Quite simply, what I want to do is the following
A = np.ones((3,3)) #arbitrary matrix
B = np.ones((2,2)) #arbitrary matrix
A[1:,1:] = A[1:,1:] + B
except in Tensorflow (where the matrices can be arbitrarily complicated tensor expressions). Neither A nor B is a Tensorflow Variable, but just a run-of-the-mill tensor.
What I have gathered so far: tensors are immutable, so I cannot assign to a submatrix. tf.scatter_nd is the current option for sub-assignment, but does not appear to support sub-matrices, only slices.
Methods that should work, but are perhaps not ideal:
- I could pad B with zeros, but I'm sure this leads to instantiation of an unnecessarily large B - can it be made sparse, maybe?
- I could use the padding idea, but write it as a low-rank decomposition, e.g. in Numpy:
A+U.dot(B).U.TwhereUis a stacked zero and identity matrix. I'm not sure this is actually advantageous. - I could split
Ainto submatrices, and stack them back together. Might be the most efficient, but sounds like the code would be convoluted.
Ideally, I want to do this operation N times for progressively smaller matrices, resulting in one large final result, but this is tangential.
I'll use one of the hacks for now, but I'm hoping someone can tell me what the idiomatic version is!
