GPU稀疏矩阵向量乘的性能模型构造

摘要

稀疏矩阵向量乘(Sparse matrix-vector multiplication,SPMV)是广泛应用于大规模线性求解系统和求解矩阵特征值等问题的基本运算,但在迭代处理过程中它也常常成为处理的瓶颈,影响算法的整体性能.对于不同形态的矩阵,选择不同的存储格式,对应的算法往往会产生较大的性能影响.通过实验分析,找到各种矩阵形态在不同存储结构下体现的性能变化特征,构建一个有效的性能度量模型,为评估稀疏矩阵运算开销、合理选择存储格式做出有效的指导.在14组CSR,COO,HYB格式和8组ELL格式的测试用例下,性能预测模型和测量之间的差异低于9％.%Sparse matrix-vector multiplication algorithm is widely used in large-scale linear system and solving matrix eigenvalue problems.It also often becomes the bottleneck of processing in iterative process and affects the whole algorithm performance.Choosing a different store format for different forms of matrix,the corresponding algorithms tend to generate large performance impact.Through experimental analysis,the variation performance characteristics were found under different storage structure,so as to build up an effective performance measurement model for assessment of sparse matrix computation overhead,and we selected reasonable storage format and made effective guidance.Based on 14 groups of CSR,COO,HYB format,8 groups of ELL format test cases,the difference between the performance prediction model and measurement is less than 9 ％.