RTToolbox

Dual-variant index class, dense tensor class, and unit tests of a tensor framework for model-based approaches to imaging with MATLAB.

The Ricci-notation tensor (RT) framework [1] comprises a dual-variant index algebra, aligned with the Ricci notation of non-Euclidean geometry but designed for numeric purposes, as well as codesigned object-oriented software, called the RTToolbox for MATLAB. Compared to a numeric tensor (NT) predecessor [2, 3, 4], the RT framework enables superior ways to model imaging problems and to thereby develop solutions. Although this release of the RTToolbox does not address sparsity, the RT framework is theoretically capable of leveraging ideas demonstrated with the NT framework [5].

[1] Dileepan Joseph, “Ricci-Notation Tensor Framework for Model-based Approaches to Imaging,” Journal of Imaging Science and Technology, vol. 68, no. 4, pp. 040504 1-17, Jul. 2024 (DOI)

[2] Adam P. Harrison and Dileepan Joseph, “Numeric tensor framework: Exploiting and extending Einstein notation,” Journal of Computational Science, vol. 16, pp. 128-139, Sep. 2016 (DOI)

[3] Richard Cairney, “PhD thesis cites Einstein and Kuhn, identifies computing paradigm,” News & Events, Faculty of Engineering, University of Alberta, Jun. 2016 (URL)

[4] Adam P. Harrison (supervised by Dileepan Joseph ), Numeric Tensor Framework: Toward a New Paradigm in Technical Computing, Ph.D. Thesis, University of Alberta, pp. i-xvi 1-199, Jun. 2016 (DOI)

[5] Adam P. Harrison and Dileepan Joseph, “High Performance Rearrangement and Multiplication Routines for Sparse Tensor Arithmetic,” SIAM Journal on Scientific Computing, vol. 40, no. 2, pp. C258-C281, Mar. 2018 (DOI)