Re: Simultaneous nonlinear Regression of two data sets

*To*: mathgroup at smc.vnet.net*Subject*: [mg19473] Re: [mg19440] Simultaneous nonlinear Regression of two data sets*From*: "Mark E. Harder" <harderm at ucs.orst.edu>*Date*: Sat, 28 Aug 1999 15:53:03 -0400*Sender*: owner-wri-mathgroup at wolfram.com

To All; Christopher, thanks for posting this. I, too, have a global fitting problem** I would like NonlinearRegress to work on, & when I read the book & the online help, I thought the idea was still worth trying. Alas, the problem *seems* to be that the function can't interpret parameter symbols and values that are lists ( which, I believe, are the most economical and direct forms for expressing the problem.). In my case, the function call returned no error messages; it simply returned a slightly expanded form of the function. Another problem I have is that my model function has to be a Mathematica function module, not a symbolic statement, since evaluation of my model, given parameter values, involves iterative numerical procedures, like root-finding; & I don't think Mathematica can handle that, even when using the FindMinimum option. I have been able to implement these kinds of fits in FORTRAN 77 & 90, using the IMSL nonlinear-fitting routine where you can pass the subroutine the name of the model function subprogram. If you want the package routing to use analytical derivatives, you pass it a function for evaluating derivatives, otherwise, it uses some internal approximate numerical algorithm for the derivatives. This can be a little complicated, requiring COMMON blocks or some such, and I would rather have it done in Mathematica. I am currently working at creating simpler test cases in Mathematica that separate these two problem variables. If I get anywhere, I'll let you know (don't hold your breath). Otherwise, I, too, would welcome enlightenment. -mark **- one term for the procedure of simultaneously fitting a set of models to multiple data sets, when some of the parameters are shared among the models -- this can be a way to make a more overdetermined system with better-defined minimum in its error surface out of a bunch of possibly poorly-determined individual fits. -----Original Message----- From: Christopher Mack <mack at tvt.tu-darmstadt.de> To: mathgroup at smc.vnet.net Subject: [mg19473] [mg19440] Simultaneous nonlinear Regression of two data sets >Hello, > >I want to fit two (if it works, I also want to fit threee and four) >mathematical functions to two (in future perhaps three and four) data >sets (gaussian >profiles); each function has eight parameters to fit, but four of them >are the same for all functions. > >I first thought of using the Mathematica-Function "NonlinearRegress"; >but after reading the Online-help I assumed that it only can fit >one function to one data set. > >Is there a functino implemented into Mathematica, which can solve the >described problem ? > > >Thanks, > >Christopher Mack, > >Department of Chemical Process Engineering, >Darmstadt University of Technology >