2019/10/29 by Ilia Sivkov, Patrick Seewald, Sivkov, Ilia +5
Computer Science · Mathematics · #Algorithms and Data Compression #Distributed #FOS: Computer and information sciences #Parallel #Parallel Computing and Optimization Techniques #Tensor decomposition and applications #and Cluster Computing (cs.DC) #cs.DC
paper · pdf · doi:10.48550/arxiv.1910.13555
10 pages, 3 figures, submitted at the ParCO2019 conference, Prague, Czech Republic, 10-13 September 2019
arxiv created 2019/10/29 · openalex publication_date 2019/10/29 · arxiv updated 2019/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient determination of the exact exchange energy. When going beyond mean field approaches, e.g. for Moller-Plesset perturbation theory, RPA and Coupled-Cluster methods, or the GW methods, it becomes necessary to manipulate higher-order sparse tensors. Very similar problems are also encountered in other domains, like signal processing, data mining, computer vision, and machine learning. With the idea that the most of the tensor operations can be mapped to matrices, we have implemented sparse tensor algebra functionalities in the frames of the sparse matrix linear algebra library DBCSR (Distributed Block Compressed Sparse Row). DBCSR has been specifically designed to efficiently perform blocked-sparse matrix operations, so it becomes natural to extend its functionality to include tensor operations. We describe the newly developed tensor interface and algorithms. In particular, we introduce the tensor contraction based on a fast rectangular sparse matrix multiplication algorithm.