# [Numpy-discussion] How to remove loops over inner()

Timothy Hochberg tim.hochberg at ieee.org
Tue Nov 27 14:45:36 EST 2007

```On Nov 26, 2007 2:30 PM, Hans-Andreas Engel <engel at physics.harvard.edu>
wrote:

> Dear all:
>
> After using numpy for several weeks, I am very happy about it and
> deeply impressed about the performance improvements it brings in my
> python code.  Now I have stumbled upon a problem, where I cannot use
> numpy to eliminate all my loops in python.
>
> Currently the return value of inner(a, b) is defined as
>   inner(a, b)[I, J] = sum_k  a[I, k] * b[J, k],
> for some super indices I and J.  Somewhat more general is the
> tensordot() function that allows to specify over which axes K is
> summed over.
>
> However, if I understand numpy correctly, the following more general
> version is currently missing:
>  inner(a, b, keep_axis=0)[H, I, J] = sum_k a[H, I, k] * b[H, J, k].
> Here H would be an additional super index (specified via the keep_axis
> keyword), on which no outer product is taken, i.e., the same index is
> used for a[] and b[].
>
> This more general definition would allow elimination of an extra level
> of loops.  For example, I wish to calculate the following
>   a = rand(200, 5, 2)
>   b = rand(200, 4, 2)
>   r = empty(a.shape[:-1] + b.shape[1:-1])
>   for h in range(a.shape[0]):
>       r[h] = inner(a[h], b[h])
> How could I eliminate the loop?  It would be great if there would be
> the mentioned generalized version of the inner() [or tensordot()]
> function, since it would eliminate this loop and make my code much
> faster.
>
> What are your opinions?  Would such a feature be desirable (or is it

Essentially, you want to operate on a stack of two dimensional arrays,
correct? I'd be mildly supportive of something like this for tensordot; I'd
prefer more descriptive name for keep_axis, but I don't know what it would
be off the top of my head. In any event it should be XXX_axes and optionally
take a sequence of axes so that more than one can be ignored. You could
trivially build more specific functions on top of tensordot, so I don't see
that inner needs to be changed as it's basically a convenience function
anyway.

--
.  __
.   |-\
.
.  tim.hochberg at ieee.org
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