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<div class="quarto-title">
<h1 class="title">References</h1>
</div>
<div class="quarto-title-meta">
</div>
</header>
<p>Consider the <em>mutable</em> Objects we have been working with in this course: Lists, Tuples, Dictionaries, DataFrames, and Series. In our style of writing code, we have been modifying our data structures as we go, like this:</p>
<div id="ab524a14" class="cell" data-execution_count="1">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> [<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>]</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>a.append(<span class="dv">4</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(a)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>[1, 2, 3, 4]</code></pre>
</div>
</div>
<p>However, consider the following pattern in which we assign <code>b</code> to <code>a</code> and then perform the append method on <code>b</code>.</p>
<div id="ad7c0f99" class="cell" data-execution_count="2">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> [<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>]</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>b <span class="op">=</span> a</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>b.append(<span class="dv">4</span>)</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(b)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>[1, 2, 3, 4]</code></pre>
</div>
</div>
<p>Let’s look at <code>a</code> also:</p>
<div id="c6893f38" class="cell" data-execution_count="3">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(a)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>[1, 2, 3, 4]</code></pre>
</div>
</div>
<p>Strange, <code>a</code> was modified also! What’s going on?</p>
<section id="assignment-by-reference" class="level2">
<h2 class="anchored" data-anchor-id="assignment-by-reference">Assignment by Reference</h2>
<p>When we created the variable <code>a</code> to equal the list <code>[1, 2, 3]</code>, it is tempting to say, “the variable ‘a’ is a list with value [1, 2, 3]”, but that is technically incorrect!</p>
<p>The correct way: “the variable ‘a’ is a <strong>reference</strong> to a list with value [1, 2, 3]”.</p>
<p>We now make a distinction between the variable and the object: the variable gives the <strong>reference</strong> information to the object, and other variables can reference the same object also! When we evaluated <code>b = a</code>, we told <code>b</code> to reference thee same object as <code>a</code>, so modifying <code>b</code> modified <code>a</code> also.</p>
<p>This <strong>reference</strong> information tells us where the object is stored in the working memory of the computer, usually in the address form of a number.</p>
<p>Let’s see this in action:</p>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=a%20%3D%20%5B1,%202,%203%5D%0Ab%20%3D%20a%0Ab.append%284%29&codeDivHeight=400&codeDivWidth=350&cumulative=false&curInstr=0&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" <="" iframe="">
<p>If it doesn’t load properly, here is the <a href="https://pythontutor.com/render.html#code=a%20%3D%20%5B1,%202,%203%5D%0Ab%20%3D%20a%0Ab.append%284%29&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false">link</a>.</p>
<p>What is happening behind the scenes:</p>
<ol type="1">
<li><code>a = [1, 2, 3]</code>
<ol type="1">
<li>The list with value [1, 2, 3] is created in the memory of the computer, with a particular memory address, say 999.</li>
<li>The variable <code>a</code> holds the reference to that memory address, 999.</li>
</ol></li>
<li><code>b = a</code>
<ol type="1">
<li>The variable <code>b</code> has the same memory address as <code>a</code>, 999.</li>
</ol></li>
<li><code>b.append(4)</code>
<ol type="1">
<li>Access the list that is addressed as 999 and append 4 to it.</li>
</ol></li>
<li><code>print(a)</code>, <code>print(b)</code>
<ol type="1">
<li>Both <code>a</code> and <code>b</code> have the same address and will access the same object.</li>
</ol></li>
</ol>
<p>We can look at the memory address of our variables via the <code>id()</code> function:</p>
<div id="d983fcf1" class="cell" data-execution_count="4">
<div class="sourceCode" id="cb7"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="bu">id</span>(a), <span class="bu">id</span>(b)</span></code></pre></div>
<div class="cell-output cell-output-display" data-execution_count="73">
<pre><code>(5141501248, 5141501248)</code></pre>
</div>
</div>
<p>They are the same.</p>
<p>Here is another visual way to think about this:</p>
<p><img src="images/references.png" class="img-fluid" alt="If you imagine variables are like boxes, you can't make sense of assignment in Python; instead, think of variables as sticky notes. Image source: Fluent Python, Chapter 8." />If you imagine variables are like boxes, you can’t make sense of assignment in Python; instead, think of variables as sticky notes. Image source: Fluent Python, Chapter 8.</p>
<section id="an-object-isnt-unique" class="level3">
<h3>An object isn’t unique</h3>
<p>Let’s see another example, using Dictionaries this time:</p>
<div id="f9720bf0" class="cell" data-execution_count="5">
<div class="sourceCode" id="cb9"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>charles <span class="op">=</span> {<span class="st">'name'</span>: <span class="st">'Charles L. Dodgson'</span>, <span class="st">'born'</span>: <span class="dv">1832</span>}</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>lewis <span class="op">=</span> charles</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="bu">id</span>(charles), <span class="bu">id</span>(lewis)</span></code></pre></div>
<div class="cell-output cell-output-display" data-execution_count="74">
<pre><code>(4395375360, 4395375360)</code></pre>
</div>
</div>
<div id="aa2c7ea3" class="cell" data-execution_count="6">
<div class="sourceCode" id="cb11"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>lewis[<span class="st">'balance'</span>] <span class="op">=</span> <span class="dv">950</span></span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>charles</span></code></pre></div>
<div class="cell-output cell-output-display" data-execution_count="75">
<pre><code>{'name': 'Charles L. Dodgson', 'born': 1832, 'balance': 950}</code></pre>
</div>
</div>
<p>As expected, we see that Charles also has a balance of 950, because both variables have the same reference to the same object.</p>
<p>Now, suppose we create a variable <code>alex</code> with a reference to a dictionary with the <em>same value</em>:</p>
<div id="38ee004e" class="cell" data-execution_count="7">
<div class="sourceCode" id="cb13"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>alex <span class="op">=</span> {<span class="st">'name'</span>: <span class="st">'Charles L. Dodgson'</span>, <span class="st">'born'</span>: <span class="dv">1832</span>, <span class="st">'balance'</span>: <span class="dv">950</span>}</span></code></pre></div>
</div>
<p>What do we expect?</p>
<div id="03030a37" class="cell" data-execution_count="8">
<div class="sourceCode" id="cb14"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="bu">id</span>(lewis), <span class="bu">id</span>(charles), <span class="bu">id</span>(alex)</span></code></pre></div>
<div class="cell-output cell-output-display" data-execution_count="77">
<pre><code>(4395375360, 4395375360, 4395006976)</code></pre>
</div>
</div>
<p>This shows that you can have objects of the same values, that is:</p>
<div id="399f2cc6" class="cell" data-execution_count="9">
<div class="sourceCode" id="cb16"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>lewis <span class="op">==</span> alex</span></code></pre></div>
<div class="cell-output cell-output-display" data-execution_count="78">
<pre><code>True</code></pre>
</div>
</div>
<p>but they are distinct objects that are stored in a different part of the memory. Therefore you can modify <code>alex</code>, but <code>lewis</code> and <code>charles</code> won’t be changed.</p>
<p>Let’s see this step-by-step:</p>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=charles%20%3D%20%7B'name'%3A%20'Charles%20L.%20Dodgson',%20'born'%3A%201832%7D%0Alewis%20%3D%20charles%0Alewis%5B'balance'%5D%20%3D%20950%0Aalex%20%3D%20%7B'name'%3A%20'Charles%20L.%20Dodgson',%20'born'%3A%201832,%20'balance'%3A%20950%7D%0Aalex%5B'balnce'%5D%20%3D%200&codeDivHeight=400&codeDivWidth=350&cumulative=false&curInstr=0&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"
</iframe>
<p>If it doesn’t load properly, here is the <a href="https://pythontutor.com/render.html#code=charles%20%3D%20%7B'name'%3A%20'Charles%20L.%20Dodgson',%20'born'%3A%201832%7D%0Alewis%20%3D%20charles%0Alewis%5B'balance'%5D%20%3D%20950%0Aalex%20%3D%20%7B'name'%3A%20'Charles%20L.%20Dodgson',%20'born'%3A%201832,%20'balance'%3A%20950%7D%0Aalex%5B'balnce'%5D%20%3D%200&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false">link</a>.</p>
<p>Here’s another illustration of the situation:</p>
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="images/references2.png" class="img-fluid figure-img"></p>
<figcaption>If you imagine variables are like boxes, you can’t make sense of assignment in Python; instead, think of variables as sticky notes. Image source: Fluent Python, Chapter 8.</figcaption>
</figure>
</div>
</section>
<section id="copying-an-object" class="level3">
<h3 class="anchored" data-anchor-id="copying-an-object">Copying an object</h3>
<p>Sometimes, you want an actual copy of an object, not a reference to the object as we have seen before. Most objects have a <code>.copy()</code> method that will allow you to create a copy of it:</p>
<div id="abeeece7" class="cell" data-execution_count="10">
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> [<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>]</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>b <span class="op">=</span> a.copy()</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>b.append(<span class="dv">4</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Now, <code>a</code> and <code>b</code> are distinct!</p>
<div id="bd363650" class="cell" data-execution_count="11">
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"a:"</span>, a)</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"b:"</span>, b)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>a: [1, 2, 3]
b: [1, 2, 3, 4]</code></pre>
</div>
</div>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=a%20%3D%20%5B1,%202,%203%5D%0Ab%20%3D%20a.copy%28%29%0Ab.append%284%29&codeDivHeight=400&codeDivWidth=350&cumulative=false&curInstr=0&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" <="" iframe="">
<p>If it doesn’t load properly, here is the <a href="https://pythontutor.com/render.html#code=a%20%3D%20%5B1,%202,%203%5D%0Ab%20%3D%20a.copy%28%29%0Ab.append%284%29&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false">link</a>.</p>
</section>
<section id="shallow-vs.-deep-copy" class="level3">
<h3>Shallow vs. Deep copy</h3>
<p>There’s a subtle problem with making copies of an object. Recall that you can put objects within lists, such as a list within a list. Well, that list within a list is a reference, so you can get some strange, unexpected situations:</p>
<div id="2d8d3408" class="cell" data-execution_count="12">
<div class="sourceCode" id="cb21"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a>sub_list <span class="op">=</span> [<span class="st">"apple"</span>, <span class="st">"pineapple"</span>]</span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> [sub_list, <span class="dv">1</span>, <span class="dv">2</span>]</span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a>b <span class="op">=</span> a.copy()</span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a>b.append(<span class="dv">3</span>)</span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a>b[<span class="dv">0</span>].append(<span class="st">"pear"</span>)</span></code></pre></div>
</div>
<div id="440ee8fb" class="cell" data-execution_count="13">
<div class="sourceCode" id="cb22"><pre class="sourceCode python cell-code"><code class="sourceCode python"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"a:"</span>, a)</span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"b:"</span>, b)</span></code></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>a: [['apple', 'pineapple', 'pear'], 1, 2]
b: [['apple', 'pineapple', 'pear'], 1, 2, 3]</code></pre>
</div>
</div>
<p>This is strange, because <code>b</code> is a copy of <code>a</code>, yet when we appended to the sublist in <code>b</code>, it still modified <code>a</code>‘s sublist! This is because the <code>.copy()</code> still kept the sublist pointing to the same object. This is called “shallow copy”, in which any nested objects’ references are still kept the same. To ensure that we get a entire new copy for nested objects, we can make a “deep copy”, via the <code>copy.deepcopy(x)</code> function.</p>
<p>Let’s visualize what shallow copy looks like:</p>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=sub_list%20%3D%20%5B%22apple%22,%20%22pineapple%22%5D%0Aa%20%3D%20%5Bsub_list,%201,%202%5D%0A%0Ab%20%3D%20a.copy%28%29%0Ab.append%283%29%0Ab%5B0%5D.append%28%22pear%22%29&codeDivHeight=400&codeDivWidth=350&cumulative=false&curInstr=0&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe>
<p>If it doesn’t load properly, here is the <a href="https://pythontutor.com/render.html#code=sub_list%20%3D%20%5B%22apple%22,%20%22pineapple%22%5D%0Aa%20%3D%20%5Bsub_list,%201,%202%5D%0A%0Ab%20%3D%20a.copy%28%29%0Ab.append%283%29%0Ab%5B0%5D.append%28%22pear%22%29&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false">link</a>.</p>
<p>Here is how we use <code>copy.deepcopy(x)</code>:</p>
<div id="d338dbc7" class="cell" data-execution_count="14">
<div class="sourceCode cell-code" id="cb24"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> copy</span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a>sub_list <span class="op">=</span> [<span class="st">"apple"</span>, <span class="st">"pineapple"</span>]</span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> [sub_list, <span class="dv">1</span>, <span class="dv">2</span>]</span>
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb24-5"><a href="#cb24-5" aria-hidden="true" tabindex="-1"></a>b <span class="op">=</span> copy.deepcopy(a)</span>
<span id="cb24-6"><a href="#cb24-6" aria-hidden="true" tabindex="-1"></a>b.append(<span class="dv">3</span>)</span>
<span id="cb24-7"><a href="#cb24-7" aria-hidden="true" tabindex="-1"></a>b[<span class="dv">0</span>].append(<span class="st">"pear"</span>)</span>
<span id="cb24-8"><a href="#cb24-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb24-9"><a href="#cb24-9" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"a:"</span>, a)</span>
<span id="cb24-10"><a href="#cb24-10" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"b:"</span>, b)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>a: [['apple', 'pineapple'], 1, 2]
b: [['apple', 'pineapple', 'pear'], 1, 2, 3]</code></pre>
</div>
</div>
<p>Let’s visualize what shallow deep copy looks like:</p>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=import%20copy%0Asub_list%20%3D%20%5B%22apple%22,%20%22pineapple%22%5D%0Aa%20%3D%20%5Bsub_list,%201,%202%5D%0A%0Ab%20%3D%20copy.deepcopy%28a%29%0Ab.append%283%29%0Ab%5B0%5D.append%28%22pear%22%29&codeDivHeight=400&codeDivWidth=350&cumulative=false&curInstr=0&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe>
<p>If it doesn’t load properly, here is the <a href="https://pythontutor.com/render.html#code=import%20copy%0Asub_list%20%3D%20%5B%22apple%22,%20%22pineapple%22%5D%0Aa%20%3D%20%5Bsub_list,%201,%202%5D%0A%0Ab%20%3D%20copy.deepcopy%28a%29%0Ab.append%283%29%0Ab%5B0%5D.append%28%22pear%22%29&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false">link</a>.</p>
</section>
<section id="notes-on-dataframes" class="level2">
<h2 class="anchored" data-anchor-id="notes-on-dataframes">Notes on Dataframes</h2>
<p>When we work with Pandas Dataframes, variables are also assigned by reference: suppose we have a small dataframe <code>simple_df</code>:</p>
<div id="a31587b0" class="cell" data-execution_count="15">
<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> pandas <span class="im">as</span> pd</span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a>simple_df <span class="op">=</span> pd.DataFrame(data<span class="op">=</span>{<span class="st">'id'</span>: [<span class="st">"AAA"</span>, <span class="st">"BBB"</span>, <span class="st">"CCC"</span>, <span class="st">"DDD"</span>, <span class="st">"EEE"</span>],</span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a> <span class="st">'case_control'</span>: [<span class="st">"case"</span>, <span class="st">"case"</span>, <span class="st">"control"</span>, <span class="st">"control"</span>, <span class="st">"control"</span>],</span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a> <span class="st">'measurement1'</span>: [<span class="fl">2.5</span>, <span class="fl">3.5</span>, <span class="dv">9</span>, <span class="fl">.1</span>, <span class="fl">2.2</span>],</span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a> <span class="st">'measurement2'</span>: [<span class="dv">0</span>, <span class="dv">0</span>, <span class="fl">.5</span>, <span class="fl">.24</span>, <span class="fl">.003</span>],</span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a> <span class="st">'measurement3'</span>: [<span class="dv">80</span>, <span class="dv">2</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">2</span>]})</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>We assign <code>analysis_df</code> as <code>simple_df</code>, and log-transform the column “measurement1”, and see how it affects both dataframes:</p>
<div id="9de8e9a9" class="cell" data-execution_count="16">
<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>analysis_df <span class="op">=</span> simple_df</span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a>analysis_df.measurement1 <span class="op">=</span> np.log(analysis_df.measurement1)</span>
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(analysis_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 0.916291 0.000 80
1 BBB case 1.252763 0.000 2
2 CCC control 2.197225 0.500 1
3 DDD control -2.302585 0.240 1
4 EEE control 0.788457 0.003 2</code></pre>
</div>
</div>
<div id="24b93730" class="cell" data-execution_count="17">
<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(simple_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 0.916291 0.000 80
1 BBB case 1.252763 0.000 2
2 CCC control 2.197225 0.500 1
3 DDD control -2.302585 0.240 1
4 EEE control 0.788457 0.003 2</code></pre>
</div>
</div>
<p>To prevent this behavior, we can use the <a href="https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.copy.html"><code>.copy()</code></a> method:</p>
<div id="15a704ea" class="cell" data-execution_count="18">
<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a>simple_df <span class="op">=</span> pd.DataFrame(data<span class="op">=</span>{<span class="st">'id'</span>: [<span class="st">"AAA"</span>, <span class="st">"BBB"</span>, <span class="st">"CCC"</span>, <span class="st">"DDD"</span>, <span class="st">"EEE"</span>],</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a> <span class="st">'case_control'</span>: [<span class="st">"case"</span>, <span class="st">"case"</span>, <span class="st">"control"</span>, <span class="st">"control"</span>, <span class="st">"control"</span>],</span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a> <span class="st">'measurement1'</span>: [<span class="fl">2.5</span>, <span class="fl">3.5</span>, <span class="dv">9</span>, <span class="fl">.1</span>, <span class="fl">2.2</span>],</span>
<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a> <span class="st">'measurement2'</span>: [<span class="dv">0</span>, <span class="dv">0</span>, <span class="fl">.5</span>, <span class="fl">.24</span>, <span class="fl">.003</span>],</span>
<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a> <span class="st">'measurement3'</span>: [<span class="dv">80</span>, <span class="dv">2</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">2</span>]})</span>
<span id="cb31-6"><a href="#cb31-6" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb31-7"><a href="#cb31-7" aria-hidden="true" tabindex="-1"></a>analysis_df <span class="op">=</span> simple_df.copy()</span>
<span id="cb31-8"><a href="#cb31-8" aria-hidden="true" tabindex="-1"></a>analysis_df.measurement1 <span class="op">=</span> np.log(analysis_df.measurement1)</span>
<span id="cb31-9"><a href="#cb31-9" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(analysis_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 0.916291 0.000 80
1 BBB case 1.252763 0.000 2
2 CCC control 2.197225 0.500 1
3 DDD control -2.302585 0.240 1
4 EEE control 0.788457 0.003 2</code></pre>
</div>
</div>
<p>So <code>simple_df</code> does not change:</p>
<div id="5be12f5f" class="cell" data-execution_count="19">
<div class="sourceCode cell-code" id="cb33"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(simple_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 2.5 0.000 80
1 BBB case 3.5 0.000 2
2 CCC control 9.0 0.500 1
3 DDD control 0.1 0.240 1
4 EEE control 2.2 0.003 2</code></pre>
</div>
</div>
<section id="copy-vs.-reference-in-dataframe-operations-and-methods" class="level3">
<h3 class="anchored" data-anchor-id="copy-vs.-reference-in-dataframe-operations-and-methods">Copy vs. Reference in Dataframe operations and methods</h3>
<p>However, some Dataframe operations and methods will automatically give you a copy, while others give you a reference.</p>
<p>For instance, when we subset via <code>.loc</code>, it returns a copy:</p>
<div id="0506d827" class="cell" data-execution_count="20">
<div class="sourceCode cell-code" id="cb35"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a>case_df <span class="op">=</span> simple_df.loc[simple_df.case_control <span class="op">==</span> <span class="st">"case"</span>]</span>
<span id="cb35-2"><a href="#cb35-2" aria-hidden="true" tabindex="-1"></a>case_df.loc[:, <span class="st">'measurement1'</span>] <span class="op">=</span> <span class="dv">5</span></span>
<span id="cb35-3"><a href="#cb35-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(case_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 5.0 0.0 80
1 BBB case 5.0 0.0 2</code></pre>
</div>
</div>
<div id="177b9174" class="cell" data-execution_count="21">
<div class="sourceCode cell-code" id="cb37"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(simple_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 2.5 0.000 80
1 BBB case 3.5 0.000 2
2 CCC control 9.0 0.500 1
3 DDD control 0.1 0.240 1
4 EEE control 2.2 0.003 2</code></pre>
</div>
</div>
<p>However, if you subset to one specific column, it gives you a reference:</p>
<div id="a70749c5" class="cell" data-execution_count="22">
<div class="sourceCode cell-code" id="cb39"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a>m1 <span class="op">=</span> simple_df[<span class="st">"measurement1"</span>]</span>
<span id="cb39-2"><a href="#cb39-2" aria-hidden="true" tabindex="-1"></a>m1[<span class="dv">0</span>] <span class="op">=</span> <span class="dv">5</span></span>
<span id="cb39-3"><a href="#cb39-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(m1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>0 5.0
1 3.5
2 9.0
3 0.1
4 2.2
Name: measurement1, dtype: float64</code></pre>
</div>
<div class="cell-output cell-output-stderr">
<pre><code>/var/folders/2v/0x2zqrfs0pj9nqgmdv3v8n5r0000gp/T/ipykernel_8823/1078013331.py:2: SettingWithCopyWarning:
A value is trying to be set on a copy of a slice from a DataFrame
See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
m1[0] = 5</code></pre>
</div>
</div>
<div id="89bc2e30" class="cell" data-execution_count="23">
<div class="sourceCode cell-code" id="cb42"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(simple_df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> id case_control measurement1 measurement2 measurement3
0 AAA case 5.0 0.000 80
1 BBB case 3.5 0.000 2
2 CCC control 9.0 0.500 1
3 DDD control 0.1 0.240 1
4 EEE control 2.2 0.003 2</code></pre>
</div>
</div>
<p>This pattern is called <a href="https://pandas.pydata.org/pandas-docs/stable/user_guide/copy_on_write.html#copy-on-write-chained-assignment">“Chained Assignment”</a>, which means doing two bracket subsetting one after the other.</p>
<p>This behavior is super inconsistent and confusing, as it’s hard to predict when you will get a reference and when you get a copy. More details of this behavior can be <a href="https://pandas.pydata.org/pandas-docs/stable/user_guide/copy_on_write.html">found here</a>. Future versions of Pandas Dataframe will remove these confusion, but for now, when you are modifying Dataframes, consider making a copy when you are unsure what its behaviors are when assigning variables to Dataframes.</p>
</section>
</section>
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anchorJS.add('.anchored');
const isCodeAnnotation = (el) => {
for (const clz of el.classList) {
if (clz.startsWith('code-annotation-')) {
return true;
}
}
return false;
}
const onCopySuccess = function(e) {
// button target
const button = e.trigger;
// don't keep focus
button.blur();
// flash "checked"
button.classList.add('code-copy-button-checked');
var currentTitle = button.getAttribute("title");
button.setAttribute("title", "Copied!");
let tooltip;
if (window.bootstrap) {
button.setAttribute("data-bs-toggle", "tooltip");
button.setAttribute("data-bs-placement", "left");
button.setAttribute("data-bs-title", "Copied!");
tooltip = new bootstrap.Tooltip(button,
{ trigger: "manual",
customClass: "code-copy-button-tooltip",
offset: [0, -8]});
tooltip.show();
}
setTimeout(function() {
if (tooltip) {
tooltip.hide();
button.removeAttribute("data-bs-title");
button.removeAttribute("data-bs-toggle");
button.removeAttribute("data-bs-placement");
}
button.setAttribute("title", currentTitle);
button.classList.remove('code-copy-button-checked');
}, 1000);
// clear code selection
e.clearSelection();
}
const getTextToCopy = function(trigger) {
const codeEl = trigger.previousElementSibling.cloneNode(true);
for (const childEl of codeEl.children) {
if (isCodeAnnotation(childEl)) {
childEl.remove();
}
}
return codeEl.innerText;
}
const clipboard = new window.ClipboardJS('.code-copy-button:not([data-in-quarto-modal])', {
text: getTextToCopy
});
clipboard.on('success', onCopySuccess);
if (window.document.getElementById('quarto-embedded-source-code-modal')) {
// For code content inside modals, clipBoardJS needs to be initialized with a container option
// TODO: Check when it could be a function (https://github.com/zenorocha/clipboard.js/issues/860)
const clipboardModal = new window.ClipboardJS('.code-copy-button[data-in-quarto-modal]', {
text: getTextToCopy,
container: window.document.getElementById('quarto-embedded-source-code-modal')
});
clipboardModal.on('success', onCopySuccess);
}
var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
var mailtoRegex = new RegExp(/^mailto:/);
var filterRegex = new RegExp('/' + window.location.host + '/');
var isInternal = (href) => {
return filterRegex.test(href) || localhostRegex.test(href) || mailtoRegex.test(href);
}
// Inspect non-navigation links and adorn them if external
var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool):not(.about-link)');
for (var i=0; i<links.length; i++) {
const link = links[i];
if (!isInternal(link.href)) {
// undo the damage that might have been done by quarto-nav.js in the case of
// links that we want to consider external
if (link.dataset.originalHref !== undefined) {
link.href = link.dataset.originalHref;
}
}
}
function tippyHover(el, contentFn, onTriggerFn, onUntriggerFn) {
const config = {
allowHTML: true,
maxWidth: 500,
delay: 100,
arrow: false,
appendTo: function(el) {
return el.parentElement;
},
interactive: true,
interactiveBorder: 10,
theme: 'quarto',
placement: 'bottom-start',
};
if (contentFn) {
config.content = contentFn;
}
if (onTriggerFn) {
config.onTrigger = onTriggerFn;
}
if (onUntriggerFn) {
config.onUntrigger = onUntriggerFn;
}
window.tippy(el, config);
}
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
for (var i=0; i<noterefs.length; i++) {
const ref = noterefs[i];
tippyHover(ref, function() {
// use id or data attribute instead here
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
try { href = new URL(href).hash; } catch {}
const id = href.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
if (note) {
return note.innerHTML;
} else {
return "";
}
});
}
const xrefs = window.document.querySelectorAll('a.quarto-xref');
const processXRef = (id, note) => {
// Strip column container classes
const stripColumnClz = (el) => {
el.classList.remove("page-full", "page-columns");
if (el.children) {
for (const child of el.children) {
stripColumnClz(child);
}
}
}
stripColumnClz(note)
if (id === null || id.startsWith('sec-')) {
// Special case sections, only their first couple elements
const container = document.createElement("div");
if (note.children && note.children.length > 2) {
container.appendChild(note.children[0].cloneNode(true));
for (let i = 1; i < note.children.length; i++) {
const child = note.children[i];
if (child.tagName === "P" && child.innerText === "") {
continue;
} else {
container.appendChild(child.cloneNode(true));
break;
}
}
if (window.Quarto?.typesetMath) {
window.Quarto.typesetMath(container);
}
return container.innerHTML
} else {
if (window.Quarto?.typesetMath) {
window.Quarto.typesetMath(note);
}
return note.innerHTML;
}
} else {
// Remove any anchor links if they are present
const anchorLink = note.querySelector('a.anchorjs-link');
if (anchorLink) {
anchorLink.remove();
}
if (window.Quarto?.typesetMath) {
window.Quarto.typesetMath(note);
}
// TODO in 1.5, we should make sure this works without a callout special case
if (note.classList.contains("callout")) {
return note.outerHTML;
} else {
return note.innerHTML;
}
}
}
for (var i=0; i<xrefs.length; i++) {
const xref = xrefs[i];
tippyHover(xref, undefined, function(instance) {
instance.disable();
let url = xref.getAttribute('href');
let hash = undefined;
if (url.startsWith('#')) {
hash = url;
} else {
try { hash = new URL(url).hash; } catch {}
}
if (hash) {
const id = hash.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
if (note !== null) {
try {
const html = processXRef(id, note.cloneNode(true));
instance.setContent(html);
} finally {
instance.enable();
instance.show();
}
} else {
// See if we can fetch this
fetch(url.split('#')[0])
.then(res => res.text())
.then(html => {
const parser = new DOMParser();
const htmlDoc = parser.parseFromString(html, "text/html");
const note = htmlDoc.getElementById(id);
if (note !== null) {
const html = processXRef(id, note);
instance.setContent(html);
}
}).finally(() => {
instance.enable();
instance.show();
});
}
} else {
// See if we can fetch a full url (with no hash to target)
// This is a special case and we should probably do some content thinning / targeting
fetch(url)
.then(res => res.text())
.then(html => {
const parser = new DOMParser();
const htmlDoc = parser.parseFromString(html, "text/html");
const note = htmlDoc.querySelector('main.content');
if (note !== null) {
// This should only happen for chapter cross references
// (since there is no id in the URL)
// remove the first header
if (note.children.length > 0 && note.children[0].tagName === "HEADER") {
note.children[0].remove();
}
const html = processXRef(null, note);
instance.setContent(html);
}
}).finally(() => {
instance.enable();
instance.show();
});
}
}, function(instance) {
});
}
let selectedAnnoteEl;
const selectorForAnnotation = ( cell, annotation) => {
let cellAttr = 'data-code-cell="' + cell + '"';
let lineAttr = 'data-code-annotation="' + annotation + '"';
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
return selector;
}
const selectCodeLines = (annoteEl) => {
const doc = window.document;
const targetCell = annoteEl.getAttribute("data-target-cell");
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
const lineIds = lines.map((line) => {
return targetCell + "-" + line;
})
let top = null;
let height = null;
let parent = null;
if (lineIds.length > 0) {
//compute the position of the single el (top and bottom and make a div)
const el = window.document.getElementById(lineIds[0]);
top = el.offsetTop;
height = el.offsetHeight;
parent = el.parentElement.parentElement;
if (lineIds.length > 1) {
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
height = bottom - top;
}
if (top !== null && height !== null && parent !== null) {
// cook up a div (if necessary) and position it
let div = window.document.getElementById("code-annotation-line-highlight");
if (div === null) {
div = window.document.createElement("div");
div.setAttribute("id", "code-annotation-line-highlight");
div.style.position = 'absolute';
parent.appendChild(div);
}
div.style.top = top - 2 + "px";
div.style.height = height + 4 + "px";
div.style.left = 0;
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
if (gutterDiv === null) {
gutterDiv = window.document.createElement("div");
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
gutterDiv.style.position = 'absolute';
const codeCell = window.document.getElementById(targetCell);
const gutter = codeCell.querySelector('.code-annotation-gutter');
gutter.appendChild(gutterDiv);
}
gutterDiv.style.top = top - 2 + "px";
gutterDiv.style.height = height + 4 + "px";
}
selectedAnnoteEl = annoteEl;
}
};
const unselectCodeLines = () => {
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
elementsIds.forEach((elId) => {
const div = window.document.getElementById(elId);
if (div) {
div.remove();
}
});
selectedAnnoteEl = undefined;
};
// Handle positioning of the toggle
window.addEventListener(
"resize",
throttle(() => {
elRect = undefined;
if (selectedAnnoteEl) {
selectCodeLines(selectedAnnoteEl);
}
}, 10)
);
function throttle(fn, ms) {
let throttle = false;
let timer;
return (...args) => {
if(!throttle) { // first call gets through
fn.apply(this, args);
throttle = true;
} else { // all the others get throttled
if(timer) clearTimeout(timer); // cancel #2
timer = setTimeout(() => {
fn.apply(this, args);
timer = throttle = false;
}, ms);
}
};
}
// Attach click handler to the DT
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
for (const annoteDlNode of annoteDls) {
annoteDlNode.addEventListener('click', (event) => {
const clickedEl = event.target;
if (clickedEl !== selectedAnnoteEl) {
unselectCodeLines();
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
if (activeEl) {
activeEl.classList.remove('code-annotation-active');
}
selectCodeLines(clickedEl);
clickedEl.classList.add('code-annotation-active');
} else {
// Unselect the line
unselectCodeLines();
clickedEl.classList.remove('code-annotation-active');
}
});
}
const findCites = (el) => {
const parentEl = el.parentElement;
if (parentEl) {
const cites = parentEl.dataset.cites;
if (cites) {
return {
el,
cites: cites.split(' ')
};
} else {
return findCites(el.parentElement)
}
} else {
return undefined;
}
};
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const citeInfo = findCites(ref);
if (citeInfo) {
tippyHover(citeInfo.el, function() {
var popup = window.document.createElement('div');
citeInfo.cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
}
});
</script>
</div> <!-- /content -->
</body></html>