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<div class="section" id="rcm">
<span id="algorithms-rcm"></span><h1>Rcm<a class="headerlink" href="#rcm" title="Permalink to this headline">ΒΆ</a></h1>
<p>[<a class="reference external" href="../../_static/examples/rcm.py">source code</a>]</p>
<div class="highlight-python"><div class="highlight"><pre><span class="c"># Cuthill-McKee ordering of matrices</span>
<span class="c"># The reverse Cuthill-McKee algorithm gives a sparse matrix ordering that</span>
<span class="c"># reduces the matrix bandwidth.</span>
<span class="c"># Requires NumPy</span>
<span class="c"># Copyright (C) 2011 by</span>
<span class="c"># Aric Hagberg <aric.hagberg@gmail.com></span>
<span class="c"># BSD License</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="kn">as</span> <span class="nn">nx</span>
<span class="kn">from</span> <span class="nn">networkx.utils</span> <span class="kn">import</span> <span class="n">reverse_cuthill_mckee_ordering</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="c"># build low-bandwidth numpy matrix</span>
<span class="n">G</span><span class="o">=</span><span class="n">nx</span><span class="o">.</span><span class="n">grid_2d_graph</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">rcm</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">reverse_cuthill_mckee_ordering</span><span class="p">(</span><span class="n">G</span><span class="p">))</span>
<span class="k">print</span> <span class="s">"ordering"</span><span class="p">,</span><span class="n">rcm</span>
<span class="k">print</span><span class="p">(</span><span class="s">"unordered Laplacian matrix"</span><span class="p">)</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">laplacian_matrix</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="n">x</span><span class="p">,</span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nonzero</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="c">#print("lower bandwidth:",(y-x).max())</span>
<span class="c">#print("upper bandwidth:",(x-y).max())</span>
<span class="k">print</span><span class="p">(</span><span class="s">"bandwidth: </span><span class="si">%d</span><span class="s">"</span><span class="o">%</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span><span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
<span class="k">print</span> <span class="n">A</span>
<span class="n">B</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">laplacian_matrix</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">nodelist</span><span class="o">=</span><span class="n">rcm</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"low-bandwidth Laplacian matrix"</span><span class="p">)</span>
<span class="n">x</span><span class="p">,</span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nonzero</span><span class="p">(</span><span class="n">B</span><span class="p">)</span>
<span class="c">#print("lower bandwidth:",(y-x).max())</span>
<span class="c">#print("upper bandwidth:",(x-y).max())</span>
<span class="k">print</span><span class="p">(</span><span class="s">"bandwidth: </span><span class="si">%d</span><span class="s">"</span><span class="o">%</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span><span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
<span class="k">print</span> <span class="n">B</span>
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