PEXSI

## General questions

Q: How do I know whether PEXSI works for my application?

A: PEXSI may not necessarily be faster than the diagonalization method or other competitive methods. The simplest way to see whether PEXSI brings acceleration for your applications is to use PEXSI to compute the selected elements of the inverse for a typical matrix from your applications. See Parallel selected inversion for a real symmetric matrix and driver_pselinv_real.c for how to do this.

Q: Can I just use the selected inversion routine?

A: The parallel selected inversion (PSelInv) is a standalone routine. See Parallel selected inversion for a real symmetric matrix for an example.

Q: Does PEXSI accelerate dense matrix computation?

A: Not likely. The acceleration is based on the sparsity of the LU factor or the Cholesky factor. PEXSI should not be fast if the matrix is dense or nearly dense.

Q: Does PEXSI work for asymmetric matrices?

A: Yes! Starting from v0.9.0, PEXSI v0.9.0 supports PSelInv for asymmetric matrices, boh structurally symmetric and fully asymmetric. See pagePselinvRealSymmetricUnsym for example. This can already be used for Kohn-Sham DFT calculations for k-point etc with an "expert-mode". The full support similar to PPEXSIDFTDriver might be available in the future, but the interface might not be as straightforward.

Q: How to control the amount of output information and which processor outputs the log file?

See Using plans and generating log files. Also the verbosity option in PPEXSIOptions control the amount of information.

## Installation

Q: The FORTRAN routine cannot compile.

A: For FORTRAN users, CPP_LIB=-lstdc++ -lmpi -lmpi_cxx is often needed. Check this first if there is link error.

## Performance

Q: What if PEXSI is numerically unstable or inaccurate for my application?

A: If you are using the pole expansion, the expansion converges exponentially with respect to the number of poles. So first increase the number of poles until the error saturates. After this step, error only comes from the selected inversion phase. The selected inversion is in principle an exact method, but may possibly suffer from numerical instability issue due to the round off erros. This is possible due to the lack of dynamic pivoting strategies. If this problem persists, please contact us as in Troubleshooting, with some description of your matrix and application.

Q: When using ParMETIS/PT-Scotch, I got segmentaiton fault in the factorization phase.

A: We have observed that when ParMETIS/PT-Scotch is used, the number of processors for symbolic factorization (npSymbFact) cannot be larger than a magic number depending on the matrix and the machine. This may to be related to the parallel symbolic factorization routine in SuperLU_DIST. If this problem happens, try to reduce npSymbFact to a small number (such as 4 or 16), or even try to use the sequential symbolic factorization if feasible.