How to get a an XY plotted curve to match another curve based on observed values?

If I have as function that is supposed to model an observable phenomenon with a variable that can be adjusted, how can I get Matlab to adjust that variable to achieve an output that can be compared to and matched as closely as possible to an observed set of data points?

Answer 1

[Matt Tearle]

Sounds like a regression/curve fitting problem? The right function to use depends a bit on the form of the model. If it's just a single parameter, I'm guessing it's a nonlinear model, in which case use nlinfit if you have Statistics Toolbox. Otherwise, you can brute force it and use fminsearch.

For example, to fit a model y = cos(kx) to data stored in vectors xdata & ydata, using an initial guess of pi for k:

f = @(k,x) cos(k*x);
kfit = nlinfit(xdata,ydata,f,pi)

or

f = @(k) norm(ydata - cos(k*xdata));
kfit = fminsearch(f,pi)