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[Q] Nonlinear Fitting in symbolic Integration ..?

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  • Subject: [mg82842] [Q] Nonlinear Fitting in symbolic Integration ..?
  • From: hwoarang <kjwan at kaist.ac.kr>
  • Date: Thu, 1 Nov 2007 05:12:02 -0500 (EST)

 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 



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