An hierarchical approach for performance analysis of ScaLAPACK-based routines using the distributed linear algebra machine

Abstract

Performance models are important in the design and analysis of linear algebra software for scalable high performance computer systems. They can be used for estimation of the overhead in a parallel algorithm and measuring the impact of machine characteristics and block sizes on the execution time. We present an hierarchical approach for design of performance models for parallel algorithms in linear algebra based on a parallel machine model and the hierarchical structure of the ScaLAPACK library. This suggests three levels of performance models corresponding to existing ScaLAPACK routines. As a proof of the concept a performance model of the high level QR factorization routine pdgeqrf is presented. We also derive performance models of lower level ScaLAPACK building blocks such as pdgeqr2, pdlarft, pdlarfb, pdlarfg, pdlarf, pdnrm2, and pdscal, which are used in the high level model for pdgeqrf. Predicted performance results are compared to measurements on an Intel Paragon XP/S system. The accuracy of the top level model is over 90% for measured matrix and block sizes and different process grid configurations.