Diamond matrix powers kernels
Diamond matrix powers kernels
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金刚石矩阵为内核提供动力
DOI：
10.1145/3368474.3368494
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Suda Reiji
中科院分区：
文献类型：
--
作者：
Vatai Emil;Singhal Utsav;Suda Reiji
矩阵幂核计算向量Akv，对于k = 1,2，…，它们是各种科学计算的核心，包括通信避免迭代求解器。本文提出了菱形矩阵幂核- DMPK，目的是将“菱形平铺”模板算法应用于一般矩阵。它也可以被认为是由Demmel等人引入的PA1和PA2算法的扩展。我们的方法使我们能够控制通信避免算法中固有的通信避免和冗余计算之间的平衡。我们提出了使用MPI例程实现该算法的概念证明。我们进行的实验表明，计算量和通信量的控制是可以实现的，并且通过更彻底的优化，DMPK是现有MPK方法的一个有前途的替代方案。
Matrix powers kernel calculates the vectors Akv, for k = 1, 2,..., m and they are the heart of various scientific computations, including communication avoiding iterative solvers. In this paper we propose diamond matrix powers kernel - DMPK, which has the purpose to apply the "diamond tiling" stencil algorithm to general matrices. It can also be considered as an extension of the PA1 and PA2 algorithms, introduced by Demmel et al. Our approach enables us to control the balance between the amount of communication avoidance and redundant computation inherently present in communication avoiding algorithms. We present a proof of concept implementation of the algorithm using MPI routines. The experiments we performed show that the control of the amount of computation and communication is achievable, and with more thorough optimisations, DMPK is a promising alternative to existing MPK approaches.