Extract hyper-cubical blocks from a numpy array with unknown number of dimensions
<p>I have a bit of python code which currently is hard-wired with two-dimensional arrays as follows:</p>

<pre><code>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
</code></pre>

<p>Now, this is hard coded for a 2-dimensional array and I would like to extend this 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 generate these sub-blocks without having to replicate this function for multidimensional data.</p>

<p>Here is my wack at this problem.  The idea behind the code below is to find the "starting indices" for each slice of data. So for 4x4x4 sub-arrays of a 5x5x5 array, the starting indices would be <code>(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,1)</code>, and the slices along each dimension would be of length 4.  </p>

<p>To get the sub-arrays, you just need to iterate over the different tuples of slice objects and pass them to the array.</p>

<pre><code>import numpy as np
from itertools import product

def iterslice(data_shape, width):
    # check for invalid width
    assert(all(sh&gt;=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]
</code></pre>

python numpy multidimensional-array