主维对矩阵运算性能的影响

The Effect of Leading Dimension to Performance of Matrix Computation

随着计算机体系结构的发展，高速缓存（ｃａｃｈｅ）的引入，分块方法成为矩阵计算中性能优化的主要方法，而矩阵主维对分块算法的性能影响很大。本文分析了矩阵主维影响性能的原因以及如何选取主维来改善性能，并与拷贝方法进行了比较。最后用矩阵乘法和ＬＵ分解进行了试算。

With the development of computer architecture and the introduction of cache, blocking has been the main method to optimize performance in matrix computing, and the effect of leading dimension becomes important to blocking algorithms' performance. This paper analyzes this effect and how to select leading dimension to improve perofrmance, and compares this method with copy method. This method is applied to matrix multiplication and LU factorization, and the practical results agree with the theoretical analysis.