Packed Storage Extension for ScaLAPACK

We describe an extension to ScaLAPACK for computing with symmetric (and hermitian) matrices stored in a packed form. This is similar to the compact storage for symmetric (and hermitian) matrices available in LAPACK [2]. This enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric matrix. The capabilities include Choleksy factorization (PxSPTRF) and solution (PxSPTRS) of symmetric (Hermitian) linear systems, the computation of eigenvalues and eigenvectors (PxSPEV), expert drivers (PxSPEVX) for generalized eigenvalue problem (PxSPGVX) for symmetric (Hermitian) matrices in packed storage. This work differs from an earlier work [5] on packed storage by considering wider block column panels of width NB * NPCOL instead of single block column of width NB in performance sensitive routines. The goal is to reduce the overhead in index calculation by increasing the granularity and operating on wider column panels. The packed storage scheme (described in §2) resembles the ScaLAPACK data distribution but physically stores only the lower (or upper) blocks. Each block column panel of width NB * NPCOL can be considered as a trapezoidal submatirx in a fully dense ScaLAPACK matrix. Section 3 contains two concrete examples on how such an arrangement can be used with conventional ScaLAPACK routines for dense storage. For some performance critical PBLAS like routines such as PxTPSM (triangular solve) and PxTPMM (multiplication by triangular matrix), block diagonal submatrices are copied into fully dense ScaLAPACK matrices to reuse standard high perform parallel BLAS routines. The right-looking Cholesky factorization re-