A distributed packed storage for large dense parallel in-core calculations

We propose in this paper a distributed packed storage format that exploits the symmetry or the triangular structure of a dense matrix. This format stores only half of the matrix while maintaining most of the efficiency compared to a full storage for a wide range of operations. This work has been motivated by the fact that, contrary to sequential linear algebra libraries (e.g. LAPACK [4]), there is no routine, no format that handles packed matrices in the current parallel distributed libraries available. The proposed algorithms exclusively use the existing ScaLAPACK [6] computational kernels which proves the generality of the approach, provides easy portability of the code, efficient re-use of existing software. The performance results obtained for the Cholesky factorization show that our packed format performs as good or better than the ScaLAPACK full algorithm for small numbers of processors. For larger number of processors, the ScaLAPACK full storage routine performs slightly better until each processor runs out of its memory.