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Re: complex function fitting?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98352] Re: complex function fitting?
  • From: dh <dh at metrohm.com>
  • Date: Wed, 8 Apr 2009 02:48:00 -0400 (EDT)
  • References: <grcgjg$pml$1@smc.vnet.net> <49D9DDF3.30605@metrohm.com> <49da0538.06025a0a.6489.123b@mx.google.com>

Hi Ned,
what I said is still valid, by default Mathematica calculates with 
complex numbers. You must have made another error. Why do you not give a 
simple complete example? I can not help you without knowing the problem. 
  Here is my working example using NonlinearModelFit:
d = Table[{x + I y, Exp[x + y I]}, {x, 0, 1, .1}, {y, 0, 1, .1}];
d = Flatten[d, 1];
pol = NonlinearModelFit[d, {c0 + c1 x + c2 x^2}, {c0, c1, c2}, x]
yc = pol[x] /. x -> d[[All, 1]];
ListPlot[{Re[#], Im[#]} & /@ (yc - d[[All, 2]]), PlotRange -> All]
Daniel

Ned Lieb wrote:
> Just a clarification of my original question: I'm referring to a specific
> issue I'm having using the NonlinearModelFit function, which fits lists of
> data-points to functions of a type specified by the user (for example, say I
> knew that my data fit an exponential equation (it doesn't, by the way, this
> is just an example) with x as an independent variable: NonLinearModelFit
> could find the constant A in the equation A*e^x that would give the function
> that most closely approximated my data). My list of data is complex-valued
> (with non-zero imaginary components). Mathematica returned an error message
> saying I could only use real numbers. I was wondering whether there was a
> way to get around this.
> 
> Thanks
> 
> -----Original Message-----
> From: dh [mailto:dh at metrohm.com] 
> Sent: Monday, April 06, 2009 6:48 AM
> To: Ned Lieb
> Subject: Re: complex function fitting?
> 
> Hi Ned,
> Mathematica works by default with complex numbres. E.g. using "Fit":
> d = Table[{x + I y, Exp[x + y I ]}, {x, 0, 1, .1}, {y, 0, 1, .1}];
> d = Flatten[d, 1];
> pol = Fit[d, {1, x, x^2}, x]
> yc = pol /. x -> d[[All, 1]];
> ListPlot[{Re[#], Im[#]} & /@  (yc - d[[All, 2]]), PlotRange -> All]
> Daniel
> 
> Ned Lieb wrote:
>> Does anyone know how I could extend the domain of Mathematica's
>> function-fitting functions so I can use complex-valued data?
>>
>>
>>
> 
> 
> 
> 
> 


-- 

Daniel Huber
Metrohm Ltd.
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CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>



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