[Numpy-discussion] poly class question

[Charles R Harris]

On Fri, Oct 2, 2009 at 12:30 PM, <josef.pktd at gmail.com> wrote:

> On Fri, Oct 2, 2009 at 2:09 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> >
> > On Fri, Oct 2, 2009 at 11:35 AM, Charles R Harris
> > <charlesr.harris at gmail.com> wrote:
> >>
> >>
> >> On Fri, Oct 2, 2009 at 11:33 AM, Charles R Harris
> >> <charlesr.harris at gmail.com> wrote:
> >>>
> >>>
> >>> On Fri, Oct 2, 2009 at 11:30 AM, Charles R Harris
> >>> <charlesr.harris at gmail.com> wrote:
> >>>>
> >>>>
> >>>> On Fri, Oct 2, 2009 at 11:08 AM, <josef.pktd at gmail.com> wrote:
> >>>>>
> >>>>> Is there a way in numpy (or scipy) to get an infinite expansion for
> >>>>> the inverse of a polynomial (for a finite number of terms)
> >>>>>
> >>>>> np.poly1d([ -0.8, 1])**(-1)
> >>>>>
> >>>>> application for example the MA representation of an AR(1)
> >>>>>
> >>>>
> >>>> Hmm, I've been working on a chebyshev class and division of a scalar
> by
> >>>> a chebyshev series is
> >>>> expressly forbidden, but it could be included if a good interface is
> >>>> proposed. Same would go for polynomials.
> >>>
> >>> In fact is isn't hard to get, for poly1d you should be able to multiply
> >>> the series by a power of x to shift it left, then divide.
> >>>
> >>
> >> That is, divide a power of x by the polynomial.
> >>
> >
> > You will also need to reverse the denominator coefficients...Chuck
>
> That's the hint I needed. However the polynomial coefficients are then
> reversed and not consistent with other polynomial operations, aren't
> they?
>
> >>> from scipy.signal import lfilter
>
> >>> (np.poly1d([1, 0])**10)/np.poly1d([1, -0.8])
> (poly1d([ 1.        ,  0.8       ,  0.64      ,  0.512     ,  0.4096    ,
>        0.32768   ,  0.262144  ,  0.2097152 ,  0.16777216,
> 0.13421773]), poly1d([ 0.10737418]))
>
> >>> lfilter([1], [1,-0.8], [1] + [0]*9)
> array([ 1.        ,  0.8       ,  0.64      ,  0.512     ,  0.4096    ,
>        0.32768   ,  0.262144  ,  0.2097152 ,  0.16777216,  0.13421773])
>
> >>> (np.poly1d([1, 0])**10)/np.poly1d([1, -0.8, 0.2])
> (poly1d([ 1.        ,  0.8       ,  0.44      ,  0.192     ,  0.0656    ,
>        0.01408   , -0.001856  , -0.0043008 , -0.00306944]),
> poly1d([-0.00159539,  0.00061389]))
> >>> lfilter([1], [1,-0.8, 0.2], [1] + [0]*9)
> array([ 1.        ,  0.8       ,  0.44      ,  0.192     ,  0.0656    ,
>        0.01408   , -0.001856  , -0.0043008 , -0.00306944, -0.00159539])
>
>
> What I meant initally doesn't necessarily mean division of a scalar.
>
> >>> np.poly1d([1])/np.poly1d([-0.8, 1])
> (poly1d([ 0.]), poly1d([ 1.]))
>
> I didn't find any polynomial division that does the expansion of the
> remainder. The same problem, I think is inherited, by the
> scipy.signal.lti, and it took me a while to find the usefulness of
> lfilter in this case.
>
> If it were possible to extend the methods for the polynomial class to
> do a longer expansions, it would make them more useful for arma and
> lti.
>
> (in some areas, I'm still trying to figure out whether some
> functionality is just hidden to me, or actually a limitation of the
> implementation or a missing feature.)
>
>
Could you describe the sort of problems you want to solve? There are lots of
curious things out there we could maybe work with. Covariances, for
instance, are closely related to Chebyshev series.

Chuck
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