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

Anne Archibald peridot.faceted@gmail....
Thu Oct 8 14:03:08 CDT 2009

2009/10/8 Charles R Harris <charlesr.harris@gmail.com>:
> Hi Anne,
> On Thu, Oct 8, 2009 at 9:37 AM, Anne Archibald <peridot.faceted@gmail.com>
> wrote:
>> 2009/10/7 David Goldsmith <d.l.goldsmith@gmail.com>:
>> > Thanks for doing that, Anne!
>> There is now a rough prototype on github:
>> http://github.com/aarchiba/scikits.polynomial
>> It certainly needs more tests and features, but it does support both
>> the power basis and the Lagrange basis (polynomials represented by
>> values at Chebyshev points).
> Just took a quick look, which is probably all I'll get to for a few days as
> I'm going out of town tomorrow. Anyway, the Chebyshev points there are type
> II, which should probably be distinguished from type I (and III & IV). I
> also had the impression that the base class could have a few more functions
> and NotImplemented bits. The Polynomial class is implemented as a wrapper,
> it might even make sense to use multiple inheritance (horrors) to get
> specific polynomial types, but anyway it caught my attention and that part
> of the design might be worth spending some time thinking about. It also
> might be worth distinguishing series as a separate base because series do
> admit the division operators //, %, and divmod. Scalar
> multiplication/division (__truedivision__) should also be built in. I've
> also been using "from __future__ import division" up at the top to be py3k
> ready. For a series basis I was thinking of using what I've got for
> Chebyshev but with a bunch of the __foo__  functions raising the
> NotImplementedError. I've also got a single function for importing the
> coefficient arrays and doing the type conversions/checking. It's worth doing
> that one way for all the implementations as it makes it easier to fix/extend
> things.

The polynomial class as a wrapper was a design decision. My reasoning
was that certain data - roots, integration schemes, weights for
barycentric interpolation, and so on - are associated with the basis
rather than any particular polynomial. The various algorithms are also
associated with the basis, of course (or rather the family of bases).
So that leaves little in the way of code to be attached to the
polynomials themselves; basically just adapter code, as you noted.
This also allows users to stick to working with plain arrays of
coefficients, as with chebint/chebder/etc. if they prefer. But the
design is very much open for discussion.

I agree, there are some good reasons to implement a class for graded
polynomial bases in which the ith polynomial has degree i. One would
presumably implement a further class for polynomial bases based on
orthogonal families specified in terms of recurrence relations.

Division operators make sense to implement, yes; there are sensible
notions of division even for polynomials in the Lagrange or Bernstein
bases. I just hadn't included those functions yet.

> I've attached the low->high version of the chebyshev.py file just for
> further reference. The Chebyshev class is at the end.

Thanks, I'll take a look at it.


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