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

[Rasmus Larsen <rmlarsen@xxxxxxxxxx>]

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.