Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels

  • Authors:

  • Azzam Haidar;Hatem Ltaief;Jack Dongarra

  • Affiliations:

  • University of Tennessee, Knoxville, TN;KAUST Supercomputing Laboratory, Thuwal, Saudi Arabia;University of Tennessee, Knoxville, TN

  • Venue:
  • Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
  • Year:
  • 2011

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Abstract

This paper introduces a novel implementation in reducing a symmetric dense matrix to tridiagonal form, which is the preprocessing step toward solving symmetric eigenvalue problems. Based on tile algorithms, the reduction follows a two-stage approach, where the tile matrix is first reduced to symmetric band form prior to the final condensed structure. The challenging trade-off between algorithmic performance and task granularity has been tackled through a grouping technique, which consists of aggregating fine-grained and memory-aware computational tasks during both stages, while sustaining the application's overall high performance. A dynamic runtime environment system then schedules the different tasks in an out-of-order fashion. The performance for the tridiagonal reduction reported in this paper is unprecedented. Our implementation results in up to 50-fold and 12-fold improvement (130 Gflop/s) compared to the equivalent routines from LAPACK V3.2 and Intel MKL V10.3, respectively, on an eight socket hexa-core AMD Opteron multicore shared-memory system with a matrix size of 24000 x 24000.