[Numpy-discussion] einsum and broadcasting

[Sebastian Berg]

On Thu, 2013-04-04 at 16:56 +0300, Jaakko Luttinen wrote:
> I don't quite understand how einsum handles broadcasting. I get the
> following error, but I don't understand why:
> 
> In [8]: import numpy as np
> In [9]: A = np.arange(12).reshape((4,3))
> In [10]: B = np.arange(6).reshape((3,2))
> In [11]: np.einsum('ik,k...->i...', A, B)
> ---------------------------------------------------------------------------
> 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
> 
> However, if I use explicit indexing, it works:
> 
> In [12]: np.einsum('ik,kj->ij', A, B)
> Out[12]:
> array([[10, 13],
>        [28, 40],
>        [46, 67],
>        [64, 94]])
> 
> It seems that it also works if I add '...' to the first operand:
> 
> In [12]: np.einsum('ik...,k...->i...', A, B)
> Out[12]:
> array([[10, 13],
>        [28, 40],
>        [46, 67],
>        [64, 94]])
> 
> However, as far as I understand, the syntax
> np.einsum('ik,k...->i...', A, B)
> should work. Have I misunderstood something or is there a bug?
> 

My guess is, it is by design because the purpose of the ellipsis is more
to allow extra dimensions that are not important to the problem itself.
A vector product is np.einsum('i,i->i') and if I write
np.einsum('...i,...i->...i') I allow generalizing that arrays of 1-d
arrays (like the new gufunc linalg stuff).
I did not check the code though, so maybe thats not the case. But in any
case I don't see a reason why it should not be possible to only allow
extra dims for some inputs (I guess it can also make sense to not
give ... for the output).
So I would say, if you want to generalize it, go ahead ;).

- Sebastian

> Thanks for your help!
> Jaakko
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