Re: Non-Linear implicit Curve Fitting

[Olaf Till]

On Sat, Nov 16, 2013 at 08:54:45AM +0100, Christian Kascha wrote:
> Am 15.11.2013 18:22, schrieb Giftig:
> >Good Day
> >
> >I have two data sets.x and F that has about 10000 points each.
> >
> >I also have the following equation:
> >F = C_CV .* alpha.^( x - 1) .* sqrt(a .* F.^2+ b * F + c)
> >
> >I want to fit that equation on the data above. everything is unknown as
> >specified.
> >Any idea on how to accomplish this?
> >
> >I tried a few methods put nothing gave me a proper fit

What did you try?

> >Thank you
> 
> I would try non-linear least squares with "fminsearch" or "fminunc"
> from the optim package.
> (http://octave.sourceforge.net/optim/index.html)
> 
> Best,
> Christian

I think Giftig has not a scalar objective function, so its worth
trying residual minimization. Rearrange the equation to return zero
and use, e.g., nonlin_residmin of the optim package (this also fits to
least squares by default). But the fit is doubtful to be well defined
if 'C_CV' and 'a' are vectors, as they seem to be by your usage of
'.*' (more unknowns than residuals) (and the problem would probably be
too large in this case anyway).

If necessary, feel free to ask for specific details.

Olaf

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