Fitting two data sets with different equation but same parameters
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Hi everyone,
I have a problem on my hands that I don't really know how to solve. I have two sets of data, one is Amplitude vs Temeprature (let's called it Amp vs Temp) and another is Phase vs Temperature (say Phi vs Temp). Right now I need to fit a non-linear model to Amp vs Temp, let's say for simplicity
Amp(Temp) = a*Temp^2+b*Temp^3, a
nd a different model to Phi vs Temp, let's say
Phi(Temp) = a*exp(-b*Temp).
But a and b are the same for both Amp and Phi because they are actual physical quantities. How should I proceed?
Thank you very much!
Jennifer
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Shashank Prasanna
2013-7-8
Jennifer, essentially you are solving a system of equations. Do you have the optimization toolbox? If you do then you can solve this either using fsolve or lsqnonlin
Create a function as follows:
function y = nonlinmodel(x,Temp,Amp,Phi)
y = [Amp - x(1)*Temp.^2 + x(2)*Temp.^3; Phi - x(1)*exp(-x(2)*Temp)];
% Where x(1) = a, and x(2) = b
Now you want to find x(1) and x(2) that minimizes the above system in a least square sense.
Temp = randn(100,1);
Amp = randn(100,1);
Phi = randn(100,1);
% Some random data for demonstration
f = @(x)nonlinmodel(x,Temp,Amp,Phi);
optimal_x = lsqnonlin(f,[0;0]);
% OR
optimal_x = fsolve(f,[0;0]);
2 个评论
Shashank Prasanna
2013-7-8
Here are links to the documentation page of lsqnonlin and fsolve:
Jennifer Yu
2013-7-9
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2013-7-8
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