1
0
Fork 0
Old engine for Continuous Time Bayesian Networks. Superseded by reCTBN. 🐍 https://github.com/madlabunimib/PyCTBN
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
This repo is archived. You can view files and clone it, but cannot push or open issues/pull-requests.
PyCTBN/docs/PyCTBN.PyCTBN.optimizers.html

338 lines
23 KiB

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xml:lang="" lang="" version="-//W3C//DTD XHTML 1.1//EN" xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>PyCTBN.PyCTBN.optimizers package &mdash; PyCTBN 2.0 documentation</title>
<link href='https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic|Roboto+Slab:400,700|Inconsolata:400,700' rel='stylesheet' type='text/css'/>
<link rel="stylesheet" href="_static/css/pdj.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="_static/css/pdj.css" type="text/css" />
<link rel="index" title="Index"
href="genindex.html"/>
<link rel="search" title="Search" href="search.html"/>
<link rel="top" title="PyCTBN 2.0 documentation" href="index.html"/>
<link rel="up" title="PyCTBN.PyCTBN package" href="PyCTBN.PyCTBN.html"/>
<link rel="next" title="PyCTBN.PyCTBN.structure_graph package" href="PyCTBN.PyCTBN.structure_graph.html"/>
<link rel="prev" title="PyCTBN.PyCTBN.estimators package" href="PyCTBN.PyCTBN.estimators.html"/>
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
<meta http-equiv="cache-control" content="public" />
<meta name="robots" content="follow, all" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<!-- Add jQuery library -->
<script type="text/javascript" src="http://code.jquery.com/jquery-latest.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/modernizr/2.6.2/modernizr.min.js"></script>
</head>
<body class="wy-body-for-nav" role="document">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-nav-search">
<a href="index.html" class="fa fa-home"> PyCTBN </a>
<div role="search">
<form id ="rtd-search-form" class="wy-form"
action="search.html" method="get">
<input type="text" name="q" placeholder="Search docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<p class="caption"><span class="caption-text">Contents:</span></p>
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="PyCTBN.PyCTBN.html">PyCTBN.PyCTBN package</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="PyCTBN.PyCTBN.html#subpackages">Subpackages</a></li>
<li class="toctree-l2"><a class="reference internal" href="PyCTBN.PyCTBN.html#module-PyCTBN.PyCTBN">Module contents</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a><ul>
<li class="toctree-l2"><a class="reference internal" href="examples.html#installation-usage">Installation/Usage</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#implementing-your-own-data-importer">Implementing your own data importer</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#parameters-estimation-example">Parameters Estimation Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#structure-estimation-example">Structure Estimation Example</a></li>
</ul>
</li>
</ul>
</div>
&nbsp;
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">
<nav class="wy-nav-top" id="barra-mobile" role="navigation" aria-label="top navigation">
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="#">Porão do Juca</a>
</nav>
<div class="wy-nav-content">
<div class="fundo-claro">
</div>
<div class="fundo-escuro">
</div>
<div class="rst-content">
<div role="navigation" aria-label="breadcrumbs navigation">
<!-- <ul class="wy-breadcrumbs"> -->
<!-- <li><a href="#">Docs</a> &raquo;</li> -->
<!-- <li>Features</li> -->
<!-- <li class="wy-breadcrumbs-aside"> -->
<!-- <a href="_sources/index.txt" rel="nofollow"> View page source</a> -->
<!-- </li> -->
<!-- </ul> -->
<!-- <hr/> -->
</div>
<div role="main" class="">
<div id="content" class="hfeed entry-container hentry">
<div class="section" id="pyctbn-pyctbn-optimizers-package">
<h1>PyCTBN.PyCTBN.optimizers package<a class="headerlink" href="#pyctbn-pyctbn-optimizers-package" title="Permalink to this headline"></a></h1>
<div class="section" id="submodules">
<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline"></a></h2>
</div>
<div class="section" id="module-PyCTBN.PyCTBN.optimizers.constraint_based_optimizer">
<span id="pyctbn-pyctbn-optimizers-constraint-based-optimizer-module"></span><h2>PyCTBN.PyCTBN.optimizers.constraint_based_optimizer module<a class="headerlink" href="#module-PyCTBN.PyCTBN.optimizers.constraint_based_optimizer" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.constraint_based_optimizer.ConstraintBasedOptimizer">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">PyCTBN.PyCTBN.optimizers.constraint_based_optimizer.</span></span><span class="sig-name descname"><span class="pre">ConstraintBasedOptimizer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node_id</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure_estimator</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><a class="reference internal" href="PyCTBN.PyCTBN.estimators.html#PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator" title="PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator"><span class="pre">PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">tot_vars_count</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.constraint_based_optimizer.ConstraintBasedOptimizer" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#PyCTBN.PyCTBN.optimizers.optimizer.Optimizer" title="PyCTBN.PyCTBN.optimizers.optimizer.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyCTBN.PyCTBN.optimizers.optimizer.Optimizer</span></code></a></p>
<p>Optimizer class that implement a CTPC Algorithm</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>node_id</strong> (<em>string</em>) – current node’s id</p></li>
<li><p><strong>structure_estimator</strong> (<em>class:'StructureEstimator'</em>) – a structure estimator object with the information about the net</p></li>
<li><p><strong>tot_vars_count</strong> (<em>int</em>) – number of variables in the dataset</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.constraint_based_optimizer.ConstraintBasedOptimizer.optimize_structure">
<span class="sig-name descname"><span class="pre">optimize_structure</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.constraint_based_optimizer.ConstraintBasedOptimizer.optimize_structure" title="Permalink to this definition"></a></dt>
<dd><p>Compute Optimization process for a structure_estimator by using a CTPC Algorithm</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>the estimated structure for the node</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>List</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="module-PyCTBN.PyCTBN.optimizers.hill_climbing_search">
<span id="pyctbn-pyctbn-optimizers-hill-climbing-search-module"></span><h2>PyCTBN.PyCTBN.optimizers.hill_climbing_search module<a class="headerlink" href="#module-PyCTBN.PyCTBN.optimizers.hill_climbing_search" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.hill_climbing_search.HillClimbing">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">PyCTBN.PyCTBN.optimizers.hill_climbing_search.</span></span><span class="sig-name descname"><span class="pre">HillClimbing</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node_id</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure_estimator</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><a class="reference internal" href="PyCTBN.PyCTBN.estimators.html#PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator" title="PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator"><span class="pre">PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_parents</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">iterations_number</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">40</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">patience</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.hill_climbing_search.HillClimbing" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#PyCTBN.PyCTBN.optimizers.optimizer.Optimizer" title="PyCTBN.PyCTBN.optimizers.optimizer.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyCTBN.PyCTBN.optimizers.optimizer.Optimizer</span></code></a></p>
<p>Optimizer class that implement Hill Climbing Search</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>node_id</strong> (<em>string</em>) – current node’s id</p></li>
<li><p><strong>structure_estimator</strong> (<em>class:'StructureEstimator'</em>) – a structure estimator object with the information about the net</p></li>
<li><p><strong>max_parents</strong> (<em>int</em><em>, </em><em>optional</em>) – maximum number of parents for each variable. If None, disabled, default to None</p></li>
<li><p><strong>iterations_number</strong> (<em>int</em><em>, </em><em>optional</em>) – maximum number of optimization algorithm’s iteration, default to 40</p></li>
<li><p><strong>patience</strong> (<em>int</em><em>, </em><em>optional</em>) – number of iteration without any improvement before to stop the search.If None, disabled, default to None</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.hill_climbing_search.HillClimbing.optimize_structure">
<span class="sig-name descname"><span class="pre">optimize_structure</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; <span class="pre">List</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.hill_climbing_search.HillClimbing.optimize_structure" title="Permalink to this definition"></a></dt>
<dd><p>Compute Optimization process for a structure_estimator by using a Hill Climbing Algorithm</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>the estimated structure for the node</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>List</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="module-PyCTBN.PyCTBN.optimizers.optimizer">
<span id="pyctbn-pyctbn-optimizers-optimizer-module"></span><h2>PyCTBN.PyCTBN.optimizers.optimizer module<a class="headerlink" href="#module-PyCTBN.PyCTBN.optimizers.optimizer" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.optimizer.Optimizer">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">PyCTBN.PyCTBN.optimizers.optimizer.</span></span><span class="sig-name descname"><span class="pre">Optimizer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node_id</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure_estimator</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><a class="reference internal" href="PyCTBN.PyCTBN.estimators.html#PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator" title="PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator"><span class="pre">PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.optimizer.Optimizer" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">abc.ABC</span></code></p>
<p>Interface class for all the optimizer’s child PyCTBN</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>node_id</strong> (<em>string</em>) – the node label</p></li>
<li><p><strong>structure_estimator</strong> (<em>class:'StructureEstimator'</em>) – A structureEstimator Object to predict the structure</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.optimizer.Optimizer.optimize_structure">
<em class="property"><span class="pre">abstract</span> </em><span class="sig-name descname"><span class="pre">optimize_structure</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; <span class="pre">List</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.optimizer.Optimizer.optimize_structure" title="Permalink to this definition"></a></dt>
<dd><p>Compute Optimization process for a structure_estimator</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>the estimated structure for the node</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>List</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="module-PyCTBN.PyCTBN.optimizers.tabu_search">
<span id="pyctbn-pyctbn-optimizers-tabu-search-module"></span><h2>PyCTBN.PyCTBN.optimizers.tabu_search module<a class="headerlink" href="#module-PyCTBN.PyCTBN.optimizers.tabu_search" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.tabu_search.TabuSearch">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">PyCTBN.PyCTBN.optimizers.tabu_search.</span></span><span class="sig-name descname"><span class="pre">TabuSearch</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node_id</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">structure_estimator</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><a class="reference internal" href="PyCTBN.PyCTBN.estimators.html#PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator" title="PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator"><span class="pre">PyCTBN.PyCTBN.estimators.structure_estimator.StructureEstimator</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_parents</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">iterations_number</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">40</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">patience</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tabu_length</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span> <span class="o"><span class="pre">=</span></span> <span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tabu_rules_duration</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.tabu_search.TabuSearch" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#PyCTBN.PyCTBN.optimizers.optimizer.Optimizer" title="PyCTBN.PyCTBN.optimizers.optimizer.Optimizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyCTBN.PyCTBN.optimizers.optimizer.Optimizer</span></code></a></p>
<p>Optimizer class that implement Tabu Search</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>node_id</strong> (<em>string</em>) – current node’s id</p></li>
<li><p><strong>structure_estimator</strong> (<em>class:'StructureEstimator'</em>) – a structure estimator object with the information about the net</p></li>
<li><p><strong>max_parents</strong> (<em>int</em><em>, </em><em>optional</em>) – maximum number of parents for each variable. If None, disabled, default to None</p></li>
<li><p><strong>iterations_number</strong> (<em>int</em><em>, </em><em>optional</em>) – maximum number of optimization algorithm’s iteration, default to 40</p></li>
<li><p><strong>patience</strong> (<em>int</em><em>, </em><em>optional</em>) – number of iteration without any improvement before to stop the search.If None, disabled, default to None</p></li>
<li><p><strong>tabu_length</strong> (<em>int</em><em>, </em><em>optional</em>) – maximum lenght of the data structures used in the optimization process, default to None</p></li>
<li><p><strong>tabu_rules_duration</strong> (<em>int</em><em>, </em><em>optional</em>) – number of iterations in which each rule keeps its value, default to None</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="PyCTBN.PyCTBN.optimizers.tabu_search.TabuSearch.optimize_structure">
<span class="sig-name descname"><span class="pre">optimize_structure</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; <span class="pre">List</span><a class="headerlink" href="#PyCTBN.PyCTBN.optimizers.tabu_search.TabuSearch.optimize_structure" title="Permalink to this definition"></a></dt>
<dd><p>Compute Optimization process for a structure_estimator by using a Hill Climbing Algorithm</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>the estimated structure for the node</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>List</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="module-PyCTBN.PyCTBN.optimizers">
<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-PyCTBN.PyCTBN.optimizers" title="Permalink to this headline"></a></h2>
</div>
</div>
</div>
<footer>
<div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
<a href="PyCTBN.PyCTBN.structure_graph.html" class="btn btn-neutral float-right" title="PyCTBN.PyCTBN.structure_graph package">Next <span class="fa fa-arrow-circle-right"></span></a>
<a href="PyCTBN.PyCTBN.estimators.html" class="btn btn-neutral" title="PyCTBN.PyCTBN.estimators package"><span class="fa fa-arrow-circle-left"></span> Previous</a>
</div>
<hr/>
<div role="contentinfo">
<p>
&copy; Copyright 2021, Bregoli Alessandro, Martini Filippo, Moretti Luca.
</p>
</div>
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/jucacrispim/sphinx_pdj_theme">theme</a> provided by <a href="http://poraodojuca.net">Porão do Juca</a>.
</footer>
</div>
</div>
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT:'./',
VERSION:'2.0',
COLLAPSE_INDEX:false,
FILE_SUFFIX:'.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="_static/documentation_options.js">
</script>
<script type="text/javascript" src="_static/jquery.js">
</script>
<script type="text/javascript" src="_static/underscore.js">
</script>
<script type="text/javascript" src="_static/doctools.js">
</script>
<script type="text/javascript"
src="_static/js/theme.js"></script>
<script type="text/javascript"
src="_static/js/pdj.js"></script>
<script type="text/javascript">
jQuery(function () {
SphinxRtdTheme.StickyNav.enable();
});
</script>
</body>
</html>