Automated operation minimization of tensor contraction expressions in electronic structure calculations

Authors:
Albert Hartono;Alexander Sibiryakov;Marcel Nooijen;Gerald Baumgartner;David E. Bernholdt;So Hirata;Chi-Chung Lam;Russell M. Pitzer;J. Ramanujam;P. Sadayappan
Affiliations:
Dept. of Computer Science and Engineering, The Ohio State University, Columbus, OH;Dept. of Computer Science and Engineering, The Ohio State University, Columbus, OH;Dept. of Chemistry, University of Waterloo, Waterloo, Ontario, Canada;Dept. of Computer Science, Louisiana State University, Baton Rouge, LA;Computer Sci. & Math. Div., Oak Ridge National Laboratory, Oak Ridge, TN;Quantum Theory Project, University of Florida, Gainesville, FL;Dept. of Computer Science and Engineering, The Ohio State University, Columbus, OH;Dept. of Chemistry, The Ohio State University, Columbus, OH;Dept. of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA;Dept. of Computer Science and Engineering, The Ohio State University, Columbus, OH
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

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Abstract

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, but the optimization problem is NP-hard. 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. In this paper, we develop an effective heuristic approach to the operation minimization problem, and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.