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From Gilles <gil...@harfang.homelinux.org>
Subject Re: [math] Levenerg-Marquardt evaluations vs. iterations
Date Fri, 20 Oct 2017 13:59:58 GMT
Hi.

On Wed, 18 Oct 2017 15:00:20 -0600, Kearns, Aaron wrote:
> Hi,
>
> I have been using the LM solver in a least-squares curve fitting 
> function.
> I have been using some debugging statements every time the function 
> (&
> Jacobian) is evaluated. I would like some clarification on what the 
> number
> of evalutations vs. iterations is. My understanding is that the 
> number of
> evaluations is the number of times the MultivariateJacobianFunction 
> used in
> the least-squares problem definition is run,

Indeed.

> whereas the number of
> iterations is the number of times a change in the input variables 
> leads to
> an improvement in the cost function / residual.

The number of iterations is incremented by one for each pass
through the algorithm's in main loop:
   
http://commons.apache.org/proper/commons-math/apidocs/src-html/org/apache/commons/math4/fitting/leastsquares/LevenbergMarquardtOptimizer.html#line.337

> Is this a correct
> interpretation?

Probably (bugs notwithstanding).

> Would we be able to get the number of iterations based on
> just looking at the change in the cost function per evaluation of the 
> MJF
> at different points and subtracting the times that a change in 
> variables
> produced a worse cost?

Calling "getIterations()" would be more straightforward:
   
http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math4/fitting/leastsquares/LeastSquaresOptimizer.Optimum.html


HTH,
Gilles



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