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Re: [Help-gsl] Understanding 'ftol' in nonlinear-least-squares fitter

From: Patrick Alken
Subject: Re: [Help-gsl] Understanding 'ftol' in nonlinear-least-squares fitter
Date: Mon, 7 Oct 2019 00:46:13 +0000
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Thunderbird/60.8.0

Hello. Only xtol and gtol are currently used by
gsl_multifit_nlinear_test(). You can see the code here:

I made a stub for ftol as well, because the book by Dennis and Schnabel
talks about a test for testing the residual vector (see comment (3) in
the header of that function). However, in practice I found that test
wasn't as useful as the xtol and gtol tests, so it is currently disabled.

Also, xtol does not measure distance to the initial guess. It measures
the distance from the previous iteration - so if the step vector is
small relative to the current position, the iteration will stop.


On 10/4/19 12:51 PM, Spencer Fleming wrote:
> Hello!
> I'm an undergraduate research student working at Boise State University.
> Keeping things brief, my job is to work on a project that aims to use the
> GNU Scientific Library to fit a large amount of data for scientific
> analysis.
> We are using the gsl_multifit_nlinear module to fit each individual unit of
> data. There are three coefficients it uses that are of interest to me
> currently: xtol, ftol and gtol.
> To my knowledge, each of these are used in a separate calculation for
> error, each of which answer a different question about how close our
> current guess is to the actual data.
> To make things a little simpler, let's say the theoretical, ideal function
> for the data we are fitting is named f(x), and the function we are
> generating to approximate it is named g(x).
> - xtol roughly answers "How close are we to the original guess? Did we
> wander too far?"
> - gtol roughly answers "For every data point x, how close is f(x) to g(x)?"
> - ftol I'm not as certain about. I was hoping I could be provided with some
> insight on this coefficient.
> Also, I apologize if my vocabulary is a bit confusing here; as a Computer
> Science major, a lot of this is new to me. However, don't shy away from
> giving me a complex answer if that's what it takes to understand ftol, or
> anything about the fitter. I can decipher it with a textbook and some grit!
> Thank you for your time!
> -Spencer Fleming

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