Global Fitting multiple nonlinear equations to multiple datasets.

*To*: mathgroup at smc.vnet.net*Subject*: [mg131238] Global Fitting multiple nonlinear equations to multiple datasets.*From*: Brandon Breitling <brandonjbreitling at gmail.com>*Date*: Thu, 20 Jun 2013 04:45:32 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hi, I have collected several time dependent data sets. At each time point there are 5 observables (XHS, XHF, XO, X, and F) which can be described by five equations (XHS(t), XHF(t), XO(t), X(t), and F(t)) These five equations are related and depend on five parameters (k1,k2,k3,k4,k5). I would like to globally fit the five data sets to the five equations to extract the five parameters. I have fitted each of the curves individually but would like to try a global fit but don't know how to do that. What I have done so far is below which shows the fit for one equation with NonlinearModelFit(I have the other equations fitted too but its a lot of code): XHS = Import["C:\\Users\\bbreitling\\Desktop\\XHS.csv"] ; XHF = Import["C:\\Users\\bbreitling\\Desktop\\XHF.csv"] ; XO = Import["C:\\Users\\bbreitling\\Desktop\\XO.csv"] ; X = Import["C:\\Users\\bbreitling\\Desktop\\X.csv"] ; F = Import["C:\\Users\\bbreitling\\Desktop\\F.csv"] ; dataXHS = XHS[[11 ;; 19, All]]; dataXHF = XHF[[11 ;; 19, All]]; dataXO = XO[[11 ;; 19, All]]; dataX = X[[11 ;; 19, All]]; dataF = F[[11 ;; 19, All]]; XHSi = dataXHS[[1, 2]]; clear[k1]; nlmXHS = NonlinearModelFit[dataXHS, E^(-k1 t) XHSi, { {k1, .005}}, t]; dataplotXHS = ListPlot[dataXHS, PlotStyle -> ColorData[1, 1], PlotMarkers -> (Style["\[FilledCircle]"])]; fitplotXHS = Plot[nlmXHS[t], {t, 0, 120}, PlotStyle -> ColorData[1, 1], PlotRange -> {{0, 120}, {100, 0}}];