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Re: Fitting with a complex equation

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

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.

f=Abs[A/(wa-x-I Ga)+k E^(I t)]^2;

NonlinearFit[data, Evaluate[f],


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.


     (\___/)     The fear of the LORD is the beginning of    
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    /|:.V.:|\    that do his commandments: his praise        
    \\::::://    endureth for ever.              Psa 111:10  
-----`"" ""`------------------------------------------------
        Lawrence A. Walker Jr., M.Eng./Ph.D. Candidate      
                   Morgan State University                  
          Clarence M. Mitchell School of Engineering        
 COMSARE (Center Of Microwave/Satellite And RF Engineering) 
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