Re: [Bug-gsl] bug report gsl_multifit_wlinear_svd

[Brian Gough]

At Tue, 10 Nov 2009 16:25:45 +0100,
Mezger Anton-Chr. wrote:
> 
> A small example. I took also the source (I hope the latest one) and a
> commented the balancing out which gives then correct results.
> 

Thanks for the program, I have studied the problem now and can see
what is happening.  

The fit results are inherently different for balanced and unbalanced
matrices in the case where singular values are removed.  The process
of removing singular values is not an invariant operation, since it
acts on an individual element of the matrix.  This introduces an
arbitrariness -- the same difference in the fit results would also
occur without automatic balancing if the scale/units of the variables
simply happened to be chosen differently (as this is equivalent to the
balancing procedure).

To avoid confusion, I have added an option to disable the balancing
(which will be in the next release).

I would be interested to know if the fit results from the balanced
case were physically bad in some way or just different from what was
expected (the residual in the test case is still small).

-- 
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/