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Optimising the fit of a function with 2 variables

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Hi,
I'm using a Gaussian derivative function of the form
A*(mu-x)*exp(-((x-mu)^2)/(2*S^2)))/S^2
to fit some existing discrete data and I want to vary A and S to minimse the RMS error of the fit.
Does anyone know of a function that would allow me to do this, and how I should use it?
I'd appreciate any help!
Thanks,
Earle

Accepted Answer

the cyclist
the cyclist on 27 Mar 2012
The function nlinfit() from the Statistics Toolbox will do this.
Here is a simple example of the use of the function:
% Define the data to be fit
x=(0:1:10)'; % Explanatory variable
y = 5 + 3*x + 7*x.^2; % Response variable (if response were perfect)
y = y + 2*randn((size(x)));% Add some noise to response variable
% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x) F(1) + F(2).*x + F(3).*x.^2;
F_fitted = nlinfit(x,y,f,[1 1 1]);
% Display fitted coefficients
disp(['F = ',num2str(F_fitted)])
% Plot the data and fit
figure(1)
plot(x,y,'*',x,f(F_fitted,x),'g');
legend('data','nonlinear fit')
Note that I am not actually using nonlinear fitting parameters here, but I hope the idea is clear enough.

More Answers (1)

Frederic Moisy
Frederic Moisy on 14 May 2012
You can also use the Ezyfit toolbox, which is free: http://www.mathworks.com/matlabcentral/fileexchange/10176
One installed, you can perform your fit like this:
f = ezfit(x,y,'A*(mu-x)*exp(-((x-mu)^2)/(2*S^2)))/S^2');
See also the example here:

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