NonlinearRegress of user functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg91518] NonlinearRegress of user functions*From*: "Ngoc Anh Lai" <ngocanh.lai at boku.ac.at>*Date*: Mon, 25 Aug 2008 05:05:57 -0400 (EDT)

Greetings all, I have problem with nolinearRegress of my functions. Could you please tell me what should I do to solve my problem?. The problem is: I have experimental data set of (Texp, pexp, rhoexp). With each value of Texp, I will calculate pcal and rhocal by using functions pcal = psT[T, A, B, C, D, E] and rhocal = rhoT[T, A, B, C, D, E]. Parameters A, B, C, D, E of the functions psT and rhoT will be found by Minimization of (1-pcal/ pexp)^2+(1- rhocal/ rhoexp)^2 for all experimental data points. rhocal and pcal is found by iteration and guessing of some value in functions psT[T, A, B, C, D, E] and rhoT[T, A, B, C, D, E] provided values of T, A, B, C, D, E are given. To solve the problem, I define + rhoT[T_,A_,B_,C_,D_,E_]:=Module[{rho}, â?? bunch of commands and iterative procedures related to T, A, B, C, D, E to find rhoâ??, rho]; + psT[T_,A_,B_,C_,D_,E_]:=Module[{ps}, â?? bunch of commands and iterative procedures related to T, A, B, C, D, E to find psâ??, ps]; + and experimental data set: tprho = {Texp, pexp, rhoexp}. Firstly, I try to Minimize as: toiuu=NMinimize[{Plus@@Table[(1-psT[tprho[[i,1]], A1,B1,C1,D1,E1]/tprho[[i,2]])^2 + (1-rhoT[tprho[[i,1]], A1,B1,C1,D1,E1]/tprho[[i,3]])^2,{i,Length[tprho[[All,1]]]}], 320.0<A1<550, 0.8<B1<1.8, 0.8<C1<1.80, 0.0<D1<20, 0.0<E1<20},{A1,B1,C1,D1,E1}]; { A,B,C,D,E }={ A1,B1,C1,D1,E1}/.Last[toiuu]; I receive { A,B,C,D,E } ={ 327.593,1.63175,1.8,20.,0.00224707} while the corrected values should be {A,B,C,D,E} ={440.2208,1.5161,1.4600,0.8646,4.9666}. I also shorten the constrained range of {A1,B1,C1,D1,E1} close to the corrected values of {A,B,C,D,E} but it is still give the wrong answers. Secondly, I try to use NoninearRegress as: tprho[[All,4]]=0; caseall=NonlinearRegress[tprho[[All,{1,2,3,4}]],(1-psT[T,A1,B1,C1,D1,E1]/pexp)^2 + (1-rhoT[T,A1,B1,C1,D1,E1]/rhoexp)^2,{T,pexp, rhoexp },{{A1,440},{B1,1.516},{C1,1.46},{D1,0.88},{E1,4.9}},RegressionReport->{BestFitParameters}]; { A,B,C,D,E }={ A1,B1,C1,D1,E1}/.BestFitParameters/.caseall; I receive { A,B,C,D,E } ={ 39094.2,341.312,96.922,27.3373,-155.741}. In my opinion, this case, the psT and rhoT may not be call correctly because the total running time of this NonlinearRegress is 0.141s while I have 22 experimental data point and each data point need 5.125s to run the function psT and 5.094s for function rhoT. The total running time have to larger than 22*(5.125+5.094)s but not 0.141s. For this case, I receive error messages as: Set::shape: Lists \ {Statistics`NonlinearFit`Private`params,Statistics`NonlinearFit`Private`start,\ \[LeftSkeleton]38\[RightSkeleton],\[LeftSkeleton]38\[RightSkeleton],\ Statistics`NonlinearFit`Private`minr,Statistics`NonlinearFit`Private`maxr} and \ {{$Failed,$Failed,$Failed,$Failed,$Failed},{$Failed,$Failed,$Failed,$Failed,$\ Failed},{$Failed,\[LeftSkeleton]3\[RightSkeleton],$Failed},{$Failed,$Failed,$Failed,$\ Failed,$Failed},{$Failed,$Failed,$Failed,$Failed,$Failed}} are not the same shape. Transpose::nmtx: The first two levels of the one-dimensional list {Statistics`NonlinearFit`Private`params,Statistics`NonlinearFit`Private`minr,\ Statistics`NonlinearFit`Private`maxr} cannot be transposed. Part::partw: Part 2 of {} does not exist NonlinearFit::srange : The starting point Statistics`NonlinearFit`Private`start for the least \ squares search for parameter estimates is outside the prescribed parameter range Transpose[Statistics`NonlinearFit`Private`minrâ?¤Statistics`NonlinearFit`\ Private`paramsâ?¤Statistics`NonlinearFit`Private`maxr]. and so on. I really do not know which command or procedure or manipulation should be implemented. Could you please give me some suggestions. Thanks and regards, LAI Ngoc Anh PS: There are some separated coefficient files and long source code for the problem. I can not attach here. However, I can send it to your email for analyzing If you give me your email's address.