基于瓦片算法的并行QR分解及其实现-科研信息化技术与应用-中国.PDF

科研信息化技术与应用 2 0 1 6 , 7 ( 2 ) : 1 6 – 2 4 TECHNOLOGY ·技术 / · QR 基于瓦片算法的并行 分解及其实现 1,2 1 1,2 曹冬冬 ，赵永华，赵莲 1. 中国科学院计算机网络信息中心，北京 100190 2. 中国科学院大学，北京 100049 摘 要：本文介绍了一种基于瓦片算法的稠密矩阵并行 QR 分解及其实现方法。瓦片算法的思想是将完整 的矩阵分块，并使每个块内的数据连续存储。各个瓦片块先独立进行分解，其他块接收当前块分 解产生的数据，来更新自身块内的矩阵。我们分别实现了串行瓦片算法和并行瓦片算法，采用基于 MPI 和 OpenMP 混合并行编程模型，在“元”超级计算机上验证了该并行算法，并与 PLASMA 软件 包进行对比，程序效率和可扩展性优于 PLASMA 。在多个节点上运行时，展现了良好的扩展性。 关键词： 瓦片算法；QR 分解；并行实现 doi: 10.11871/j.issn.1674-9480.2016.02.003 Parallel QR Factorization Based on Tile Algorithm 1, 2 1 1, 2 Cao Dongdong , Zhao Yonghua , Zhao Lian 1. Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China 2. University of Chinese Academy of Sciences, Beijing, 100049, China Abstract: In this paper, a dense matrix parallel QR factorization method based on tile algorithm are presented. The ideal of tile algorithm is to make the matrix storage by blocks, and each block data are continuously stored. The matrix decomposition of each tile block is executed independently, meanwhile, the other blocks receive data from the current block decomposition, and update itself matrix. We implemented a serial tile algorithm and a parallel tile algorithm respectively. Adopting MPI and OpenMP hybrid parallel programming model, our algorithm has verified on the supercomputer Era. Compared with PLASMA package, it shows that the efficiency and scalability of