[Top][All Lists]

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

RE: [Help-gsl] Weighted Levenberg Marquardt

From: Tom Banwell
Subject: RE: [Help-gsl] Weighted Levenberg Marquardt
Date: Wed, 19 Aug 2009 09:17:34 +0000

Hi Brian,

Thanks for you reply, it sounds similar to my solution.  I found out that if I 
perform Cholesky Decomposition on my covariance matrix V = LL^T, then I can 
perform regular least squares on the modified state and jacobian as follows:

F~ = L^-1 F
J~ = L^-1 J

This should simply be a case of multiplying the matrices/vectors before I 
return control back to the solver.



> Date: Wed, 19 Aug 2009 08:56:16 +0100
> From: address@hidden
> To: address@hidden
> CC: address@hidden
> Subject: Re: [Help-gsl] Weighted Levenberg Marquardt
> 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
> result.
> -- 
> Brian Gough
> (GSL Maintainer)
> Support freedom by joining the FSF

Windows Live Messenger: Thanks for 10 great years—enjoy free winks and 

reply via email to

[Prev in Thread] Current Thread [Next in Thread]