Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices

摘要

A task-based formulation of Scalable Universal Matrix MultiplicationAlgorithm (SUMMA), a popular algorithm for matrix multiplication (MM), isapplied to the multiplication of hierarchy-free, rank-structured matrices thatappear in the domain of quantum chemistry (QC). The novel features of ourformulation are: (1) concurrent scheduling of multiple SUMMA iterations, and(2) fine-grained task-based composition. These features make it tolerant of theload imbalance due to the irregular matrix structure and eliminate allartifactual sources of global synchronization.Scalability of iterativecomputation of square-root inverse of block-rank-sparse QC matrices isdemonstrated; for full-rank (dense) matrices the performance of our SUMMAformulation usually exceeds that of the state-of-the-art dense MMimplementations (ScaLAPACK and Cyclops Tensor Framework).