641 lines
113 KiB
HTML
641 lines
113 KiB
HTML
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<div class="quarto-title">
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<h1 class="title">Applications with scalar functions</h1>
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</div>
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<div class="quarto-title-meta">
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</div>
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</header>
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<p>This section uses these add-on packages:</p>
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<div id="14" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">CalculusWithJulia</span></span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Plots</span></span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">plotly</span>()</span>
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<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">SymPy</span></span>
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<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Roots</span></span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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</div>
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<section id="example" class="level5">
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<h5 class="anchored" data-anchor-id="example">Example</h5>
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<p>Consider the function <span class="math inline">\(f(x,y) = x^2 + 3y^2 -x\)</span> over the region <span class="math inline">\(x^2 + y^2 \leq 1\)</span>. This is a continuous function over a closed set, so will have both an absolute maximum and minimum. Find these from an investigation of the critical points and the boundary points.</p>
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<p>The gradient is easily found: <span class="math inline">\(\nabla{f} = \langle 2x - 1, 6y \rangle\)</span>, and is <span class="math inline">\(\vec{0}\)</span> only at <span class="math inline">\(\vec{a} = \langle 1/2, 0 \rangle\)</span>. The Hessian is:</p>
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<p><span class="math display">\[
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H =
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\begin{bmatrix}
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2 & 0\\
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0 & 6
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\end{bmatrix}.
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\]</span></p>
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<p>At <span class="math inline">\(\vec{a}\)</span> this has positive determinant and <span class="math inline">\(f_{xx} > 0\)</span>, so <span class="math inline">\(\vec{a}\)</span> corresponds to a <em>local</em> minimum with values <span class="math inline">\(f(\vec{a}) = (1/2)^2 + 3(0) - 1/2 = -1/4\)</span>. The absolute maximum and minimum may occur here (well, not the maximum) or on the boundary, so that must be considered. In this case we can easily parameterize the boundary and turn this into the univariate case:</p>
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<div id="16" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">fₗ</span>(x,y) <span class="op">=</span> x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">2</span>y<span class="op">^</span><span class="fl">2</span> <span class="op">-</span> x</span>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">gammaₗ</span>(t) <span class="op">=</span> [<span class="fu">cos</span>(t), <span class="fu">sin</span>(t)] <span class="co"># traces out x^2 + y^2 = 1 over [0, 2pi]</span></span>
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<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>gₗ <span class="op">=</span> <span class="fu">splat</span>(fₗ) <span class="op">∘</span> gammaₗ</span>
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<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>cpsₗ <span class="op">=</span> <span class="fu">find_zeros</span>(gₗ<span class="ch">', 0, 2pi) # critical points of g</span></span>
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<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="fu">append!</span>(cpsₗ, [<span class="fl">0</span>, <span class="fl">2</span>pi])</span>
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<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a><span class="fu">unique!</span>(cpsₗ)</span>
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<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a><span class="fu">gₗ</span>.(cpsₗ)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<pre><code>5-element Vector{Float64}:
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0.0
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2.25
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2.0
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2.25
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0.0</code></pre>
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</div>
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</div>
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<p>We see that maximum value is <code>2.25</code> and that the interior point, <span class="math inline">\(\vec{a}\)</span>, will be where the minimum value occurs. To see exactly where the maximum occurs, we look at the values of gamma:</p>
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<div id="18" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb4"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>inds <span class="op">=</span> [<span class="fl">2</span>,<span class="fl">4</span>]</span>
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<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>cpsₗ[inds]</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<pre><code>2-element Vector{Float64}:
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2.0943951023931953
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4.1887902047863905</code></pre>
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</div>
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</div>
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<p>These are multiples of <span class="math inline">\(\pi\)</span>:</p>
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<div id="20" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb6"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>cpsₗ[inds]<span class="op">/</span><span class="cn">pi</span></span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<pre><code>2-element Vector{Float64}:
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0.6666666666666666
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1.3333333333333333</code></pre>
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</div>
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</div>
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<p>So we have the maximum occurs at the angles <span class="math inline">\(2\pi/3\)</span> and <span class="math inline">\(4\pi/3\)</span>. Here we visualize, using a hacky trick of assigning <code>NaN</code> values to the function to avoid plotting outside the circle:</p>
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<div id="22" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb8"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hₗ</span>(x,y) <span class="op">=</span> <span class="fu">fₗ</span>(x,y) <span class="op">*</span> (x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> y<span class="op">^</span><span class="fl">2</span> <span class="op"><=</span> <span class="fl">1</span> ? <span class="fl">1</span> <span class="op">:</span> <span class="cn">NaN</span>)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<pre><code>hₗ (generic function with 1 method)</code></pre>
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</div>
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</div>
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<div id="24" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb10"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">gr</span>()</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<pre><code>Plots.GRBackend()</code></pre>
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</div>
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</div>
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<div id="26" class="cell" data-hold="true" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb12"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>xs <span class="op">=</span> ys <span class="op">=</span> <span class="fu">range</span>(<span class="op">-</span><span class="fl">1</span>,<span class="fl">1</span>, length<span class="op">=</span><span class="fl">100</span>)</span>
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<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>plt <span class="op">=</span> <span class="fu">surface</span>(xs, ys, hₗ)</span>
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<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>ts <span class="op">=</span> cpsₗ <span class="co"># 2pi/3 and 4pi/3 by above</span></span>
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<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>xs, ys <span class="op">=</span> <span class="fu">cos</span>.(ts), <span class="fu">sin</span>.(ts)</span>
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<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>zs <span class="op">=</span> <span class="fu">fₗ</span>.(xs, ys)</span>
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<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a><span class="fu">scatter3d!</span>(xs, ys, zs)</span>
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<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a><span class="co">#tuple.(xs, ys, zs)</span></span>
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<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a><span class="co">#plot!(plt, tuple.(xs, ys, zs); linetype=:scatter)</span></span>
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<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a><span class="co">#plt</span></span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<img 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">
|
|
</div>
|
|
</div>
|
|
<p>A contour plot also shows that some—and only one—extrema happens on the interior:</p>
|
|
<!--
|
|
|
|
```lqoxmri
|
|
#| hold: true
|
|
xs = ys = range(-1,1, length=100)
|
|
contour(xs, ys, hₗ)
|
|
```
|
|
|
|
The extrema are identified by the enclosing regions, in this case the one around the point $(1/2, 0)$.
|
|
-->
|
|
</section>
|
|
|
|
</main>
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|
<!-- /main column -->
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<script id="quarto-html-after-body" type="application/javascript">
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window.document.addEventListener("DOMContentLoaded", function (event) {
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const icon = "";
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const anchorJS = new window.AnchorJS();
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anchorJS.options = {
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placement: 'right',
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icon: icon
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};
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anchorJS.add('.anchored');
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const isCodeAnnotation = (el) => {
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for (const clz of el.classList) {
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if (clz.startsWith('code-annotation-')) {
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return true;
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}
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}
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return false;
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}
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const onCopySuccess = function(e) {
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// button target
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const button = e.trigger;
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// don't keep focus
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button.blur();
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// flash "checked"
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button.classList.add('code-copy-button-checked');
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var currentTitle = button.getAttribute("title");
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button.setAttribute("title", "Copied!");
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let tooltip;
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if (window.bootstrap) {
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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 outerScaffold = trigger.parentElement.cloneNode(true);
|
|
const codeEl = outerScaffold.querySelector('code');
|
|
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')) {
|
|
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);
|
|
}
|
|
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> |