Identifying Cost-Effective Common Subexpressions to Reduce Operation Count in Tensor Contraction Evaluations
Identifying Cost-Effective Common Subexpressions to Reduce Operation Count in Tensor Contraction Evaluations
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识别具有成本效益的公共子表达式以减少张量收缩评估中的操作次数
DOI：
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发表时间：
2006
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通讯作者：
P. Sadayappan
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作者：
Albert Hartono;Q. Lu;X. Gao;S. Krishnamoorthy;M. Nooijen;Gerald Baumgartner;D. Bernholdt;Venkatesh Choppella;R. Pitzer;J. Ramanujam;A. Rountev;P. Sadayappan
复杂的张量收缩表达式出现在量子化学中精确的电子结构模型中，例如耦合团簇方法。使用交换性和结合性的代数性质的变换可以用于显著减少计算这些表达式所需的算术运算的数量。操作最小化是张量收缩引擎的重要优化步骤，张量收缩引擎是一种正在开发的工具，用于将高级张量收缩表达式自动转换为高效程序。在一组张量收缩表达式中识别公共子表达式可以导致评估张量收缩所需的操作总数的减少。在本文中，我们开发了一个有效的算法，共同的子表达式识别，并证明其有效性的张量压缩表达式耦合集群方程。
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed for the automatic transformation of high-level tensor contraction expressions into efficient programs. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. In this paper, we develop an effective algorithm for common subexpression identification and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.