The Matrix Template Library: A generic programming approach to high performance numerical linear algebra

We present a unified approach for building high-performance numerical linear algebra routines for large classes of dense and sparse matrices. As with the Standard Template Library [1], we separate algorithms from data structures using generic programming techniques. Such an approach does not hinder high performance; rather, writing portable high-performance codes is enabled because the performance-critical code can be isolated from the algorithms and data structures. We address the performance portability problem for architecture-dependent algorithms such as matrix-matrix multiply. Recently, code generation systems, such as PHiPAC [2] and ATLAS [3], have allowed algorithms to be tuned to particular architectures. Our approach is to use template metaprograms [4] to directly express performance-critical, architecture-dependent, sections of code.