Knowledge-based automatic generation of Partitioned Matrix Expressions,” http://www.aices.rwth-aachen.de/preprints, Aachen Institute for Advanced Study

Abstract. We target the automatic generation of formally correct algorithms and routines for linear algebra operations. Given the broad variety of architectures and configurations with which scientists deal, there does not exist one algorithmic variant that is suitable for all scenarios. Therefore, we aim to generate a family of algorithmic variants to attain high-performance for a broad set of scenarios. One of the authors has previously demonstrated that automatic derivation of a family of algorithms is possible when the Partitioned Matrix Expression (PME) of the target operation is available. The PME is a recursive definition that states the relations between submatrices in the input and the output operands. In this paper we describe all the steps involved in the automatic derivation of PMEs, thus making progress towards a fully automated system