_tricks import as_strided

arr = np.arange(1, 25).reshape(4, 6) % 10
sub_shape = (3, 3)
view_shape = tuple(np.subtract(arr.shape, sub_shape) + 1) + sub_shape
arr_view = as_strided(arr, view_shape, arr.strides * 2
arr_view = arr_view.reshape((-1,) + sub_shape)

>>> arr_view
array([[[[1, 2, 3],
         [7, 8, 9],
         [3, 4, 5]],

        [[2, 3, 4],
         [8, 9, 0],
         [4, 5, 6]],

        ...

        [[9, 0, 1],
         [5, 6, 7],
         [1, 2, 3]],

        [[0, 1, 2],
         [6, 7, 8],
         [2, 3, 4]]]])

The good part of doing it like this is that you are not copying any data, you are simply accessing the data of your original array in a different way. For large arrays this can result in tremendous memory savings.