The Generation of Optimized Codes using Nonzero Structure Analysis

In this paper we consider techniques for improving the performance of codes for general sparse problems by extracting both local and global structure information from a sparse matrix instance. This information can be used to improve the performance of the primitives through the utilization of specialized methods for the component parts which result from the matrix decomposition. A calculus is defined for controlling the decompositions and algorithms are presented for implementing the techniques within a code development environment. 1 Introduction The development of libraries for high-performance computers and their effective use in application codes is an iterative process involving the refinement of the algorithms and implementations, and the tuning of parameters to match the machine architecture and the application context. This process includes the complex algorithm prototyping stage and continues during the lifetime of the library, as the algorithms are updated and ported between..