##
Library Designs for Generic C++
Sparse Matrix Computations of Iterative Methods

Roldan Pozo
National Institute of Standards and Technology
A new library design is presented for generic sparse matrix
C++ objects for use in iterative algorithms and preconditioners.
This design extends previous work on C++ numerical libraries
(SparseLib++[3], IML++[4], Lapack++[5]) by providing a framework
in which efficient algorithms can be written *independent* of the
matrix layout or format. That is, rather than supporting different
codes for each (element type) / (matrix format) combination,
only one version of the algorithm need be maintained. This not only
reduces the effort for library developers, but also simplifies the
calling interface seen by library users. Furthermore, the underlying
matrix library can be naturally extended to support user-defined
objects, such as hierarchical block-structured matrices, or
application-specific preconditioners. Utilizing optimized
kernels[1,7] whenever possible, the resulting performance of
such framework can be shown to be competitive with optimized Fortran
programs.
[1] S. Carney, M. A. Heroux, G. Li, K. Wu, "A Revised Proposal for a Sparse
BLAS Toolkit", Army High Performance Computing Research Center Technical
Report 94-034, June 1994.
[2] Barrett, et. al, "Templates for the Solution of Linear Systems: Building
Blocks for Iterative Methods," SIAM Press, 1994.
[3] J. Dongarra, A. Lumsdaine, R. Pozo, K. Remington, "A Sparse
Matrix Library in C++ for High Performance Linear Algebra," Proceedings
of the Object Oriented Numerics Conference, 1994, pp. 214-218.
[4] J. Dongarra, A. Lumsdaine, R. Pozo, K. Remginton, "IML++: Iterative
Methods Library Reference Guide", 1995, available from
http://math.nist.gov/pozo/iml++.html.
[5] J. Dongarra, R. Pozo, D. Walker, "Lapack++: A Design Overview
of Object-Oriented Extensions for High Performance Linear Algebra",
Proceedings of Supercomputing '93.
[6] R. Pozo, K. Remington, "C Sparse BLAS", source code available from
http://math.nist.gov/pozo/sparse_blas/sparse_blas.html