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Re: [Q] Nonlinear Fitting in symbolic Integration ..?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82942] Re: [Q] Nonlinear Fitting in symbolic Integration ..?
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sun, 4 Nov 2007 06:09:06 -0500 (EST)
  • References: <fgc9f7$8g1$1@smc.vnet.net>

hwoarang schrieb:
>  Dear Mathgroup, 
>  
>  I have experiment data and am trying to fit data to convoluted equation. 
>  The equation contains UnitStep and symbolic Integrate function. 
>  I think that these functions have some compolited problems according to searching 
>  about related problems in archives. 
>  But still, I have no idea whether the problem is in UnitStep, symbolic Integrate or NonlinearRegress.. -_-. 
>  Does anybody out there have any ideas for this ? 
>  Any help would be appreciated. 
>  
>  I pasted math code.
>  
>  Sincerely, yours 
>  Hwoarang. 
>  
>  Math Code : 
>  ----------------------------------------------------------------------------- 
>  Remove["Global`*"]; 
>  << "Statistics`NonlinearFit`" 
>  k0 = 1; k1 =. ; k2 =. ; tau1 =. ; tau2 =. ; 
>  response[t_, x_] := (UnitStep[t - x]*{k2*(1 - E^(-((t - x)/tau2))) + 
>  (k1*(1 - E^(-((t - x)/tau1))))/E^((t - x)/tau2)})/E^(x^2/(2*0.1^2)) 
>  convol[t_] = Integrate[(k0*response[t, x])/(2*Pi*0.1^0.5), {x, -1, 0}, 
>  Assumptions -> {{t, k1, k2, tau1, tau2} ¡ô Reals && t > 0 && tau1 > 0 && 
>  tau2 > 0 && k1 > 0 && k2 > 0}, GenerateConditions -> False] + 
>  Integrate[(k0*response[t, x])/(2*Pi*0.1^0.5), {x, 0, 20}, 
>  Assumptions -> {{t, k1, k2, tau1, tau2} ¡ô Reals && t > 0 && tau1 > 0 && 
>  tau2 > 0 && k1 > 0 && k2 > 0}, GenerateConditions -> False] 
>  dat = Import["Reflsmooth.txt", "Table"]; 
>  ListPlot[dat]; 
>  NonlinearRegress[dat, convol, t, {{k1, 0.4, 0.35, 0.45}, 
>  {k2, 0.04, 0.035, 0.045}, {tau1, 0.35, 0.3, 0.4}, {tau2, 0.25, 0.2, 0.3}}, 
>  ShowProgress -> True] 
> 
> -------------------------------------------------------------------------- 
> Jiwan Kim, Ph. D. Candidate,
> Dept. of Physics and Center for Nanospinics of Spintronic Materials, 
> KAIST 373-1, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Republic of Korea 
> Tel: +82-42-869-8163
> Cel: +82-16-870-7419
> Fax: +82-42-869-8162 
> E-mail: hwoarang at kaist.ac.kr 
> 
> 

Hi,

there are some details I do not understand:

1.) Why is response[] defined to return a list with one element? I would
replace the curly braces with parentheses. Maybe NonlinearRegress
doesn't like lists in models...

2.) Why do you add the integrals from -1 to 0 and from 0 to 20 instead
of integrating from -1 to 20? (Or my eyes become old and I overlooked a
difference in the integrands).

We do not know the content of Reflsmooth.txt; so any help beyond the
integrals is nearly impossible. But it might help to add the Option
WorkingPrecision->20 (or higher) to the call of NonlinearRegress.

HTH,
Peter


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