Add an ordering for cuDSS

[amontoison]

@frapac @sshin23 @michel2323

[sshin23]

Thanks, @amontoison! I only have small comments

[amontoison]

@sshin23 How can I test this new option with the following tests:
https://github.com/MadNLP/MadNLP.jl/blob/master/lib/MadNLPGPU/test/madnlpgpu_test.jl#L4-L8
?

[sshin23]

It can be done by adding

    [
        "LapackGPU-CUSOLVERRF",
        ()->MadNLP.Optimizer(
            linear_solver=MadNLPGPU.CUDSSSolver,
            print_level=MadNLP.ERROR
            ordering=MadNLPGPU.METIS
        ),
        [],
    ],

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 69.80%. Comparing base (fcbbbda) to head (30c493c).

❗ Your organization needs to install the Codecov GitHub app to enable full functionality.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #317   +/-   ##
=======================================
  Coverage   69.80%   69.80%           
=======================================
  Files          39       39           
  Lines        3888     3888           
=======================================
  Hits         2714     2714           
  Misses       1174     1174           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[amontoison]

We have a segmentation fault with cuDSS if we provide our own permutation... :(

[sshin23]

Hmm... maybe1-based indexing is causing an issue again? If it is possible to turn off the ordering, manual ordering is always an option.

https://github.com/MadNLP/MadNLP.jl/blob/master/lib/MadNLPGPU/src/cusolverrf.jl#L237-L252

[amontoison]

Hmm... maybe1-based indexing is causing an issue again? If it is possible to turn off the ordering, manual ordering is always an option.

https://github.com/MadNLP/MadNLP.jl/blob/master/lib/MadNLPGPU/src/cusolverrf.jl#L237-L252

cuDSS uses METIS internally but we want to compare the linear solvers on CPU / GPU with the same ordering.
The goal of this PR is to provide a permutation determined outside cuDSS.

[sshin23]

Right. That can be implemented by turning off the ordering from the CUDSS side (if possible) and manually reordering the matrix before sending it to CUDSS, based on whatever ordering method we want to apply

[amontoison]

Right. That can be implemented by turning off the ordering from the CUDSS side (if possible) and manually reordering the matrix before sending it to CUDSS, based on whatever ordering method we want to apply

We can't turn off the ordering with the version 0.1.0 or 0.2.0. I will send an email to ask this feature for the next release.

[amontoison]

@sshin23 @frapac
The issue was that SparseMatrixCSC was not exported, so AMD/METIS were not called, and the permutation was Cint[]. CUDSS didn't like this permutation, and due to the segmentation fault, the error related to SparseMatrixCSC was not displayed...

[sshin23]

Looks great! Thanks @amontoison for the contribution. I'll merge it once the naming is fixed