We describe a new data formats for storing triangular,
symmetric, and Hermitian matrices. The standard two dimensional arrays
of Fortran and C (also known as a full format) that are used to store
triangular, symmetric, and Hermitian 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
the new formats to obtain high performance using L3 (level~3). Also,
these new formats require exactly the same minimal storage as LAPACK
packed format. These new formats even out perform the LAPACK full
format for some computer platforms.