[Numpy-discussion] numpy.polynomial.Polynomial

[Charles R Harris]

On Fri, Oct 22, 2010 at 11:47 AM, <josef.pktd at gmail.com> wrote:

> On Fri, Oct 22, 2010 at 12:26 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> >
> > On Fri, Oct 22, 2010 at 9:51 AM, <josef.pktd at gmail.com> wrote:
> >>
> >> I'm subclassing numpy.polynomial.Polynomial. So far it works well.
> >>
> >> One question on inplace changes
> >>
> >> Is it safe to change coef directly without creating a new instance?
> >> I'm not trying to change anything else in the polynomial, just for
> >> example pad, truncate or invert the coef inplace, e.g
> >>
> >> def pad(self, maxlag):
> >>    self.coef = np.r_[self.coef, np.zeros(maxlag - len(self.coef))]
> >>
> >> Currently, I have rewritten this to return a new instance.
> >>
> >
> > You can (currently) modify the coef and it should work, but I think it
> best
> > to regard the Polynomial class as immutable. I'm even contemplating
> making
> > the coef attribute read only just to avoid such things. Another tip is to
> > use // instead of / for division, polynomials are rather like integers
> that
> > way and don't have a true divide so plain old / will fail for python 3.x
> >
> > Note that most operations will trim trailing zeros off the result.
> >
> > In [6]: P((1,1,1,0,0,0))
> > Out[6]: Polynomial([ 1.,  1.,  1.,  0.,  0.,  0.], [-1.,  1.])
> >
> > In [7]: P((1,1,1,0,0,0)) + 1
> > Out[7]: Polynomial([ 2.,  1.,  1.], [-1.,  1.])
> >
> > The reason the constructor doesn't was because trailing zeros can be of
> > interest in least squares fits. Is there a particular use case for which
> > trailing zeros are important for you? The polynomial modules aren't
> finished
> > products yet, I can still add some functionality if you think it useful.
>
> I need "long" division, example was A(L)/B(L) for lag-polynomials as I
> showed before.
>
>
OK, I kinda thought that was what you wanted. It would be a version of
"true" division, the missing pieces are how to extend that to other basis,
there are several possibilities... But I suppose they could just be marked
not implemented for the time being. There also needs to be a way to specify
"precision" and the location of the "decimal" point.


> My current version (unfinished since I got distracted by
> stats.distribution problems):
>
> from numpy import polynomial as npp
>
>
> class LagPolynomial(npp.Polynomial):
>
>    #def __init__(self, maxlag):
>
>    def pad(self, maxlag):
>        return LagPolynomial(np.r_[self.coef,
> np.zeros(maxlag-len(self.coef))])
>
>    def padflip(self, maxlag):
>        return LagPolynomial(np.r_[self.coef,
> np.zeros(maxlag-len(self.coef))][::-1])
>
>    def flip(self):
>        '''reverse polynomial coefficients
>        '''
>        return LagPolynomial(self.coef[::-1])
>
>    def div(self, other, maxlag=None):
>        '''padded division, pads numerator with zeros to maxlag
>        '''
>        if maxlag is None:
>            maxlag = max(len(self.coef), len(other.coef)) + 1
>        return (self.padflip(maxlag) / other.flip()).flip()
>
>    def filter(self, arr):
>        return (self * arr)  #trim to end
>
>
> another method I haven't copied over yet is the adjusted fromroots
> (normalized lag-polynomial from roots)
>
> Essentially, I want to do get the AR and ARMA processes in several
> different ways because I don't trust (my interpretation) of any single
> implementation and eventually to see which one is fastest.
>
>

I could also implement "polyz" polynomials that would use negative powers of
z. The Chebyshev polynomials are currently implemented with symmetric
z-series using both positive and negative powers, but I may change that.

Another possibility is some sort of factory function that emits polynomial
classes with certain additional properties, I'm thinking of something like
that for Jacobi polynomials.

Chuck
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