基于CUDA编程模型的稀疏对角矩阵向量乘优化

稀疏矩阵向量乘是很多科学计算问题中的核心问题。本文针对稀疏对角矩阵,在DIA存储格式的基础上,设计了一种新型压缩存储格式CDIA,结合CUDA编程模型的特点,在计算线程上进行了细粒度的任务分配,同时为满足CUDA对存储器的合并访问要求,将压缩矩阵做了相应的转置处理,设计了细粒度算法与程序,并根据稀疏矩阵向量乘特点,做了相应的程序优化。实验数据显示,这种存储格式能够很好地发挥CUDA在数据处理方面的优势,在测试数据中,最高获得了单精度39.6Gflop/s和双精度19.6Gflop/s的浮点计算性能,性能在Nathan Bell和Michael Garland的基础上分别提高了7.6%和17.4%。

Optimization of Sparse Diagonal Matrix-Vector Multiplication Based on the CUDA Program Model

Sparse matrix-vector multiplication is often an important computational kernel in many scientific applications.This paper faces the n-diagonal sparse matrix,uses the CUDA program model and describes a new compress format of sparse matrix based on the DIA compress format(CDIA),and gives each thread fine-grained task distribution.In order to fulfill the characteristics of the align access of memory in CUDA,we transpose the compress matrix and design a fine-grained algorithm and program and do some optimization to the program.In the data experiment,our best implementation achieves up to 39.6Gflop/s in single-precision and 19.6Gflop/s in double-precision,and enhances the performance by about 7.6% and 17.4% that of Nathan Bell’s and Michael Garland’s respectively.