New Data Structures for Matrices and Specialized Inner Kernels: Low Overhead for High Performance

Dense linear algebra codes are often expressed and coded in terms of BLAS calls. This approach, however, achieves suboptimal performance due to the overheads associated to such calls. Taking as an example the dense Cholesky factorization of a symmetric positive definite matrix we show that the potential of non-canonical data structures for dense linear algebra can be better exploited with the use of specialized inner kernels. The use of non-canonical data structures together with specialized inner kernels has low overhead and can produce excellent performance.