Fitting in MatLAB

Hi

I have a dataset, which I am trying to fit to a function having the form

A*cos(a*x) + B*sin(b*x) + C/x + exp(-D*x).

Fitting in MatLAB has always been difficult for me. Generally I have been able to fit functions "manually" like this:

**************************************************************************************************

t = 0:7 ; rel = [629 537 460 375 334 286 249 227];

fh = @(x,p) p(1) + p(2)*exp(-x./p(3))

errfh = @(p,x,y) sum((y(:)-fh(x(:),p)).^2)

p0 = [mean(rel) (max(rel)-min(rel)) (max(t) - min(t))/2];

P = fminsearch(errfh,p0,[],t,rel)

plot(t,rel,'bo',t,fh(t,P),'r-')

**************************************************************************************************

But I have never been able to get errorbars out with this method + I have run into problems regarding the number of iterations needed for convergence. Can I get a hint to how I would go about fitting my function above to my data set?

Best, Niles.

[Oleg Komarov]

This is a duplicate of the active thread (2 answers): http://www.mathworks.com/matlabcentral/answers/37920-help-with-fminsearch

Please edit your original question, do not duplicate posts.

[Sargondjani]

this is actually quite a different question....

Answer 1

[Sargondjani]

the problem is that fminsearch is not well suited to optimize for more than a couple of parameters, BUT there are special tools for curve fitting:

lsqcurvefit

lsqnonlin

or if you want something else than least squares, you would need some other algorithm to optimize for more than a couple of variables: if you have the optimization toolbar, you can use fminunc

otherwise im afraid you will have to program an optimizer yourself, like Newton Raphson algorithm

[Niles Martinsen]

Thanks. In that case, do you know how I would get the uncertainties on the fitted parameters out with the above method?

[Sargondjani]

i editted my answer: lsqcurvefit and lsqnonlin are sepcial tools. they should be able to do the trick... sorry for confusion (i dont do much curvefitting myself, so i should actually shut up)