[SciPy-dev] Generic polynomials class (was Re: Volunteer for Scipy Project)

[Charles R Harris]

On Tue, Oct 6, 2009 at 6:57 PM, Fernando Perez <fperez.net at gmail.com> wrote:

> On Tue, Oct 6, 2009 at 5:46 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> >
> > On Tue, Oct 6, 2009 at 6:32 PM, Fernando Perez <fperez.net at gmail.com>
> wrote:
>
> >> - the correct choice of coefficient order
> >
> > OK, I'm changing that now.
>
> Thank you!
>
> >> - that is stable and fast both for point-wise and for array-wise
> >> evaluations
> >>
> >
> > Just to be clear, you mean 1 polynomial in 1 variable evaluated at many
> > points ? The current code evaluates at an arbitrary ndarray of points,
> but
> > is a bit wasteful of memory: there are essentially three active copies of
> > the data points at any one time.
>
> I had a peculiar need: I needed to evaluate a family of all Legendre
> polynomials of order up to n-1, at an array with n points.  This was
> fairly performance-critical, so I rolled my own code, though I could
> have done the loop over polynomial index.  But ideally, we'd have the
> evaluation code (fast, stable) for whole arrays accessible in
> C(ython),


That wouldn't make it much faster for large arrays of data points, the code
is just multiply and add applied repeatedly to whole arrays. Well, OK, maybe
the ndarray multiply and add overhead might slow things down.


> so that a funky use case like mine could be implemented both
> easily and efficiently with a Cython loop that would do pure C calls
> without jumping up into the python layer.
>
> Dreaming here :)
>
>
> >> would be great, as I wouldn't (for example) have had to roll my own.
> >> Others with more extensive needs and experience on this, like Anne,
> >> can pitch in with more informed ideas for the API than I can come up
> >> with right now.
>

If you happen to have an example still lying around I could try running a
benchmark.


> >>
> >
> > Do you ever use the indexing in poly1d? I'm thinking of dropping that.
> After
> > all, the coefficient array is available if one wants to cheat.
>
> I didn't, but this is a sample of 1, so take it for what it's worth :)
>
>
Can't decide on that one. It's easy enough, but one can just change out the
coefficient array or, better I think, create new objects. Unless object
creation was a bottle neck.

Chuck
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