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## PARDISO Schur Complement BUG

Here's the following sparse CSR matrix.

n = 10

ia = {0, 3, 6, 9, 12, 15, 18, 19, 20, 21, 22 };

ja = { 4, 7, 8, 0, 5, 7, 1, 6, 8, 0, 2, 7, 1, 2, 8, 2, 3, 4, 3, 5, 6, 4 };

a = { -1, 1, 1, 1, 1, 5.5, 1, 1, 4, 1, -1, -2, 1, -1, -4, 1, -1, -6, 1, 1, 1, 1 };

perm = {0, 0,0, 0,0,0 ,0,1,1,1}

The exact Schur complement is {-13.5,-6,0,-6,-14,0,1,1,0}.

When calculating the Schur complement, Pardiso is handling a pivoting issue.

A/ If Pardiso perturbs the pivot elements with 1E-13, then I get {-7.5, 1.72432057769409E-10, 0,0,-8,0,0,1,0

B/ If Pardiso perturbs the pivot elements with 1E-6, then I get {-13.5009434324193, -6.0009554327987, 0,-6,-14.0002128945854,0,1,1.00000000046566,0}

If I include all the zeros in the sparse matrix (full matrix with a sparse matrix representation of 100 coefficients) then I get the exact right answer.

If I am doing the factorization of the upper left corner (7x7) of the matrix and calculating myself the Schur complement

then I get the exact right answer.

What's happening? Is it a bug?

Yvan

Employee
61 Views

Hello Yvan,

Could you please provide us also the values of iparm and mtype which you have used? And, also, what was your configuration on which you ran the code? I managed to get different results for the Schur complement with your test matrix but for me only one entry #4 varied significantly with different pivoting.

We'll have a look at it.

Best,
Kirill