mphodlr_exp

This repository contains the fully reproducible experimental code for the paper “Mixed precision HODLR matrices” [1].

Download

mphodlr_exp contains large files storage. To download the full repository, please ensure git lfs is properly set up (see here for details) and use the following commands:

GIT_LFS_SKIP_SMUDGE=1 git clone https://github.com/inEXASCALE/mphodlr_exp.git
cd mphodlr_exp
git lfs pull

Full repository containning all code and data can also be obtained in here.

Requirements

Due to large files storage, the software @precision, @hodlr, and @ampholdr, which can be downloaded from https://github.com/chenxinye/mhodlr. MATLAB 2024a or newer (with Statistics and Machine Learning Toolbox) is required. The experimental code was simulated in terms of the version Commit 706333a.

Instruction

Detailed guidance is referred to index:

• The scripts plot_saylr3.m and plot_LeGresley.m are used to generate [Fig. 4.1, 1].

• The scripts exp_rcerr.m and plot_exp_rcerr.m are used to generate the results for [Fig. 5.1, 1] (run in order).

• The scripts exp_mvprod.m and plot_exp_mvprod.m are used to generate the results for [Fig. 5.2, 1] (run in order).

• The scripts exp_lu.m and plot_exp_lu.m are used to generate the results for [Fig. 5.3, 1] (run in order).

• The scripts exp_storage.m and plot_exp_storage.m are used to generate the results for [Fig. 5.4, 1] (run in order).

All test matrices stored in the folder data are from Amestoy et al. [2] and SuiteSparse collection [4]. The low precision arithmetics are simulated by chop [3]. One can perform all experiments at one go by running the command run_all. The generated results and figures are separately stored in results and figures, respectively.

References

[1] C. Erin, X. Chen and X. Liu, Mixed precision HODLR matrices, arXiv:2407.21637, (2024), https://doi.org/10.48550/arXiv.2407.21637.

[2] P. Amestoy, O. Boiteau, A. Buttari, M. Gerest, F. J´ez´equel, J.-Y. L’Excellent, and T. Mary, Mixed precision low-rank approximations and their application to block lowrank LU factorization, IMA J. Numer. Anal., 43 (2022), pp. 2198–2227, https://doi.org/10.1093/imanum/drac037.

[3] N. J. Higham and S. Pranesh, Simulating low precision floating-point arithmetic, SIAM J. Sci. Comput., 41 (2019), pp. C585–C602, https://doi.org/10.1137/19M1251308.

[4] T. A. Davis and Y. Hu, The University of Florida Sparse Matrix Collection, ACM Trans. Math. Software, 38 (2011), https://doi.org/10.1145/2049662.2049663.