Re: [Numpy-discussion] Polyfit

[Greg W. <gre...@gm...>]

On 10/12/06, Charles R Harris <cha...@gm...> wrote:
>
> And here is the location of the problem in numpy/linalg/linalg.py :
>
> def lstsq(a, b, rcond=1.e-10):
>
> The 1e-10 is a bit conservative. On the other hand, I will note that the
> condition number of the dot(V^T ,V) matrix is somewhere around 1e22, which
> means in general terms that you need around 22 digits of accuracy. Inverting
> it only works sorta by accident in the current case. Generally, using
> Vandermonde matrices and polynomial fits it a bad idea when the dynamic
> range of the interval gets large and the degree gets up around 4-5 as it
> leads to ill conditioned sets of equations. When you really need the best
> start with chebychev polynomials or, bestest, compute a set of polynomials
> orthogonal over the sample points. Anyway, I think rcond should be something
> like 1e-12 or 1e-13 by default and be available as a keyword in the polyfit
> function. If no one complains I will make this change, although it is just a
> bandaid and things will fall apart again as soon as you call polyfit(x,y,4).
>
>

Hey that's great.  I'm glad you tracked it down.

Pardon my ignorance of polyfit algorithm details.
Is there a way of choosing rcond based on N that would give sensible
defaults for a variety of N?
Greg