Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions
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Other documents of the author: Di Napoli, Edoardo; Fabregat Traver, Diego; Quintana-Ortí, Gregorio; Bientinesi, Paolo
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Title
Towards an Efficient Use of the BLAS Library for Multilinear Tensor ContractionsDate
2014Publisher
Aachen UniversityBibliographic citation
DI NAPOLI, Edoardo…[et al]. Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions. Applied Mathematics and Computation, Volume 235 (2014), pp 454-468Type
info:eu-repo/semantics/articlePublisher version
http://publications.rwth-aachen.de/record/234423Subject
Abstract
Mathematical operators whose transformation rules constitute the building blocks
of a multi-linear algebra are widely used in physics and engineering applications where
they are very often represented as tensors. ... [+]
Mathematical operators whose transformation rules constitute the building blocks
of a multi-linear algebra are widely used in physics and engineering applications where
they are very often represented as tensors. In the last century, thanks to the advances
in tensor calculus, it was possible to uncover new research fields and make remarkable
progress in the existing ones, from electromagnetism to the dynamics of fluids and from
the mechanics of rigid bodies to quantum mechanics of many atoms. By now, the formal
mathematical and geometrical properties of tensors are well defined and understood;
conversely, in the context of scientific and high-performance computing, many tensorrelated
problems are still open. In this paper, we address the problem of efficiently
computing contractions among two tensors of arbitrary dimension by using kernels from
the highly optimized BLAS library. In particular, we establish precise conditions to
determine if and when GEMM, the kernel for matrix products, can be used. Such
conditions take into consideration both the nature of the operation and the storage
scheme of the tensors, and induce a classification of the contractions into three groups.
For each group, we provide a recipe to guide the users towards the most effective use of
BLAS. [-]
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Applied Mathematics and Computation, Volume 235 (2014)Rights
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