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Numeric tensor framework: Exploiting and extending Einstein notation
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DOI：10.1016/j.jocs.2016.05.004.png)
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Abstract
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The numeric tensor (NT) framework addresses and unifies a growing body of work on high-dimensional algebra and software for technical computing. Its NT algebra exploits and extends Einstein notation, offering unmatched capabilities, including N-dimensional operators, associativity, commutativity, entrywise products, and linear invertibility. High-performance C++ and MATLAB NT software allows practitioners to directly program with NT algebra. The advantages of NT algebra are highlighted using the example of canonical-polyadic (CP) tensor decomposition. Corresponding dense benchmarks demonstrate that the NT software matches or surpasses leading competitors, i.e., the MATLAB Tensor Toolbox, NumPy, and Blitz++, while supporting a more general set of arithmetic operations. (C) 2016 Elsevier B.V. All rights reserved.
Keywords:
Tensor algebra
Tensor computations
Tensor inversion
C plus plus classes
MATLAB classes
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