       Re: Fitting with a complex equation

• To: mathgroup at smc.vnet.net
• Subject: [mg18713] Re: Fitting with a complex equation
• From: Lawrence Walker <lwalker701 at earthlink.net>
• Date: Sat, 17 Jul 1999 02:36:35 -0400
• Organization: Morgan State University: COMSARE
• References: <7luhrb\$kdk@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Gibum,

You might want to weight the points and/or window off a
portion of the data you want fitted very well.
You could weight the points at this point --
Apply[(model[A,wa,Ga,k,t,#1]-#2)^2 &, data,{1}].

Alternatively, the package Statistics`NonlinearFit` has the
desired Weights option.

data={{x1,f1},{x2,f2},...};
f=Abs[A/(wa-x-I Ga)+k E^(I t)]^2;

NonlinearFit[data, Evaluate[f],
{x},
{{A,8.1,8.5},{wa,2958,2962},{Ga,8.2,8.6},{k,0.3,0.4},{t,32,35}},
Weights->{1,1,.9,.8,...}];

Lawrence

Gibum Kim wrote:
>
> Hi, there.
> I'm having a trouble with the determining parameters of the equation with
> the experimental data.
> This is my equation.
>
> f(x)=Abs[A/(wa-x-I Ga)+k E^(I t)]^2
>
> A,wa,Ga,k and t are parameters I want to find.
> I know the best guess of the parameters.
> Even with the best guess values,  I got totally wrong values of them using
> "FindMinimum".
> Here's the program I got from mathematica support.
>
> ClearAll[A,wa,Ga,k,t]
> data=ReadList ["onepeak.dat", Number, RecordLists-> True]
>  f=Abs[A/(wa + x - I Ga) +  k E^(I t)]^2
> <<Statistics`
> model[A_?NumberQ,wa_?NumberQ,Ga_?NumberQ,
> k_?NumberQ,t_?NumberQ,x_?NumberQ]:=
>   Abs[A/(wa + x - I Ga) +  k E^(I t)]^2
> sse[A_,wa_,Ga_,k_,t_]=
>   Plus @@ Apply[(model[A,wa,Ga,k,t,#1]-#2)^2 &, data,{1}];
> FindMinimum[sse[A,wa,Ga,k,t],
> {A,8.1,8.5},{wa,2958,2962},{Ga,8.2,8.6},
> {k,0.3,0.4},{t,32,35},MaxIterations->500]
>
> Do you have any idea?
> Your any suggestion would be grateful.

--

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Lawrence A. Walker Jr., M.Eng./Ph.D. Candidate
Morgan State University
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COMSARE (Center Of Microwave/Satellite And RF Engineering)
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```

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