[Numpy-discussion] Iterative Matrix Multiplication

[Friedrich Romstedt]

2010/3/5 Ian Mallett <geometrian at gmail.com>:
> Cool--this works perfectly now :-)

:-)

> Unfortunately, it's actually slower :P  Most of the slowest part is in the
> removing doubles section.

Hmm.  Let's see ... Can you tell me how I can test the time calls in a
script take?  I have no idea.

> #takes 0.04 seconds
> inner = np.inner(ns, v1s - some_point)

I think I can do nothing about that at the moment.

> #0.0840001106262
> sum_1 = sum.reshape((len(sum), 1)).repeat(len(sum), axis = 1)
>
> #0.0329999923706
> sum_2 = sum.reshape((1, len(sum))).repeat(len(sum), axis = 0)
>
> #0.0269999504089
> comparison_sum = (sum_1 == sum_2)

We can leave out the repeat() calls and leave only the reshape() calls
there.  Numpy will substitute dimi == 1 dimensions with stride == 0,
i.e., it will effectively repeat those dimension, just as we did it
explicitly.

> #0.0909998416901
> diff_1 = diff.reshape((len(diff), 1)).repeat(len(diff), axis = 1)
>
> #0.0340001583099
> diff_2 = diff.reshape((1, len(diff))).repeat(len(diff), axis = 0)
>
> #0.0269999504089
> comparison_diff = (diff_1 == diff_2)

Same here.  Delete the repeat() calls, but not the reshape() calls.

> #0.0230000019073
> same_edges = comparison_sum * comparison_diff

Hmm, maybe use numpy.logical_and(comparison_sum, comparison_diff)?  I
don't know, but I guess it is in some way optimised for such things.

> #0.128999948502
> doublet_count = same_edges.sum(axis = 0)

Maybe try axis = 1 instead.  I wonder why this is so slow.  Or maybe
it's because he does the conversion to ints on-the-fly, so maybe try
same_edges.astype(numpy.int8).sum(axis = 0).

Hope this gives some improvement.  I attach the modified version.

Ah, one thing to mention, have you not accidentally timed also the
printout functions?  They should be pretty slow.

Friedrich