python - Numpy elementwise product of 3d array

Question

I have two 3d arrays A and B with shape (N, 2, 2) that I would like to multiply element-wise according to the N-axis with a matrix product on each of the 2x2 matrix. With a loop implementation, it looks like

C[i] = dot(A[i], B[i])

Is there a way I could do this without using a loop? I've looked into tensordot, but haven't been able to get it to work. I think I might want something like tensordot(a, b, axes=([1,2], [2,1])) but that's giving me an NxN matrix.

Answer 1

It seems you are doing matrix-multiplications for each slice along the first axis. For the same, you can use np.einsum like so -

np.einsum('ijk,ikl->ijl',A,B)

We can also use np.matmul -

np.matmul(A,B)

On Python 3.x, this matmul operation simplifies with @ operator -

A @ B

Benchmarking

Approaches -

def einsum_based(A,B):
    return np.einsum('ijk,ikl->ijl',A,B)

def matmul_based(A,B):
    return np.matmul(A,B)

def forloop(A,B):
    N = A.shape[0]
    C = np.zeros((N,2,2))
    for i in range(N):
        C[i] = np.dot(A[i], B[i])
    return C

Timings -

In [44]: N = 10000
    ...: A = np.random.rand(N,2,2)
    ...: B = np.random.rand(N,2,2)

In [45]: %timeit einsum_based(A,B)
    ...: %timeit matmul_based(A,B)
    ...: %timeit forloop(A,B)
100 loops, best of 3: 3.08 ms per loop
100 loops, best of 3: 3.04 ms per loop
100 loops, best of 3: 10.9 ms per loop