Multiplying Tensors Containing Images In Numpy

I have the following 3rd order tensors. Both tensors matrices the first tensor containing 100 10x9 matrices and the second containing 100 3x10 matrices (which I have just filled wi

Solution 1:

Did you try?

In [96]: np.einsum('ijk,ilj->ilk',T1,T2).shape
Out[96]: (100, 3, 9)

The way I figure this out is look at the shapes:

(100, 10, 9))  (i, j, k)
(100, 3, 10)   (i, l, j)
-------------
(100, 3, 9)    (i, l, k)

the two j sum and cancel out. The others carry to the output.

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For 4d arrays, with dimensions like (100,3,2,24 ) there are several options:

Reshape to 3d, T1.reshape(300,2,24), and after reshape back R.reshape(100,3,...). Reshape is virtually costless, and a good numpy tool.

Add an index to einsum: np.einsum('hijk,hilj->hilk',T1,T2), just a parallel usage to that of i.

Or use elipsis: np.einsum('...jk,...lj->...lk',T1,T2). This expression works with 3d, 4d, and up.