Re: [eigen] Re: Complete orthogonal decomposition rank computation corner case

[Simon Rutishauser <simon.rutishauser@xxxxxxxxx>]

Cool, thanks for the update, I'll give it a try in the beginning of next week.

I'll also cross-check with the most current Eigen 3.2.x

- Simon

On Friday 24 June 2016 08.35:49 Rasmus Larsen wrote:
> You'd also need
> 
> https://bitbucket.org/eigen/eigen/commits/6901ee7288f847d56d96046113a9c3d6281fd1bb
> 
> 
> On Fri, Jun 24, 2016 at 8:33 AM, Rasmus Larsen <rmlarsen@xxxxxxxxxx> wrote:
> 
> > Yes, I am going to investigate this issue. The 3.2.x version you patched
> > it into does not have the improvements to the norm updating formula (and
> > thus rank determination) in CPQR I submitted in
> > https://bitbucket.org/eigen/eigen/commits/9da6c621d055e425605362c92c5dd1f7768e9681.
> > You should first try backporting that to your codebase (or even better to
> > the Eigen 3.2 branch). That being said, I can envision corner cases where
> > applying the final orthogonal transformation in COD (which mathematically
> > do not affect the rank) could push a close value across the threshold.
> >
> > Rasmus
> >
> > On Fri, Jun 24, 2016 at 1:01 AM, Gael Guennebaud <
> > gael.guennebaud@xxxxxxxxx> wrote:
> >
> >> Hi,
> >>
> >> In my opinion this is hiding a more fundamental issue, and this patch
> >> would just hide it for eternity... We should rather try to understand why
> >> the rank does change, but since the issue does not occur with 3.3, maybe
> >> the problem comes from 3.2.6's ColPivHouseholderQR or from a shortcoming in
> >> your backport. What if you upgrade to 3.2's head?
> >>
> >> gael
> >>
> >> On Fri, Jun 24, 2016 at 12:43 AM, Rasmus Larsen <rmlarsen@xxxxxxxxxx>
> >> wrote:
> >>
> >>> Hi Simon,
> >>>
> >>> Thanks for the patch. I've just gotten back from vacation, but it seems
> >>> reasonable to me. I'll look more carefully shortly.
> >>>
> >>> Rasmus
> >>>
> >>> On Wed, Jun 15, 2016 at 11:41 PM, Simon Rutishauser <
> >>> simon.rutishauser@xxxxxxxxx> wrote:
> >>>
> >>>> Hi list and Rasmus,
> >>>>
> >>>> I have been playing around with the complete orthogonal decomposition
> >>>> that was recently added to Eigen,
> >>>> and I think I have ran into a corner case:
> >>>>
> >>>> I have a matrix of size 70 where the rank() in the
> >>>> CompleteOrthogonalDecomposition::compute() method is 69,
> >>>> it thus performs the additional Householder reflections. After those
> >>>> reflections, the rank() method returns 70.
> >>>>
> >>>> Next I run the pseudoInverse() method, which in consequence skips the
> >>>> applyZAdjointOnTheLeftInPlace() step.
> >>>> The resulting matrix is completely wrong.
> >>>>
> >>>> The solution, as far as I can see it, would be to the rank() obtained
> >>>> directly after the QR decomposition
> >>>> and then stick with it.
> >>>>
> >>>> What do you think? I have attached a proposed patch.
> >>>>
> >>>> Simon
> >>>>
> >>>> P.S. I'd love to provide an example matrix that triggers this
> >>>> behaviour, but unfortunately I only observe
> >>>> this corner-case on Eigen 3.2.6 with a backported
> >>>> CompleteOrthogonalDecomposition. So the issues I am
> >>>> observing may also have other origins.
> >>>
> >>>
> >>>
> >>
> >

-- 
Simon Rutishauser

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