Re: [Matplotlib-users] polyfit implementation

[<and...@ti...>]

Hello Jean-Michel,

>Anyway it seems that my polyfit troubles come from computation precision=

>issues. Indeed my polynomial may be of too high order than data actually=

>
>need so that some coefficients are very low (eg. 1e-20). I made some 
>experiments that show the results depend on the use of Numeric/numarray:=

>
>* Numeric
>I must use polyfit(x,y,N) with Float64 for x because it crashes with 
>Float32, but results are very inaccurate
>
>* numarray
>I can use either Float64 or Float32, but only Float32 give good results

>(may someone have an explanation...)
>
>Compared to Matlab, polynomial fitting with Python is not as good in 
>this case. For people who are interested in testing my data I provided

>an attached text file of x and y, the polynomial order is 6.

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 wit=
h
a simple trial that your data are bad conditioned. As an example, if x,
y are the 2 rows of your data:

x =3D x(:);
y =3D y(:);

% Construct the Vardermonde Matrix
V(:,n+1) =3D ones(length(x),1);
for j =3D n:-1:1
   V(:,j) =3D x.*V(:,j+1);
end

[Q,R] =3D qr(V,0);
p =3D R\(Q'*y);
Warning: Matrix is close to singular or badly scaled.
         Results may be inaccurate. RCOND =3D 2.575966e-026.

In fact, try to take a look at the condition number of your matrix R:

condest(R)

ans =3D

     3.89823249817041e+025

That's too high. Neither Matlab, Python or whatever software will give yo=
u
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.

HTH.

Andrea.