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03-Functions.html
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<h1 class="title">Functions</h1>
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<div class="quarto-title-meta">
</div>
</header>
<p>After learning how to use other people’s functions, it’s time to write our own! We will look at the anatomy of how a function is constructed, and see bunch of examples in action.</p>
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="https://moffett4understandingmath.com/wp-content/uploads/2017/06/function-machine.png" class="img-fluid figure-img" width="300"></p>
<figcaption>Source: https://moffett4understandingmath.com/wp-content/uploads/2017/06/function-machine.png</figcaption>
</figure>
</div>
<p>First, we remind ourselves why we write functions in the first place. We write functions for two main, often overlapping, reasons:</p>
<ol type="1">
<li><p>Following DRY (Don’t Repeat Yourself) principle: If you find yourself repeating similar patterns of code, you should write a function that executes that pattern. This saves time and the risk of mistakes.</p></li>
<li><p>Create modular structure and abstraction: Having all of your code in one place becomes increasingly complicated as your program grows. Think of the function as a mini-program that can perform without the rest of the program. Organizing your code by functions gives modular structure, as well as abstraction: you only need to know the function name, inputs, and output to use it and don’t have to worry how it works.</p></li>
</ol>
<p>Some advice on writing functions:</p>
<ul>
<li><p>Code that has a well-defined set of inputs and outputs make a good function.</p></li>
<li><p>A function should do only one, well-defined task.</p></li>
</ul>
<section id="anatomy-of-a-function-definition" class="level2">
<h2 class="anchored" data-anchor-id="anatomy-of-a-function-definition">Anatomy of a function definition</h2>
<p>This is how you define a function:</p>
<pre><code>def <function name>(<input arguments>):
""" documentation string """
code block
return <variable></code></pre>
<ul>
<li><p><code><function name></code> is the function’s name you are creating.</p></li>
<li><p><code><input arguments></code> specify the input arguments for the function as variable, separated by commas.</p></li>
<li><p><code>""" documentation string """</code> describes what the function is doing. It is considered optional but highly recommended.</p></li>
<li><p><code>code block</code> performs the action of the function, typically using the input arguments of the function.</p></li>
<li><p><code>return <variable></code> it the output of the function.</p></li>
</ul>
<p>Here’s an simple example to define a function that adds two numbers together:</p>
<div id="472a9fde" class="cell" data-execution_count="1">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> add_numbers(num1, num2):</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> <span class="co">""" Adds two input numbers together. """</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> result <span class="op">=</span> num1 <span class="op">+</span> num2</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> result</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>When this code is run, <code>add_numbers()</code> is stored in the environment, but the function is never run. To run the function,</p>
<div id="3eae762a" 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>add_numbers(<span class="dv">3</span>, <span class="dv">4</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display" data-execution_count="2">
<pre><code>7</code></pre>
</div>
</div>
<p>When the function is called, the input values 3 and 4 are reassigned to function input arguments <code>num1</code> and <code>num2</code> to be used within the function.</p>
<p>We need to introduce the concept of local and global environments to distinguish variables used only for a function from variables used for the entire program.</p>
</section>
<section id="local-and-global-environments" class="level2">
<h2 class="anchored" data-anchor-id="local-and-global-environments">Local and global environments</h2>
<p>Within a function, all input arguments and any new variables defined are stored in a “<strong>local environment</strong>”, and is only accessible within the function’s body. The overall environment of the program is called the “<strong>global environment</strong>” and can be also accessed within the function.</p>
<p>The reason of having some of this “privacy” in the local environment is to make functions modular - they are independent little tools that should not interact with the rest of the global environment. Imagine someone writing a tool that they want to give someone else to use, but the tool depends on your environment, vice versa.</p>
<p>To illustrate the distinguish between a the local and global environment, the following tool allows you to step through Python code execution line-by-line and see the relationship between order of execution, variables, and environments. The “Global frame” refers to the global environment, and “add_numbers” refer to the local environment for the function <code>add_numbers()</code>.</p>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=def%20add_numbers%28num1,%20num2%29%3A%0A%20%20%22%22%22%20Adds%20two%20input%20numbers%20together.%20%22%22%22%0A%20%20result%20%3D%20num1%20%2B%20num2%0A%20%20return%20result%0A%20%20%0Aadd_numbers%283,%204%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=def%20add_numbers%28num1,%20num2%29%3A%0A%20%20%22%22%22%20Adds%20two%20input%20numbers%20together.%20%22%22%22%0A%20%20result%20%3D%20num1%20%2B%20num2%0A%20%20return%20result%0A%20%20%0Aadd_numbers%283,%204%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="function-arguments-create-modularity" class="level2">
<h2 class="anchored" data-anchor-id="function-arguments-create-modularity">Function arguments create modularity</h2>
<p>First time writers of functions might ask: why are variables we use for the arguments of a function <em>reassigned</em> for function arguments in the local environment? Here is an example when that process is skipped - what are the consequences?</p>
<div id="97918386" 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>x <span class="op">=</span> <span class="dv">3</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> <span class="dv">4</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> add_numbers(num1, num2):</span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a> <span class="co">""" Adds two input numbers together. """</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a> result <span class="op">=</span> x <span class="op">+</span> y</span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> result</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Let’s try this function out for a few values:</p>
<div id="f849e1ae" class="cell" data-execution_count="4">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>add_numbers(x, y)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display" data-execution_count="4">
<pre><code>7</code></pre>
</div>
</div>
<div id="d2b38959" class="cell" data-execution_count="5">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>add_numbers(<span class="dv">10</span>, <span class="op">-</span><span class="dv">5</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display" data-execution_count="5">
<pre><code>7</code></pre>
</div>
</div>
<p>Why is this happening? Let’s try to step through this interactively:</p>
<iframe width="800" height="500" frameborder="0" src="https://pythontutor.com/iframe-embed.html#code=x%20%3D%203%0Ay%20%3D%204%0A%0Adef%20add_numbers%28num1,%20num2%29%3A%0A%20%20%22%22%22%20Adds%20two%20input%20numbers%20together.%20%22%22%22%0A%20%20result%20%3D%20x%20%2B%20y%0A%20%20return%20result%0A%20%20%0Aadd_numbers%28x,%20y%29%0A%0Aadd_numbers%2810,%20-5%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=x%20%3D%203%0Ay%20%3D%204%0A%0Adef%20add_numbers%28num1,%20num2%29%3A%0A%20%20%22%22%22%20Adds%20two%20input%20numbers%20together.%20%22%22%22%0A%20%20result%20%3D%20x%20%2B%20y%0A%20%20return%20result%0A%20%20%0Aadd_numbers%28x,%20y%29%0A%0Aadd_numbers%2810,%20-5%29&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false">link</a>.</p>
<p>The function did not work as expected because we used hard-coded variables (<code>x</code>, <code>y</code>) from the global environment and not function argument variables unique to the function use!</p>
</section>
<section id="exercises" class="level2">
<h2 class="anchored" data-anchor-id="exercises">Exercises</h2>
<ul>
<li><p>Write a function, <code>my_abs(x)</code> that computes the absolute value of an input numeric value and returns it. Use cases: <code>my_abs(-3) = 3</code>, <code>my_abs(0) = 0</code>, <code>my_abs(33) = 33</code>. You will need to use conditional statements within the body of the function.</p></li>
<li><p>Write a function, <code>my_abs_iterated(x)</code> that takes in a list of numerical values and use <code>my_abs(x)</code> to take the absolute value of each element. Use cases: <code>my_abs_itereated([3, -9, 2]) = [3, -9, 2]</code>.</p></li>
<li><p>Write a function, <code>is_in(element, iterable)</code> that checks whether <code>element</code> is found in an <code>iterable</code> using For-Loops and conditional statements, and returns <code>True</code> if so and <code>False</code> otherwise. Use cases: <code>is_in(3, [3, 4, 5]) = True</code>, <code>is_in("hi", ("hello", "bonjour")) = False</code>, <code>is_in("fred", {"hank": 34, "george": 23, "fred": 2}) = True</code>.</p></li>
</ul>
</section>
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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>