Exploiting data sparsity for large-scale matrix computations

K. Akbudak, H. Ltaief, A. Mikhalev, A. Charara, A. Esposito, D. Keyes
European Conference on Parallel Processing, pp. 721-734, (2018)

Exploiting data sparsity for large-scale matrix computations

Keywords

HiCMA

Abstract

​Exploiting data sparsity in dense matrices is an algorithmic bridge between architectures that are increasingly memory-austere on a per-core basis and extreme-scale applications. The Hierarchical matrix Computations on Manycore Architectures (HiCMA) library tackles this challenging problem by achieving significant reductions in time to solution and memory footprint, while preserving a specified accuracy requirement of the application. HiCMA provides a high-performance implementation on distributed-memory systems of one of the most widely used matrix factorization in large-scale scientific applications, i.e., the Cholesky factorization. It employs the tile low-rank data format to compress the dense data-sparse off-diagonal tiles of the matrix. It then decomposes the matrix computations into interdependent tasks and relies on the dynamic runtime system StarPU for asynchronous out-of-order scheduling, while allowing high user-productivity. Performance comparisons and memory footprint on matrix dimensions up to eleven million show a performance gain and memory saving of more than an order of magnitude for both metrics on thousands of cores, against state-of-the-art open-source and vendor optimized numerical libraries. This represents an important milestone in enabling large-scale matrix computations toward solving big data problems in geospatial statistics for climate/weather forecasting applications.

Code

DOI: 10.1007/978-3-319-96983-1_51

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