# PH-roadmap

<h3> Project founder: </h3>

Nina Otter (For contact information, see <a href="http://people.maths.ox.ac.uk/otter/"> here</a>.)

<h3> Description </h3>

This project was created to host data sets and scripts used in the paper <a href="#roadmap">[1]</a> and the accompanying supplementary information. The paper can be found <a href="https://epjdatascience.springeropen.com/articles/10.1140/epjds/s13688-017-0109-5"> here</a>. The accompanying <a href="https://static-content.springer.com/esm/art%3A10.1140%2Fepjds%2Fs13688-017-0109-5/MediaObjects/13688_2017_109_MOESM2_ESM.pdf"> tutorial</a> explains how to download/install the libraries Dionyus, DIPHA, GUDHI, javaPlex, Hera, jHoles, Perseus and Ripser, how to compute persistent homology for weighted networks, point clouds as well as digital images, how to plot barcodes and persistence diagrams obtained with these libraries, as well as how to compute bottleneck and Wasserstein distances. 




<h3> Software for PH </h3>
In the following you can find all libraries to compute PH that I know of. If you know a package that is not listed here, please contact me. I was inspired to write this list by Felsenstein's comprehensive  <a href="http://evolution.genetics.washington.edu/phylip/software.html">list of phylogeny programs</a>.

<table align="center" border="0" cellpadding="10" cellspacing="2" width="100%">
<tr bgcolor="#E5EAED">
<td align="center" valign="middle" width="20%"><a href="#intro">Brief introduction</a></td> &nbsp;&nbsp;
<td align="center" valign="middle" width="20%"><a href="#complexes">By complexes</a></td> &nbsp;&nbsp;
<td align="center" valign="middle" width="20%"><a href="#language">By language</a></td> &nbsp;&nbsp;
<td align="center" valign="middle" width="20%"><a href="#statistics">Statistical tools</a></td>
</tr>
</table>


<a name="intro">&nbsp;</a><br>
<h3> Brief Introduction </h3>

If you are new to the computation of persistent homology a good idea is to start with javaPlex, which is the new library of the Plex family:


<ul>

<p>
<li>
<a href="http://appliedtopology.github.io/javaplex/"> javaPlex</a>

<p>
<li>
<a href="http://www.math.duke.edu/~hadams/jplex/index.html"> jPlex</a>

<p>
<li>
<a href="http://mii.stanford.edu/research/comptop/programs/"> Plex</a>
</ul>


After that you could try out Perseus, which implements Morse theoretic reductions to reduce the size of the complex:

<ul>
<p>
<li>
<a href="http://www.sas.upenn.edu/~vnanda/perseus/"> Perseus</a>

</ul>

<p>
If you are familiar with R you might want to try out these two libraries:
<ul>
<p>
<li>
<a href="http://rpackages.ianhowson.com/cran/phom/man/phom-package.html"> pHom</a>


<p>
<li>
<a href="https://cran.r-project.org/web/packages/TDA/"> TDA</a> (See <a href="tda package tutorial"> here</a> for the accompanying tutorial.) This library implements many tools for the statistical interpretation of the computation of PH.


</ul>

....and if you are familiar with GAP  this one:

<p>
<ul>
<li>
<a href="http://www-circa.mcs.st-and.ac.uk/~mik/persistence/"> GAP Persistence</a>
</ul>
</p>


The following is a powerful toolbox of algorithms for the computation of barcodes from the boundary matrix (the first package to implement parallel computation in a shared setting):

<ul>
<li>
<a href="https://code.google.com/p/phat/"> PHAT</a>
</ul>

....if you do not want to compute the boundary matrix yourself, you can use its spin-off library (which implements algorithms for parallel computations in a distributed setting):
<ul>
<p>
<li>
<a href="https://code.google.com/p/dipha/"> DIPHA</a>
</ul>

<p>
Another powerful software is this:
<p>
<ul>
<li>
<a href="https://project.inria.fr/gudhi/software/"> GUDHI</a>
</ul>


This is the only software to implement, among other things, the computation of PH with the &#268;ech complex, and vineyards:

<ul>
<p>
<li>
<a href="http://www.mrzv.org/software/dionysus/"> Dionysus</a>
</ul>
<p>

...while the following library implements, among other things, a <a href="http://arxiv.org/abs/1407.2275">parallel computation of homology</a> based on the Mayer-Vietoris principle and the computation of PH over finite fields:


<ul>
<p>
<li>
<a href="http://ctl.appliedtopology.org/">CTL</a>
</ul>
<p>

The following is a module for the <a href="https://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/">Kenzo</a> library which implements computation of PH in a more general setting, i.e. with integer coefficients and for infinite spaces (provided their homology is <a href="https://www-fourier.ujf-grenoble.fr/~sergerar/Papers/Constructive-AT.pdf">effective</a>):
<ul>
<p>
<li>
 <a href="http://www.unirioja.es/cu/anromero/persistent-homology.zip"> Kenzo module for PH</a> (see the companion <a href="http://arxiv.org/pdf/1403.7086v2.pdf"> preprint</a> for instructions)
</ul>

<p class="bottom-three">
</p>





Finally some more libraries:
</p>


....to do statistics on persistence diagrams:


<ul>
<p>
<li>
<a href="https://www.math.upenn.edu/~dlotko/persistenceLandscape.html"> The Persistence Landscape Toolbox</a>
</p>
</ul>

....for simplicial maps:

<ul>

<p>
<li>
<a href="http://web.cse.ohio-state.edu/~tamaldey/SimpPers/SimpPers-software/"> SimpPers</a>
</p>
</ul>

....to compute the weight rank clique filtration for networks:


<ul>
<p>
<li>
<a href="http://cuda.unicam.it/jHoles"> jHoles</a>
</p>
</ul>

....and its older version:

<ul>
<p>
<li>
<a href="http://lordgrilo.github.io/Holes/"> Holes </a>
</p>
</ul>

....for fast computation of PH with alpha complexes in 1-D:
<ul>

<li>
<a href="http://kurlin.org/projects/persistent-skeletons.php"> HOPES</a>
</ul>


<a name="complexes">&nbsp;</a><br>
<h3> By complexes </h3>
..to be added soon
<a name="language">&nbsp;</a><br>
<h3> By language </h3>
..to be added soon
<a name="statistics">&nbsp;</a><br>
<h3> Statistical tools </h3>
..to be added soon
<h3> References </h3>
<a name="roadmap">[1]</a> A roadmap for the computation of persistent homology. N. Otter, M. Porter, U. Tillmann, P. Grindrod, H. Harrington, <i>EPJ Data Science</i> 2017 <b>6</b>:17