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

*To*: mathgroup at smc.vnet.net*Subject*: [mg126812] Re: Fitting complex functions or simultaneous fit of functions with identical parameters with Mathematica*From*: Sseziwa Mukasa <mukasa at gmail.com>*Date*: Sat, 9 Jun 2012 03:06:19 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201206080735.DAA13711@smc.vnet.net>

Replies inline below... On Jun 8, 2012, at 3:35 AM, 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. By doing this you've lost the phase information. > > 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. Because once you've lost the phase information it's unlikely that a good fit to your model is also a good fit to the original data. Fortunately, NonlinearModelFit can fit to complex valued functions already: In[2]:= NonlinearModelFit[RandomComplex[{-1-I,1+I},{10}],a+Ib,{a,b},x] Out[2]= FittedModel[0.257386 -0.15977 I] Regards, Ssezi

**References**:**Fitting complex functions or simultaneous fit of functions with identical parameters with Mathematica***From:*eastman <eastriverman@hotmail.com>