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## Re: Non-Linear implicit Curve Fitting

**From**: |
Olaf Till |

**Subject**: |
Re: Non-Linear implicit Curve Fitting |

**Date**: |
Sat, 16 Nov 2013 22:52:42 +0100 |

**User-agent**: |
Mutt/1.5.21 (2010-09-15) |

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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