Fitting two data sets with different equation but same parameters

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

Answer 1

[Shashank Prasanna]

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]);

[Shashank Prasanna]

Here are links to the documentation page of lsqnonlin and fsolve:

http://www.mathworks.com/help/optim/ug/lsqnonlin.html

http://www.mathworks.com/help/optim/ug/fsolve.html

[Jennifer Yu]

That's exactly what I'm looking for. Thank you!