Creating a 4D view on 2D array to divide it into cells of fixed size

Question

I have a 2D array t in numpy:

>>> t = numpy.array(range(81)).reshape((9,9))
>>> t
array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8],
       [ 9, 10, 11, 12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23, 24, 25, 26],
       [27, 28, 29, 30, 31, 32, 33, 34, 35],
       [36, 37, 38, 39, 40, 41, 42, 43, 44],
       [45, 46, 47, 48, 49, 50, 51, 52, 53],
       [54, 55, 56, 57, 58, 59, 60, 61, 62],
       [63, 64, 65, 66, 67, 68, 69, 70, 71],
       [72, 73, 74, 75, 76, 77, 78, 79, 80]])

It is indexed by two numbers: row and column index.

>>> t[2,3]
21
>>> t.shape
(9, 9)
>>> t.strides
(72, 8)

What I want to do is to divide the array into rectangular cells of fixed size, 3×3 for example. I'd like to avoid memory copying. The way I try to achieve this is creating a view onto t with correspondent shape and strides ((3,3,3,3) and (216,24,72,8) respectively). This way the first two indexes of the view would mean the position of 3×3 cell in the larger grid and the last two would mean the position of element inside the cell. For example, t[0,1,:,:] would return

array([[ 3,  4,  5],
       [12, 13, 14],
       [21, 22, 23]])

So my question is — how to create the described view? Am I missing a simpler method? Can this be done elegantly with slicing syntax?

Answer 1

Edit: A way that does not require you to figure out the strides yourself is

numpy.rollaxis(t.reshape(3, 3, 3, 3), 2, 1)

[end of edit]

Another way to achieve this is to use numpy.lib.stride_tricks.as_strided:

>>> t = numpy.arange(81.).reshape((9,9))
>>> numpy.lib.stride_tricks.as_strided(t, shape=(3,3,3,3), strides=(216,24,72,8))
array([[[[  0.,   1.,   2.],
         [  9.,  10.,  11.],
         [ 18.,  19.,  20.]],

        [[  3.,   4.,   5.],
         [ 12.,  13.,  14.],
         [ 21.,  22.,  23.]],

        [[  6.,   7.,   8.],
         [ 15.,  16.,  17.],
         [ 24.,  25.,  26.]]],


       [[[ 27.,  28.,  29.],
         [ 36.,  37.,  38.],
         [ 45.,  46.,  47.]],

        [[ 30.,  31.,  32.],
         [ 39.,  40.,  41.],
         [ 48.,  49.,  50.]],

        [[ 33.,  34.,  35.],
         [ 42.,  43.,  44.],
         [ 51.,  52.,  53.]]],


       [[[ 54.,  55.,  56.],
         [ 63.,  64.,  65.],
         [ 72.,  73.,  74.]],

        [[ 57.,  58.,  59.],
         [ 66.,  67.,  68.],
         [ 75.,  76.,  77.]],

        [[ 60.,  61.,  62.],
         [ 69.,  70.,  71.],
         [ 78.,  79.,  80.]]]])

Note that the strides you provided are correct only for float arrays (itemsize == 8), while the example t in your post is an int array (which might or might no have itemsize == 8).

Answer 2

You can do:

t = np.arange(81).reshape(9,9)
t.shape = (3, 3, 3, 3)
t = t.transpose((0, 2, 1, 3))

>>> print t.strides
(108, 12, 36, 4)

>>> print t
[[[[ 0  1  2]
   [ 9 10 11]
   [18 19 20]]

  [[ 3  4  5]
   [12 13 14]
   [21 22 23]]

  [[ 6  7  8]
   [15 16 17]
   [24 25 26]]]


 [[[27 28 29]
   [36 37 38]
   [45 46 47]]

  [[30 31 32]
   [39 40 41]
   [48 49 50]]

  [[33 34 35]
   [42 43 44]
   [51 52 53]]]


 [[[54 55 56]
   [63 64 65]
   [72 73 74]]

  [[57 58 59]
   [66 67 68]
   [75 76 77]]

  [[60 61 62]
   [69 70 71]
   [78 79 80]]]]

transpose will return a view whenever possible, that way you don't have to worry about knowing the data type.