This repository contains the fully reproducible experimental code for the paper [1].
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
Due to large files storage, the software @precision, @hodlr, and @ampholdr, which can be downloaded from https://github.com/chenxinye/mhodlr. Full repo (old version) for all experiment as well as software can be directly downloaded from
Full repository containning all old code and data (the new version of mhodlr might not be compatible to this experimental code) can also be obtained in here.
MATLAB 2024a or newer (with Statistics and Machine Learning Toolbox) is required. The experimental code was simulated in terms of the version Commit 706333a.
Detailed guidance is referred to index:
-
The scripts
plot_saylr3.mandplot_LeGresley.mare used to generate [Fig. 4.1, 1]. -
The scripts
exp_rcerr.mandplot_exp_rcerr.mare used to generate the results for [Fig. 5.1, 1] (run in order). -
The scripts
exp_mvprod.mandplot_exp_mvprod.mare used to generate the results for [Fig. 5.2, 1] (run in order). -
The scripts
exp_lu.mandplot_exp_lu.mare used to generate the results for [Fig. 5.3, 1] (run in order). -
The scripts
exp_storage.mandplot_exp_storage.mare 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.
[1] C. Erin, X. Chen and X. Liu, Mixed precision HODLR matrices, SIAM Journal on Scientific Computing, (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.