在GPU上使用CUDA處理稀疏矩陣 計算函式

Sparse Computing Function for GPU processing with CUDA

劉世華(Shih-Hwa Liu)

指導教授 ： 張榮貴

國立中正大學/工學院/資訊工程學系/碩士(2013年)

摘要

矩陣運算不管是在數學運算或者是圖形處理等地方都佔有了很重要的地位，因此如何快速的處理矩陣運算成了一個很重要的課題。稀疏矩陣視為現今科學與工程領域中經常出現的大型矩陣，這類的矩陣有個特性，就是大部份的元素皆為零，也因為這個特性導致在運算時有許多多餘的運算。

為了使得這類型的運算能有快速的運算能力，我們建立了稀疏矩陣專用的library，參考fortran2003的函式庫，在現今擁有最高速平行運算能力的GPU上利用CUDA執行，並利用我們提出的五個針對GPU上的優化方法來達到高效能的表現。

關鍵詞：稀疏矩陣、平行運算、函式庫

關鍵字

函式庫 ； 平行運算 ； 稀疏矩陣

並列摘要

Sparse matrix computing is an important role in mathematic computing or other graph processing. How to processing sparse matrix computing faster becoming a important issue. Sparse matrix is usually used in modern scientific knowledge and Engineering. This matrix has a special feature that most of the elements in the matrix are zero; this feature let the sparse matrix computing has many unnecessary computing.

To let this kind of matrix has better computing ability, we construct a library for sparse matrix computing only, reference by fortran2003 handbook, and the CUDA on GPU is the platform which has the best Parallel Computing nowadays. We also propose five optimizing methods to improve the library which we construct for sparse matrix computing.

Keywords: GPU, sparse matrix, function library

並列關鍵字

function library ； sparse matrix ； GPU

參考文獻

[1] R.-G. Chang, T.-R. Chuang, and J. K. Lee. Compiler optimizations for parallel sparse programs with array intrinsics of Fortran 90. In Proceedings of the 1999 International Conference on Parallel Processing, Aizu-Wakamatsu City, Japan, pp. 103-110, 1999.

[3] L. Buatois, G. Caumon, and B. Levy. Concurrent number cruncher: a GPU implementation of a general sparse linear solver. Int. J. Parallel Emerg. Distrib. Syst., 24(3):205-223, 2009.

[7] Z. Wang, X. Xu, W. Zhao, Y. Zhang, and S. He. Optimizing Sparse Matrix-Vector Multiplication on CUDA.. In ICETE : Proceeding of the 2

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[13] Vazquez, F., G. Ortega, J. J. Fernandez, and E. M. Garzon, "Improving the performance of the sparse matrix vector product with GPUs," IEEE 10th International Conference on Computer and Information Technology (CIT), 1146-1151, 2010.