[Q] Nonlinear Fitting in symbolic Integration ..?

• To: mathgroup at smc.vnet.net
• 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
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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