I have numpy ndarrays which could be 3 or 4 dimensional. I'd like to find maximum values and their indices in a moving subarray window with specified strides.
For example, suppose I have a 4x4 2d array and my moving subarray window is 2x2 with stride 2 for simplicity:
[[ 1, 2, 3, 4],
[ 5, 6, 7, 8],
[ 9,10,11,12],
[13,14,15,16]].
I'd like to find
[[ 6 8],
[14 16]]
for max values and
[(1,1), (3,1),
(3,1), (3,3)]
for indices as output.
Is there a concise, efficient implementation for this for ndarray without using loops?
Here's a solution using stride_tricks:
def make_panes(arr, window):
arr = np.asarray(arr)
r,c = arr.shape
s_r, s_c = arr.strides
w_r, w_c = window
if c % w_c != 0 or r % w_r != 0:
raise ValueError("Window doesn't fit array.")
shape = (r / w_r, c / w_c, w_r, w_c)
strides = (w_r*s_r, w_c*s_c, s_r, s_c)
return np.lib.stride_tricks.as_strided(arr, shape, strides)
def max_in_panes(arr, window):
w_r, w_c = window
r, c = arr.shape
panes = make_panes(arr, window)
v = panes.reshape((-1, w_r * w_c))
ix = np.argmax(v, axis=1)
max_vals = v[np.arange(r/w_r * c/w_c), ix]
i = np.repeat(np.arange(0,r,w_r), c/w_c)
j = np.tile(np.arange(0, c, w_c), r/w_r)
rel_i, rel_j = np.unravel_index(ix, window)
max_ix = i + rel_i, j + rel_j
return max_vals, max_ix
A demo:
>>> vals, ix = max_in_panes(x, (2,2))
>>> print vals
[[ 6 8]
[14 16]]
>>> print ix
(array([1, 1, 3, 3]), array([1, 3, 1, 3]))
Note that this is pretty untested, and is designed to work with 2d arrays. I'll leave the generalization to n-d arrays to the reader...
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