EigenKernel - A middleware for parallel generalized eigenvalue solvers to attain high scalability and usability

An open-source middleware named EigenKernel was developed for use with parallel generalized eigenvalue solvers or large-scale electronic state calculation to attain high scalability and usability. The middleware enables the users to choose the optimal solver, among the three parallel eigenvalue libraries of ScaLAPACK, ELPA, EigenExa and hybrid solvers constructed from them, according to the problem specification and the target architecture. The benchmark was carried out on the Oakforest-PACS supercomputer and reveals that ELPA, EigenExa and their hybrid solvers show a strong scaling property, while the conventional ScaLAPACK solver has a severe bottleneck in scalability. A performance prediction function was also developed so as to predict the elapsed time $T$ as the function of the number of used nodes $P$ ($T=T(P)$). The prediction is based on Bayesian inference and the test calculation indicates that the method is applicable not only to performance interpolation but also to extrapolation. Such a middleware is of crucial importance for application-algorithm-architecture co-design among the current next-generation (exascale), and future-generation (post-Moore era) supercomputers.