An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms
IBM Journal of Research and Development
Matrix computations (3rd ed.)
Applied numerical linear algebra
Applied numerical linear algebra
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
A recursive formulation of Cholesky factorization of a matrix in packed storage
ACM Transactions on Mathematical Software (TOMS)
LAPACK95 users' guide
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
High-performance linear algebra algorithms using new generalized data structures for matrices
IBM Journal of Research and Development
A fully portable high performance minimal storage hybrid format Cholesky algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format
ACM Transactions on Mathematical Software (TOMS)
Supermatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Minimal-storage high-performance Cholesky factorization via blocking and recursion
IBM Journal of Research and Development
Minimal data copy for dense linear algebra factorization
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Rectangular full packed format for LAPACK algorithms timings on several computers
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
A new array format for symmetric and triangular matrices
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Cache-Oblivious algorithms and matrix formats for computations on interval matrices
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
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We describe a new data format for storing triangular, symmetric, and Hermitian matrices called Rectangular Full Packed Format (RFPF). 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. Also, RFPF requires exactly the same minimal storage as packed the format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full-format routine and two calls to Level 3 BLAS routines. This means no new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution, and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using the standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines.