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

The software @precision, @hodlr, and @ampholdr, which can be downloaded from here. MATLAB 2024a or newer (with Statistics and Machine Learning Toolbox) is required.

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.