Re: Fitting complex functions or simultaneous fit of functions with identical parameters with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg126813] Re: Fitting complex functions or simultaneous fit of functions with identical parameters with Mathematica
• From: danl at wolfram.com
• Date: Sat, 9 Jun 2012 03:06:39 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```On Friday, June 8, 2012 2:36:22 AM UTC-5, eastman wrote:
> Greetings to all!
>
> I have failed to solve a stubborn problem in fitting a complex- valued
> Drude-Lorentz model (DLM) to experimental data using the
> NonLinearFitModel of Mathematica. I'd prefer to do the fit with this
> procedure since the errors of the experimental data are also known and
> that procedure allows for weighting the fit with these errors.
>
> The problem is as follows:
>
> In terms of mathematics, the DLM is a complex-valued function of real
> arguments or a set of two real-valued functions  i.e. real and
> imaginary part. Obviously, both parts share the same set of
> parameters.
>
> Also obviously, fitting the real and imaginary part is not a good
> idea, since one generally gets different parameter values for Re and
> Im.
>
> My idea was to put the real and imaginary part into one new real
> function and I chose the square of the absolute value i.e. Re^2 +
> Im^2. Transforming the experimental data correspondingly as well as
> transforming the error data using the error propagation law, the fit
> results showed excellent coincidence of the combined function to the
> transformed data.
>
> So far, so good. But the problem is: Inserting the parameter values of
> this fit into Re and Im, the coincidence with the corresponding
> experimental data is much less impressive, if not crappy.
>
> So, this does not work.
>
> What I then need is a recipe
>
> (a) that urges NonLinearFitModel to fit Re and Im to the corresponding
> experimental data simultaneously and putting out one set of parameter
> vaules for both of them.
>
> or
>
> (b) urging NonLinearFitModel to fit the complex DLM directly.
>
> I was looking for help in the net for quite a while and tried all the
> proposals I found, but they simply do not work.
>
> I have the suspicion that my problem is not that rare and so I'd like
> to ask the experts in this group for some enlightment.
>
> If possible, I'd prefer a do- it-yourself solution and not something
> extended with libraries since I want to fiddle around with a potential
> solution to customize it for my needs.
>
>
> cu
> eastman

See:

http://forums.wolfram.com/mathgroup/archive/2012/May/msg00289.html

Several notes relevant to this topic show up if you read this group via groups.google.com, and search comp-soft-sys.math.mathematica for 'simultaneous fit' (sans quotes). So I guess one viable hint would be "Check the group archives".

Not my call really, but I agree it would be nice if the various Fit/Regress functions had direct support for complex-valued functions.

Daniel Lichtblau
Wolfram Research

```

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