[Numpy-discussion] vectorizing loops

[Charles R Harris]

Hi,

On 10/26/07, Timothy Hochberg <tim.hochberg at ieee.org> wrote:
>
>
> On 10/26/07, Sebastian Haase <haase at msg.ucsf.edu> wrote:
> > On 10/26/07, David Cournapeau <david at ar.media.kyoto-u.ac.jp> wrote:
> > > P.S: IMHO, this is one of the main limitation of numpy (or any language
> > > using arrays for speed; and this is really difficult to optimize: you
> > > need compilation, JIT or similar to solve those efficiently).
> >
> > This is where the scipy - sandbox numexpr  project comes in
> > - if I'm not misaken ....
> >
> > http://www.scipy.org/SciPyPackages/NumExpr
> >
> > Description
> > The scipy.sandbox.numexpr package supplies routines for the fast
> > evaluation of array expressions elementwise by using a vector-based
> > virtual machine. It's comparable to scipy.weave.blitz (in Weave), but
> > doesn't require a separate compile step of C or C++ code.
> >
> >
> > I hope that more noise around this  will result  in more interest and
> > subsequentially result in more support.
> > I think numexpr  might be one of the most powerful ideas in numpy /
> > scipy  "recently".
> > Did you know about numexpr - David ?
>
> Sadly, I don't think numexpr will help here; It basically handles the same
> cases as numpy; only faster because it can avoid a lot of temporaries. I
> think he's going to need Psyco,  Pyrex, Weave or similar.
>
>
>
This problem of efficient recursion turns up often. The only versions
we support now are the reduce and accumulate methods for ufuncs. I
wonder if we can think of some way of offering support that will speed
it up? The problem space is big enough that there is probably no
method that will solve all problems, but maybe we can toss around some
thoughts. For 2-D sorts of things recursion based on functions on
"half squares" preceding the current value could be useful. A reverse
recursion would also be useful in evaluating a lot of series. The
posted problem is sort of a matrix recursion, though not necessarily
linear. Some sort of accumulate method using a vector of function
calls would probably do the trick. Hmmm... I think that would not be
too hard to do, although the calls to python functions would probably
keep the speedup down to a factor of 2-3x if implemented in C.

In a sense, I am thinking of accumulate and reduce type methods
attached to vectors of functions with more than 2 arguments, iterated
multidimensional maps, if you will.

Chuck