Fastest way to multiply arrays of matrices in Python (numpy)

Question

I have two arrays of 2-by-2 complex matrices, and I was wondering what would be the fastest method of multiplying them. (I want to do matrix multiplication on the elements of the matrix arrays.) At present, I have

numpy.array(map(lambda i: numpy.dot(m1[i], m2[i]), range(l)))

But can one do better than this?

Thanks,

v923z

Answer 1

numpy.einsum is the optimal solution for this problem, and it is mentioned way down toward the bottom of DaveP's reference. The code is clean, very easy to understand, and an order of magnitude faster than looping through the array and doing the multiplication one by one. Here is some sample code:

import numpy
l = 100

m1 = rand(l,2,2)
m2 = rand(l,2,2)

m3 = numpy.array(map(lambda i: numpy.dot(m1[i], m2[i]), range(l)))
m3e = numpy.einsum('lij,ljk->lik', m1, m2)

%timeit numpy.array(map(lambda i: numpy.dot(m1[i], m2[i]), range(l)))
%timeit numpy.einsum('lij,ljk->lik', m1, m2)

print np.all(m3==m3e)

Here are the return values when run in an ipython notebook:
1000 loops, best of 3: 479 µs per loop
10000 loops, best of 3: 48.9 µs per loop
True