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An open-source middleware EigenKernel was developed for use with parallelgeneralized eigenvalue solvers or large-scale electronic state calculation toattain high scalability and usability. The middleware enables the users tochoose the optimal solver, among the three parallel eigenvalue libraries ofScaLAPACK, ELPA, EigenExa and hybrid solvers constructed from them, accordingto the problem specification and the target architecture. The benchmark wascarried out on the Oakforest-PACS supercomputer and reveals that ELPA, EigenExaand their hybrid solvers show better performance, when compared with pureScaLAPACK solvers. The benchmark on the K computer is also used for discussion.In addition, a preliminary research for the performance prediction wasinvestigated, so as to predict the elapsed time T as the function of the numberof used nodes P (T=T(P)). The prediction is based on Bayesian inference usingthe Markov Chain Monte Carlo (MCMC) method and the test calculation indicatesthat the method is applicable not only to performance interpolation but also toextrapolation. Such a middleware is of crucial importance forapplication-algorithm-architecture co-design among the current, next-generation(exascale), and future-generation (post-Moore era) supercomputers.

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