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<div class="section" id="wavelet-packets">
<span id="reg-wp"></span><h1>Wavelet Packets<a class="headerlink" href="#wavelet-packets" title="Permalink to this headline">¶</a></h1>
<div class="section" id="import-pywt">
<h2>Import pywt<a class="headerlink" href="#import-pywt" title="Permalink to this headline">¶</a></h2>
<blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pywt</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">def</span> <span class="nf">format_array</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
<span class="gp">... </span> <span class="sd">"""Consistent array representation across different systems"""</span>
<span class="gp">... </span> <span class="kn">import</span> <span class="nn">numpy</span>
<span class="gp">... </span> <span class="n">a</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">numpy</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o"><</span> <span class="mf">1e-5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
<span class="gp">... </span> <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array2string</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">precision</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">separator</span><span class="o">=</span><span class="s">' '</span><span class="p">,</span> <span class="n">suppress_small</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
</pre></div>
</div>
</blockquote>
</div>
<div class="section" id="create-wavelet-packet-structure">
<h2>Create Wavelet Packet structure<a class="headerlink" href="#create-wavelet-packet-structure" title="Permalink to this headline">¶</a></h2>
<p>Ok, let’s create a sample <a title="pywt.WaveletPacket" class="reference external" href="../ref/wavelet-packets.html#pywt.WaveletPacket"><tt class="xref docutils literal"><span class="pre">WaveletPacket</span></tt></a>:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<p>The input <em>data</em> and decomposition coefficients are stored in the
<tt class="xref docutils literal"><span class="pre">WaveletPacket.data</span></tt> attribute:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">data</span>
<span class="go">[1, 2, 3, 4, 5, 6, 7, 8]</span>
</pre></div>
</div>
<p><a title="pywt.Node" class="reference external" href="../ref/wavelet-packets.html#pywt.Node"><tt class="xref docutils literal"><span class="pre">Nodes</span></tt></a> are identified by <tt class="xref docutils literal"><span class="pre">paths</span></tt>. For the root
node the path is <tt class="docutils literal"><span class="pre">''</span></tt> and the decomposition level is <tt class="docutils literal"><span class="pre">0</span></tt>.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="nb">repr</span><span class="p">(</span><span class="n">wp</span><span class="o">.</span><span class="n">path</span><span class="p">)</span>
<span class="go">''</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">level</span>
<span class="go">0</span>
</pre></div>
</div>
<p>The <em>maxlevel</em>, if not given as param in the constructor, is automatically
computed:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">maxlevel</span>
<span class="go">3</span>
</pre></div>
</div>
</div>
<div class="section" id="traversing-wp-tree">
<h2>Traversing WP tree:<a class="headerlink" href="#traversing-wp-tree" title="Permalink to this headline">¶</a></h2>
<div class="section" id="accessing-subnodes">
<h3>Accessing subnodes:<a class="headerlink" href="#accessing-subnodes" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<p>First check what is the maximum level of decomposition:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">maxlevel</span>
<span class="go">3</span>
</pre></div>
</div>
<p>and try accessing subnodes of the WP tree:</p>
<blockquote>
<ul>
<li><p class="first">1st level:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'a'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span>
<span class="go">[ 2.12132034 4.94974747 7.77817459 10.60660172]</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'a'</span><span class="p">]</span><span class="o">.</span><span class="n">path</span>
<span class="go">a</span>
</pre></div>
</div>
</li>
<li><p class="first">2nd level:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'aa'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span>
<span class="go">[ 5. 13.]</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'aa'</span><span class="p">]</span><span class="o">.</span><span class="n">path</span>
<span class="go">aa</span>
</pre></div>
</div>
</li>
<li><p class="first">3rd level:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'aaa'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span>
<span class="go">[ 12.72792206]</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'aaa'</span><span class="p">]</span><span class="o">.</span><span class="n">path</span>
<span class="go">aaa</span>
</pre></div>
</div>
<p>Ups, we have reached the maximum level of decomposition and got an
<tt class="xref docutils literal"><span class="pre">IndexError</span></tt>:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'aaaa'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="c">...</span>
<span class="nc">IndexError</span>: <span class="n-Identifier">Path length is out of range.</span>
</pre></div>
</div>
</li>
</ul>
</blockquote>
<p>Now try some invalid path:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ac'</span><span class="p">]</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="c">...</span>
<span class="nc">ValueError</span>: <span class="n-Identifier">Subnode name must be in ['a', 'd'], not 'c'.</span>
</pre></div>
</div>
<p>which just yielded a <tt class="xref docutils literal"><span class="pre">ValueError</span></tt>.</p>
</div>
<div class="section" id="accessing-node-s-attributes">
<h3>Accessing Node’s attributes:<a class="headerlink" href="#accessing-node-s-attributes" title="Permalink to this headline">¶</a></h3>
<p><a title="pywt.WaveletPacket" class="reference external" href="../ref/wavelet-packets.html#pywt.WaveletPacket"><tt class="xref docutils literal"><span class="pre">WaveletPacket</span></tt></a> object is a tree data structure, which evaluates to a set
of <a title="pywt.Node" class="reference external" href="../ref/wavelet-packets.html#pywt.Node"><tt class="xref docutils literal"><span class="pre">Node</span></tt></a> objects. <a title="pywt.WaveletPacket" class="reference external" href="../ref/wavelet-packets.html#pywt.WaveletPacket"><tt class="xref docutils literal"><span class="pre">WaveletPacket</span></tt></a> is just a special subclass
of the <a title="pywt.Node" class="reference external" href="../ref/wavelet-packets.html#pywt.Node"><tt class="xref docutils literal"><span class="pre">Node</span></tt></a> class (which in turn inherits from the <a title="pywt.BaseNode" class="reference external" href="../ref/wavelet-packets.html#pywt.BaseNode"><tt class="xref docutils literal"><span class="pre">BaseNode</span></tt></a>).</p>
<p>Tree nodes can be accessed using the <em>obj[x]</em> (<tt class="xref docutils literal"><span class="pre">Node.__getitem__()</span></tt>) operator.
Each tree node has a set of attributes: <tt class="xref docutils literal"><span class="pre">data</span></tt>, <tt class="xref docutils literal"><span class="pre">path</span></tt>,
<a title="pywt.Node.node_name" class="reference external" href="../ref/wavelet-packets.html#pywt.Node.node_name"><tt class="xref docutils literal"><span class="pre">node_name</span></tt></a>, <tt class="xref docutils literal"><span class="pre">parent</span></tt>, <tt class="xref docutils literal"><span class="pre">level</span></tt>,
<tt class="xref docutils literal"><span class="pre">maxlevel</span></tt> and <tt class="xref docutils literal"><span class="pre">mode</span></tt>.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span>
<span class="go">[-2. -2.]</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">path</span>
<span class="go">ad</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">node_name</span>
<span class="go">d</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">path</span>
<span class="go">a</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">level</span>
<span class="go">2</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">maxlevel</span>
<span class="go">3</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">mode</span>
<span class="go">sym</span>
</pre></div>
</div>
</div>
<div class="section" id="collecting-nodes">
<h3>Collecting nodes<a class="headerlink" href="#collecting-nodes" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<p>We can get all nodes on the particular level either in <tt class="docutils literal"><span class="pre">natural</span></tt> order:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="p">[</span><span class="n">node</span><span class="o">.</span><span class="n">path</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">wp</span><span class="o">.</span><span class="n">get_level</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="s">'natural'</span><span class="p">)]</span>
<span class="go">['aaa', 'aad', 'ada', 'add', 'daa', 'dad', 'dda', 'ddd']</span>
</pre></div>
</div>
<p>or sorted based on the band frequency (<tt class="docutils literal"><span class="pre">freq</span></tt>):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="p">[</span><span class="n">node</span><span class="o">.</span><span class="n">path</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">wp</span><span class="o">.</span><span class="n">get_level</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="s">'freq'</span><span class="p">)]</span>
<span class="go">['aaa', 'aad', 'add', 'ada', 'dda', 'ddd', 'dad', 'daa']</span>
</pre></div>
</div>
<p>Note that <a title="pywt.WaveletPacket.get_level" class="reference external" href="../ref/wavelet-packets.html#pywt.WaveletPacket.get_level"><tt class="xref docutils literal"><span class="pre">WaveletPacket.get_level()</span></tt></a> also performs automatic decomposition
until it reaches the specified <em>level</em>.</p>
</div>
</div>
<div class="section" id="reconstructing-data-from-wavelet-packets">
<h2>Reconstructing data from Wavelet Packets:<a class="headerlink" href="#reconstructing-data-from-wavelet-packets" title="Permalink to this headline">¶</a></h2>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<p>Now create a new <a title="pywt.WaveletPacket" class="reference external" href="../ref/wavelet-packets.html#pywt.WaveletPacket"><tt class="xref docutils literal"><span class="pre">Wavelet</span> <span class="pre">Packet</span></tt></a> and set it’s nodes with
some data.</p>
<blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">new_wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">new_wp</span><span class="p">[</span><span class="s">'aa'</span><span class="p">]</span> <span class="o">=</span> <span class="n">wp</span><span class="p">[</span><span class="s">'aa'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span>
<span class="gp">>>> </span><span class="n">new_wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">]</span>
</pre></div>
</div>
</blockquote>
<p>For convenience, <tt class="xref docutils literal"><span class="pre">Node.data</span></tt> gets automatically extracted from the
<a title="pywt.Node" class="reference external" href="../ref/wavelet-packets.html#pywt.Node"><tt class="xref docutils literal"><span class="pre">Node</span></tt></a> object:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">new_wp</span><span class="p">[</span><span class="s">'d'</span><span class="p">]</span> <span class="o">=</span> <span class="n">wp</span><span class="p">[</span><span class="s">'d'</span><span class="p">]</span>
</pre></div>
</div>
<p>And reconstruct the data from the <tt class="docutils literal"><span class="pre">aa</span></tt>, <tt class="docutils literal"><span class="pre">ad</span></tt> and <tt class="docutils literal"><span class="pre">d</span></tt> packets.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">new_wp</span><span class="o">.</span><span class="n">reconstruct</span><span class="p">(</span><span class="n">update</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="go">[ 1. 2. 3. 4. 5. 6. 7. 8.]</span>
</pre></div>
</div>
<p>If the <em>update</em> param in the reconstruct method is set to <tt class="xref docutils literal"><span class="pre">False</span></tt>, the node’s
<tt class="xref docutils literal"><span class="pre">data</span></tt> will not be updated.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">new_wp</span><span class="o">.</span><span class="n">data</span>
<span class="go">None</span>
</pre></div>
</div>
<p>Otherwise, the <tt class="xref docutils literal"><span class="pre">data</span></tt> attribute will be set to the reconstructed
value.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">new_wp</span><span class="o">.</span><span class="n">reconstruct</span><span class="p">(</span><span class="n">update</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="go">[ 1. 2. 3. 4. 5. 6. 7. 8.]</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">new_wp</span><span class="o">.</span><span class="n">data</span>
<span class="go">[ 1. 2. 3. 4. 5. 6. 7. 8.]</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="p">[</span><span class="n">n</span><span class="o">.</span><span class="n">path</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">new_wp</span><span class="o">.</span><span class="n">get_leaf_nodes</span><span class="p">(</span><span class="bp">False</span><span class="p">)]</span>
<span class="go">['aa', 'ad', 'd']</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="p">[</span><span class="n">n</span><span class="o">.</span><span class="n">path</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">new_wp</span><span class="o">.</span><span class="n">get_leaf_nodes</span><span class="p">(</span><span class="bp">True</span><span class="p">)]</span>
<span class="go">['aaa', 'aad', 'ada', 'add', 'daa', 'dad', 'dda', 'ddd']</span>
</pre></div>
</div>
</div>
<div class="section" id="removing-nodes-from-wavelet-packet-tree">
<h2>Removing nodes from Wavelet Packet tree:<a class="headerlink" href="#removing-nodes-from-wavelet-packet-tree" title="Permalink to this headline">¶</a></h2>
<p>Let’s create a sample data:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<p>First, start with a tree decomposition at level 2. Leaf nodes in the tree are:</p>
<blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">dummy</span> <span class="o">=</span> <span class="n">wp</span><span class="o">.</span><span class="n">get_level</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">wp</span><span class="o">.</span><span class="n">get_leaf_nodes</span><span class="p">(</span><span class="bp">False</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">print</span> <span class="n">n</span><span class="o">.</span><span class="n">path</span><span class="p">,</span> <span class="n">format_array</span><span class="p">(</span><span class="n">n</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="go">aa [ 5. 13.]</span>
<span class="go">ad [-2. -2.]</span>
<span class="go">da [-1. -1.]</span>
<span class="go">dd [ 0. 0.]</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">node</span> <span class="o">=</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="n">node</span>
<span class="go">ad: [-2. -2.]</span>
</pre></div>
</div>
</blockquote>
<p>To remove a node from the WP tree, use Python’s <cite>del obj[x]</cite>
(<tt class="xref docutils literal"><span class="pre">Node.__delitem__</span></tt>):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">del</span> <span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span>
</pre></div>
</div>
<p>The leaf nodes that left in the tree are:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">wp</span><span class="o">.</span><span class="n">get_leaf_nodes</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">print</span> <span class="n">n</span><span class="o">.</span><span class="n">path</span><span class="p">,</span> <span class="n">format_array</span><span class="p">(</span><span class="n">n</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="go">aa [ 5. 13.]</span>
<span class="go">da [-1. -1.]</span>
<span class="go">dd [ 0. 0.]</span>
</pre></div>
</div>
<p>And the reconstruction is:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">reconstruct</span><span class="p">()</span>
<span class="go">[ 2. 3. 2. 3. 6. 7. 6. 7.]</span>
</pre></div>
</div>
<p>Now restore the deleted node value.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">wp</span><span class="p">[</span><span class="s">'ad'</span><span class="p">]</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">data</span>
</pre></div>
</div>
<p>Printing leaf nodes and tree reconstruction confirms the original state of the
tree:</p>
<blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">wp</span><span class="o">.</span><span class="n">get_leaf_nodes</span><span class="p">(</span><span class="bp">False</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">print</span> <span class="n">n</span><span class="o">.</span><span class="n">path</span><span class="p">,</span> <span class="n">format_array</span><span class="p">(</span><span class="n">n</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="go">aa [ 5. 13.]</span>
<span class="go">ad [-2. -2.]</span>
<span class="go">da [-1. -1.]</span>
<span class="go">dd [ 0. 0.]</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">reconstruct</span><span class="p">()</span>
<span class="go">[ 1. 2. 3. 4. 5. 6. 7. 8.]</span>
</pre></div>
</div>
</blockquote>
</div>
<div class="section" id="lazy-eveluation">
<h2>Lazy eveluation:<a class="headerlink" href="#lazy-eveluation" title="Permalink to this headline">¶</a></h2>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">This section is for demonstration of pywt internals purposes
only. Do not rely on the attribute access to nodes as presented in
this example.</p>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">wp</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">WaveletPacket</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">wavelet</span><span class="o">=</span><span class="s">'db1'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sym'</span><span class="p">)</span>
</pre></div>
</div>
<ol class="arabic">
<li><p class="first">At first the wp’s attribute <cite>a</cite> is None</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">a</span>
<span class="go">None</span>
</pre></div>
</div>
<p><strong>Remember that you should not rely on the attribute access.</strong></p>
</li>
<li><p class="first">At first attempt to access the node it is computed via decomposition
of it’s parent node (the wp object itself).</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="p">[</span><span class="s">'a'</span><span class="p">]</span>
<span class="go">a: [ 2.12132034 4.94974747 7.77817459 10.60660172]</span>
</pre></div>
</div>
</li>
<li><p class="first">Now the <cite>wp.a</cite> is set to the newly created node:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">a</span>
<span class="go">a: [ 2.12132034 4.94974747 7.77817459 10.60660172]</span>
</pre></div>
</div>
<p>And so is <cite>wp.d</cite>:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="n">wp</span><span class="o">.</span><span class="n">d</span>
<span class="go">d: [-0.70710678 -0.70710678 -0.70710678 -0.70710678]</span>
</pre></div>
</div>
</li>
</ol>
</div>
</div>
</div>
</div>
</div>
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<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference external" href="#">Wavelet Packets</a><ul>
<li><a class="reference external" href="#import-pywt">Import pywt</a></li>
<li><a class="reference external" href="#create-wavelet-packet-structure">Create Wavelet Packet structure</a></li>
<li><a class="reference external" href="#traversing-wp-tree">Traversing WP tree:</a><ul>
<li><a class="reference external" href="#accessing-subnodes">Accessing subnodes:</a></li>
<li><a class="reference external" href="#accessing-node-s-attributes">Accessing Node’s attributes:</a></li>
<li><a class="reference external" href="#collecting-nodes">Collecting nodes</a></li>
</ul>
</li>
<li><a class="reference external" href="#reconstructing-data-from-wavelet-packets">Reconstructing data from Wavelet Packets:</a></li>
<li><a class="reference external" href="#removing-nodes-from-wavelet-packet-tree">Removing nodes from Wavelet Packet tree:</a></li>
<li><a class="reference external" href="#lazy-eveluation">Lazy eveluation:</a></li>
</ul>
</li>
</ul>
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