Re: convolution vs. NMinimize

• To: mathgroup at smc.vnet.net
• Subject: [mg52405] Re: [mg52397] convolution vs. NMinimize
• From: DrBob <drbob at bigfoot.com>
• Date: Fri, 26 Nov 2004 01:04:34 -0500 (EST)
• References: <200411251051.FAA21591@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Does anybody know what "4*&#960;*t^3" means?

Bobby

On Thu, 25 Nov 2004 05:51:03 -0500 (EST), julia <db at ict.fhg.de> wrote:

> Hello,
>
> I've had some problems with the nonlinear fit of my measuresd data
> before.
> Now, i have worked it out. I have to use a numerical global
> optimization.
> The fit with NMinimize leads to very good results.
> The problem now is, that the fit needs about 6 hours computation time.
> I'm sure this could be faster, but i don't have an idea how...
>
> i've generated a sum of squares from the measured data and the model.
> The model consists of the actual model and a numerical convolution of
> the
> model with a measured input signal. The convolution should be the the
> time-consuming
> step. I don't know what mathematica is doing exactly (e.g., which
> steps are calculated
> symbolical or numerical). The optimization should be fast, if the
> model with the actual
> parameters, and the convolution would be evaluated numerically.
> I've attached the code for the optimization.
>
> In[11]:=
> pred[Pe_,tau_]:=Module[{model,pred1,falt},
>     model=(Pe*tau/(4*&#960;*t^3))^0.5*Exp[-Pe/(4*t/tau)*(1-t/tau)^2];
>     pred1=Map[model/.{t->#}&,time];falt=ListConvolve[inp,pred1,1];falt
>     ]
>
>
> In[15]:=soln=NMinimize[Plus@@Table[((yc[Pe,tau][[i]])-respconvdata[[i,2]])^2,
> 	{i,Length[time]}],{{tau,15,20},{Pe,95,110}},MaxIterations->50,Method->"DifferentialEvolution"]//Timing
>
>
> "inp" is the input signal
> "pred" is the predicted Convolution product
> "respconvdata" is the measured curve
>
> Does anybody have an idea?
> (e.g., how to apply the convolution on a different way..)
>
> Thanks,
>
> julia
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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