Synopsis

TiledArray is a scalable, block-sparse tensor library that is designed to aid in rapid composition of high-performance tensor expressions, appearing for example in many-body quantum mechanics. It allows users to compose tensor expressions of arbitrary complexity in native C++ code that closely resembles the standard mathematical notation. The library is designed to scale from a single multicore computer to a massive cluster.

TiledArray is built on top of MADNESS parallel runtime (MADWorld), part of MADNESS numerical calculus framework.

TiledArray is a work in progress.

Design Goals

• Simple implementation of tensor algebra in C++
• Dense, and structured/unstructured sparse tensors
• Intra- and inter-node scalability
• General purpose

Example Code

The following are example expressions written in C++ with TiledArray. TiledArray use the Einstein summation convention when evaluating tensor expressions.

• Matrix-matrix multiplication

  C("m,n") = 2.0 * A("m,k") * B("k,n");

• Matrix-vector multiplication

  C("n") = A("k") * B("k,n");

• Complex tensor expression

  E("m,n") = 2.0 * A("m,k") * B("k,n") + C("k,n") * D("k,m");

Developers

TiledArray is developed by the Valeev Group at Virginia Tech.

How to Cite

Cite TiledArray as

"TiledArray: A general-purpose scalable block-sparse tensor library", Justus A. Calvin and Edward F. Valeev, https://github.com/valeevgroup/tiledarray .

Inner workings of TiledArray are partially described in the following publications:

• Justus A. Calvin, Cannada A. Lewis, and Edward F. Valeev, "Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices." http://arxiv.org/abs/1509.00309 .
• Justus A. Calvin and Edward F. Valeev, "Task-Based Algorithm for Matrix Multiplication: A Step Towards Block-Sparse Tensor Computing." http://arxiv.org/abs/1504.05046 .

The MADNESS parallel runtime is described in the following publication:

• Robert J. Harrison, Gregory Beylkin, Florian A. Bischoff, Justus A. Calvin, George I. Fann, Jacob Fosso-Tande, Diego Galindo, Jeff R. Hammond, Rebecca Hartman-Baker, Judith C. Hill, Jun Jia, Jakob S. Kottmann, M-J. Yvonne Ou, Junchen Pei, Laura E. Ratcliff, Matthew G. Reuter, Adam C. Richie-Halford, Nichols A. Romero, Hideo Sekino, William A. Shelton, Bryan E. Sundahl, W. Scott Thornton, Edward F. Valeev, Álvaro Vázquez-Mayagoitia, Nicholas Vence and Yukina Yokoi, "madness: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation.", http://arxiv.org/abs/1507.01888 .

Acknowledgements

Development of TiledArray is made possible by past and present contributions from the National Science Foundation (awards CHE-0847295, CHE-0741927, OCI-1047696, CHE-1362655, ACI-1047696), the Alfred P. Sloan Foundation, and the Camille and Henry Dreyfus Foundation.