Re: How to fit complex valued data?

• To: mathgroup at smc.vnet.net
• Subject: [mg64144] Re: How to fit complex valued data?
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Thu, 2 Feb 2006 00:07:07 -0500 (EST)
• References: <drq0b1\$mpt\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```NMinimize[Norm[1/(1 + I b*data[[All,1]]) - data[[All,2]]]^2, {b}]

{1.5401072015490602*^-13, {b -> 1.0000000069007826}}

James McCambridge wrote:
> 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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