Fitting a function of the form x-a for unknown a
1 view (last 30 days)
Show older comments
We have data which is roughly exponential for x<a, and approximately a power law (x-a)^b for x>a, but I'm unclear how (or if it's even possible) to find a adaptively.
Clearly fitting a function of the form Ce^(bx)+ c(x-a)^d is a problem (if for no other reason than the fact that 0<x<a gives complex value), but short of brute force trial and error to find a, I'm not quite sure where to start.
I guess I'm looking to optimize the value of a by simultaneously fitting the exponential below and the power law above until both converge (though I'm pretty sure that's not possible without a fair amount of work).
0 Comments
Accepted Answer
Roger Wohlwend
on 4 Sep 2014
Yes, you're looking for an optimization, and I can assure you that it is not a fair amount of work. However it won't work with the function you mention in your question. Instead use the optimization function lsqcurvefit with the following function you want to fit:
function y = myoptfunc(coeff, xdata)
y = NaN(length(xdata),1);
q = xdata < coeff(1);
y(q) = coeff(2) * exp(coeff(3) * xdata(q));
y(~q) = coeff(4) * (xdata(~q) - coeff(1)).^coeff(5);
end
The vector coeff contains your coefficients. The first one is your parameter a.
More Answers (0)
See Also
Categories
Find more on Fourier Analysis and Filtering in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!