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>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Does anybody know what "4*π*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*π*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

**References**:**convolution vs. NMinimize***From:*db@ict.fhg.de (julia)