# hm-toolbox

**Repository Path**: alphakappa/hm-toolbox

## Basic Information

- **Project Name**: hm-toolbox
- **Description**: Toolbox for HODLR and HSS matrices in MATLAB
- **Primary Language**: Unknown
- **License**: GPL-3.0
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2020-03-20
- **Last Updated**: 2020-12-19

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# Hierarchical matrix toolbox

[![Build status](https://api.travis-ci.org/numpi/hm-toolbox.svg?branch=master)](https://travis-ci.org/numpi/hm-toolbox)

The <code>hm-toolbox</code> is a toolbox implementing the arithmetic of HODLR and HSS matrices in MATLAB. 

The HODLR case is handled in the @hodlr class, and correspond to H-matrices with partitioning
recursively done in 2 x 2 blocks, where the off-diagonal blocks are of low-rank. The HSS 
arithmetic uses the same partitioning (with nested bases), and is available through the
@hss class. 

Routines to compute matrix functions [1] and to solve matrix equations are included [1,2]. 

# Installation instructions

To install the toolbox download the latest revision from Github by running
```
 git clone https://github.com/numpi/hm-toolbox.git
```

or downloading the ZIP file from the webpage [github.com/numpi/hm-toolbox](https://github.com/numpi/hm-toolbox). 
Rename the folder to <code>hm-toolbox</code> if needed. Then, add it to your MATLAB path by running
```Matlab
 >> addpath /path/to/hm-toolbox
```

You are now ready to create new @hodlr and @hss objects. Check some examples in the
<code>examples/</code> folder. 

## Octave compatibility
The toolbox is compatible with GNU Octave >= 4.4. The easiest way to get a
recent version of Octave on Linux is to enable Flatpak following the instructions
[here](https://flatpak.org/setup/), and then run the command 
```
 flatpak install flathub org.octave.Octave
```
You can then run Octave from the menu or by typing <code>flatpak run org.octave.Octave</code> in a terminal. 
Some functions require dependencies found in additional packages, namely <code>octave-control</code>
(for the solvers of Lyapunov and Sylvester equations) and <code>octave-statistics</code> (for
the ACA code that is used inside the HODLR handle constructor). 

# References

1. Massei, S., Palitta, D., & Robol, L. (2018). Solving Rank-Structured Sylvester and Lyapunov Equations. SIAM Journal on Matrix Analysis and Applications, 39(4), 1564-1590.
2. Kressner, D., Massei, S., & Robol, L. (2019). Low-rank updates and a divide-and-conquer method for linear matrix equations. SIAM Journal on Scientific Computing 41 (2), A848-A876.
3. Kressner, D., Massei, S., & Robol, L. (2019). hm-toolbox: Matlab software for HODLR and HSS matrices, arXiv preprint arXiv:1909.07909.