Re: Fittings 2 sets of equations and 2 data sets with nonlinearmodelfit

*To*: mathgroup at smc.vnet.net*Subject*: [mg121711] Re: Fittings 2 sets of equations and 2 data sets with nonlinearmodelfit*From*: Ray Koopman <koopman at sfu.ca>*Date*: Mon, 26 Sep 2011 20:06:24 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j5pcf8$8h2$1@smc.vnet.net>

On Sep 26, 1:17 am, JamesE <haywan... at excite.com> wrote: > Hi, > > My names is James Ellison; and I have 2 nonlinear equations of the > type: > > y[1]=x+a*x[1]^2+b*x[1]^3 and y[2]=a*x[2]^3+b*x[2]^5 with the real > valued parameters a and b for both equations. > > I further have 2 data sets > > data[1] for y[1] and > data[2] for y[2] > > I can use NonlinearModelFit in order to fit each data[i] set to > its function y[i] and get good fits. But the parameters a and b > should be the same. > > How can I create a simple code with Mathematica, so that I can do > a simultaneous fit resulting in the parameters a and b to be the > same. > > I am a Mathematica beginner and would be pleased, if someone could > answer my question for beginners. > > Best regards, James Although your models are nonlinear in x they are linear in the unknown parameters, and it is the latter that matters here. Write your model as w = a*u + b*v, where {u, v, w} = {x^2, x^3, y-x} for data[1] and {x^3, x^5, y} for data[2]. If data[1] and data[2] contain {x,y} pairs then Join[{#1^2, #1^3, #2-#1}& @@@ data[1], {#1^3, #1^5, #2 }& @@@ data[2]}] will give you a data matrix that can be input to LinearModelFit. Be sure to specify IncludeConstantBasis->False.