CODEWITHSUNDEEP
pythonarraysnumpymatrixscipy
Aleksandar Bojchevski
Aleksandar Bojchevski

Reputation: 53

Scipy/numpy: two dense, one sparse dot product

Let's say we have a matrix A of size NxN, and A is sparse and N is very large. So we naturally want to store is as as scipy sparse matrix.

We also have a dense numpy array q of size NxK, where K is relatively smaller.

How do we most efficiently perform q.T * A * q, where * is matrix multiplication, to obtain a KxK result?

One part of what we want can be done efficiently, that is just A * q, but once you do that you materialize a dense array that you then need to multiply with another dense array.

Any way to do it faster than q.T.dot(A.dot(q))?

Upvotes: 0

Views: 170

Answers (1)

hpaulj
hpaulj

Reputation: 231738

So you have

(k,N) * (N,N) * (N,k) => (k,k)

One of those dot product results in a dense array; that times another dense is also dense. With a multiplication like this you quickly loose the sparsity.

If q has a lot of 0s, and you want to preserve the sparse matrix nature of the problem, make q sparse before doing this multiplication.

Upvotes: 0

Related Questions