Fast tensor rotation with NumPy

Question

At the heart of an application (written in Python and using NumPy) I need to rotate a 4th order tensor. Actually, I need to rotate a lot of tensors many times and this is my

Answer 1

Thanks to hard work by M. Wiebe, the next version of Numpy (which will probably be 1.6) is going to make this even easier:

>>> Trot = np.einsum('ai,bj,ck,dl,abcd->ijkl', g, g, g, g, T)

Philipp's approach is at the moment 3x faster, though, but perhaps there is some room for improvement. The speed difference is probably mostly due to tensordot being able to unroll the whole operation as a single matrix product that can be passed on to BLAS, and so avoiding much of the overhead associated with small arrays --- this is not possible for general Einstein summation, as not all operations that can be expressed in this form resolve to a single matrix product.