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I would like to use PARDISO to compute the SCHUR complement. I am trying to understand the documentation and I have questions:
- I understand that the Schur complement matrix is obtained in the solution vector. I had a look on PARDISO 5.0 (not the Intel software) documentation and the SCHUR complement is returned as a sparse matrix. Is MKL PARDISO returning a full matrix or a sparse matrix ? Also which element is where in the matrix.
- I will probably need to access the full factorization ie the Schur complement but also the other matrices (L11, L21, U11,U12 from the documentation). I understand it is possible to compute these matrices, but how can we access those and in which form.
- do you have a code example of PARDISO for computation of the SCHUR complement and access to all the matrices.
Thanks a lot.
Marc
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Hi Maria,
It's Konstantin again. I am still having problems with the Schur complement. If the matrix size is below 50K it works well, e.g
A22 * A22_inv = I (identity matrix). However, when the size is greater than 50K the product of the Schur times the original matrix does not give identity matrix. I am using the lower triangle of the Schur matrix. Any thoughts?
Regards,
Konstantin
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Hi Konstantin,
Could you please clarify how you compute A22_inv?
Also, it would be great if you provide a reproducer for this case.
Best regards,
Maria
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Hi Maria,
I have again problems with schur complement. Below is the code I used.
With the second example, n = 10, nonz = 28, the Schur complement is calculated correctly.
With the first example, n = 9, nonz = 18. I get some weired matrix.
The Schur should be:
1.83 0.50 0.00 -1.00 -0.67 0.00
0.50 1.50 0.00 -1.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
-1.00 -1.00 0.00 2.00 0.00 0.00
-0.67 0.00 0.00 0.00 1.33 0.00
0.00 0.00 0.00 0.00 0.00 1.00
The result from the program is :
Schur matrix:
0.00 1.83 0.50 -1.00 -0.66 0.00
0.00 0.50 1.50 -1.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.00 -1.00 0.00 2.00 0.00
0.00 -0.66 0.00 0.00 0.00 1.33
0.00 0.00 0.00 1.00 0.00 0.00
Can you have a look at the code. I am doing something wrong, I guess. Thanks in advance.
The code:
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Hi Maria,
Did you have a chance to look at my schur problem?
Regards,
Konstantin
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with the version of Intel MKL 2018 u3 as well as with the newest 2019 beta, I see this Schur complement:
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Hi Konstantin,
I'm sorry for the delayed reply!
I've checked you program and the output is correct for the small (N = 9) case with the latest MKL version.
Can you please double check on your side and let us know what you find out?
Best regards,
Maria
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