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

Understand

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format).

• The standard two dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of 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 is no Level 3 packed BLAS.
• We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full format representation.