MMatrix Matlab toolbox

A toolbox for fast and accurate computations using M-matrices in Matlab, by Bruno Iannazzo, Mehdi Najafi-Kalyani, and Federico Poloni. The toolbox is described in

The mmatrix toolbox: componentwise accurate algorithms for M-matrices with triplet representation, Bruno Iannazzo, Mehdi Najafi Kalyani, Federico Poloni, arXiv:2607.05437.

Installation

To install the toolbox, download the source files from the Releases page into a folder, and add that folder to the Matlab search path.

If you have a working Fortran compiler set up on your computer to use with Matlab, you can compile the Mex files yourself with

>> build_mex

Otherwise, you can download pre-compiled versions for Windows and Linux from the Releases page. (Producing a pre-compiled version for Mac is more complicated, unfortunately, since Matlab does not support building Mex-files using GFortran on Mac machines.) Download the mex-???.zip file that matches your operating system, and unzip its contents into the +mmex folder.

After installation, you can run the automated tests to check everything is working:

>> runtests('tests/');

Automated installation inside Matlab

To download and install the most recent development version of the toolbox automatically, you can also run:

unzip('https://github.com/numpi/mmatrix/archive/main.zip');
movefile('mmatrix-main', 'mmatrix-toolbox');
addpath(fullfile('mmatrix-toolbox'));
savepath;

Descriptions of the Fortran files

Right triplet algorithms:

• dmmtf2.f: basic unblocked (BLAS level-2) version.
• dmmtrf2.f: recursive cache-oblivious version. Needs a temporary buffer WORK of size 2n.
• dmmtrf.f: blocked version (BLAS level-3) which calls dmmtf2.f on the single blocks. Needs a temporary buffer WORK of size nb, where nb is the user-specified block size.
• dmmtrff.f: blocked version (BLAS level-3) which calls dmmtrf2.f on the single blocks (this one should be the fastest). Needs a temporary buffer WORK of size 2*nb, where nb is the user-specified block size.

Left triplet algorithms:

• dmltf2.f: basic unblocked (BLAS level-2) version.
• dmltrf2.f: recursive cache-oblivious version.
• dmltrf.f: blocked version (BLAS level-3) which calls dmltf2.f on the single blocks. Needs a temporary buffer WORK of size nb, where nb is the user-specified block size.
• dmltrff.f: blocked version (BLAS level-3) which calls dmltrf2.f on the single blocks. Needs a temporary buffer WORK of size nb, where nb is the user-specified block size.