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Re: NonlinearFit problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg66527] Re: NonlinearFit problem
*From*: dh <dh at metrohm.ch>
*Date*: Fri, 19 May 2006 03:39:17 -0400 (EDT)
*References*: <e4ekoe$9fa$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Oliver,
to fit a complex function f you may e.g. use NMinimize and minimize the
absolute value of some "error" function.
E.g., assume f depends on the independent variable z and a parameter p:
f[z,p]. Further, you have data d={{z,f[z]},..}. You may the define an
"error" function:
ff[p] = Norm[ d[[All, 2]] - (f[#, p] & /@ d[[All, 1]]) ];
here we used Norm to get the "length of the error". Finally:
NMinimize[ff[p],p]
gets the optimal p value.
Daniel
Oliver Friedrich wrote:
> Hallo,
>
> I want to use the NonlinearFit algorithm to obtain the parameters of a
> lossy line. There is a model
>
> Cell[BoxData[
> RowBox[{
> SqrtBox[
> FractionBox[
> RowBox[{
> RowBox[{"2", " ", "\[ImaginaryI]", " ", "f", " ", "L", " ",
> "\[Pi]"}], "+",
> RowBox[{
> SqrtBox["f"], " ",
> SqrtBox[
> RowBox[{"2", " ", "\[Pi]"}]], " ",
> SubscriptBox["R", "skin"]}]}],
> RowBox[{"G", "+",
> RowBox[{"2", " ", "\[ImaginaryI]", " ", "C", " ", "f", " ",
> "\[Pi]"}]}]]], " ",
> RowBox[{"Tanh", "[",
> RowBox[{"1.`", " ",
> SqrtBox[
> RowBox[{
> RowBox[{"(",
> RowBox[{"G", "+",
> RowBox[{"2", " ", "\[ImaginaryI]", " ", "C", " ", "f",
> " ", "\[Pi]"}]}], ")"}], " ",
> RowBox[{"(",
> RowBox[{
> RowBox[{"2", " ", "\[ImaginaryI]", " ", "f", " ", "L",
> " ", "\[Pi]"}], "+",
> RowBox[{
> SqrtBox["f"], " ",
> SqrtBox[
> RowBox[{"2", " ", "\[Pi]"}]], " ",
> SubscriptBox["R", "skin"]}]}], ")"}]}]]}], "]"}]}]],
> "Output",
> CellLabel->"Out[166]="]
>
> that describes the input impedance of a lossy line when shorted at the
> end. The line parameters to obtain are Rskin,L,G and C. f is the
> independant variable. I have data of the line of the form {{f1,Z1},
> {f2,Z2},...} where Z is of course complex.
> Unfortunately NonlinearFit seems to have problems with complex numbers
> since it returns with messages saying "Objective function isn't real
> at...".
> Does anyone knows how to fix NonlinearFit for complex numbers or any
> other numerical method that could solve my problem?.
>
> Thank you
> Oliver
>
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