Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels
Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels
复制标题
使用聚合细粒度和内存感知内核并行简化对称特征值问题的压缩形式
DOI：
10.1145/2063384.2063394
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Dongarra
中科院分区：
文献类型：
--
作者：
A. Haidar;H. Ltaief;J. Dongarra
本文介绍了一种将对称稠密矩阵约简为三对角形式的新方法，这是求解对称特征值问题的预处理步骤。基于瓦片算法，减少遵循两阶段的方法，其中瓦片矩阵首先减少到对称带的形式之前，最终的压缩结构。算法性能和任务粒度之间具有挑战性的权衡已经通过分组技术得到解决，该技术包括在这两个阶段聚合细粒度和内存感知的计算任务，同时保持应用程序的整体高性能。动态运行时环境系统然后以无序的方式调度不同的任务。本文报道的三对角约简的性能是前所未有的。在矩阵大小为24000 x 24000的八插槽六核AMD Opteron多核共享内存系统上，与LAPACK V3.2和Intel MKL V10.3的等效例程相比，我们的实现分别获得了高达50倍和12倍的改进（130 Gflop/s）。
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 × 24000.
DOI：
10.1177/1094342010391989
发表时间：
2011-02-01
影响因子：
3.1
作者：
Dongarra, Jack;Beckman, Pete;Yelick, Kathy
通讯作者：
Yelick, Kathy