6

I have numpy compiled with OpenBlas and I am wondering why einsum is much slower than dot (I understand in the 3 indices case, but I dont understand why it is also less performant in the two indices case)? Here an example:

import numpy as np
A = np.random.random([1000,1000])
B = np.random.random([1000,1000])

%timeit np.dot(A,B)

Out: 10 loops, best of 3: 26.3 ms per loop

%timeit np.einsum("ij,jk",A,B)

Out: 5 loops, best of 3: 477 ms per loop

Is there a way to let einsum use OpenBlas and parallelization like numpy.dot? Why does np.einsum not just call np.dot if it notices a dot product?

varantir
  • 6,624
  • 6
  • 36
  • 57
  • Related: http://stackoverflow.com/questions/20149201/why-is-numpys-einsum-slower-than-numpys-built-in-functions – Alex Riley May 27 '15 at 13:38
  • That is true, but my question rather related to the two indices case. The answers in the given post give me the impression that there are issues with three indices. I was surprised that the difference of speeds in this specific exampe is so impressive. – varantir May 27 '15 at 13:42
  • 4
    Because einsum is written to be generic and does not special case the two index dot product to use blas. That is really the bottom line. If you know you only have two indices, just use dot. – BeRecursive May 27 '15 at 15:13

1 Answers1

3

einsum parses the index string, and then constructs an nditer object, and uses that to perform a sum-of-products iteration. It has special cases where the indexes just perform axis swaps, and sums ('ii->i'). It may also have special cases for 2 and 3 variables (as opposed to more). But it does not make any attempt to invoke external libraries.

I worked out a pure python work-a-like, but with more focus on the parsing than the calculation special cases.

tensordot reshapes and swaps, so it can then call dot to the actual calculations.

hpaulj
  • 221,503
  • 14
  • 230
  • 353