Feature request: RBF - Allow to set the initial guess for optimal sigma calculation

[gutierrad]

When using RBF interpolation for locations that are very close to each other, it may be advantageous to be able to provide an initial optimization estimate based on the value calculated for a location close the the problem one.

[gutierrad]

Hi @tausiaj,

I have reviewed the commits and I have seen that in the new version the function used to minimize when x0 (sigma_opt) is prescribed is fmin, as opposed to fminbound, used when x0 is not prescribed.
Why is this? I'd say that the bounds should still apply no matter if x0 is prescribed or not.
In general, the bounds will not be reached, but under some circumstances, the optimization could not converge.
i.e.: Iterating along a coastline, using the previous optimal sigma and going around a cape. The sigmas at both sides of the cape could be very different and using one of them as a guess for the other may lead to non-convergence.

I think it may be worth checking if scipy.optimize.minimize should be used instead?
With the Nelder-Mead method options, but through the more general minimize (instead of the more specific fmin and fminbound).

Cheers,
D