An update:
A little more tuning resulted in determinant and inverse being about 80x
faster than the original numarray code and about 5 times faster than
using NumPy for the same test cases I was using before (1000x4x4
matrices). If anyone is interested, let me know and I'll send you the code.
-tim
Tim Hochberg wrote:
>
> I discovered that some (all?) of the functions in
> numarray.linear_algebra are very slow when operating on small
> matrices. In particular, determinant and inverse are both more than 15
> times slower than their NumPy counterparts when operating on 4x4
> matrices. I assume that this is simply a result of numarray's higher
> overhead.
>
> Normally the overhead of numarray is not much of a problem since when
> I'm operating on lots of small data chunks I can usually agregate them
> into larger chunks and operate on the big chunks. This is, of course,
> the standard way to get decent performance in either numarray or
> NumPy. However, because the functions in linear_algebra take only
> rank-2 (or 1 in some cases) arrays, their is no way to aggregate the
> small operations and thus things run quite slow.
>
> In order to address this I rewrote some of the functions in
> linear_algebra to allow an additional, optional, dimension on the
> input arrays. Rank-3 arrays are treated as being a set of matrices
> that are indexed along the first axis of A. Thus determinant(A) is
> essentially equivalent to array(map(determinant, A)) when A is rank-3.
> See the attached file for more detail.
>
> By this trick and by some relentless tuning, I got the numarray
> functions to run at about the same speed as their NumPy counterparts
> when computing the determinants and inverses of 1000 4x4 matrices.
> That's a humungous speedup.
>
> Is this approach worth pursuing for linear_algebra in general? I'll be
> using these myself since I need the speed, although I may back out
> some of the more aggresive tuning so I don't get bit if numarray's
> internals change. I'll gladly donate this code to numarray if it's
> wanted, and I'm willing to help convert the rest, although it probaly
> wouldn't happen as fast as this stuff since I don't need it myself
> presently.
>
> -tim
>
> [Use this with caution at this point -- I just got finished with a
> tuning spree and there may well be some bugs]
>
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>
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