Multidimensional matrix multiplication on numpy array

Question

I'm implementing a neural network in python, as a part of backpropagation I need to multiply a 3D matrix,call it A, dimension (200, 100, 1) , by a 2D matrix, call it W,dimension (100, 200) the result should have dimensions (200, 200, 1).

A is an error vector, W is a weight matrix, the product is to be used to calculate the updates for the previous layer.

I tried solving it using matrix_multiply(from numpy.core.umath_tests), I tried reshaping W to (100,200,1) and then multiplying, but that throws

ValueError: matrix_multiply: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (m,n),(n,p)->(m,p) (size 100 is different from 1).

How can I solve this?

Do you have a compelling reason for keeping the shape of A as (200, 100, 1), instead of dropping the trivial dimension and making its shape (200, 100)? — Warren Weckesser
– Warren Weckesser, Commented Feb 11, 2017 at 15:21
@WarrenWeckesser I didn't consider that option. Thanks for the suggestion, I'll explore it. — Effective_cellist
– Effective_cellist, Commented Feb 11, 2017 at 15:59

Divakar · Accepted Answer · 2017-02-11 15:19:58Z

4

You could use np.tensordot and then permute axes with swapaxes or simply reshape -

np.tensordot(A,W,axes=((1),(0))).swapaxes(1,2)
np.tensordot(A,W,axes=((1),(0))).reshape(A.shape[0],W.shape[1],1)

Alternatively, we can use np.dot using the only slice along the last axis of A and then after matrix-multiplication extend into 3D -

A[:,:,0].dot(W)[...,None]

Or we can use np.einsum -

np.einsum('ijk,jl->ilk',A,W)

edited Feb 11, 2017 at 15:19

answered Feb 11, 2017 at 15:14

Divakar

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