A Block-Oriented Language and Runtime System for Tensor Algebra with Very Large Arrays

Sanders, Beverly A.; Bartlett, R. J.; Deumens, Erik; Lotrich, Victor F.; Ponton, Mark

doi:10.1109/sc.2010.3

Cited by 16 publications

(17 citation statements)

References 19 publications

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“…However, while the working set size 2 of a finite element local assembly kernel rarely exceeds a megabyte, the tensors in quantum chemistry computations are typically huge, even reaching petabytes in size. Consequently, the optimized implementation of individual tensor operations on distributed-memory parallel computers is usually the major concern, as is the case with SIAL [48], libtensor [14], and CTF [50]. Similarly, TensorFlow [1] serves to instrument tensor computations for machine learning purposes on large-scale heterogeneous computing systems, so most of their challenges do not overlap with ours.…”

Section: Related Workmentioning

confidence: 99%

TSFC: A Structure-Preserving Form Compiler

Homolya¹,

Mitchell²,

Luporini³

et al. 2018

SIAM J. Sci. Comput.

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A form compiler takes a high-level description of the weak form of partial differential equations and produces low-level code that carries out the finite element assembly. In this paper we present the Two-Stage Form Compiler (TSFC), a new form compiler with the main motivation to maintain the structure of the input expression as long as possible. This facilitates the application of optimizations at the highest possible level of abstraction. TSFC features a novel, structure-preserving method for separating the contributions of a form to the subblocks of the local tensor in discontinuous Galerkin problems. This enables us to preserve the tensor structure of expressions longer through the compilation process than other form compilers. This is also achieved in part by a two-stage approach that cleanly separates the lowering of finite element constructs to tensor algebra in the first stage, from the scheduling of those tensor operations in the second stage. TSFC also efficiently traverses complicated expressions, and experimental evaluation demonstrates good compile-time performance even for highly complex forms.Algorithm 1 Generated loop nests for the expression (4.2).1: for all q do 2:3: for all q, r do 4: 1) q,r * c r 5: for all q do 6:J (1,2) [q] ← 0 7: for all q, r do 8: 2) q,r * c r 9: for all q do 10: J (2,1) [q] ← 0 11: for all q, r do 12: J (2,1) [q] += C (2,1) q,r * c r 13: for all q do 14: J (2,2) [q] ← 0 15: for all q, r do 16: J (2,2) [q] += C (2,2) q,r * c r

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Section: Related Workmentioning

confidence: 99%

TSFC: A Structure-Preserving Form Compiler

Homolya¹,

Mitchell²,

Luporini³

et al. 2018

SIAM J. Sci. Comput.

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“…This section presents the block tensor, an approach that partitions the modes of a tensor consistently so that the subtensors (“blocks”) have the same dimensionality as the original tensor. The approach, first introduced by Windus and Pople and then used in BlockTensor library and SIAL, is thus a multidimensional generalization of matrix tiling as illustrated in Figure .…”

Section: Data Structures and Algorithmsmentioning

confidence: 99%

“…developed in 1997–1998 following Windus and Pople's ideas. Similar libraries were developed by the NWCHEM (including optimization of tensor expressions), ACES III, and PSI4 teams.…”

Section: Introductionmentioning

confidence: 99%

New implementation of high‐level correlated methods using a general block tensor library for high‐performance electronic structure calculations

et al. 2013

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This article presents an open‐source object‐oriented C++ library of classes and routines to perform tensor algebra. The primary purpose of the library is to enable post‐Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide‐and‐conquer‐type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q‐Chem electronic structure software uses this library to drive coupled‐cluster, equation‐of‐motion, and algebraic‐diagrammatic construction methods. © 2013 Wiley Periodicals, Inc.

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“…One should note that the fragmentation of the system in our case serves a completely different purpose then it does in fragment‐based local many‐body methods. Namely, there are two reasons why we introduce a formal fragmentation of the system: (1) we can adjust (lower/raise) the quality of the basis set locally (within a fragment) and (2) splitting the full orbital range into contiguous segments naturally partitions all tensors into subtensors (tensor blocks) and this can be exploited efficiently in massively parallel computations (splitting a tensor into tensor blocks, that is, block‐partitioning of tensors, is a higher‐dimensional analog of matrix tiling). Furthermore, since the range of each index (dimension) of a tensor block is associated with a specific local spatial domain (fragment), one can efficiently exploit tensor sparsity and introduce the concept of the tensor block strength, based on some spatial metric, for example, in some analogy with the measures used by Pulay and Szaebo for orbital domains .…”

Section: Theorymentioning

confidence: 99%

Scale‐adaptive tensor algebra for local many‐body methods of electronic structure theory

Lyakh

2014

Int J of Quantum Chemistry

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While the formalism of multiresolution analysis, based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this article, we present a formalism called scaleadaptive tensor algebra, which introduces an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability of certain local correlated many-body methods of electronic structure theory, for example, those directly based on atomic orbitals (or any other localized basis functions in general).

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A Block-Oriented Language and Runtime System for Tensor Algebra with Very Large Arrays

Cited by 16 publications

References 19 publications

TSFC: A Structure-Preserving Form Compiler

TSFC: A Structure-Preserving Form Compiler

New implementation of high‐level correlated methods using a general block tensor library for high‐performance electronic structure calculations

Scale‐adaptive tensor algebra for local many‐body methods of electronic structure theory

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