Re: HELP! Strange evaluations

*To*: mathgroup at smc.vnet.net*Subject*: [mg33600] Re: HELP! Strange evaluations*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 3 Apr 2002 01:13:24 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <a89174$p7h$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de*Sender*: owner-wri-mathgroup at wolfram.com

Hi, it can't work, because your function has no derivatives ? Or does it not work, because FindRoot[] can return complex values for the the solution, and you can't minimize with a complex valued function. The minimization used by NonlinearRegress[] must evaluate the derivative to know the direction in the parameter space. You can try to find an approximate gradient eqn = x /. Solve[Normal[Series[Cos[a x] - b x, {x, 0, 10}]] == 0, x] // Simplify[#, a > 0 && b > 0] &; grad = D[#, a] & /@ eqn; (BestFitParameters /. NonlinearRegress[data, goo[a, b], a, {b, {0.25, 1.}}, RegressionReport -> BestFitParameters, Gradient -> #] &) /@ grad beside some error messages about a complex objective function this works fine. Regards Jens "Lawrence A. Walker Jr." wrote: > > Hi, > > For the life of me I can't figure out how to get the following to work > correctly. I also tried using various combinations of Hold and Evaluate > -- but to no avail. > > << Statistics`NonlinearFit` > > (* This works ok *) > goo[a_, b_] := > FindRoot[( Cos[a x]) == b x, {x, 0}][[1, 2]]; > > (* Here are some sample data *) > data = Table[{i, goo[i, .5]}, {i, 0, 1, .2}]; > > (* This doesn't work -- I expect b->.5 to be returned. *) > BestFitParameters /. > NonlinearRegress[data, goo[a, b], a, {b, {0., 1.}}, > RegressionReport -> BestFitParameters] > > After executing the above, I get the following error messages: > > FindRoot::frnum: Function {0. b+Cos[0. a]} is not a length 1 list of > numbers at {x} = {0.}. > > NonlinearRegress::nonnum: The model is not numerical at {b->0., a->0.}. > Check that all model parameters are included in the parameter list... > > How do I get the above to work.