Packed storage extension for ScaLAPACK

摘要

The authors describe a new extension to ScaLAPACK for computing with symmetric (Hermitian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric (Hermitian) matrix. The packed storage scheme distributes the matrix by block column panels. Within each panel, the matrix is stored as a regular ScaLAPACK matrix. This storage arrangement simplifies the subroutine interface and code reuse. Routines PxPPTRF/PxPPTRS implement the Cholesky factorization and solution for symmetric (Hermitian) linear systems in packed storage. Routines PxSPEV/PxSPEVX (PxHPEV/PxHPEVX) implement the computation of eigenvalues and eigenvectors for symmetric (Hermitian) matrices in packed storage. Routines PxSPGVX (PxHPGVX) implement the expert driver for the generalized eigenvalue problem for symmetric (Hermitian) matrices in packed storage. Performance results on the Intel Paragon suggest that the packed storage scheme incurs only a small time overhead over the full storage scheme.