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MathGroup Archive 2006

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Fitting a complex Function with FindMinimum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65692] Fitting a complex Function with FindMinimum
  • From: "petitsun1" <r.bactavatchalou at mx.uni-saarland.de>
  • Date: Sun, 16 Apr 2006 01:44:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
I would like to fit experimental data with a complex function.
I have first give the experimental data: {x, real(y),Imag{y}} as
following:

\!\({{10.24`, 12.611`, 0.1344`}, {20.48`, 12.595`, 0.17804`}, {40.96`,
\
12.557`, 0.29196`}, {81.92`, 12.463`, 0.50528`}, {163.84`, 12.234`, \
0.83546`}, {327.68`, 11.773`, 1.2298`}, {655.36`, 11.054`, 1.5477`},
{1310.7`,
       10.191`, 1.6657`}, {2621.4`, 9.3468`, 1.5783`}, {5242.9`,
8.6333`, \
1.3658`}, {10486, 8.0744`, 1.1128`}, {20972, 7.6556`, 0.87569`},
{41943,
    7.3466`, 0.67967`}, {83886, 7.1146`, 0.53152`}, {167770,
    6.9339`, 0.42835`}, {335540, 6.7872`, 0.36402`}, {671090,
    6.6575`, 0.3308`}, {
      1.3422`*^6, 6.5308`, 0.32231`}, {2.6844`*^6, 6.4072`, 0.33302`},
\
{5.3687`*^6, 6.3103`, 0.37133`}}\)

After that, I define the function y=eps and the real and imaginary part
of esp :

eps[Eu1_, Es1_, tau1_, alpha1_, tau1_, fr_] := Eu1 + (Es1 - Eu1)/(1 +
(I*2*p*
    fr*tau1)^alpha1)^beta1
f[Eu1_, Es1_, tau1_, alpha1_,
       tau1_, fr_] := Re[eps[Eu1, Es1, tau1, alpha1, tau1, fr]]
g[Eu1_, Es1_,
 tau1_, alpha1_, tau1_, fr_] := -Im[eps[Eu1, Es1, tau1, alpha1, tau1,
fr]]

I define a new function that I would like to minimize (least squares
fit):

<< Statistics`
ssq[Eu1_, Es1_, tau1_, alpha1_, tau1_] = Plus @@ Apply[((f[Eu1,
    Es1, tau1, alpha1,
   tau1, #[[
    1]]] - #[[2]])^2 + (g[Eu1, Es1, tau1, alpha1, tau1, #[[
                    1]]] - #[[3]])^2) &, t1]

He gives me the error:
Set write:Tg plus in (...) is protected

Now, I would like to fit with minimizing the function as:

FindMinimum[ssq[Eu1, Es1, tau1, alpha1, tau1], {Eu1, 6, 7}, {
    Es1, 12, 13}, {tau1, 0.0001, 0.001}, {alpha1, 0, 1}, {beta1, 0, 1}]

Buet he can´t ...
Have someone one Idee??

Thank you, 
Ravi


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