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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