       NonlinearModelFit and Complex Data

• To: mathgroup at smc.vnet.net
• Subject: [mg126244] NonlinearModelFit and Complex Data
• From: Maria <rouelli at gmail.com>
• Date: Thu, 26 Apr 2012 05:33:05 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi,

I am trying to fit complex data to a complex function.

Here's a snippet:

data = Import["http://apps.getcloudigniter.com/data/data.csv";];

fitData =
Table[{data[[i, 1]], data[[i, 2]] + I*data[[i, 3]]}, {i, 1,
Dimensions[data][]}];

fitEqn[x_] := (aR + I aI) + ( bR + I bI)*(Abs[x - 79800.3]/
1585.02) - (
par1 (x - par1))/((cR + I cI)*((x - par1)^2 -
I par2/2 (x - par1) - 435093.75^2));

fit = NonlinearModelFit[fitData,
fitEqn[x] , {aR, aI, bR, bI, cR, cI, par1, par2}, x,
WorkingPrecision -> 100, MaxIterations -> 10000]

This gives me an error:

"The function value {....} is not a list of real numbers..."

On the other hand, FindFit gives me the same error but it works quite well by setting NormFunction -> (Norm[Abs[#^2]] &):

(* This works *)
fit = FindFit[fitData,
fitEqn[x] , {aR, aI, bR, bI, cR, cI, par1, par2}, x,
NormFunction -> (Norm[Abs[#^2]] &), WorkingPrecision -> 100,
MaxIterations -> 10000]

And I get a fairly nice fit:

Show[ListPlot[
Table[{data[[i]][], data[[i]][]}, {i, 1,
Dimensions[data][]}], PlotStyle -> Red],
Plot [Re[fitEqn[x] /. fit], {x, data[[Dimensions[data][]]][],
data[[1, 1]]}, PlotStyle -> Blue]]

Show[ListPlot[Table[{data[[i]][],data[[i]][]},{i,1,Dimensions[\
data][]}],PlotStyle->Red],Plot \
[Im[fitEqn[x]/.fit],{x,data[[Dimensions[data][]]][],data[[1,1]]}\
,PlotStyle->Blue]]

However, I can't do the same modification to NonlinearModelFit(which I prefer to use since I need the additional information on fitting, e.g. ANOVA). Any tips on making it work?

Thanks,
Maria

```

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