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arXiv · 1509.00309

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

Justus A. Calvin·Cannada A. Lewis·Edward F. Valeev
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Abstract

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).

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Justus A. Calvin, Cannada A. Lewis, Edward F. Valeev. 2015-09-01. Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices. https://doi.org/10.1145/2833179.2833186

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