Tuning the Blocksize for Dense Linear Algebra Factorization Routines with the Roofline Model

摘要

The optimization of dense linear algebra operations is a fundamental task in the solution of many scientific computing applications. The Roofline Model is a tool that provides an estimation of the performance that a computational kernel can attain on a hardware platform. Therefore, the RM can be used to investigate whether a computational kernel can be further accelerated. We present an approach, based on the RM, to optimize the algorithmic parameters of dense linear algebra kernels. In particular, we perform a basic analysis to identify the optimal values for the kernel parameters. As a proof-of-concept, we apply this technique to optimize a blocked algorithm for matrix inversion via Gauss-Jordan elimination. In addition, we extend this technique to multi-block computational kernels. An experimental evaluation validates the method and shows its convenience. We remark that the results obtained can be extended to other computational kernels similar to Gauss-Jordan elimination such as, e.g., matrix factorizations and the solution of linear least squares problems.