I am trying to make sense of np.einsum, and there does not appear to be examples related to my specific context. There are many good examples in the numpy docs, a guide here, here, and a stackoverflow answer here.
There is no example similar to my problem which is np.einsum("ijij->ij", padded_matrix)
where when I output padded_matrix I get
>> padded_matrix
>> [[[[[1. 0. 0. 0.33333333 0. 0.33333333]]
[[0. 1. 0. 0. 0. 0. ]]
[[0. 0. 1. 0. 0. 0. ]]
[[0.33333333 0. 0. 1. 0. 0.33333333]]
[[0. 0. 0. 0. 1. 0. ]]
[[0.33333333 0. 0. 0.33333333 0. 1. ]]]]]
padded_matrix is length of 1, and is <class 'numpy.ndarray'>. Unfortunately copying the output for padded matrix does not work. In the actual program, padded_matrix is a call to a function too complicated to include here, hence, why I have copied its output.
The result is [[1. 1. 1. 1. 1. 1.]] but I cannot figure out how the elements were multiplied and then which axis was summed.
Given that I have not provided a working MWE, if anyone can just tell me what "ijij->ij" should do in the context of the given padded_matrix as a <class 'numpy.ndarray'>, I would be grateful.
np.einsum("ii->i,A") views the diagonal of Matrix A, so does this mean that in this usage, i is effectively replaced by ij due to all the padding, so that np.einsum("ijij->ij",padded_matrix) is a view of the diaganol?
There's no multiplication since there's only one argument:
In [25]: arr = np.arange(36).reshape(1,6,1,6)
In [26]: arr
Out[26]:
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]]]])
In [27]: np.einsum('ijij->ij', arr)
Out[27]: array([[ 0, 7, 14, 21, 28, 35]])
This einsum is effectively a diagonal.
In [29]: np.einsum('ii->i', arr.squeeze())
Out[29]: array([ 0, 7, 14, 21, 28, 35])
In [30]: np.diagonal(arr.squeeze())
Out[30]: array([ 0, 7, 14, 21, 28, 35])