Sparse extensions to the FORTRAN Basic Linear Algebra Subprograms

Reviewer: Mohamed E. El-Hawary

Adopting a standardized set of basic routines for problems in linear algebra is acknowledged to improve program clarity, portability, modularity, and maintainability. The original set is known as the Basic Linear Algebra Subprograms (BLAS) and deals with dense linear algebraic operations. Many codes now exist for solving sparse linear systems. The authors point out justifications for sparse extensions to the BLAS. The paper is a proposal for standardization that has been under discussion for quite a few years. An examination of available sparse linear algebra codes reveals that a few basic operations occur frequently and dominate the computation. Standardizing these operations is treated in this paper. In Section 2, the authors review the basis for storage of sparse vectors in compressed form as compared to the original BLAS representation. Section 3 discusses the scope of the sparse BLAS. Here conventions for data types and operations are introduced. Conventions for storage, error handling, and naming are given in Section 4. In Section 5, the authors offer examples of specifications for the sparse BLAS. This paper is clearly written. It is mainly suited for those interested in efficient sparse implementations of linear algebraic operations.