A set of level 3 basic linear algebra subprograms for sparse matrices

This paper proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. We discuss the design, implementation and use of subprograms for the multiplication of a full matrix by a sparse one and for the solution of sparse triangular systems with one or more (full) right-hand sides. We include routines for checking the input data, generating a new sparse data structure from that input, and scaling a sparse matrix. The new data structure for the transformation can be specified by the user or can be chosen automatically by vendors to be efficient on their machines. We also include routines for permuting the columns of a sparse matrix and one for permuting the rows of a full matrix. A major aim is to establish standards to enable efficient, and portable, implementations of iterative algorithms for sparse matrices on high-performance computers. We have designed the routines so that the developer of mathematical software need not be concerned with the complexities of the various data structures used for sparse matrices. We have kept the interface and suite of codes as simple as possible while at the same time including sufficient functionality to cover most of the requirements of iterative solvers, and sufficient flexibility to cover most sparse matrix data structures. Fortran 77 code implementing this proposal is available by anonymous ftp