article-powmde

This repository includes programs for experiments in the preprint Computing the matrix fractional power based on the double exponential formula, arXiv: 2012.01667.

How to run the programs?

1. Install Julia and set path.
2. git clone https://github.com/f-ttok/article-powmde.git (or download zip file from https://github.com/f-ttok/article-powmde/archive/master.zip, and extract the zip file.)
3. cd article-powmde
4. julia install_packages.jl
5. julia download_matrices.jl
   • If you use Windows, uncomment l.28 and l.31.
6. julia generate_matrices.jl
7. julia run_alltests.jl

Details

Our environment is as follows:

• OS: Linux (Ubuntu 20.04)
• CPU: Intel(R) Core(TM) i7-9700K
• Memory: 16GB
• Julia version: 1.5.1

The programs are written in Julia Language. Hence, Julia Language has to be installed in your computer.

In addition, some additional packages of Julia are required.

• Arpack.jl
• Elliptic.jl
• FastGaussQuadrature.jl
• MatrixMarket.jl
• SuiteSparse.jl

To install these packages, run julia install_packages.jl in your terminal.

The test matrices have to be in matrix directory in .mtx format, for example, matrix/ex5.mtx. If you want to download, extract and put these matrices automatticaly, run julia download_matrices.jl.

In order to generate test matrices, SPD_(well|ill), NS_(well|ill), poisson200, run julia generate_matrices.jl.

In order to run all tests, run julia run_alltests.jl in your terminal.

Some Comments

Test 5

Julia compile the code before running the code for the first time. Hence, it may affect the computational time. In order to avoid the effect, we measure the computational time twice for poisson200 and cell1.

Other comments

Figures are plotted via Jupyter notebook. Their results are in notebooks directory.