[Numpy-discussion] Speed up function on cross product of two sets?
zpincus at stanford.edu
Sun Apr 2 17:17:06 CDT 2006
Thanks for your suggestions -- that all makes good sense.
It sounds like the general take home message is, as always: "the
first thing to try is to vectorize your inner loop."
>> I have a inner loop that looks like this:
>> out = 
>> for elem1 in l1:
>> for elem2 in l2:
>> out.append(do_something(l1, l2))
> this is do_something(elem1, elem2), correct?
>> result = do_something_else(out)
>> where do_something and do_something_else are implemented with
>> only numpy ufuncs, and l1 and l2 are numpy arrays.
>> As an example, I need to compute the median distance from any
>> element in one set to any element in another set.
>> What's the best way to speed this sort of thing up with numpy
>> (e.g. push as much down into the underlying C as possible)? I
>> could re- write do_something with the numexpr tools (which are
>> very cool), but that doesn't address the fact that I've still got
>> nested loops living in Python.
> The exact approach I'd take would depend on the sizes of l1 and l2
> and a certain amount of trial and error. However, the first thing
> I'd try is:
> n1 = len(l1)
> n2 = len(l2)
> out = numpy.zeros([n1*n2], appropriate_dtype)
> for i, elem1 in enumerate(l1):
> out[i*n2:(i+1)*n2] = do_something(elem1, l1)
> result = do_something_else(out)
> That may work as is, or you may have to tweak do_something slightly
> to handle l1 correctly. You might also try to do the operations in
> place and stuff the results into out directly by using X= and three
> argument ufuncs. I'd not do that at first though.
> One thing to consider is that, in my experience, numpy works best
> on chunks of about 10,000 elements. I believe that this is a
> function of cache size. Anyway, this may choice of which of l1 and
> l2 you continue to loop over, and which you vectorize. If they both
> might get really big, you could even consider chopping up l1 when
> you vectorize it. Again I wouldn't do that unless it really looks
> like you need it.
> If that all sounds opaque, feel free to ask more questions. Or if
> you have questions about microoptimizing the guts of do_something,
> I have a bunch of experience with that and I like a good puzzle.
>> Perhaps there's some way in numpy to make one big honking array
>> that contains all the pairs from the two lists, and then just run
>> my do_something on that huge array, but that of course scales
> I know of at least one way, but it's a bit of a kludge. I don't
> think I'd try that though. As you said, it scales poorly. As long
> as you can vectorize your inner loop, it's not necessary and
> sometimes makes things worse, to vectorize your outer loop as well.
> That's assuming your inner loop is large, it doesn't help if your
> inner loop is 3 elements long for instance, but that doesn't seem
> like it should be a problem here.
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