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.