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Re: Re: [Help-gsl] about nonlinear fit of several functions simultaneou


From: Francesco Abbate
Subject: Re: Re: [Help-gsl] about nonlinear fit of several functions simultaneously
Date: Tue, 27 Jul 2010 17:11:09 +0200

2010/7/27  <address@hidden>:
> Hi,
>
> Thanks a lot! Actually, I met another situation in the so called
> ellipsometry. There people often do like this: evaluate ki_squared as the
> sum over [F1(i)-f1(i)]^2+[F2(i)-f2(i)]^2 then divided by (2N-P) where N is
> the number of f1(or f2) and P the number of parameters. I just wonder
> whether this can be extended to a more generall case where one has M dataset
> to be fitted and ki_squared =
> 1/(M*N-P)*sum{(F1-f1)^2+(F2-f2)^2+...(FM-fM)^2}. How about this approach?
>
> Liu

Well, it is funny but the software I have developed is about ellipsometry :-)

In ellipsometry the problem arise because you often work with complex
number or with couple of real numbers.

I believe that the solution to calculate the square is suboptimal
because you lose the details about how each function behaves
separately. Note also that GSL should obtain an f_i which is the
difference between the model and the observed value y_i. This
difference can be therefore positive or negative and it will be GSL,
internally, that calculates its square. If you calculate the square by
yourself you alter subtly the nature of the problem. I believe also
the to divide by N or N-P is totally pointless for the sake of the
minimisation since both are fixed numbers.

So, I think that it is more correct to just "collate" the functions in sequence.

Byr
Francesco



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