numpy einsum与'...'

Question

The code below is meant to conduct a linear coordinate transformation on a set of 3d coordinates. The transformation matrix is A , and the array containing the coordinates is x . The zeroth axis of x runs over the dimensions x, y, z. It can have any arbitrary shape beyond that.

Here's my attempt:

A = np.random.random((3, 3))
x = np.random.random((3, 4, 2))

x_prime = np.einsum('ij,j...->i...', A, x)

The output is:

    x_prime = np.einsum('ij,j...->i...', A, x)

ValueError: operand 0 did not have enough dimensions
to match the broadcasting, and couldn't be extended
because einstein sum subscripts were specified at both
the start and end

If I specify the additional subscripts in x explicitly, the error goes away. In other words, the following works:

x_prime = np.einsum('ij,jkl->ikl', A, x)

I'd like x to be able to have any arbitrary number of axes after the zeroth axis, so the workaround I give about is not optimal. I'm actually not sure why the first einsum example is not working. I'm using numpy 1.6.1. Is this a bug, or am I misunderstanding the documentation ?

Answer 1

Yep, it's a bug. It was fixed in this pull request: https://github.com/numpy/numpy/pull/4099

This was only merged a month ago, so it'll be a while before it makes it to a stable release.

EDIT : As @hpaulj mentions in the comment, you can work around this limitation by adding an ellipsis even when all indices are specified:

np.einsum('...ij,j...->i...', A, x)