A Case Study on Modeling the Performance of Dense Matrix Computation: Tridiagonalization in the EigenExa Eigensolver on the K Computer

Modeling the performance of a program is an important task in the field of automatic performance tuning. These days, performance modeling on a large-scale supercomputer system is in great demand but is challenging because the performance of large-scale parallel computation consists of several factors (e.g. the cost for floating point operations and communications). In this paper, we report a case study in which we model the performance of the tridiagonalization routine in the EigenExa eigensolver on the K computer. We assume several situations in which different amounts of limited information are available for performance modeling, and we construct models using this information. We evaluate the models by comparing the estimated time of the routine with the timing results measured during the development of EigenExa. We clarify the characteristics of each model and reveal knowledge that will help model the performance of other dense matrix computations.