Reshaping/Combining several sub-matrices to one matrix in multi-dimensional space

Question

I have a 5D binary array 'a' of size (2, 2, 4, 2, 2). The structure looks like this, for example:

a[0,0]:
[[[ 0.  1.]
  [ 0.  0.]]

 [[ 0.  0.]
  [ 0.  1.]]

 [[ 0.  0.]
  [ 0.  1.]]

 [[ 0.  0.]
  [ 1.  0.]]]

What I want to do is to make a (2,2,4,4) matrix that combines the 2x2 matrices in the last two axis, but in a squared structure.

The result should look like this:

result[0,0]:
[[0. 1. 0. 0.]
 [0. 0. 0. 1.]
 [0. 0. 0. 0.]
 [0. 1. 1. 0.]]

I hope this is clear enough. If I put the brackets of original matrices in results, it looks like this:

result[0,0]:
[[[0. 1. [0. 0.]
 [0. 0.] 0. 1.]]
 [[0. 0. [0. 0.]
 [0. 1.] 1. 0.]]]

No it isn't clear enough. It would help if you gave a test case that we can use with a simple cut-n-paste. Otherwise we are likely to miss some nuance of your goal. — hpaulj, Jan 05 '16 at 08:06
That last addition of brackets is more confusing that helpful. — hpaulj, Jan 05 '16 at 08:08

Divakar · Accepted Answer · 2016-01-05T08:19:28.430

3

It seems you are breaking the third axis from (4) into (2,2) and bringing in the first half of the split axes to the second last axes position. So, there are two ways to achieve such an output using np.reshape and np.transpose, like so -

out = a.reshape(2,2,2,2,2,2).transpose(0,1,3,4,2,5).reshape(2,2,4,4)

out = a.reshape(2,2,2,-1,2).transpose(0,1,3,2,4).reshape(2,2,4,4)

Sample run -

In [69]: a[0][0]
Out[69]: 
array([[[49, 91],
        [10, 32]],

       [[71, 27],
        [50, 64]],

       [[ 9, 41],
        [73, 52]],

       [[54, 85],
        [53, 36]]])

In [70]: out1 = a.reshape(2,2,2,2,2,2).transpose(0,1,3,4,2,5).reshape(2,2,4,4)

In [71]: out2 = a.reshape(2,2,2,-1,2).transpose(0,1,3,2,4).reshape(2,2,4,4)

In [72]: out1[0][0]
Out[72]: 
array([[49, 91,  9, 41],
       [10, 32, 73, 52],
       [71, 27, 54, 85],
       [50, 64, 53, 36]])

In [73]: out2[0][0]
Out[73]: 
array([[49, 91,  9, 41],
       [10, 32, 73, 52],
       [71, 27, 54, 85],
       [50, 64, 53, 36]])

edited Jan 05 '16 at 08:19

answered Jan 05 '16 at 08:08

Divakar

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Thank you so much! This is almost what I want. My question was ambiguous in terms of mentioning the order of combination. So you are stacking them on top first and then you move to the right. Is it possible to do it the other way around so that the out[0,0] looks like: ```[[49, 91, 71, 27], [10, 32, 50, 64], [9, 41, 54, 85], [50, 64, 53, 36]]``` – Babak Jan 05 '16 at 08:50
@Babak Shouldn't the last one be `[73, 52, 53, 36]`? Assuming that, this should do it - `a.reshape(2,2,2,2,2,2).transpose(0,1,2,4,3,5).reshape(2,2,4,4) `. – Divakar Jan 05 '16 at 08:58
Thank you so much! You are a true wizard – Babak Jan 05 '16 at 09:07

hpaulj · Answer 2 · 2016-01-05T08:25:40.793

First, it is better to index your array like a[0,0] or a[0,0,...] or a[0,0,:,:].

Does a.reshape(2,2, 4,4) do what you want? That retains all values, but reshapes the inner most (2,2) arrays into (4,) arrays.

Looking more closely it looks like you want to reorder values in the inner arrays. That is not entirely obvious from your description. I had to carefully match up values between the displays. In particular it's only 2 of the subarrays that are unabiguous:

[[ 0.  0.]
  [ 0.  1.]]

 [[ 0.  0.]
  [ 1.  0.]]]

[0. 0. 0. 0.]
 [0. 1. 1. 0.]]

What we will need to do is transpose the last 2 axes before reshaping.

This might do the trick:

a.transpose(0,1,2,4,3).reshape(2,2,4,4)

It works with np.ones((2,2,4,2,2)), but I haven't tested it with numbers that duplicate your question - because you did not give a test case that can be cut-n-pasted.

oops - looks like Divakar got it right. We need to break up the 4 dimension into 2,2, and perform the transpose across dimensions.

In [290]: a=np.array([[[0,1],[0,0]],[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[1,0]]])
In [291]: a
Out[291]: 
array([[[0, 1],
        [0, 0]],

       [[0, 0],
        [0, 1]],

       [[0, 0],
        [0, 1]],

       [[0, 0],
        [1, 0]]])
In [292]: a.reshape(2,2,2,2).transpose(0,2,1,3).reshape(4,4)
Out[292]: 
array([[0, 1, 0, 0],
       [0, 0, 0, 1],
       [0, 0, 0, 0],
       [0, 1, 1, 0]])

Here's a clearer example:

In [303]: a=np.arange((4*2*2)).reshape(4,2,2)
In [304]: a.reshape(2,2,2,2).transpose(0,2,1,3).reshape(4,4)
Out[304]: 
array([[ 0,  1,  4,  5],
       [ 2,  3,  6,  7],
       [ 8,  9, 12, 13],
       [10, 11, 14, 15]])

It would be even better if each of the dimensions was different, so there'd even less ambiguity as to which ones are being combined.

In [308]: a=np.arange((6*5*7)).reshape(6,5,7)
In [309]: a.reshape(2,3,5,7).transpose(0,2,1,3).reshape(10,21)

Thank you. Sorry about indexing my arrays. I fixed that – Babak Jan 05 '16 at 09:10 — Babak, Jan 05 '16 at 09:10

Reshaping/Combining several sub-matrices to one matrix in multi-dimensional space

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