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Re: [Help-gsl] Weighted Levenberg Marquardt

From: Brian Gough
Subject: Re: [Help-gsl] Weighted Levenberg Marquardt
Date: Wed, 19 Aug 2009 08:56:16 +0100
User-agent: Wanderlust/2.14.0 (Africa) Emacs/22.2 Mule/5.0 (SAKAKI)

At Mon, 17 Aug 2009 09:57:33 +0000,
Tom Banwell wrote:
> I have solved the problem using an unweighted Least-squares but
> would prefer to use weighted as some of my data have larger relative
> uncertainties.  I have seen on the GSL reference manual that I can
> perform weighted Least-Squares using a scalar, but I wanted to use
> the full covariance matrix, Vi. 

We should really provided a separate correlated fitter to take care of
the case with a full covariance matrix.  

It is possible to use the existing routine by factorising the
covariance matrix to get an expression of the form (U [ y - f(x,a)])^T
W (U [ y - f(x,a)]) and working with the transformed variables Y=U y
and F=U f(x,a), transforming the final values back to get the desired

Brian Gough
(GSL Maintainer)

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