[petsc-users] Mat/Vec with empty ranks

[Florian Lindner]

Am 03.10.2017 um 16:05 schrieb Matthew Knepley:
> On Mon, Oct 2, 2017 at 10:11 PM, Florian Lindner <mailinglists at xgm.de <mailto:mailinglists at xgm.de>> wrote:
> 
> 
> 
>     Am 02.10.2017 um 21:04 schrieb Matthew Knepley:
>     > On Mon, Oct 2, 2017 at 6:21 AM, Florian Lindner <mailinglists at xgm.de <mailto:mailinglists at xgm.de>
>     <mailto:mailinglists at xgm.de <mailto:mailinglists at xgm.de>>> wrote:
>     >
>     >     Hello,
>     >
>     >     I have a matrix and vector that live on 4 ranks, but only rank 2 and 3 have values:
>     >
>     >     Doing a simple LSQR solve does not converge. However, when the values are distributed equally, it converges
>     within 3
>     >     iterations.
>     >
>     >     What can I do about that?
>     >
>     >     I have attached a simple program and creates the matrix and vector or loads them from a file.
>     >
>     >
>     > There are a few problems with this program. I am attaching a cleaned up version. However, convergence still
>     differs starting
>     > at iteration 2. It appears that LSQR has a problem with this system, or we have a bug that I cannot see.
> 
>     Thanks for having a look at it!
> 
>     And good to hear it's not by design. If I can be of any more help tracking this down, pleae let me know.
> 
>     In the meantime, what could be a good way to work around this? This is admittedly a very malformed example. Is there a
>     way to force solving on a single CPU and then distribute the results resp. KSP object to the original parallel layout?
>     Of course, we would first try to solve in parallel, but we have little influence about the actual parallel layout, since
>     we are just a library and other solvers give us the data.
> 
> 
> I need to be more clear. I do not think convergence has anything to do with being on 1 process. I think this is an
> ill-conditioned
> example and convergence is an accident in one case. Unless you see this in a bunch of cases, I would not worry about
> gathering
> to a single process. However, that can be done using PCREDUNDANT if this is really a problem.

Why do think it is ill-conditioned? The condition number is around 5, The singular values are [5.93710645,  1.85088733,
1.15107911] (both according to NumPy) and QR decomposition with NumPy works fine.

I believe you're right about that, giving your proficiency in the subject, just want to learn and maybe fix my input
data, if it's possible.

Thanks,
Florian