Re: inability to pass argument(s) to functions..

*To*: mathgroup at smc.vnet.net*Subject*: [mg29897] Re: inability to pass argument(s) to functions..*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 18 Jul 2001 02:08:42 -0400 (EDT)*Organization*: Universitaet Leipzig*References*: <9j05is$esk$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, Mark Harder wrote: > > Just to set the stage, I am trying to use NonlinearRegression > (again, alas) to fit a model with shared parameters to 2 sets of data, > which are distinguished from each other by an integer index which > appears in the data list in the NLR arguments as an extra independent > variable, which will be passed to the model function in the usual > fashion. This simple scheme fails, although I have tried several > alternative formulations of the model function because, apparently, NLR > is unable to pass the integer index into the model function. I have > enclosed a trial function which reproduces this behavior. I hope > someone can show me what I am doing "wrong" and how I can fix my > problem: > > (* definition of function *) > > In[478]:= > Clear[trialfn, i, ii, c, cc]; > trialfn[aN_List, c, i] := (Print[i]; > Return[c*aN\[LeftDoubleBracket]i\[RightDoubleBracket]] ) c and i should be a Pattern[] and the Return[] is useless because the function value will be the last evaluated expression Clear[trialfn, i, ii, c, cc]; trialfn[aN_List, c_, i_Integer] := (Print[i];c*aN[[i]]) > > (* aN is a list *) > > In[405]:= {aN1,aN2}; > > {c, i, aN} > Out[405]= {c, i, {aN1, aN2}} > > (* pass numeric values explicitly *) > > In[482]:= > trialfn[{-3.4, -4.}, 0., 1 ] > Out[482]= > trialfn[{-3.4, -4.}, 0., 1] (* Doesn't understand command *) With your definition the pattern will only match for a variables c and i that have no values. > > (* passed by replacement ( I think this is how NLR does it) *) > > In[487]:= > trialfn[aN, c, i ] /. {aN1 -> -3.4`, aN2 -> -4.`, c -> 1.`, i -> 2`} > an integer nor a list \ > of integers." > Out[487]= -4. (* correct evaluation, for i=2!! *) It is not the correct evaluation. first trialfn[aN,c,i] is evaluated and gives c*aN[[i]]. Since i has no value you get an error message and than the ReplaceAll insert the numeric value for i into c*aN[[i]] and gives you the result. > > note the result of printing out the value of i, although the function > *is* evaluated. This doesn't work in NLR, however: > > fitData2 = {{0, 1, -3.320248485`}, {1, 1, -3.215648485`}, {2, > 1, -3.375939394`}, {0, 2, -4.312424242`}, {1, 2, -3.985844444`}, > {2, > 2, -4.300822222`}}; (* trial data for fitting *) > > In[476]:= best3D = NonlinearRegress[fitData2, trialfn[aN, c, i ] > , > {c, i}, { {aN1, {-3.4, -3.}}, {aN2, {-4., -3.}} }, > Method -> Gradient, Compiled -> False] > > an integer nor a list \ > of integers. > > "From In[476]:= > FindMinimum::"fmgs": "Could not symbolically find the gradient of > \!\(#1\\ \(\ > \(\(\({aN1, aN2}\)\) \[LeftDoubleBracket] #2 > \[RightDoubleBracket]\)\)\). Try \ > using the default method, giving two starting values for each variable." This is no wonder, because Part[] will never have a derivative with respect to i. But you give {c, i} as variables *and* say that a gradient with respect to both variables should be evaluated. What do you want ? Mathematica has no algorithms for integer optimization. If you wish to have two function you should fit against a linear combination of the two functions, if you wisth to fit to function 1 *or* function 2 you should do two fits't and look for the smaller residual. Regards Jens