Re: How to do a Nonlinear Complex Fit ?
- To: mathgroup at smc.vnet.net
- Subject: [mg22443] Re: [mg22411] How to do a Nonlinear Complex Fit ?
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Wed, 8 Mar 2000 02:21:44 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Ronald,
Unfortunately, NonlinearRegress (& NonlinearFit) don't take observations
of the form {x,f(x),g(x) }, but you can arrange your f(x) and g(x) values in
one list, f(x) first, followed by g(x). In this case NonlinearRegress will
supply indices (1. through (Length[f(x)]+Length[g(x)]) ) one at a time to
your model function, which should be written to generate the proper x, f(x),
and g(x) values in order. I hope the example I worked out will make this
clear:
<<Statistics`
(* x-values & the real and imaginary parts *)
xdat= N[Table[x,{x,0.,Pi,Pi/10} ] ]
rePart=3. Cos[1.1 xdat];
imPart=3. Sin[1.1 xdat];
(* the data vector *)
ydata=Flatten[Append[rePart,imPart ] ];
(* the model function for the real parts, followed by the imaginary parts
*)
ClearAll[model];
model[x_List,i_,limit_Integer,a_,b_]:= If[ i<= limit,a Cos[b x[[i]] ], a
Sin[b x[[i-limit]] ] ];
(* set the limit dividing real from imaginary parts in the list, and fit
*)
limit=Length[xdat];
NonlinearRegress[ydata,Evaluate[model[xdat,i,limit,a,b] ],i,{a,b}]
Important note: although i is an index, Mathematica will substitute real
values for i; you must allow model to accept non-integer i-values.
I didn't add any noise to the data, and the regression returned exactly 3.
and 1.1 for a & b.
-mark harder
-----Original Message-----
From: Ronald Sastrawan <sastra at fmf.uni-freiburg.de>
To: mathgroup at smc.vnet.net
Subject: [mg22443] Re: [mg22411] How to do a Nonlinear Complex Fit ?
>Hello Mark,
>
>thanks for your answer !
>My data is real. I measure the real and the imaginary part in dependance of
x
>(in my case the frequency, I am doing impedance measurements). So my data
looks
>like (x, f(x), g(x)), where f and g are the imaginary and complex part
>respectively, but all of it is real. My model yields expressions for both
f(x,
>k1,k2,k3,k4,k5) and g(x,k1,k2,k3,k4,k5), where the k are the fit parameters
>(they should be the same for both f and g).
>
>Thanks for your effort,
>
>Ronald
>
>Mark Harder schrieb:
>
>> In mg22411 you wrote
>> "I am trying to fit a complex function to real data. The data consists of
>> real and imaginary part."
>>
>> Before I think about this, I need to know more. Is the data a vector of
>> complex numbers (with "real & imaginary part" or real? In the former
case,
>> I think you will have to create a data vector with real and complex parts
>> separated, and real and complex parts of the model function separated in
the
>> same way -- Mathematica's NonlinearFit[] won't accept multi-valued data,
>> and I think it sees complex numbers as 2D vectors over the reals (not
>> certain, that's what I need to play with).
>>
>> Any questions or clarification, just e-mail me. I didn't submit this
note
>> to the whole group.
>> mark harder
>> harderm at ucs.orst.edu
>
>--
>Ronald Sastrawan
>
>Freiburg Materials Research Center
>Stefan-Meier-Str. 21
>D-79104 Freiburg
>Germany
>Tel: ++49/761/203-4802
>FAX: ++49/761/203-4801
>EMAIL: sastra at fmf.uni-freiburg.de
>http://www.fmf.uni-freiburg.de/~biomed/FSZ/forschung-FSZ.html
>
>