[Numpy-discussion] How to remove loops over inner()
Tue Nov 27 13:45:36 CST 2007
On Nov 26, 2007 2:30 PM, Hans-Andreas Engel <email@example.com>
> 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):
> 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
> What are your opinions? Would such a feature be desirable (or is it
> already implemented)?
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
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