Performance Evaluation of the Eigen Exa Eigensolver on Oakleaf-FX: Tridiagonalization Versus Pentadiagonalization

The solution of real symmetric dense Eigen value problems is one of the fundamental matrix computations. To date, several new high-performance Eigen solvers have been developed for peta and postpeta scale systems. One of these, the Eigen Exa Eigen solver, has been developed in Japan. Eigen Exa provides two routines: eigens, which is based on traditional tridiagonalization, and eigensx, which employs a new method via a pentadiagonal matrix. Recently, we conducted a detailed performance evaluation of Eigen Exa by using 4,800 nodes of the Oak leaf-FX supercomputer system. In this paper, we report the results of our evaluation, which is mainly focused on investigating the differences between the two routines. The results clearly indicate both the advantages and disadvantages of eigensx over eigens, which will contribute to further performance improvement of Eigen Exa. The obtained results are also expected to be useful for other parallel dense matrix computations, in addition to Eigen value problems.