[petsc-users] Action of inverse of Cholesky factors in parallel

[Jose E. Roman]

As far as I know, the solveForward/Backward operations are not implemented for external packages.

What are you trying to do? One may be tempted to use the Cholesky decomposition to transform a symmetric-definite generalized eigenvalue problem into a standard eigenvalue problem, as is done e.g. in LAPACK https://netlib.org/lapack/lug/node54.html - But note that in SLEPc you do not need to do this, as EPSSolve() will take care of symmetry using Cholesky without having to apply solveForward/Backward separately.

Jose




> El 2 dic 2022, a las 13:32, Johannes Haubner <haubnerj at simula.no> escribió:
> 
> Given a s.p.d. matrix A and a right-hand-side b, we want to compute (L^T)^{-1}b and L^{-1}b, where A= L L^T is the Cholesky decomposition of A. In serial, we are able to do this using pc_factor_mat_solver_type petsc and using "solveForward" and "solveBackward" (see https://github.com/JohannesHaubner/petsc-cholesky/blob/main/main.py). In parallel, we are not able to do this yet. According to p. 52 https://slepc.upv.es/documentation/slepc.pdf , PETSc's Cholesky factorization is not parallel. However, using "mumps" or "superlu_dist" prevents us from using "solveForward" or "solveBackward". Is there a way of using solveBackward in parallel with a distributed matrix (MPI)?