Re: [eigen] JacobiSVD with nearly rank-deficient matrix

[Jim Bosch <talljimbo@xxxxxxxxx>]

On 02/12/2011 10:32 AM, Benoit Jacob wrote:
> I understand that LAPACK cuts off very small singular values, but I
> don't think that we should do the same in Eigen. The algorithm that
> LAPACK uses makes these small singular values very unreliable, but the
> same is not true with our algorithm.
>
> There are many different notions of "goodness/badness" tests of
> solutions, depending on your use cases, and the path we've chosen in
> Eigen is to let the user perform his own tests, like in the example
> program above where I compute the relative error on the right-hand
> side.

There are times when one doesn't trust the values one has fed into the 
SVD algorithm well enough to trust such small eigenvalues either, 
regardless of the reliability of the algorithm.  I have to admit I also 
never use Eigen's SVD::solve routines, because I always wrap the SVD in 
something that imposes a cutoff on small singular values as well, so I'd 
love to see an option to supply such a cutoff to solve, even if it 
defaults to zero.

That said, if Eigen's philosophy is that such tests should take place 
outside Eigen, I can certainly accept that.

Jim