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We describe a new data format for storing triangular, symmetric, andHermitian matrices called RFPF (Rectangular Full Packed Format). The standardtwo dimensional arrays of Fortran and C (also known as full format) that areused to represent triangular and symmetric matrices waste nearly half of thestorage space but provide high performance via the use of Level 3 BLAS.Standard packed format arrays fully utilize storage (array space) but providelow performance as there is no Level 3 packed BLAS. We combine the goodfeatures of packed and full storage using RFPF to obtain high performance viausing Level 3 BLAS as RFPF is a standard full format representation. Also, RFPFrequires exactly the same minimal storage as packed format. Each LAPACK fulland/or packed triangular, symmetric, and Hermitian routine becomes a single newRFPF routine based on eight possible data layouts of RFPF. This new RFPFroutine usually consists of two calls to the corresponding LAPACK full formatroutine and two calls to Level 3 BLAS routines. This means {\it no} newsoftware is required. As examples, we present LAPACK routines for Choleskyfactorization, Cholesky solution and Cholesky inverse computation in RFPF toillustrate this new work and to describe its performance on several commonlyused computer platforms. Performance of LAPACK full routines using RFPF versusLAPACK full routines using standard format for both serial and SMP parallelprocessing is about the same while using half the storage. Performance gainsare roughly one to a factor of 43 for serial and one to a factor of 97 for SMPparallel times faster using vendor LAPACK full routines with RFPF than withusing vendor and/or reference packed routines.

Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion