The matrix template library: A generic programming approach to high performance numerical linear algebra

Abstract

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 algo- rithms from data structures using generic programming techniques. Such an approach does not hinder high performance, rather, writing porta- ble high-performance codes is enabled because the performance-critical code can be isolated from the algorithms and data structures. We ad- dress 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.