Re: Using LevenbergMarquardt Method with a complicated function

*To*: mathgroup at smc.vnet.net*Subject*: [mg52799] Re: Using LevenbergMarquardt Method with a complicated function*From*: iguess at noreply.com (guess)*Date*: Mon, 13 Dec 2004 04:23:15 -0500 (EST)*References*: <c42fu1475r5h@legacy>, <v8ou5u4a7soi@legacy>*Sender*: owner-wri-mathgroup at wolfram.com

From the message, I guess ChiSQ can allow only one Sum when using LevenbergMarquardt method in FindMinimum. Did you try to mimic that there is only one Sum[] function? On 9 Dec 04 06:09:46 -0500 (EST), algaba wrote: >Hi. >I have defined a very long function like this: > >ChiSquare[Per0_?NumericQ, Ppa0_?NumericQ, Ecc0_?NumericQ] := > > (some steps and definitions here) > >ChiSQ = Sum[ResAlpha[[i]]^2 + ResDelta[[i]]^2, {i, 1, Length[ > TExp]}] + Sum[ResAlphaComp[[i]]^2 + > ResDeltaComp[[i]]^2, {i, 1, Length[TComp]}]); > >which tries to find the Chi-Square of an array of data. Now, I want to >minimize it and I use FindMinimum, which works well. The problem >arises when I want to use the Levenberg-Marquardt method, which seems >to be better for this kind of functions (As you can see, it is a sum >of squares) But when I run Mathematica 5 it gives me the next error >message: > >FindMinimum::notlm: The objective function for the method >LevenbergMarquardt \ >must be in a least-squares form: Sum[f[i][x]^2,{i,1,n}] or Sum[w[i] \ >f[i][x]^2,{i,1,n}] with positive w[i]. > >I think the function accomplishes all the requirements. Why I get this >error? Is it maybe because of the long definition of the function? Is >it because Mathematica doesn't see this function as a sum of squares >but as a sequence of steps? >What can I do to solve this problem? I do want to use this method to >minimize the Chi-Square. Thanks. > > >****************************************** >algaba at alumni.uv.es >Universitat de Valencia >Departamento de Astronomía y Astrofísica