Fitting a function of the form x-a for unknown a
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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).
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Roger Wohlwend
2014-9-4
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.
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