JuliaKurs23/notebooks/nb-types.ipynb.html

616 lines
25 KiB
HTML
Raw Permalink Normal View History

2023-05-12 20:12:56 +02:00
<!DOCTYPE html>
<html
xmlns="http://www.w3.org/1999/xhtml"
lang="de"
xml:lang="de"
>
<head>
<meta charset="utf-8" />
<meta name="generator" content="quarto-99.9.9" />
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
<title>Julia für Numerik nb-types</title> <style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
div.columns{display: flex; gap: min(4vw, 1.5em);}
div.column{flex: auto; overflow-x: auto;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
ul.task-list li input[type="checkbox"] {
width: 0.8em;
margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */
vertical-align: middle;
}
/* CSS for syntax highlighting */
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
}
pre.numberSource { margin-left: 3em; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
</style>
<style>
.quarto-embed-header {
height: 3em;
width: 100%;
display: flex;
justify-content: space-between;
align-items: center;
border-bottom: solid 1px;
}
.quarto-embed-header h6 {
font-size: 1em;
padding-top: 0.6em;
margin-left: 1em;
margin-right: 1em;
font-weight: 300;
}
.quarto-embed-header a.quarto-download-embed {
font-size: 0.7em;
margin-top: 1em;
margin-bottom: 1em;
margin-left: 1em;
margin-right: 1em;
}
</style>
<!-- htmldependencies:E3FAD763 -->
<script id="quarto-search-options" type="application/json">{
"language": {
"search-no-results-text": "Keine Treffer",
"search-matching-documents-text": "Treffer",
"search-copy-link-title": "Link in die Suche kopieren",
"search-hide-matches-text": "Zusätzliche Treffer verbergen",
"search-more-match-text": "weitere Treffer in diesem Dokument",
"search-more-matches-text": "weitere Treffer in diesem Dokument",
"search-clear-button-title": "Zurücksetzen",
"search-detached-cancel-button-title": "Abbrechen",
"search-submit-button-title": "Abschicken"
}
}</script>
<link rel="stylesheet" href="../css/styles.css" />
</head>
<body>
<div class="quarto-embed-header">
<h6><i class="bi bi-journal-code"></i> nb-types.ipynb</h6>
<a
href="../images/nb-types.ipynb"
class="btn btn-primary quarto-download-embed"
data-noresolveinput="true"
download="nb-types.ipynb"
>Download Notebook</a
>
</div>
<div id="quarto-search-results"></div>
<header id="quarto-header" class="headroom fixed-top">
<nav class="quarto-secondary-nav">
<div class="container-fluid d-flex">
<button type="button" class="quarto-btn-toggle btn"
data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass"
aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Seitenleiste umschalten"
onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
<i class="bi bi-layout-text-sidebar-reverse"></i>
</button>
<h1 class="quarto-secondary-nav-title"></h1>
<a class="flex-grow-1" role="button" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass"
aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Seitenleiste umschalten"
onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
</a>
</div>
</nav>
</header>
<!-- content -->
<div id="quarto-content" class="quarto-container page-columns page-rows-contents page-layout-article">
<!-- sidebar -->
<nav id="quarto-sidebar" class="sidebar collapse collapse-horizontal sidebar-navigation floating overflow-auto">
<div class="pt-lg-2 mt-2 text-left sidebar-header sidebar-header-stacked">
<a href="/index.html" class="sidebar-logo-link">
<img src="/images/julia-logo-color.svg" alt="" class="sidebar-logo py-0 d-lg-inline d-none"/>
</a>
<div class="sidebar-title mb-0 py-0">
<a href="/">
Julia für Numerik
</a>
<div class="sidebar-tools-main tools-wide">
<a href="/Julia-f%C3%BCr-Numerik.pdf" title="" class="quarto-navigation-tool px-1" aria-label=""><i class="bi bi-download"></i></a>
<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>
<a href="" class="quarto-color-scheme-toggle quarto-navigation-tool px-1" onclick="window.quartoToggleColorScheme(); return false;" title="Dunkelmodus umschalten"><i class="bi"></i></a>
</div>
</div>
</div>
<div class="sidebar-menu-container">
<ul class="list-unstyled mt-1">
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="/index.html" class="sidebar-item-text sidebar-link">
<span class="menu-text">Was ist Julia?</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="/chapters/types.html" class="sidebar-item-text sidebar-link">
<span class="menu-text">&lt;span class=&#39;chapter-number&#39;&gt;1&lt;/span&gt;  &lt;span class=&#39;chapter-title&#39;&gt;Das Typsystem von Julia&lt;/span&gt;</span></a>
</div>
</li>
</ul>
</div>
</nav>
<div id="quarto-sidebar-glass" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass" ></div>
<!-- margin-sidebar -->
<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
<div id="quarto-toc-target"></div>
</div>
<!-- main -->
<main class="content" id="quarto-document-content"> <div id="nb1" class="cell" data-execution_count="1">
<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>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">println</span>(<span class="st">&quot; &quot;</span><span class="op">^</span>i, T)</span>
<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>
<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>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">end</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
<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>
<div class="cell-output cell-output-stdout">
<pre class=""><code class=" ansi">Number
Complex
Real
AbstractFloat
BigFloat
Float16
Float32
Float64
AbstractIrrational
Irrational
Integer
Bool
Signed
BigInt
Int128
Int16
Int32
Int64
Int8
Unsigned
UInt128
UInt16
UInt32
UInt64
UInt8
Rational</code></pre>
</div>
</div>
<div id="nb2" class="cell" data-execution_count="2">
<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>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a></span>
<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>
<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>
<div class="cell-output cell-output-stdout">
<pre class=""><code class=" ansi">Number
├─ Complex
└─ Real
├─ AbstractFloat
│ ├─ BigFloat
│ ├─ Float16
│ ├─ Float32
│ └─ Float64
├─ AbstractIrrational
│ └─ Irrational
├─ Integer
│ ├─ Bool
│ ├─ Signed
│ │ ├─ BigInt
│ │ ├─ Int128
│ │ ├─ Int16
│ │ ├─ Int32
│ │ ├─ Int64
│ │ └─ Int8
│ └─ Unsigned
│ ├─ UInt128
│ ├─ UInt16
│ ├─ UInt32
│ ├─ UInt64
│ └─ UInt8
└─ Rational</code></pre>
</div>
</div>
<div id="quarto-navigation-envelope" class="hidden">
<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 />
</span></p>
</div>
<div id="quarto-meta-markdown" class="hidden">
<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>
</div>
</main> <!-- /main --> <script id = "quarto-html-after-body" type="application/javascript">
window.document.addEventListener("DOMContentLoaded", function (event) {
const toggleBodyColorMode = (bsSheetEl) => {
const mode = bsSheetEl.getAttribute("data-mode");
const bodyEl = window.document.querySelector("body");
if (mode === "dark") {
bodyEl.classList.add("quarto-dark");
bodyEl.classList.remove("quarto-light");
} else {
bodyEl.classList.add("quarto-light");
bodyEl.classList.remove("quarto-dark");
}
}
const toggleBodyColorPrimary = () => {
const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
if (bsSheetEl) {
toggleBodyColorMode(bsSheetEl);
}
}
toggleBodyColorPrimary();
const disableStylesheet = (stylesheets) => {
for (let i=0; i < stylesheets.length; i++) {
const stylesheet = stylesheets[i];
stylesheet.rel = 'prefetch';
}
}
const enableStylesheet = (stylesheets) => {
for (let i=0; i < stylesheets.length; i++) {
const stylesheet = stylesheets[i];
stylesheet.rel = 'stylesheet';
}
}
const manageTransitions = (selector, allowTransitions) => {
const els = window.document.querySelectorAll(selector);
for (let i=0; i < els.length; i++) {
const el = els[i];
if (allowTransitions) {
el.classList.remove('notransition');
} else {
el.classList.add('notransition');
}
}
}
const toggleColorMode = (alternate) => {
// Switch the stylesheets
const alternateStylesheets = window.document.querySelectorAll('link.quarto-color-scheme.quarto-color-alternate');
manageTransitions('#quarto-margin-sidebar .nav-link', false);
if (alternate) {
enableStylesheet(alternateStylesheets);
for (const sheetNode of alternateStylesheets) {
if (sheetNode.id === "quarto-bootstrap") {
toggleBodyColorMode(sheetNode);
}
}
} else {
disableStylesheet(alternateStylesheets);
toggleBodyColorPrimary();
}
manageTransitions('#quarto-margin-sidebar .nav-link', true);
// Switch the toggles
const toggles = window.document.querySelectorAll('.quarto-color-scheme-toggle');
for (let i=0; i < toggles.length; i++) {
const toggle = toggles[i];
if (toggle) {
if (alternate) {
toggle.classList.add("alternate");
} else {
toggle.classList.remove("alternate");
}
}
}
// Hack to workaround the fact that safari doesn't
// properly recolor the scrollbar when toggling (#1455)
if (navigator.userAgent.indexOf('Safari') > 0 && navigator.userAgent.indexOf('Chrome') == -1) {
manageTransitions("body", false);
window.scrollTo(0, 1);
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">
&nbsp;
</div>
<div class="nav-footer-right">
<div class='footer-contents'>Created with [Quarto](https://quarto.org/)
</div>
</div>
</div>
</footer>
</body>
</html>