Re: How to fit complex valued data?

• To: mathgroup at smc.vnet.net
• Subject: [mg64147] Re: [mg64096] How to fit complex valued data?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 2 Feb 2006 02:17:05 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```You could try fitting the absolute value since it depends on both the real and
imaginary parts. You must test the result since you might get the sign of b
wrong.

expr[b_,x_]:=(1+I b x)^-1;

b=Random[]

0.9831217471019718

data={#,expr[b,#]}&/@Range[10]//N;

Clear[b];

Off[FindFit::fmgz];

FindFit[{#[[1]],Abs[#[[2]]]}&/@data,
ComplexExpand[Abs[expr[b,x]]],b,x]

{b -> 0.9831217471019714}

Bob Hanlon

>
> From: James McCambridge <James.McCambridge at usa.dupont.com>
To: mathgroup at smc.vnet.net
> Subject: [mg64147] [mg64096] How to fit complex valued data?
>
>
> Esteemed Colleagues,
>
> I would like to fit a complex valued data set with FindFit (I'm willing to
> try other methods too, but I thought I'd start out with the basics). Is
> this possible?
>
> For example, I am interested in fitting the complex permittivity of liquid
> polymers vs frequency, which has a functional form:
>
> In[1]:=    expr[b_,x_]:=(1+I b x)^-1;
>
> Using this form to generate data, with b = 1.0, I get:
>
> In[2]:=    data ={{1,0.5 -0.5 I},{2.,0.2 -0.4 I},{3.,0.1 -0.3 I
> },{4.,0.0588235 -0.235294 I},{5.,0.0384615 -0.192308 I},{6.,0.027027
> -0.162162 I},{7.,0.02 -0.14 I},{8.,0.0153846 -0.123077 I},{9.,0.0121951
> -0.109756 I},{10.,0.00990099 -0.0990099 I}};
>
> Using FindFit, I come up against an error message.
>
> In[3]:=   FindFit[data,expr[b,y],{{b,1.}}, y]
>
> has the output
>
> Out[3]:=   FindFit::nrlnum: The function value {0.+0. I, 0.+0. I, -1.38778
> 10^-17+0. I, <<4>>, 0.+0. I, 0.+0. I, 0.+0. I} is not a list of real
> numbers with dimensions {10} at {b} = {0.}
>
> The form expr[0.,x] doesn't look poorly behaved, so what gives?
>
> I could separately fit the real and imaginary components, but this often
> gives two somewhat different sets of parameters; I would like to obtain
> the parameters which optimize the fit to BOTH the real and imaginary
> parts.
>
>
> Jim McCambridge
>
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```

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