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From Greg Sterijevski <>
Subject Re: [Math] "LUDecomposition" in "AbstractLeastSquaresOptimizer"
Date Thu, 08 Sep 2011 14:49:12 GMT
Cholesky, in my opinion, is not robust as you have discovered. When it
encounters a non-psd matrix it gives up. Maybe that is the correct course of
action, but I still think that when you are using the getCovariance to
estimate the curvature in the neighborhood of a point it would be okay to
take the generalized inverse and not worry too much about why your matrix is
bordering on non-PSDness... If your optimization stops on that point, that
is another story and should be flagged.

> A possibly more robust option here is to use Cholesky decomposition,
> > which is known to be stable for symmetric positive definite
> > matrices, which the covariance matrix being inverted here should
> > be.  The exceptions thrown will be different; but they will give
> > more specific information about what is wrong with the covariance
> > matrix.
> I've tried it with my problem, and it also throws an exception.
> However, I would like to obtain the covariance matrix anyway, because I've
> no other clue as to what might be wrong.
> So I think that, at least, users should be able to set the positive
> definiteness threshold in order to avoid raising an exception.

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