       Re: Fitting experimental data

• To: mathgroup at smc.vnet.net
• Subject: [mg85544] Re: Fitting experimental data
• From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
• Date: Wed, 13 Feb 2008 04:28:42 -0500 (EST)
• Organization: University System of Maryland
• References: <fopb53\$bhu\$1@smc.vnet.net>

Here is the way I usually do this for a particular example. I generally
roll my own least-squares fit:

points={{23400.,273.2},{6800.0,298.2},{2400.0,323.2}};
(*Plot the data points,but don't show the plot*)
p1=ListPlot[points,PlotStyle->{Red,PointSize[0.025]}];

(*The function that I wish to fit*)
f[B_,Ro_,x_]:=B/Log[x/Ro]

(*The LSQ fit function.*)
(*Note that you can plot this for a range of B and Ro values*)
lsFit[B_,Ro_]:=Plus@@Apply[Abs[f[B,Ro,#1]-#2]^2&,points,1]

(*Finally,fit the data by finding the minimum*)
(* The output comes in two parts. The first is *)
(* the sum of the squares; the second, the best fit parameters *)
sol=FindMinimum[lsFit[B,Ro],{B,1},{Ro,1}]

(* g[R] is the fitting function with the best fit parameters *)
g[x_]=f[B,Ro,x]/.sol[];

(*Plot the fit along with the original data points*)
Plot[g[R],{R,1000,25000},PlotStyle->{Blue,AbsoluteThickness},\
Epilog->p1[],Frame->True,
FrameStyle->AbsoluteThickness,
GridLines->Automatic,
BaseStyle->{FontFamily->"Arial",FontSize->12,FontWeight->Bold},\
FrameLabel->{"R","g(R)"},PlotLabel->"LSQ Demo"
]

Hope this helps,

Kevin

Ausman, Kevin wrote:
> I am trying to fit experimental data (a list of {x,y} points) with a
> model that produces a similar list of points. It seems that FindMinimum
> with a Levenberg Marquardt method makes the most sense; unfortunately, I
> can't seem to get it to work.
>
> soln=FindMinimum[Sum[(xptData[[i,2]]-(simulatedData[xaxis,testInstFunc,
> k1auto,a1initauto])[[i]])^2,{i,1,Length[xaxis]}],{{k1auto,0.04},{a1initauto,0.9}}]
>
> In this example, xptData is the list of experimental data. simulatedData
> returns just the y axis as a list (assuming the same x axis), and the
> resulting list, as you might imagine, depends on k1auto and a1initauto.
> However, this results in a number of errors, I think because it tries to
> evaluate simulatedData for the general case rather than for specific
> instances of k1auto and a1initauto. simulatedData requires the use of
> ListConvolve, NDSolve, and a number of other functions that seem to
> preclude a general solution rather than a specific solution.
>
> Does anyone have any thoughts on how to overcome this problem? Thanks!
>
> Kevin Ausman
> ausman at okstate.edu

--

Kevin J. McCann
Research Associate Professor
JCET/Physics
Physics Building
University of Maryland, Baltimore County
1000 Hilltop Circle
Baltimore, MD 21250

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