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Date: Thu, 8 Sep 2011 17:22:04 +0200
From: Gilles Sadowski <gilles@harfang.homelinux.org>
To: dev@commons.apache.org
Subject: Re: [Math] "LUDecomposition" in "AbstractLeastSquaresOptimizer"
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On Thu, Sep 08, 2011 at 09:49:12AM -0500, Greg Sterijevski wrote:
> 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.
> 

In fact, in my current case (which is a unit test), the point is supposed to
be the minimum, by construction.  I'm trying to figure out where the
problem comes from (namely, whether the Jacobian matrix is correct)...

Gilles

> 
> > 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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