theano - Operate Two Matrix By Rule like T.dot

Question

I want to operate two matrix by rule as T.dot, like:

op( [v1, v2, v3] ,  [u1, u2, u3].T )
(v & u are all vectors)

and return the matrix:

[[op(v1, u1), op(v1, u2), op(v1, u3)],
 [op(v2, u1), op(v2, u2), op(v2, u3)],
 [op(v3, u1), op(v3, u2), op(v3, u3)]]

But, instead dot between two vectors, I want the op is the function to compute cosine similarity.

Is there any function can do this in theano?

=======

The cosine similarity function is:

import theano.tensor as T
x = T.vector()
y = T.vector()
result, _ = T.dot(x, y) / (x.norm(2) * y.norm(2))
cosine_similarity = theano.function(inputs=[x,y], outputs=[result])

Answer 1

You should probably do this with the matrices directly:

Define

V = (v1, v2, v3)
U = (u1, u2, u3)

Then

import theano.tensor as T
import numpy as np

U = T.fmatrix()
V = T.fmatrix()

cos_sim = T.dot(U, V.T) / (T.sqrt((U ** 2).sum(0)) * T.sqrt((V ** 2).sum(0).reshape((-1, 1))))

u = np.arange(9.).reshape(3, 3)

cos_sim.eval({U: u.astype('float32'), V: u.astype('float32')})