616 lines
25 KiB
HTML
616 lines
25 KiB
HTML
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"language": {
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"search-no-results-text": "Keine Treffer",
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"search-matching-documents-text": "Treffer",
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"search-copy-link-title": "Link in die Suche kopieren",
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"search-hide-matches-text": "Zusätzliche Treffer verbergen",
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<h6><i class="bi bi-journal-code"></i> nb-types.ipynb</h6>
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Julia für Numerik
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</a>
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<a href="/Julia-f%C3%BCr-Numerik.pdf" title="" class="quarto-navigation-tool px-1" aria-label=""><i class="bi bi-download"></i></a>
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<a href="/Julia-für-Numerik.pdf" title="Download PDF" class="quarto-navigation-tool px-1" aria-label="Download PDF"><i class="bi bi-file-pdf"></i></a>
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<span class="menu-text">Was ist Julia?</span></a>
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<a href="/chapters/types.html" class="sidebar-item-text sidebar-link">
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<span class="menu-text"><span class='chapter-number'>1</span> <span class='chapter-title'>Das Typsystem von Julia</span></span></a>
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<!-- main -->
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<main class="content" id="quarto-document-content"> <div id="nb1" class="cell" data-execution_count="1">
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<div class="sourceCode" id="cb1"><pre class="sourceCode julia cell-code"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> <span class="fu">show_subtype_tree</span>(T, i<span class="op">=</span><span class="fl">0</span>)</span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">println</span>(<span class="st">" "</span><span class="op">^</span>i, T)</span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> Ts <span class="op">∈</span> <span class="fu">subtypes</span>(T)</span>
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<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">show_subtype_tree</span>(Ts, i<span class="op">+</span><span class="fl">1</span>)</span>
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<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">end</span></span>
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<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span>
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<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="fu">show_subtype_tree</span>(<span class="dt">Number</span>)</span></code></pre></div>
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<div class="cell-output cell-output-stdout">
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<pre class=""><code class=" ansi">Number
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Complex
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Real
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AbstractFloat
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BigFloat
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Float16
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Float32
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Float64
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AbstractIrrational
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Irrational
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Integer
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Bool
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Signed
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|||
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BigInt
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|||
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Int128
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Int16
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|||
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Int32
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Int64
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Int8
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Unsigned
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UInt128
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UInt16
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UInt32
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UInt64
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UInt8
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Rational</code></pre>
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</div>
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</div>
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<div id="nb2" class="cell" data-execution_count="2">
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<div class="sourceCode" id="cb2"><pre class="sourceCode julia cell-code"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">AbstractTrees</span></span>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>AbstractTrees.<span class="fu">children</span>(x<span class="op">::</span><span class="dt">Type</span>) <span class="op">=</span> <span class="fu">subtypes</span>(x)</span>
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<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="fu">print_tree</span>(<span class="dt">Number</span>)</span></code></pre></div>
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<div class="cell-output cell-output-stdout">
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<pre class=""><code class=" ansi">Number
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├─ Complex
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└─ Real
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├─ AbstractFloat
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│ ├─ BigFloat
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│ ├─ Float16
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│ ├─ Float32
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│ └─ Float64
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├─ AbstractIrrational
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│ └─ Irrational
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├─ Integer
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│ ├─ Bool
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│ ├─ Signed
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│ │ ├─ BigInt
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│ │ ├─ Int128
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│ │ ├─ Int16
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│ │ ├─ Int32
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│ │ ├─ Int64
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│ │ └─ Int8
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│ └─ Unsigned
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│ ├─ UInt128
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│ ├─ UInt16
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│ ├─ UInt32
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│ ├─ UInt64
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│ └─ UInt8
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└─ Rational</code></pre>
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</div>
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</div>
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<div id="quarto-navigation-envelope" class="hidden">
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<p><span class="hidden" data-render-id="quarto-int-sidebar-title">Julia für Numerik</span> <span class="hidden" data-render-id="quarto-int-navbar-title">Julia für Numerik</span> <span class="hidden" data-render-id="quarto-int-sidebar:/index.html">Was ist Julia?</span> <span class="hidden" data-render-id="quarto-int-sidebar:/chapters/types.html"><span class="chapter-number">1</span> <span class="chapter-title">Das Typsystem von Julia</span></span> <span class="hidden" data-render-id="footer-left">All content licenced under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>.</span> <span class="hidden" data-render-id="footer-right">Created with <a href="https://quarto.org/">Quarto</a><br />
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</span></p>
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</div>
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<div id="quarto-meta-markdown" class="hidden">
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<p><span class="hidden" data-render-id="quarto-twittercardtitle"></span> <span class="hidden" data-render-id="quarto-ogcardtitle"></span> <span class="hidden" data-render-id="quarto-metasitename">Julia für Numerik</span> <span class="hidden" data-render-id="quarto-twittercarddesc"></span> <span class="hidden" data-render-id="quarto-ogcardddesc"></span></p>
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|||
|
setTimeout(() => {
|
|||
|
window.scrollTo(0, 0);
|
|||
|
manageTransitions("body", true);
|
|||
|
}, 40);
|
|||
|
}
|
|||
|
}
|
|||
|
const isFileUrl = () => {
|
|||
|
return window.location.protocol === 'file:';
|
|||
|
}
|
|||
|
const hasAlternateSentinel = () => {
|
|||
|
let styleSentinel = getColorSchemeSentinel();
|
|||
|
if (styleSentinel !== null) {
|
|||
|
return styleSentinel === "alternate";
|
|||
|
} else {
|
|||
|
return false;
|
|||
|
}
|
|||
|
}
|
|||
|
const setStyleSentinel = (alternate) => {
|
|||
|
const value = alternate ? "alternate" : "default";
|
|||
|
if (!isFileUrl()) {
|
|||
|
window.localStorage.setItem("quarto-color-scheme", value);
|
|||
|
} else {
|
|||
|
localAlternateSentinel = value;
|
|||
|
}
|
|||
|
}
|
|||
|
const getColorSchemeSentinel = () => {
|
|||
|
if (!isFileUrl()) {
|
|||
|
const storageValue = window.localStorage.getItem("quarto-color-scheme");
|
|||
|
return storageValue != null ? storageValue : localAlternateSentinel;
|
|||
|
} else {
|
|||
|
return localAlternateSentinel;
|
|||
|
}
|
|||
|
}
|
|||
|
let localAlternateSentinel = 'default';
|
|||
|
// Dark / light mode switch
|
|||
|
window.quartoToggleColorScheme = () => {
|
|||
|
// Read the current dark / light value
|
|||
|
let toAlternate = !hasAlternateSentinel();
|
|||
|
toggleColorMode(toAlternate);
|
|||
|
setStyleSentinel(toAlternate);
|
|||
|
};
|
|||
|
// Ensure there is a toggle, if there isn't float one in the top right
|
|||
|
if (window.document.querySelector('.quarto-color-scheme-toggle') === null) {
|
|||
|
const a = window.document.createElement('a');
|
|||
|
a.classList.add('top-right');
|
|||
|
a.classList.add('quarto-color-scheme-toggle');
|
|||
|
a.href = "";
|
|||
|
a.onclick = function() { try { window.quartoToggleColorScheme(); } catch {} return false; };
|
|||
|
const i = window.document.createElement("i");
|
|||
|
i.classList.add('bi');
|
|||
|
a.appendChild(i);
|
|||
|
window.document.body.appendChild(a);
|
|||
|
}
|
|||
|
// Switch to dark mode if need be
|
|||
|
if (hasAlternateSentinel()) {
|
|||
|
toggleColorMode(true);
|
|||
|
} else {
|
|||
|
toggleColorMode(false);
|
|||
|
}
|
|||
|
const icon = "";
|
|||
|
const anchorJS = new window.AnchorJS();
|
|||
|
anchorJS.options = {
|
|||
|
placement: 'right',
|
|||
|
icon: icon
|
|||
|
};
|
|||
|
anchorJS.add('.anchored');
|
|||
|
const isCodeAnnotation = (el) => {
|
|||
|
for (const clz of el.classList) {
|
|||
|
if (clz.startsWith('code-annotation-')) {
|
|||
|
return true;
|
|||
|
}
|
|||
|
}
|
|||
|
return false;
|
|||
|
}
|
|||
|
const clipboard = new window.ClipboardJS('.code-copy-button', {
|
|||
|
text: function(trigger) {
|
|||
|
const codeEl = trigger.previousElementSibling.cloneNode(true);
|
|||
|
for (const childEl of codeEl.children) {
|
|||
|
if (isCodeAnnotation(childEl)) {
|
|||
|
childEl.remove();
|
|||
|
}
|
|||
|
}
|
|||
|
return codeEl.innerText;
|
|||
|
}
|
|||
|
});
|
|||
|
clipboard.on('success', 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", "Kopiert");
|
|||
|
let tooltip;
|
|||
|
if (window.bootstrap) {
|
|||
|
button.setAttribute("data-bs-toggle", "tooltip");
|
|||
|
button.setAttribute("data-bs-placement", "left");
|
|||
|
button.setAttribute("data-bs-title", "Kopiert");
|
|||
|
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();
|
|||
|
});
|
|||
|
function tippyHover(el, contentFn) {
|
|||
|
const config = {
|
|||
|
allowHTML: true,
|
|||
|
content: contentFn,
|
|||
|
maxWidth: 500,
|
|||
|
delay: 100,
|
|||
|
arrow: false,
|
|||
|
appendTo: function(el) {
|
|||
|
return el.parentElement;
|
|||
|
},
|
|||
|
interactive: true,
|
|||
|
interactiveBorder: 10,
|
|||
|
theme: 'quarto',
|
|||
|
placement: 'bottom-start'
|
|||
|
};
|
|||
|
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);
|
|||
|
return note.innerHTML;
|
|||
|
});
|
|||
|
}
|
|||
|
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";
|
|||
|
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;
|
|||
|
};
|
|||
|
// 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 -->
|
|||
|
<footer class="footer">
|
|||
|
<div class="nav-footer">
|
|||
|
<div class="nav-footer-left">
|
|||
|
<div class='footer-contents'>All content licenced under [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/).
|
|||
|
</div>
|
|||
|
</div>
|
|||
|
<div class="nav-footer-center">
|
|||
|
|
|||
|
</div>
|
|||
|
<div class="nav-footer-right">
|
|||
|
<div class='footer-contents'>Created with [Quarto](https://quarto.org/)
|
|||
|
</div>
|
|||
|
</div>
|
|||
|
</div>
|
|||
|
</footer>
|
|||
|
</body>
|
|||
|
</html>
|