Hierarchical Performance Modeling for Ranking Dense Linear Algebra Algorithms

A large class of dense linear algebra operations, such as LU decomposition or inversion of a triangular matrix, are usually performed by blocked algorithms. For one such operation, typically, not only one but many algorithmic variants exist; depending on computing architecture, libraries and problem size, each variant attains a different performances. We propose methods and tools to rank the algorithmic variants according to their performance for a given scenario without executing them. For this purpose, we identify the routines upon which the algorithms are built. A first tool - the Sampler - measures the performance of these routines. Using the Sampler, a second tool models their performance. The generated models are then used to predict the performance of the considered algorithms. For a given scenario, these predictions allow us to correctly rank the algorithms according to their performance without executing them. With the help of the same tools, algorithmic parameters such as block-size can be optimally tuned.