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......@@ -790,13 +790,14 @@ Chapter 12 of Combinatorial Scientific Computing, Chapman and Hall/CRC, pp. 321-
<hr>
<p>
Last updated: 29st of August, 2013.<br><br>
Last updated: September 27, 2016.<br><br>
June 9, 2009 by Rob Bisseling,<br>
December 2, 2010 by Bas Fagginger Auer,<br>
December 10, 2010 by A. N. Yzelman,<br>
March 27, 2012 by Bas Fagginger Auer,<br>
April 18, 2013 by Dani&euml;l M. Pelt,<br>
August 29, 2013 by Rob Bisseling and Bas Fagginger Auer.<br><br>
August 29, 2013 by Rob Bisseling and Bas Fagginger Auer,<br>
September 27, 2016 by Marco van Oort.<br><br>
To <a href="http://www.staff.science.uu.nl/~bisse101/Mondriaan">
the Mondriaan package home page</a>.</p>
......
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<title>User's guide MondriaanOpt</title>
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<body>
<h2>User's guide MondriaanOpt</h2>
<div id="top">
<div><a href="#inst">Installing</a></div>
<div><a href="#outp">Output</a></div>
<div><a href="#opts">Options</a></div>
<div><a href="#matl">MATLAB</a></div>
</div>
<hr>
<p>
This page is continuously being improved and updated;
therefore, a more recent version may be obtained
<a href="http://www.staff.science.uu.nl/~bisse101/Mondriaan/Docs/USERS_GUIDE_OPT.html">
online</a>.
This offline version is bundled with the software for your convenience.
</p>
<hr>
<h3><a name="inst">How to install MondriaanOpt</a></h3>
<p>
MondriaanOpt comes packaged with the Mondriaan software. Refer to <a href="./USERS_GUIDE.html">this page</a> for
instructions on using Mondriaan. MondriaanOpt is automatically compiled when you compile Mondriaan. The executable
is then available at <tt>tools/MondriaanOpt</tt>.
</p>
<p>
Whereas Mondriaan uses heuristics to obtain good partitionings for sparse matrix-vector multiplication for any number of processors,
MondriaanOpt will calculate an actual optimal solution for this partitioning problem with 2 processors. More precisely, it will
calculate a partitioning with minimum volume among all solutions that obey the imbalance constraint.
</p>
<h3><a name="run">How to run MondriaanOpt</a></h3>
<p>
Go inside the directory <tt>Mondriaan4</tt> and type
</p>
<ul>
<li><tt>% cd tools</tt></li>
<li><tt>% ./MondriaanOpt -m ../tests/arc130.mtx -e 0.03 -v 20</tt></li>
</ul>
<p>
if you want to partition the <tt>arc130.mtx</tt> matrix (Matrix Market file format)
for 2 processors with at most 3% load imbalance, knowing that solutions must exist with
volume at most 20. The matrix should be the full relative path; <em>in the above example
output is saved in the Mondriaan tests folder</em> (<tt>../tests/</tt>).
</p>
<h3><a name="outp">Output</a></h3>
<p>The <tt>MondriaanOpt</tt> tool yields, after a successful run on an input matrix,
various output files. All possible output files are described below. Typically,
the output filenames are that of the input matrix filename, modified with a small
descriptor and the number of parts <i>x(=2)</i>.</p>
<h4>Processor indices (<tt>_P2.mtx</tt>)</h4>
<p> The <tt>MondriaanOpt</tt> program also writes the processor indices of each
nonzero to the Matrix Market file <tt>input_P2.mtx</tt> where the value of each
nonzero is replaced by the processor index to which the nonzero has been assigned.
</p>
<h4>Graphical output</h4>
<p>Besides textual output, also an SVG graphic is written to the file <tt>input_P2.svg</tt>,
containing a visualisation of the partitioning.
</p>
<h4><i>(Optional)</i> Distributed matrix (<tt>-Px</tt>)</h4>
<p> When the <tt>convert</tt> flag is passed, the <tt>MondriaanOpt</tt> program
writes the distributed matrix to a file called <tt>input-Px</tt>,
where <tt>input</tt> is the name of the input matrix, where x equals 3 when the
distribution includes free nonzeros, and x equals 2 otherwise.
We use an adapted Matrix Market format, with this structure:
<br>
<tt>%%MatrixMarket distributed-matrix coordinate real general<br>
m n nnz P<br>
Pstart[0]</tt> ( this should be 0 )<br>
...<br>
...<br>
...<br>
<tt>Pstart[P]</tt>( this should be nnz )<br>
<tt>A.i[0] A.j[0] A.value[0]</tt>
...<br>
...<br>
...<br>
<tt>A.i[nnz-1] A.j[nnz-1] A.value[nnz-1]</tt>
<br>
Here, <tt>Pstart[k]</tt> points to the start of the nonzeroes
of processor k.
</p>
<h4><i>(Optional)</i> Processor indices (<tt>-Ix</tt>)</h4>
<p> When the <tt>convert</tt> flag is passed, the <tt>MondriaanOpt</tt> program
also writes the processor indices of each nonzero to the Matrix Market file <tt>input-Ix</tt>
where the value of each nonzero is replaced by the processor index to which
the nonzero has been assigned. The order of the nonzeroes is exactly that of the distributed matrix (<tt>-Px</tt>).
</p>
<h4><i>(Optional)</i> Cartesian submatrices (<tt>-Cx</tt>)</h4>
<p>When the <tt>convert</tt> flag is passed, the program writes the row index sets I(q)
and column index sets J(q) of the Cartesian submatrix I(q) x J(q)
for the processors q=1,...,P to the file called <tt>input-Cx</tt>.
This file is additional information, useful e.g. for visualisation,
and you may not need it.
</p>
<h3><a name="opts">Program options</a></h3>
<p>
The MondriaanOpt options can be passed in the command line.
An overview of the options is given below.
</p>
<table>
<thead>
<tr>
<th>Option</th>
<th>Value</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td>-m</td>
<td>Matrix file</td>
<td><i>Required.</i> The input matrix file in Matrix Market (.mtx) format</td>
</tr>
<tr>
<td>-v</td>
<td>Volume</td>
<td><i>Required.</i> The starting upper bound volume</td>
</tr>
<tr>
<td>-e</td>
<td>Load imbalance</td>
<td><i>Required if -k is not passed.</i> The allowed load imbalance</td>
</tr>
<tr>
<td>-k</td>
<td>Number of nonzeros</td>
<td><i>Required if -e is not passed.</i> The maximum allowed number of nonzeros per part</td>
</tr>
<tr>
<td>-t</td>
<td>Seconds</td>
<td>Max running time in seconds</td>
</tr>
<tr>
<td>-r</td>
<td>Dumpfile</td>
<td>Resume with given dumpfile</td>
</tr>
<tr>
<td>-h</td>
<td><i>None</i></td>
<td>Show help</td>
</tr>
<tr>
<td>-c</td>
<td><i>None</i></td>
<td>After computation is complete, convert results to Mondriaan output.</td>
</tr>
<tr>
<td>-C</td>
<td><i>None</i></td>
<td>Do not compute anything; convert previously obtained results to Mondriaan output.
(When passed, only -m is required.)</td>
</tr>
</tbody>
</table>
<h3><a name="matl">Using MondriaanOpt in MATLAB</a></h3>
<p>
For more information about MATLAB usage, please see the <a href="MATLAB.html">Mondriaan MATLAB guide</a>.
MondriaanOpt is available in Matlab using the <tt>MatlabMondriaanOpt</tt> MEX routine. Example matlab files
are given as <tt>mondriaanOpt.m</tt> and <tt>mondriaanOptPlot.m</tt>.
</p>
<h3>References</h3>
<p>
[<a name="cite1" href="http://doi.org/10.1016/j.jpdc.2015.06.005">1</a>]
<em>An exact algorithm for sparse matrix bipartitioning</em>,
Daniel M. Pelt and Rob H. Bisseling, <i>Journal of Parallel and Distributed Computing</i>, <b>85</b> (2015) pp. 79-90.
</p>
<hr>
<p>
Last updated: September 27, 2016.<br><br>
September 27, 2016 by Marco van Oort.<br><br>
To <a href="http://www.staff.science.uu.nl/~bisse101/Mondriaan">
the Mondriaan package home page</a>.</p>
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