Re: Fitting to complex values

• To: mathgroup at smc.vnet.net
• Subject: [mg30801] Re: Fitting to complex values
• From: "Lawrence A. Walker Jr." <lwalker701_remove_ at earthlink.net>
• Date: Wed, 19 Sep 2001 00:16:41 -0400 (EDT)
• References: <9nalpb\$npj\$1@smc.vnet.net> <9ncgqf\$q1g\$1@smc.vnet.net> <9nf6i0\$sfj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Kevin,

Both NonlinearFit and Fit functions perform the least squares fit.  I
found that both can be used on complex data directly.  Its just that Fit
does it with basis functions that are linear combinations and
NonLinearFit does it with a function you pick.  The method I proposed is
one of perhaps many.  I chose this method because I felt it offered the
flexibility in that the real part and imag part may very well have
distinct behaviors which is conducive for two distinct functions or models.

On a side note however, I kept getting the following error when I tried
to use NonlinearFit on the complex data directly:
"Less::nord: Invalid comparison with ... attempted."  Yet, Mathematica
returned an 'exceptable' solution.  Should I disregard the error message?

Thanks,
Lawrence

Kevin J. McCann wrote:

> What about just doing a least squares fit? I have done this for complex data
> and it works fine.
>
> Kevin
>
> "Lawrence A. Walker Jr." wrote:
>>Hi Max,
>>
>>Try dividing the complex data into two data sets: real and imaginary.
>>Then you can apply the NonlinearFit function twice.
>>
>>For example
>>
>>data = {{1, 1+2 I},{2, 3+4 I}, {3, 4+5 I}};
>>dataRe=Map[{#[[1]],Re[#[[2]]]}&,data];
>>dataIm=Map[{#[[1]],Im[#[[2]]]}&,data];
>>
>>NonlinearFit[dataRe, func1, ...];
>>NonlinearFit[dataIm, func2, ...];
>>
>>Note, you must specify the functions apriori.
>>
>>Lawrence
>>
>>
>>Max Ulbrich wrote:
>>
>>
>>>Hi,
>>>
>>>I have complex data (re+im) from a lock-in amplifier and want to fit
>>>them
>>>to a complex function. Though, the NonlinearFit function doesn't work
>>>with complex data. Has anyone a solution?
>>>
>>>Max
>>>

```

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