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