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

• Published in: arXiv.org
• Main Authors: Calvin, Justus A, Lewis, Cannada A, Valeev, Edward F
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 09.10.2015
• Subjects: Algorithms; Computer Science - Distributed, Parallel, and Cluster Computing; Iterative methods; Multiplication; Multiplication & division; Organic chemistry; Quantum chemistry; Sparse matrices; Structured matrices; Synchronism; Task scheduling; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1509.00309

A task-based formulation of Scalable Universal Matrix Multiplication Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is applied to the multiplication of hierarchy-free, rank-structured matrices that appear in the domain of quantum chemistry (QC). The novel features of our formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and (2) fine-grained task-based composition. These features make it tolerant of the load imbalance due to the irregular matrix structure and eliminate all artifactual sources of global synchronization.Scalability of iterative computation of square-root inverse of block-rank-sparse QC matrices is demonstrated; for full-rank (dense) matrices the performance of our SUMMA formulation usually exceeds that of the state-of-the-art dense MM implementations (ScaLAPACK and Cyclops Tensor Framework).