Sparse Schur Complement is Computed Wrong

[Havlu]

Hi,

[Apologies for cross-posting, I don't know which board would be proper to use]

I am trying to use pardiso to compute the Schur complement of a matrix. I had some stability issues for some large matrices, so I decided to put in a tiny matrix and see if I can figure out the issue. However, it looks like for the small matrix I have, the Schur complement is computed wrong.

This matrix is real symmetric and 8-by-8. The code is attached, and it is commented for ease of reading. Any help is appreciated.

Thank you,
Abdullah

[Havlu]

Hi,

[Apologies for cross-posting, I don't know which board would be proper to use]

I am trying to use pardiso to compute the Schur complement of a matrix. I had some stability issues for some large matrices, so I decided to put in a tiny matrix and see if I can figure out the issue. However, it looks like for the small matrix I have, the Schur complement is computed wrong.

This matrix is real symmetric and 8-by-8. The code is attached, and it is commented for ease of reading. Any help is appreciated.

Thank you,
Abdullah

[MRajesh_intel]

Hi,

Thanks for posting your query. I have executed your sample code and the results are attached below. If these are not the right values, can you please provide us the right results? Can you please also share the MKL version used, OS version used?

Thanks

Rajesh.

[Havlu]

Hi Rajesh,

Thank you for the reply. The matrix outputted is wrong, and to my knowledge, it is not even a valid CSR3 matrix.

Here is the correct Schur complement to 3 digits after the point:

// [ 1.667 0.167 -0.204]
// [ 0.167 1.667 0.204]
// [-0.204 0.204 1.500]

You can also find this in the source code, it is provided there for convenience. Since it is symmetric, according to the documentation, Pardiso should return the lower triangular part of this matrix in the CSR3 format.

I am on Fedora Linux, and I am using MKL 2021.3.0.

Best,
Abdullah

[Khang_N_Intel]

Hi Abdullah,

Just want to let you know that I am discussing with the engineering team right now and will let you know what the next step is.

Khang

[Havlu]

Hi Khang,

Thanks for the update. I am looking forward to hearing from you.

Best,
Abdullah

[Havlu]

Hi Khang,

Just checking in. Are there any updates, or news on the next steps?

Best,
Abdullah

[Khang_N_Intel]

Hi Abdullah,

The issue has been confirmed. We have already escalated it to the engineering team. We will let you know when we receive any information from the engineering team.

Best,

Khang

[Havlu]

Hey Khang,

Hope all is well. Are there any updates on this matter? I was hoping to see a bugfix in the releases since, but I haven't seen anything regarding this issue and it seems to persist in the latest version.

Best,

Abdullah

[Gennady_F_Intel]

Abdullah,

there are no updates on this issue at this moment. we will keep this thread informed as soon as any updates.

-Gennady