Fitting Complex-valued data with NonlinearModelFit.

Questions
,
1

One can do fits to complex data with FindFit by using a NormFunction for complex numbers.

However, NonlinearModelFit, doesn’t appear to have a NormFunction option. I’d like to have access to the extra functionality that FittedModel provides.

Does anyone know how I could get NonlinearModelFit to generalize the following FindFit example (this is a simple RC circuit impedance example):

fitModel = 1/(1/r + I c w); 

noisyData = Table[{w, (fitModel + Random[Complex, {0, 0.1}] /. {r -> 2, c -> 1})}, {w, 0.01, 3, 0.05}]

FindFit[noisyData, fitmodel, {r, c}, w, NormFunction -> (Norm[Abs[#1^2]] &)]

Thanks, Craig

2

As long as you’re fitting normed data, how about fitting it to a normed model?
Your model:

fitModel = 1/(1/r + I c w);

and your data:

noisyData = 
  Table[{w, (fitModel + Random[Complex, {0, 0.1}] /. {r -> 2, 
       c -> 1})}, {w, 0.01, 3, 0.05}];

I fit it as you did to get the rule:

fitRule = 
 FindFit[noisyData, fitModel, {r, c}, w, 
  NormFunction -> (Norm[Abs[#1^2]] &)]

Now create a normed model:

fitModelconj = fitModel /. I -> -I;
normFitModel = Sqrt[Simplify[fitModelconj fitModel]]

and also norm the data:

normNoisyData = Map[Norm, noisyData, {2}];

Now fit the normed model to the normed data:

fittedModel = 
  NonlinearModelFit[normNoisyData, normFitModel, {r, c}, {w}];
Normal[fittedModel]

If you compare the output above to the normed model with the earlier fit, you see they don’t quite agree, but almost:

normFitModel /. fitRule

Best regards,
David

3

David,
That’s very clever. I wish I had thought of that,
Thanks, Craig