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

Hans-Andreas Engel engel@physics.harvard....
Mon Nov 26 15:30:11 CST 2007

```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