blob: 0890934e81d750569286bdb71fc5cd87afad55e8 [file] [log] [blame]
<!DOCTYPE html>
<html class="writer-html5" lang="en" >
<head>
<meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>CountMin Sketch &mdash; datasketches 0.1 documentation</title>
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<!--[if lt IE 9]>
<script src="_static/js/html5shiv.min.js"></script>
<![endif]-->
<script src="_static/jquery.js"></script>
<script src="_static/_sphinx_javascript_frameworks_compat.js"></script>
<script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/sphinx_highlight.js"></script>
<script src="_static/js/theme.js"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="prev" title="Frequent Items" href="frequent_items.html" />
</head>
<body class="wy-body-for-nav">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search" >
<a href="index.html" class="icon icon-home">
datasketches
</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" aria-label="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="Navigation menu">
<ul>
<li class="toctree-l1"><a class="reference internal" href="hyper_log_log.html">HyperLogLog</a></li>
<li class="toctree-l1"><a class="reference internal" href="cpc.html">Compressed Probabilistic Counting (CPC)</a></li>
<li class="toctree-l1"><a class="reference internal" href="theta.html">Theta Sketch</a></li>
</ul>
<ul>
<li class="toctree-l1"><a class="reference internal" href="kll.html">KLL Sketch</a></li>
</ul>
<ul>
<li class="toctree-l1"><a class="reference internal" href="frequent_items.html">Frequent Items</a></li>
</ul>
<ul class="current">
<li class="toctree-l1 current"><a class="current reference internal" href="#">CountMin Sketch</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#datasketches.count_min_sketch"><code class="docutils literal notranslate"><span class="pre">count_min_sketch</span></code></a><ul>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.deserialize"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.deserialize()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_estimate"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_estimate()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_lower_bound"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_lower_bound()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_num_buckets"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_num_buckets()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_num_hashes"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_num_hashes()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_relative_error"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_relative_error()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_seed"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_seed()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_serialized_size_bytes"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_serialized_size_bytes()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_total_weight"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_total_weight()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.get_upper_bound"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.get_upper_bound()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.is_empty"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.is_empty()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.merge"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.merge()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.serialize"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.serialize()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.suggest_num_buckets"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.suggest_num_buckets()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.suggest_num_hashes"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.suggest_num_hashes()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.to_string"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.to_string()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#datasketches.count_min_sketch.update"><code class="docutils literal notranslate"><span class="pre">count_min_sketch.update()</span></code></a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="index.html">datasketches</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="Page navigation">
<ul class="wy-breadcrumbs">
<li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
<li class="breadcrumb-item active">CountMin Sketch</li>
<li class="wy-breadcrumbs-aside">
<a href="_sources/frequency_estimation.rst.txt" rel="nofollow"> View page source</a>
</li>
</ul>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<section id="countmin-sketch">
<h1>CountMin Sketch<a class="headerlink" href="#countmin-sketch" title="Permalink to this heading"></a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="datasketches.count_min_sketch">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">_datasketches.</span></span><span class="sig-name descname"><span class="pre">count_min_sketch</span></span><a class="headerlink" href="#datasketches.count_min_sketch" title="Permalink to this definition"></a></dt>
<dd><dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.deserialize">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">deserialize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bytes</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></span><a class="headerlink" href="#datasketches.count_min_sketch.deserialize" title="Permalink to this definition"></a></dt>
<dd><p>Reads a bytes object and returns the corresponding count_min_sketch</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_estimate">
<span class="sig-name descname"><span class="pre">get_estimate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#datasketches.count_min_sketch.get_estimate" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded function.</p>
<ol class="arabic simple">
<li><p>get_estimate(self: _datasketches.count_min_sketch, item: int) -&gt; float</p></li>
</ol>
<p>Returns an estimate of the frequency of the provided 64-bit integer value</p>
<ol class="arabic simple" start="2">
<li><p>get_estimate(self: _datasketches.count_min_sketch, item: str) -&gt; float</p></li>
</ol>
<p>Returns an estimate of the frequency of the provided string</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_lower_bound">
<span class="sig-name descname"><span class="pre">get_lower_bound</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#datasketches.count_min_sketch.get_lower_bound" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded function.</p>
<ol class="arabic simple">
<li><p>get_lower_bound(self: _datasketches.count_min_sketch, item: int) -&gt; float</p></li>
</ol>
<p>Returns an lower bound on the estimate for the given 64-bit integer value</p>
<ol class="arabic simple" start="2">
<li><p>get_lower_bound(self: _datasketches.count_min_sketch, item: str) -&gt; float</p></li>
</ol>
<p>Returns an lower bound on the estimate for the provided string</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_num_buckets">
<span class="sig-name descname"><span class="pre">get_num_buckets</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.get_num_buckets" title="Permalink to this definition"></a></dt>
<dd><p>Returns the configured number of buckets for the sketch</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_num_hashes">
<span class="sig-name descname"><span class="pre">get_num_hashes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.get_num_hashes" title="Permalink to this definition"></a></dt>
<dd><p>Returns the configured number of hashes for the sketch</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_relative_error">
<span class="sig-name descname"><span class="pre">get_relative_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.get_relative_error" title="Permalink to this definition"></a></dt>
<dd><p>Returns the maximum permissible error for any frequency estimate query</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_seed">
<span class="sig-name descname"><span class="pre">get_seed</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.get_seed" title="Permalink to this definition"></a></dt>
<dd><p>Returns the base hash seed for the sketch</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_serialized_size_bytes">
<span class="sig-name descname"><span class="pre">get_serialized_size_bytes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.get_serialized_size_bytes" title="Permalink to this definition"></a></dt>
<dd><p>Returns the size in bytes of the serialized image of the sketch</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_total_weight">
<span class="sig-name descname"><span class="pre">get_total_weight</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.get_total_weight" title="Permalink to this definition"></a></dt>
<dd><p>Returns the total weight currently inserted into the stream</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.get_upper_bound">
<span class="sig-name descname"><span class="pre">get_upper_bound</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#datasketches.count_min_sketch.get_upper_bound" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded function.</p>
<ol class="arabic simple">
<li><p>get_upper_bound(self: _datasketches.count_min_sketch, item: int) -&gt; float</p></li>
</ol>
<p>Returns an upper bound on the estimate for the given 64-bit integer value</p>
<ol class="arabic simple" start="2">
<li><p>get_upper_bound(self: _datasketches.count_min_sketch, item: str) -&gt; float</p></li>
</ol>
<p>Returns an upper bound on the estimate for the provided string</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.is_empty">
<span class="sig-name descname"><span class="pre">is_empty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.is_empty" title="Permalink to this definition"></a></dt>
<dd><p>Returns True if the sketch has seen no items, otherwise False</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.merge">
<span class="sig-name descname"><span class="pre">merge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">other</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.merge" title="Permalink to this definition"></a></dt>
<dd><p>Merges the provided other sketch into this one</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.serialize">
<span class="sig-name descname"><span class="pre">serialize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bytes</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.serialize" title="Permalink to this definition"></a></dt>
<dd><p>Serializes the sketch into a bytes object</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.suggest_num_buckets">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">suggest_num_buckets</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">relative_error</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.suggest_num_buckets" title="Permalink to this definition"></a></dt>
<dd><p>Suggests the number of buckets needed to achieve an accuracy within the provided relative_error. For example, when relative_error = 0.05, the returned frequency estimates satisfy the ‘relative_error’ guarantee that never overestimates the weights but may underestimate the weights by 5% of the total weight in the sketch. Returns the number of hash buckets at every level of the sketch required in order to obtain the specified relative error.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.suggest_num_hashes">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">suggest_num_hashes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">confidence</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.suggest_num_hashes" title="Permalink to this definition"></a></dt>
<dd><p>Suggests the number of hashes needed to achieve the provided confidence. For example, with 95% confidence, frequency estimates satisfy the ‘relative_error’ guarantee. Returns the number of hash functions that are required in order to achieve the specified confidence of the sketch. confidence = 1 - delta, with delta denoting the sketch failure probability.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.to_string">
<span class="sig-name descname"><span class="pre">to_string</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#datasketches.count_min_sketch" title="_datasketches.count_min_sketch"><span class="pre">_datasketches.count_min_sketch</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="headerlink" href="#datasketches.count_min_sketch.to_string" title="Permalink to this definition"></a></dt>
<dd><p>Produces a string summary of the sketch</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="datasketches.count_min_sketch.update">
<span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#datasketches.count_min_sketch.update" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded function.</p>
<ol class="arabic simple">
<li><p>update(self: _datasketches.count_min_sketch, item: int, weight: float = 1.0) -&gt; None</p></li>
</ol>
<p>Updates the sketch with the given 64-bit integer value</p>
<ol class="arabic simple" start="2">
<li><p>update(self: _datasketches.count_min_sketch, item: str, weight: float = 1.0) -&gt; None</p></li>
</ol>
<p>Updates the sketch with the given string</p>
</dd></dl>
</dd></dl>
</section>
</div>
</div>
<footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
<a href="frequent_items.html" class="btn btn-neutral float-left" title="Frequent Items" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
</div>
<hr/>
<div role="contentinfo">
<p>&#169; Copyright 2023, charlie.</p>
</div>
Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
<a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
provided by <a href="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<script>
jQuery(function () {
SphinxRtdTheme.Navigation.enable(true);
});
</script>
</body>
</html>