Re: NonlinearRegress

*To*: mathgroup at smc.vnet.net*Subject*: [mg13028] Re: [mg12936] NonlinearRegress*From*: "Carl K.Woll" <carlw at fermi.phys.washington.edu>*Date*: Tue, 30 Jun 1998 00:26:25 -0400*Organization*: Department of Physics*References*: <199806240744.DAA03179@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Peter, I assume the problem you are running into is that Mathematica is unable to calculate symbolic derivatives of your function, since it is defined with conditions. There are two standard ways to proceed here, and one nonstandard way which I prefer. First, the standard approaches. You will need to use the option Method->FindMinimum for these approaches. Then, you can either give two starting points for your parameters, in which case the method FindMinimum won't calculate symbolic derivatives, or you can feed NonlinearRegress the symbolic gradients with the option Gradient->{ list of gradients } I should mention that I don't know how to get the second method above to work. The problems with the above approaches is that they are restricted to the method FindMinimum, the two starting point approach is slow, and of course I can't even get the Gradient method to work. This leads to the "nonstandard" approach, which is to simply override Mathematica's derivatives with your own definitions. Before describing an example of this approach, let me describe it's virtues. It works for both the default Levenberg-Marquardt method and the FindMinimum method, and is in general faster than the two starting point approach. Here is an almost nontrivial example. Suppose your model is given by a numerical integration routine, such as f[x_?NumericQ,a_?NumericQ]:=NIntegrate[E^(a q^2),{q,0,x}] Obviously, Mathematica is unable to calculate derivatives of the above function. On the other hand, we know that the derivative of the above function with respect to a is simply fa[x_?NumericQ,a_?NumericQ]:=NIntegrate[q^2 E^(a q^2),{q,0,x}] The question is how do we communicate this knowledge to Mathematica? The answer is to use an upvalue f /: D[f[x_,a_],a_]:=fa[x,a] Suppose the data is given simply by data = Table[{x,f[x,2]},{x,0,2,.1}]; Then with the above definition for the derivative, the following works: NonlinearRegress[data,f[x,a],x,{a}] Of course, Mathematica complains, since the data has no error, but that won't be a problem with real data. If you try the above with the method FindMinimum, you will also need to give the definition Derivative[0,1][f][x_,a_]:=fa[x,a] I hope the above helps answer your question. If you have problems trying to apply it, send an example. Carl Woll Dept of Physics U of Washington Klamser wrote: > Hello, how can I do a non Linear Regress not on a Function but on a > Module, because the Function can not be defined without Conditions?? > > Peter Klamser

**References**:**NonlinearRegress***From:*Klamser@t-online.de (Klamser)

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**NonlinearRegress**

**Numerical Determinants**