[petsc-users] Inaccurate Matrix Inversion using MatMatSolve

[Rakesh Halder]

Hi all,

I'm using PETSc for matrix calculations as part of a model order reduction
code. An algorithm I'm using requires that I compute the explicit inverse
of a matrix, as it needs to be used in matrix-matrix products.

The matrix is small (I'll show a 5x5 example), and I first find the LU
factorization of it as follows:

  MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);
  MatFactorInfoInitialize(&info);
  MatLUFactor(A,perm,iperm,&info);

I then find the inverse of it:

  MatMatSolve(A,I,B);

Where I is the identity matrix, and B is the inverse. The subroutine does
calculate an inverse, although not accurately; the matrix A I looked at is:

5.23E-02 1.86E-02 2.67E-02 4.58E-02 3.55E-02
6.37E-03 5.86E-02 5.07E-03 1.64E-02 1.36E-02
-4.07E-02 3.99E-03 5.50E-02 1.77E-02 -3.21E-02
1.96E-02 -5.53E-03 4.02E-02 -5.37E-02 1.80E-02
1.51E-02 1.70E-02 -1.57E-02 -3.75E-03 -5.64E-02

And when I take the product A*B, I don't recover the identity matrix, but
rather:

9.97E-01 2.77E-04 -1.66E-03 1.25E-04 -1.10E-03
-6.79E-04 9.99E-01 -1.72E-04 6.24E-04 1.16E-03
2.70E-03 -3.98E-04 9.98E-01 -1.51E-04 6.82E-04
-3.35E-04 -4.82E-04 -1.03E-03 9.99E-01 9.80E-05
-9.50E-04 -8.70E-04 8.37E-04 -3.68E-04 9.99E-01

I believe this is causing large inaccuracies in my program, as the diagonal
and off-diagonal entries have large errors associated with them. I am
wondering if there is a way to perhaps tighten the tolerance of the
subroutine, or if there are other methods I can use. I would like to avoid
using KSP and solving for the inverse vector-by-vector if possible.

Thanks,

Rakesh Halder
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