The sparse matrix vector multiplication (SpMV) is inevitable in almost all kinds of scientific computation, such as iterative methods for solving linear systems and eigenvalue problems. With the emergence and developm...The sparse matrix vector multiplication (SpMV) is inevitable in almost all kinds of scientific computation, such as iterative methods for solving linear systems and eigenvalue problems. With the emergence and development of Graphics Processing Units (GPUs), high efficient formats for SpMV should be constructed. The performance of SpMV is mainly determinted by the storage format for sparse matrix. Based on the idea of JAD format, this paper improved the ELLPACK-R format, reduced the waiting time between different threads in a warp, and the speed up achieved about 1.5 in our experimental results. Compared with other formats, such as CSR, ELL, BiELL and so on, our format performance of SpMV is optimal over 70 percent of the test matrix. We proposed a method based on parameters to analyze the performance impact on different formats. In addition, a formula was constructed to count the computation and the number of iterations.展开更多
It is an important task to improve performance for sparse matrix vector multiplication （SpMV）, and it is a difficult task because of its irregular memory access. Gen- eral purpose GPU （GPGPU） provides high computi...It is an important task to improve performance for sparse matrix vector multiplication （SpMV）, and it is a difficult task because of its irregular memory access. Gen- eral purpose GPU （GPGPU） provides high computing abil- ity and substantial bandwidth that cannot be fully exploited by SpMV due to its irregularity. In this paper, we propose two novel methods to optimize the memory bandwidth for SpMV on GPGPU. First, a new storage format is proposed to exploit memory bandwidth of GPU architecture more effi- ciently. The new storage format can ensure that there are as many non-zeros as possible in the format which is suitable to exploit the memory bandwidth of the GPU. Second, we pro- pose a cache blocking method to improve the performance of SpMV on GPU architecture. The sparse matrix is partitioned into sub-blocks that are stored in CSR format. With the block- ing method, the corresponding part of vector x can be reused in the GPU cache, so the time to access the global memory for vector x is reduced heavily. Experiments are carried out on three GPU platforms, GeForce 9800 GX2, GeForce GTX 480, and Tesla K40. Experimental results show that both new methods can efficiently improve the utilization of GPU mem- ory bandwidth and the performance of the GPU.展开更多
矩阵主特征向量(principal eigenvectors computing,PEC)的求解是科学与工程计算中的一个重要问题。随着图形处理单元通用计算(general-purpose computing on graphics pro cessing unit,GPGPU)的兴起,利用GPU来优化大规模稀疏矩阵的图...矩阵主特征向量(principal eigenvectors computing,PEC)的求解是科学与工程计算中的一个重要问题。随着图形处理单元通用计算(general-purpose computing on graphics pro cessing unit,GPGPU)的兴起,利用GPU来优化大规模稀疏矩阵的图形处理单元求解得到了广泛关注。分别从应用特征和GPU体系结构特征两方面分析了PEC运算的性能瓶颈,提出了一种面向GPU的稀疏矩阵存储格式——GPU-ELL和一个针对GPU的线程优化映射策略,并设计了相应的PEC优化执行算法。在ATI HD Radeon5850上的实验结果表明,相对于传统CPU,该方案获得了最多200倍左右的加速,相对于已有GPU上的实现,也获得了2倍的加速。展开更多
稀疏矩阵与向量相乘(Sp MV)是科学计算和工程应用中一个重要问题,而且非常适宜进行并行计算,目前在GPU对Sp M V的实现和优化是一个研究热点.针对准对角矩阵存在的一些不规则性,采用CSR+DLA混合存储格式来进行Sp M V计算,能够提高压缩的...稀疏矩阵与向量相乘(Sp MV)是科学计算和工程应用中一个重要问题,而且非常适宜进行并行计算,目前在GPU对Sp M V的实现和优化是一个研究热点.针对准对角矩阵存在的一些不规则性,采用CSR+DLA混合存储格式来进行Sp M V计算,能够提高压缩的效果.为了发挥CPU多核的并行计算能力,采用一种CPU+GPU混合计算模式,这样可以把混合存储格式不同格式的数据分割到CPU和GPU上,从而提高了资源的利用效能.本文另外还在分析CPU+GPU异构计算模式的特征基础上,提出一些优化策略,能够改进准对角矩阵与向量相乘在异构计算环境中的计算性能.展开更多
文摘The sparse matrix vector multiplication (SpMV) is inevitable in almost all kinds of scientific computation, such as iterative methods for solving linear systems and eigenvalue problems. With the emergence and development of Graphics Processing Units (GPUs), high efficient formats for SpMV should be constructed. The performance of SpMV is mainly determinted by the storage format for sparse matrix. Based on the idea of JAD format, this paper improved the ELLPACK-R format, reduced the waiting time between different threads in a warp, and the speed up achieved about 1.5 in our experimental results. Compared with other formats, such as CSR, ELL, BiELL and so on, our format performance of SpMV is optimal over 70 percent of the test matrix. We proposed a method based on parameters to analyze the performance impact on different formats. In addition, a formula was constructed to count the computation and the number of iterations.
文摘稀疏矩阵向量乘(SpMV)是科学与工程计算中一个重要的核心函数,但在当前基于存储器层次结构的计算平台上,传统CSR(Compressed Sparse Row)存储的稀疏矩阵向量乘性能较低,运行效率往往远低于硬件浮点峰值的10%.目前现有的处理器架构一般都采用SIMD向量化技术进行加速,但是传统CSR格式的稀疏矩阵向量乘由于访存的不规则性,不能直接采用向量化技术进行加速,为了利用SIMD技术,对具有局部性特征的稀疏矩阵,提出了新的稀疏矩阵存储格式CSRL(Compressed Sparse Row with Local information),该格式可以减少SpMV时内存访问次数,并且能够充分利用硬件的SIMD向量化技术进行读取和计算,提高了SpMV性能.实验表明,该方法相比国际著名商业库Intel MKL10.3版平均性能提升达到29.5%,最高可达89%的性能提升.
文摘It is an important task to improve performance for sparse matrix vector multiplication （SpMV）, and it is a difficult task because of its irregular memory access. Gen- eral purpose GPU （GPGPU） provides high computing abil- ity and substantial bandwidth that cannot be fully exploited by SpMV due to its irregularity. In this paper, we propose two novel methods to optimize the memory bandwidth for SpMV on GPGPU. First, a new storage format is proposed to exploit memory bandwidth of GPU architecture more effi- ciently. The new storage format can ensure that there are as many non-zeros as possible in the format which is suitable to exploit the memory bandwidth of the GPU. Second, we pro- pose a cache blocking method to improve the performance of SpMV on GPU architecture. The sparse matrix is partitioned into sub-blocks that are stored in CSR format. With the block- ing method, the corresponding part of vector x can be reused in the GPU cache, so the time to access the global memory for vector x is reduced heavily. Experiments are carried out on three GPU platforms, GeForce 9800 GX2, GeForce GTX 480, and Tesla K40. Experimental results show that both new methods can efficiently improve the utilization of GPU mem- ory bandwidth and the performance of the GPU.
文摘矩阵主特征向量(principal eigenvectors computing,PEC)的求解是科学与工程计算中的一个重要问题。随着图形处理单元通用计算(general-purpose computing on graphics pro cessing unit,GPGPU)的兴起,利用GPU来优化大规模稀疏矩阵的图形处理单元求解得到了广泛关注。分别从应用特征和GPU体系结构特征两方面分析了PEC运算的性能瓶颈,提出了一种面向GPU的稀疏矩阵存储格式——GPU-ELL和一个针对GPU的线程优化映射策略,并设计了相应的PEC优化执行算法。在ATI HD Radeon5850上的实验结果表明,相对于传统CPU,该方案获得了最多200倍左右的加速,相对于已有GPU上的实现,也获得了2倍的加速。
文摘稀疏矩阵与向量相乘(Sp MV)是科学计算和工程应用中一个重要问题,而且非常适宜进行并行计算,目前在GPU对Sp M V的实现和优化是一个研究热点.针对准对角矩阵存在的一些不规则性,采用CSR+DLA混合存储格式来进行Sp M V计算,能够提高压缩的效果.为了发挥CPU多核的并行计算能力,采用一种CPU+GPU混合计算模式,这样可以把混合存储格式不同格式的数据分割到CPU和GPU上,从而提高了资源的利用效能.本文另外还在分析CPU+GPU异构计算模式的特征基础上,提出一些优化策略,能够改进准对角矩阵与向量相乘在异构计算环境中的计算性能.
