How does matlab cftool (curve fitting toolbox) determine StartPoint for Sum of Sin fit?

For example given a data set:

y = {3,4,7,8,5,2,0,-1,-4,-2,0} t = {1,2,3,4,5,6,7,8,9,10,11}

I want to model the data with:

a1*sin(b1*x+c1) + a2*sin(b2*x+c2).

I have found information on the Levenberg-Marquardt and Gauss-Newton methods to perform this optimization, but none speak of how to obtain the initial guess.

When I use the cftool to do the above in Fit options it seems to have a pretty good initial guess, can anyone shed light on how it obtains its startpoint?

I realize this might be proprietary information, but I would really like to be able to perform this kind of optimization by hand, for intellectual reasons, if anyone could help me or point me to a place that might, that would be grand.

Regards,

Michael Motes

Answer 1

[Tom Lane]

It's not that proprietary. It's implemented in MATLAB code that's shipped with the product, in particular in the @fittype/private/sethandles function. It uses fft to find the frequencies, as you will see by looking in this file.

If you do try a variant on this yourself, I'd be interested in hearing about it by e-mail.