batch pairwise dot product using numpy

Question

I have two batches of vectors: W= [w1,w2, w3,...]

and

V= [v1,v2,v3,...].

Both batches are expressed in numpy 2D vectors [[x1, y1], [x2,y2]...]

I want to calculate the pairwise dot product between any element in W and a element in V, and i want a matrix of possible combinations, ie

[ w1.v1, w1.v2, w1.v3,...

w2.v1, w2.v2, w2.v3,...

w3.v1, w3.v2, w3.v3,...

....................................... ]

if w and v are simple scalars then this is easy.

But the problem is w and v are 1D vectors: [x, y]

How do I implement this in numpy?

Thanks

Answer 1

Assuming that you want to compute the dot products of row vectors,

np.einsum('ji,ki-> jk', V, W)

If column vectors

np.einsum('ij,ik-> jk', V, W)