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