Rakesh, Can you find the condition number of your matrix A? Hong ________________________________ From: petsc-users <[email protected]> on behalf of Rakesh Halder <[email protected]> Sent: Thursday, June 25, 2020 2:43 PM To: [email protected] <[email protected]> Subject: [petsc-users] Inaccurate Matrix Inversion using MatMatSolve
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
