CRPC-TR98752						April 1998

Title: Packed Storage Extensions for ScaLAPACK

Authors: E.F. D'Azevedo and J.J. Dongarra

Submitted August 1998; Available as LAPACK Working Note 135 and UTK
CS-98-385

Abstract:
We describe a new extension to ScaLAPACK (2) 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/PxEPEVX) implement the computation of 
eigenvalues and eigenvectors for symmetric (Hermitian) matrices in packed 
storage.  Routines PxSPGVX (PxEPGVX) implement the expert driver for the 
generalized eigenvalue problem for symmetric (Hermitian) matrices in 
packed storage.  Routines PFxSPGVX/PFxSPEVX (PFxHPGVX/PFxHPEVX) uses the 
packed storage and perform out-of-core computation of eigenvectors.  
Performance results on the Intel Paragon suggest that the packed storage 
scheme incurs only a small time overhead over the full storage scheme.

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E.F. D'Azevedo
dazevedoef@ornl.gov
Mathematical Sciences Section
Oak Ridge National Laboratory

J.J. Dongarra
dongarra@cs.utk.edu
Department of Computer Science
University of Tennessee - Knoxville