Scalable task-based algorithm for multiplication of block-rank-sparse matrices
By Justus A. Calvin, C. Lewis, Edward F. Valeev. 2015
46 citations recorded by the source corpus.
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).
Subfields: Computational Theory and Mathematics, Computer Networks and Communications, ML Systems & Hardware, Numerical Methods & Scientific Computing
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Citations in the corpus
- Mesh-TensorFlow: Deep Learning for Supercomputers (2018, methodology): “This technique is sometimes called iteration space tiling [2], replication [6], or task parallelism [11].”