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Massively parallel sparse matrix function calculations with NTPoly

机译：用NTPOLY大规模并行稀疏矩阵函数计算

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摘要

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.
机译：我们呈现NTPOLY，一种用于计算稀疏，对称矩阵的功能的大规模并行库。矩阵函数理论是一种开发的框架，具有各种应用，包括微分方程，图形理论和电子结构计算。一个特别重要的应用区域是量子化学中的对角化方法。当矩阵函数的输入和输出稀疏时，基于多项式扩展的方法可用于计算线性时间中的矩阵函数。我们介绍一个基于这些方法的库，可以计算各种矩阵函数。分布式存储器并行化基于避免稀疏矩阵乘法算法的通信。 OpenMP任务Parallellization用于实施混合并行化。我们描述了NTPOLY的界面，并展示了如何与以许多不同的编程语言编写的程序集成。我们通过对K计算机执行大规模计算来展示NTPOLY的优点。

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