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. Thanks, Tom > Date: Wed, 19 Aug 2009 08:56:16 +0100 > From: [email protected] > To: [email protected] > CC: [email protected] > 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 > http://www.fsf.org/associate/support_freedom/join_fsf?referrer=37 _________________________________________________________________ Windows Live Messenger: Thanks for 10 great years—enjoy free winks and emoticons. http://clk.atdmt.com/UKM/go/157562755/direct/01/_______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
