[petsc-users] Reasons for breakdown in preconditioned LSQR

Tue May 7 07:32:55 CDT 2024

On Tue, May 7, 2024 at 8:28 AM Mark Adams <mfadams at lbl.gov> wrote:

> "A^T A being similar to a finite difference Poisson matrix if the rows
> were permuted randomly."
> Normal eqs are a good option in general for rectangular systems and we
> have Poisson solvers.
>

I missed that. Why not first permute back to the Poisson matrix? Then it
would be trivial.

  Thanks,

    Matt

> I'm not sure what you mean by "permuted randomly." A random permutation
> of the matrix can kill performance but not math.
>
> Mark
>
>
> On Tue, May 7, 2024 at 8:03 AM Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Tue, May 7, 2024 at 5: 12 AM Pierre Jolivet <pierre@ joliv. et>
>> wrote: On 7 May 2024, at 9: 10 AM, Marco Seiz <marco@ kit. ac. jp>
>> wrote: Thanks for the quick response! On 07. 05. 24 14: 24, Pierre Jolivet
>> wrote: On 7 May 2024,
>> ZjQcmQRYFpfptBannerStart
>> This Message Is From an External Sender
>> This message came from outside your organization.
>>
>> ZjQcmQRYFpfptBannerEnd
>> On Tue, May 7, 2024 at 5:12 AM Pierre Jolivet <pierre at joliv.et> wrote:
>>
>>> On 7 May 2024, at 9: 10 AM, Marco Seiz <marco@ kit. ac. jp> wrote:
>>> Thanks for the quick response! On 07. 05. 24 14: 24, Pierre Jolivet wrote:
>>> On 7 May 2024, at 7: 04 AM, Marco Seiz <marco@ kit. ac. jp> wrote: This
>>> Message Is From an External
>>> ZjQcmQRYFpfptBannerStart
>>> This Message Is From an External Sender
>>> This message came from outside your organization.
>>>
>>> ZjQcmQRYFpfptBannerEnd
>>>
>>>
>>> On 7 May 2024, at 9:10 AM, Marco Seiz <marco at kit.ac.jp> wrote:
>>>
>>> Thanks for the quick response!
>>>
>>> On 07.05.24 14:24, Pierre Jolivet wrote:
>>>
>>>
>>>
>>> On 7 May 2024, at 7:04 AM, Marco Seiz <marco at kit.ac.jp> wrote:
>>>
>>> This Message Is From an External Sender
>>> This message came from outside your organization.
>>> Hello,
>>>
>>> something a bit different from my last question, since that didn't
>>> progress so well:
>>> I have a related model which generally produces a rectangular matrix A,
>>> so I am using LSQR to solve the system.
>>> The matrix A has two nonzeros (1, -1) per row, with A^T A being similar
>>> to a finite difference Poisson matrix if the rows were permuted randomly.
>>> The problem is singular in that the solution is only specified up to a
>>> constant from the matrix, with my target solution being a weighted zero
>>> average one, which I can handle by adding a nullspace to my matrix.
>>> However, I'd also like to pin (potentially many) DOFs in the future so I
>>> also tried pinning a single value, and afterwards subtracting the
>>> average from the KSP solution.
>>> This leads to the KSP *sometimes* diverging when I use a preconditioner;
>>> the target size of the matrix will be something like ([1,20] N) x N,
>>> with N ~ [2, 1e6] so for the higher end I will require a preconditioner
>>> for reasonable execution time.
>>>
>>> For a smaller example system, I set up my application to dump the input
>>> to the KSP when it breaks down and I've attached a simple python script
>>> + data using petsc4py to demonstrate the divergence for those specific
>>> systems.
>>> With `python3 lsdiv.py -pc_type lu -ksp_converged_reason` that
>>> particular system shows breakdown, but if I remove the pinned DOF and
>>> add the nullspace (pass -usens) it converges. I did try different PCs
>>> but they tend to break down at different steps, e.g. `python3 lsdiv.py
>>> -usenormal -qrdiv -pc_type qr -ksp_converged_reason` shows the breakdown
>>> for PCQR when I use MatCreateNormal for creating the PC mat, but
>>> interestingly it doesn't break down when I explicitly form A^T A (don't
>>> pass -usenormal).
>>>
>>>
>>> What version are you using? All those commands are returning
>>>  Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1
>>> So I cannot reproduce any breakdown, but there have been recent changes
>>> to KSPLSQR.
>>>
>>> For those tests I've been using PETSc 3.20.5 (last githash was
>>> 4b82c11ab5d ).
>>> I pulled the latest version from gitlab ( 6b3135e3cbe ) and compiled it,
>>> but I had to drop --download-suitesparse=1 from my earlier config due to
>>> errors.
>>> Should I write a separate mail about this?
>>>
>>> The LU example still behaves the same for me (`python3 lsdiv.py -pc_type
>>> lu -ksp_converged_reason` gives DIVERGED_BREAKDOWN, `python3 lsdiv.py
>>> -usens -pc_type lu -ksp_converged_reason` gives CONVERGED_RTOL_NORMAL)
>>> but the QR example fails since I had to remove suitesparse.
>>> petsc4py.__version__ reports 3.21.1 and if I rebuild my application,
>>> then `ldd app` gives me `libpetsc.so
>>> <https://urldefense.us/v3/__http://libpetsc.so/__;!!G_uCfscf7eWS!auri5B6VaP-JYC4fuoLQd6QGnMRYi45UVg6GvK8V2FIlWo6HdPSPwjqjQnRiV2HkM5lAHgRRgpwXScugHRUKcQ$>.3.21
>>> =>
>>> /opt/petsc/linux-c-opt/lib/libpetsc.so
>>> <https://urldefense.us/v3/__http://libpetsc.so/__;!!G_uCfscf7eWS!auri5B6VaP-JYC4fuoLQd6QGnMRYi45UVg6GvK8V2FIlWo6HdPSPwjqjQnRiV2HkM5lAHgRRgpwXScugHRUKcQ$>.3.21`
>>> so it should be using the
>>> newly built one.
>>> The application then still eventually yields a DIVERGED_BREAKDOWN.
>>> I don't have a ~/.petscrc and PETSC_OPTIONS is unset, so if we are on
>>> the same version and there's still a discrepancy it is quite weird.
>>>
>>>
>>> Quite weird indeed…
>>> $ python3 lsdiv.py -pc_type lu -ksp_converged_reason
>>>   Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1
>>> $ python3 lsdiv.py -usens -pc_type lu -ksp_converged_reason
>>>   Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1
>>> $ python3 lsdiv.py -pc_type qr -ksp_converged_reason
>>>   Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1
>>> $ python3 lsdiv.py -usens -pc_type qr -ksp_converged_reason
>>>   Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1
>>>
>>> For the moment I can work by adding the nullspace but eventually the
>>> need for pinning DOFs will resurface, so I'd like to ask where the
>>> breakdown is coming from. What causes the breakdowns? Is that a generic
>>> problem occurring when adding (dof_i = val) rows to least-squares
>>> systems which prevents these preconditioners from being robust? If so,
>>> what preconditioners could be robust?
>>> I did a minimal sweep of the available PCs by going over the possible
>>> inputs of -pc_type for my application while pinning one DOF. Excepting
>>> unavailable PCs (not compiled for, other setup missing, ...) and those
>>> that did break down, I am left with ( hmg jacobi mat none pbjacobi sor
>>> svd ).
>>>
>>> It’s unlikely any of these preconditioners will scale (or even converge)
>>> for problems with up to 1E6 unknowns.
>>> I could help you setup https://urldefense.us/v3/__https://epubs.siam.org/doi/abs/10.1137/21M1434891__;!!G_uCfscf7eWS!Yw9Mv8kLlC8eKJnJjK2drMrR2BsrOWhEvxW7gJShAxCS1rsRjmRcgAPRoq5fq9fQtr8Xhz9nIKh-AdPZRchJ$ 
>>> <https://urldefense.us/v3/__https://epubs.siam.org/doi/abs/10.1137/21M1434891__;!!G_uCfscf7eWS!auri5B6VaP-JYC4fuoLQd6QGnMRYi45UVg6GvK8V2FIlWo6HdPSPwjqjQnRiV2HkM5lAHgRRgpwXScvk6kPrWA$>
>>> if you are willing to share a larger example (the current Mat are extremely
>>> tiny).
>>>
>>> Yes, that would be great. About how large of a matrix do you need? I can
>>> probably quickly get something non-artificial up to O(N) ~ 1e3,
>>>
>>>
>>> That’s big enough.
>>> If you’re in luck, AMG on the normal equations won’t behave too badly,
>>> but I’ll try some more robust (in theory) methods nonetheless.
>>>
>>
>> We have also had good luck forming and factoring a block diagonal
>> approximation of the normal equations. It depends on your problem. What is
>> this problem?
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> Thanks,
>>> Pierre
>>>
>>> bigger
>>> matrices will take some time since I purposefully ignored MPI previously.
>>> The matrix basically describes the contacts between particles which are
>>> resolved on a uniform grid, so the main memory hog isn't the matrix but
>>> rather resolving the particles.
>>> I should mention that the matrix changes over the course of the
>>> simulation but stays constant for many solves, i.e. hundreds to
>>> thousands of solves with variable RHS between periods of contact
>>> formation/loss.
>>>
>>>
>>> Thanks,
>>> Pierre
>>>
>>>
>>>
>>> Best regards,
>>> Marco
>>>
>>> <lsdiv.zip>
>>>
>>>
>>>
>>> Best regards,
>>> Marco
>>>
>>>
>>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Yw9Mv8kLlC8eKJnJjK2drMrR2BsrOWhEvxW7gJShAxCS1rsRjmRcgAPRoq5fq9fQtr8Xhz9nIKh-AQY4i0p0$ 
>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!fB-MI7viuwcYPEUg4w1S4_woxMQH7Kg5wnygmQdQdtqlCY5hQY4bFmFI3dJtuNZX9R-0i_z0Hq4eR-ODWjrB$>
>>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Yw9Mv8kLlC8eKJnJjK2drMrR2BsrOWhEvxW7gJShAxCS1rsRjmRcgAPRoq5fq9fQtr8Xhz9nIKh-AQY4i0p0$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Yw9Mv8kLlC8eKJnJjK2drMrR2BsrOWhEvxW7gJShAxCS1rsRjmRcgAPRoq5fq9fQtr8Xhz9nIKh-AeiW0RBO$ >
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20240507/4816264f/attachment-0001.html>