Rectangular Full Packed Format for LAPACK Algorithms Timings on Several Computers | Fred G. Gustavson, Jerzy Wasniewski
| | Abstract | We describe a new data format for storing
triangular and symmetric matrices called RFP (Rectangular Full
Packed). The standard two dimensional arrays of Fortran and C (also
known as full format) that are used to store triangular and symmetric
matrices waste nearly half the storage space but provide high performance via
the use of level~3 BLAS. Standard packed format arrays fully utilize storage
(array space) but provide low performance as there are no level~3
packed BLAS. We combine the good features of packed and full storage
using RFP format to obtain high performance using L3 (level~3) BLAS as
RFP is full format. Also, RFP format requires exactly the same
minimal storage as packed format. Each full and/or packedsymmetric/triangular routine becomes a single new RFP routine. We
present LAPACK routines for Cholesky factorization, inverse and solution
computation in RFP format to illustrate this new work and to describe
its performance on the IBM, Itanium, NEC, and SUN platforms.
Performance of RFP versus LAPACK full routines for both serial and SMP
parallel processing is about the same while
using half the storage. Performance is roughly one to a factor of 33 for
serial and one to a factor of 100 for SMP parallel
times faster than LAPACK packed routines. Existing LAPACK routines
and vendor
LAPACK routines were used in the serial and the SMP parallel study
respectively. In both studies Vendor L3 BLAS were used. | | Keywords | Symmetric matrices, Factorization, Cholesky Algoritm, Inversion, Solution | | Type | Conference paper [With referee] | | Conference | In Conference Proceedings of PARA'06 (is coming) | | Year | 2006 Month June pp. 10 Ed. Springer | | Publisher | Springer | | Address | Para06, Umea, Sweden | | Series | LNCS of Springer | | BibTeX data | [bibtex] | | IMM Group(s) | Scientific Computing |
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