A64FX稀疏多线程Cholesky分解的优化
Optimization of the Sparse Multi-Threaded Cholesky Factorization for A64FX
摘要：
稀疏线性代数例程是各种科学应用的基本构建块。直接求解器是通过将矩阵分解为三角矩阵的乘积来求解线性系统的方法，通常在许多情况下使用。Cholesky分解是求解对称正定矩阵的最快的直接方法。提出了一种基于稀疏矩阵结构确定并行Cholesky分解最优任务粒度的方法--选择性嵌套。我们提出了OPT-D-COST算法，自动和动态地应用选择性排样。OPT-D-COST利用矩阵稀疏性在直接求解器的上下文中驱动基于复杂任务的并行工作负载。我们运行一个广泛的评估活动，考虑一组异构的60稀疏矩阵和并行机具有A64 FX处理器。OPT-D-COST相对于运行直接求解器的最佳并行方法，平均性能加速比为1.46 $\times$。
英文摘要：
Sparse linear algebra routines are fundamental building blocks of a large variety of scientific applications. Direct solvers, which are methods for solving linear systems via the factorization of matrices into products of triangular matrices, are commonly used in many contexts. The Cholesky factorization is the fastest direct method for symmetric and definite positive matrices. This paper presents selective nesting, a method to determine the optimal task granularity for the parallel Cholesky factorization based on the structure of sparse matrices. We propose the OPT-D-COST algorithm, which automatically and dynamically applies selective nesting. OPT-D-COST leverages matrix sparsity to drive complex task-based parallel workloads in the context of direct solvers. We run an extensive evaluation campaign considering a heterogeneous set of 60 sparse matrices and a parallel machine featuring the A64FX processor. OPT-D-COST delivers an average performance speedup of 1.46$\times$ with respect to the best state-of-the-art parallel method to run direct solvers.
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