Rank revealing Cholesky should be effectively about as good as an eigen solution. The pivoting results in non-increasing diagonals and a sharp rank indicator. You can do pseudo inverse things with the result as well.
Getting the actual pseudo inverse isn't a bad thing. I just don't see it as entirely necessary. On Thu, Sep 8, 2011 at 7:49 AM, Greg Sterijevski <gsterijev...@gmail.com>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. > > > > > 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. > > > > > > >
