Re: [Matplotlib-users] polyfit implementation

[Jean-Michel P. <jea...@ar...>]

Hello Andrea,

and...@ti... a écrit :
> That does not depend on Numeric, numarray or Matlab. Is your data. If you
> try, in Matlab, to see how polyfit works (type polyfit), you will see with
> a simple trial that your data are bad conditioned. As an example, if x,
> y are the 2 rows of your data:
> 
> In fact, try to take a look at the condition number of your matrix R:
> 
> condest(R)
> 
> ans =
> 
>      3.89823249817041e+025
> 
> That's too high. Neither Matlab, Python or whatever software will give you
> a result on which you can rely. Maybe at a first glance Matlab seems to
> be more powerful (and, in general, this is the case), but be aware that
> you should not trust on results that are affected by so bad conditioning
> number/numerical errors.
> Try to reduce the number of points (some of them are too close), or try
> a non-linear regression (as lsqnonlin), even if you should not need such
> a tool in order to do the job.

I totally agree to the fact that my problem is highly badly conditioned. 
But as this may not always be the case, I would have preferred polyfit 
to give reliable results without having to track the condition number. 
Do you know how to get it from within Python?

Indeed I do not use the fitted polynomials directly but their
derivatives. Doing so, fitting errors are increased and I noticed that
Matlab keeps providing reliable results for the few input data I tested.
This is not the case with Numeric or numarray.


JM.