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index.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
<head>
<meta charset="utf-8"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta http-equiv="X-UA-Compatible" content="IE=Edge,chrome=1"/>
<meta name="generator" content="distill" />
<style type="text/css">
/* Hide doc at startup (prevent jankiness while JS renders/transforms) */
body {
visibility: hidden;
}
</style>
<!--radix_placeholder_import_source-->
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<style type="text/css">code{white-space: pre;}</style>
<style type="text/css" data-origin="pandoc">
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;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ color: #00769e; background-color: #f1f3f5; }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span { color: #00769e; } /* Normal */
code span.al { color: #ad0000; } /* Alert */
code span.an { color: #5e5e5e; } /* Annotation */
code span.at { color: #657422; } /* Attribute */
code span.bn { color: #ad0000; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #00769e; } /* ControlFlow */
code span.ch { color: #20794d; } /* Char */
code span.cn { color: #8f5902; } /* Constant */
code span.co { color: #5e5e5e; } /* Comment */
code span.cv { color: #5e5e5e; font-style: italic; } /* CommentVar */
code span.do { color: #5e5e5e; font-style: italic; } /* Documentation */
code span.dt { color: #ad0000; } /* DataType */
code span.dv { color: #ad0000; } /* DecVal */
code span.er { color: #ad0000; } /* Error */
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code span.im { } /* Import */
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code span.op { color: #5e5e5e; } /* Operator */
code span.ot { color: #00769e; } /* Other */
code span.pp { color: #ad0000; } /* Preprocessor */
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code span.ss { color: #20794d; } /* SpecialString */
code span.st { color: #20794d; } /* String */
code span.va { color: #111111; } /* Variable */
code span.vs { color: #20794d; } /* VerbatimString */
code span.wa { color: #5e5e5e; font-style: italic; } /* Warning */
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<title>Wilson Yip</title>
<meta property="description" itemprop="description" content="My personal blog on Mathematics and Data Science"/>
<link rel="icon" type="image/vnd.microsoft.icon" href="favicons/favicon.ico"/>
<!-- https://developers.facebook.com/docs/sharing/webmasters#markup -->
<meta property="og:title" content="Wilson Yip"/>
<meta property="og:type" content="article"/>
<meta property="og:description" content="My personal blog on Mathematics and Data Science"/>
<meta property="og:image" content="img/preview.png"/>
<meta property="og:locale" content="en_US"/>
<meta property="og:site_name" content="Wilson Yip's Blog"/>
<!-- https://dev.twitter.com/cards/types/summary -->
<meta property="twitter:card" content="summary_large_image"/>
<meta property="twitter:title" content="Wilson Yip"/>
<meta property="twitter:description" content="My personal blog on Mathematics and Data Science"/>
<meta property="twitter:image" content="img/preview.png"/>
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</script>
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<meta name="distill:offset" content=""/>
<script type="application/javascript">
window.headroom_prevent_pin = false;
window.document.addEventListener("DOMContentLoaded", function (event) {
// initialize headroom for banner
var header = $('header').get(0);
var headerHeight = header.offsetHeight;
var headroom = new Headroom(header, {
tolerance: 5,
onPin : function() {
if (window.headroom_prevent_pin) {
window.headroom_prevent_pin = false;
headroom.unpin();
}
}
});
headroom.init();
if(window.location.hash)
headroom.unpin();
$(header).addClass('headroom--transition');
// offset scroll location for banner on hash change
// (see: https://github.com/WickyNilliams/headroom.js/issues/38)
window.addEventListener("hashchange", function(event) {
window.scrollTo(0, window.pageYOffset - (headerHeight + 25));
});
// responsive menu
$('.distill-site-header').each(function(i, val) {
var topnav = $(this);
var toggle = topnav.find('.nav-toggle');
toggle.on('click', function() {
topnav.toggleClass('responsive');
});
});
// nav dropdowns
$('.nav-dropbtn').click(function(e) {
$(this).next('.nav-dropdown-content').toggleClass('nav-dropdown-active');
$(this).parent().siblings('.nav-dropdown')
.children('.nav-dropdown-content').removeClass('nav-dropdown-active');
});
$("body").click(function(e){
$('.nav-dropdown-content').removeClass('nav-dropdown-active');
});
$(".nav-dropdown").click(function(e){
e.stopPropagation();
});
});
</script>
<style type="text/css">
/* Theme (user-documented overrideables for nav appearance) */
.distill-site-nav {
color: rgba(255, 255, 255, 0.8);
background-color: #0F2E3D;
font-size: 15px;
font-weight: 300;
}
.distill-site-nav a {
color: inherit;
text-decoration: none;
}
.distill-site-nav a:hover {
color: white;
}
@media print {
.distill-site-nav {
display: none;
}
}
.distill-site-header {
}
.distill-site-footer {
}
/* Site Header */
.distill-site-header {
width: 100%;
box-sizing: border-box;
z-index: 3;
}
.distill-site-header .nav-left {
display: inline-block;
margin-left: 8px;
}
@media screen and (max-width: 768px) {
.distill-site-header .nav-left {
margin-left: 0;
}
}
.distill-site-header .nav-right {
float: right;
margin-right: 8px;
}
.distill-site-header a,
.distill-site-header .title {
display: inline-block;
text-align: center;
padding: 14px 10px 14px 10px;
}
.distill-site-header .title {
font-size: 18px;
min-width: 150px;
}
.distill-site-header .logo {
padding: 0;
}
.distill-site-header .logo img {
display: none;
max-height: 20px;
width: auto;
margin-bottom: -4px;
}
.distill-site-header .nav-image img {
max-height: 18px;
width: auto;
display: inline-block;
margin-bottom: -3px;
}
@media screen and (min-width: 1000px) {
.distill-site-header .logo img {
display: inline-block;
}
.distill-site-header .nav-left {
margin-left: 20px;
}
.distill-site-header .nav-right {
margin-right: 20px;
}
.distill-site-header .title {
padding-left: 12px;
}
}
.distill-site-header .nav-toggle {
display: none;
}
.nav-dropdown {
display: inline-block;
position: relative;
}
.nav-dropdown .nav-dropbtn {
border: none;
outline: none;
color: rgba(255, 255, 255, 0.8);
padding: 16px 10px;
background-color: transparent;
font-family: inherit;
font-size: inherit;
font-weight: inherit;
margin: 0;
margin-top: 1px;
z-index: 2;
}
.nav-dropdown-content {
display: none;
position: absolute;
background-color: white;
min-width: 200px;
border: 1px solid rgba(0,0,0,0.15);
border-radius: 4px;
box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.1);
z-index: 1;
margin-top: 2px;
white-space: nowrap;
padding-top: 4px;
padding-bottom: 4px;
}
.nav-dropdown-content hr {
margin-top: 4px;
margin-bottom: 4px;
border: none;
border-bottom: 1px solid rgba(0, 0, 0, 0.1);
}
.nav-dropdown-active {
display: block;
}
.nav-dropdown-content a, .nav-dropdown-content .nav-dropdown-header {
color: black;
padding: 6px 24px;
text-decoration: none;
display: block;
text-align: left;
}
.nav-dropdown-content .nav-dropdown-header {
display: block;
padding: 5px 24px;
padding-bottom: 0;
text-transform: uppercase;
font-size: 14px;
color: #999999;
white-space: nowrap;
}
.nav-dropdown:hover .nav-dropbtn {
color: white;
}
.nav-dropdown-content a:hover {
background-color: #ddd;
color: black;
}
.nav-right .nav-dropdown-content {
margin-left: -45%;
right: 0;
}
@media screen and (max-width: 768px) {
.distill-site-header a, .distill-site-header .nav-dropdown {display: none;}
.distill-site-header a.nav-toggle {
float: right;
display: block;
}
.distill-site-header .title {
margin-left: 0;
}
.distill-site-header .nav-right {
margin-right: 0;
}
.distill-site-header {
overflow: hidden;
}
.nav-right .nav-dropdown-content {
margin-left: 0;
}
}
@media screen and (max-width: 768px) {
.distill-site-header.responsive {position: relative; min-height: 500px; }
.distill-site-header.responsive a.nav-toggle {
position: absolute;
right: 0;
top: 0;
}
.distill-site-header.responsive a,
.distill-site-header.responsive .nav-dropdown {
display: block;
text-align: left;
}
.distill-site-header.responsive .nav-left,
.distill-site-header.responsive .nav-right {
width: 100%;
}
.distill-site-header.responsive .nav-dropdown {float: none;}
.distill-site-header.responsive .nav-dropdown-content {position: relative;}
.distill-site-header.responsive .nav-dropdown .nav-dropbtn {
display: block;
width: 100%;
text-align: left;
}
}
/* Site Footer */
.distill-site-footer {
width: 100%;
overflow: hidden;
box-sizing: border-box;
z-index: 3;
margin-top: 30px;
padding-top: 30px;
padding-bottom: 30px;
text-align: center;
}
/* Headroom */
d-title {
padding-top: 6rem;
}
@media print {
d-title {
padding-top: 4rem;
}
}
.headroom {
z-index: 1000;
position: fixed;
top: 0;
left: 0;
right: 0;
}
.headroom--transition {
transition: all .4s ease-in-out;
}
.headroom--unpinned {
top: -100px;
}
.headroom--pinned {
top: 0;
}
/* adjust viewport for navbar height */
/* helps vertically center bootstrap (non-distill) content */
.min-vh-100 {
min-height: calc(100vh - 100px) !important;
}
</style>
<script src="site_libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
<link href="site_libs/font-awesome-6.4.0/css/all.min.css" rel="stylesheet"/>
<link href="site_libs/font-awesome-6.4.0/css/v4-shims.min.css" rel="stylesheet"/>
<script src="site_libs/headroom-0.9.4/headroom.min.js"></script>
<script src="site_libs/autocomplete-0.37.1/autocomplete.min.js"></script>
<script src="site_libs/fuse-6.4.1/fuse.min.js"></script>
<script type="application/javascript">
function getMeta(metaName) {
var metas = document.getElementsByTagName('meta');
for (let i = 0; i < metas.length; i++) {
if (metas[i].getAttribute('name') === metaName) {
return metas[i].getAttribute('content');
}
}
return '';
}
function offsetURL(url) {
var offset = getMeta('distill:offset');
return offset ? offset + '/' + url : url;
}
function createFuseIndex() {
// create fuse index
var options = {
keys: [
{ name: 'title', weight: 20 },
{ name: 'categories', weight: 15 },
{ name: 'description', weight: 10 },
{ name: 'contents', weight: 5 },
],
ignoreLocation: true,
threshold: 0
};
var fuse = new window.Fuse([], options);
// fetch the main search.json
return fetch(offsetURL('search.json'))
.then(function(response) {
if (response.status == 200) {
return response.json().then(function(json) {
// index main articles
json.articles.forEach(function(article) {
fuse.add(article);
});
// download collections and index their articles
return Promise.all(json.collections.map(function(collection) {
return fetch(offsetURL(collection)).then(function(response) {
if (response.status === 200) {
return response.json().then(function(articles) {
articles.forEach(function(article) {
fuse.add(article);
});
})
} else {
return Promise.reject(
new Error('Unexpected status from search index request: ' +
response.status)
);
}
});
})).then(function() {
return fuse;
});
});
} else {
return Promise.reject(
new Error('Unexpected status from search index request: ' +
response.status)
);
}
});
}
window.document.addEventListener("DOMContentLoaded", function (event) {
// get search element (bail if we don't have one)
var searchEl = window.document.getElementById('distill-search');
if (!searchEl)
return;
createFuseIndex()
.then(function(fuse) {
// make search box visible
searchEl.classList.remove('hidden');
// initialize autocomplete
var options = {
autoselect: true,
hint: false,
minLength: 2,
};
window.autocomplete(searchEl, options, [{
source: function(query, callback) {
const searchOptions = {
isCaseSensitive: false,
shouldSort: true,
minMatchCharLength: 2,
limit: 10,
};
var results = fuse.search(query, searchOptions);
callback(results
.map(function(result) { return result.item; })
);
},
templates: {
suggestion: function(suggestion) {
var img = suggestion.preview && Object.keys(suggestion.preview).length > 0
? `<img src="${offsetURL(suggestion.preview)}"</img>`
: '';
var html = `
<div class="search-item">
<h3>${suggestion.title}</h3>
<div class="search-item-description">
${suggestion.description || ''}
</div>
<div class="search-item-preview">
${img}
</div>
</div>
`;
return html;
}
}
}]).on('autocomplete:selected', function(event, suggestion) {
window.location.href = offsetURL(suggestion.path);
});
// remove inline display style on autocompleter (we want to
// manage responsive display via css)
$('.algolia-autocomplete').css("display", "");
})
.catch(function(error) {
console.log(error);
});
});
</script>
<style type="text/css">
.nav-search {
font-size: x-small;
}
/* Algolioa Autocomplete */
.algolia-autocomplete {
display: inline-block;
margin-left: 10px;
vertical-align: sub;
background-color: white;
color: black;
padding: 6px;
padding-top: 8px;
padding-bottom: 0;
border-radius: 6px;
border: 1px #0F2E3D solid;
width: 180px;
}
@media screen and (max-width: 768px) {
.distill-site-nav .algolia-autocomplete {
display: none;
visibility: hidden;
}
.distill-site-nav.responsive .algolia-autocomplete {
display: inline-block;
visibility: visible;
}
.distill-site-nav.responsive .algolia-autocomplete .aa-dropdown-menu {
margin-left: 0;
width: 400px;
max-height: 400px;
}
}
.algolia-autocomplete .aa-input, .algolia-autocomplete .aa-hint {
width: 90%;
outline: none;
border: none;
}
.algolia-autocomplete .aa-hint {
color: #999;
}
.algolia-autocomplete .aa-dropdown-menu {
width: 550px;
max-height: 70vh;
overflow-x: visible;
overflow-y: scroll;
padding: 5px;
margin-top: 3px;
margin-left: -150px;
background-color: #fff;
border-radius: 5px;
border: 1px solid #999;
border-top: none;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion {
cursor: pointer;
padding: 5px 4px;
border-bottom: 1px solid #eee;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion:last-of-type {
border-bottom: none;
margin-bottom: 2px;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item {
overflow: hidden;
font-size: 0.8em;
line-height: 1.4em;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item h3 {
font-size: 1rem;
margin-block-start: 0;
margin-block-end: 5px;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-description {
display: inline-block;
overflow: hidden;
height: 2.8em;
width: 80%;
margin-right: 4%;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview {
display: inline-block;
width: 15%;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview img {
height: 3em;
width: auto;
display: none;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview img[src] {
display: initial;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion.aa-cursor {
background-color: #eee;
}
.algolia-autocomplete .aa-dropdown-menu .aa-suggestion em {
font-weight: bold;
font-style: normal;
}
</style>
<!--/radix_placeholder_navigation_in_header-->
<!--radix_placeholder_distill-->
<style type="text/css">
body {
background-color: white;
}
.pandoc-table {
width: 100%;
}
.pandoc-table>caption {
margin-bottom: 10px;
}
.pandoc-table th:not([align]) {
text-align: left;
}
.pagedtable-footer {
font-size: 15px;
}
d-byline .byline {
grid-template-columns: 2fr 2fr;
}
d-byline .byline h3 {
margin-block-start: 1.5em;
}
d-byline .byline .authors-affiliations h3 {
margin-block-start: 0.5em;
}
.authors-affiliations .orcid-id {
width: 16px;
height:16px;
margin-left: 4px;
margin-right: 4px;
vertical-align: middle;
padding-bottom: 2px;
}
d-title .dt-tags {
margin-top: 1em;
grid-column: text;
}
.dt-tags .dt-tag {
text-decoration: none;
display: inline-block;
color: rgba(0,0,0,0.6);
padding: 0em 0.4em;
margin-right: 0.5em;
margin-bottom: 0.4em;
font-size: 70%;
border: 1px solid rgba(0,0,0,0.2);
border-radius: 3px;
text-transform: uppercase;
font-weight: 500;
}
d-article table.gt_table td,
d-article table.gt_table th {
border-bottom: none;
font-size: 100%;
}
.html-widget {
margin-bottom: 2.0em;
}
.l-screen-inset {
padding-right: 16px;
}
.l-screen .caption {
margin-left: 10px;
}
.shaded {
background: rgb(247, 247, 247);
padding-top: 20px;
padding-bottom: 20px;
border-top: 1px solid rgba(0, 0, 0, 0.1);
border-bottom: 1px solid rgba(0, 0, 0, 0.1);
}
.shaded .html-widget {
margin-bottom: 0;
border: 1px solid rgba(0, 0, 0, 0.1);
}
.shaded .shaded-content {
background: white;
}
.text-output {
margin-top: 0;
line-height: 1.5em;
}
.hidden {
display: none !important;
}
d-article {
padding-top: 2.5rem;
padding-bottom: 30px;
}
d-appendix {
padding-top: 30px;
}
d-article>p>img {
width: 100%;
}
d-article h2 {
margin: 1rem 0 1.5rem 0;
}
d-article h3 {
margin-top: 1.5rem;
}
d-article iframe {
border: 1px solid rgba(0, 0, 0, 0.1);
margin-bottom: 2.0em;
width: 100%;
}
/* Tweak code blocks */
d-article div.sourceCode code,
d-article pre code {
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
}
d-article pre,
d-article div.sourceCode,
d-article div.sourceCode pre {
overflow: auto;
}
d-article div.sourceCode {
background-color: white;
}
d-article div.sourceCode pre {
padding-left: 10px;
font-size: 12px;
border-left: 2px solid rgba(0,0,0,0.1);
}
d-article pre {
font-size: 12px;
color: black;
background: none;
margin-top: 0;
text-align: left;
white-space: pre;
word-spacing: normal;
word-break: normal;
word-wrap: normal;
line-height: 1.5;
-moz-tab-size: 4;
-o-tab-size: 4;
tab-size: 4;
-webkit-hyphens: none;
-moz-hyphens: none;
-ms-hyphens: none;
hyphens: none;
}
d-article pre a {
border-bottom: none;
}
d-article pre a:hover {
border-bottom: none;
text-decoration: underline;
}
d-article details {
grid-column: text;
margin-bottom: 0.8em;
}
@media(min-width: 768px) {
d-article pre,
d-article div.sourceCode,
d-article div.sourceCode pre {
overflow: visible !important;
}
d-article div.sourceCode pre {
padding-left: 18px;
font-size: 14px;
}
d-article pre {
font-size: 14px;
}
}
figure img.external {
background: white;
border: 1px solid rgba(0, 0, 0, 0.1);
box-shadow: 0 1px 8px rgba(0, 0, 0, 0.1);
padding: 18px;
box-sizing: border-box;
}
/* CSS for d-contents */
.d-contents {
grid-column: text;
color: rgba(0,0,0,0.8);
font-size: 0.9em;
padding-bottom: 1em;
margin-bottom: 1em;
padding-bottom: 0.5em;
margin-bottom: 1em;
padding-left: 0.25em;
justify-self: start;
}
@media(min-width: 1000px) {
.d-contents.d-contents-float {
height: 0;
grid-column-start: 1;
grid-column-end: 4;
justify-self: center;
padding-right: 3em;
padding-left: 2em;
}
}
.d-contents nav h3 {
font-size: 18px;
margin-top: 0;
margin-bottom: 1em;
}
.d-contents li {
list-style-type: none
}
.d-contents nav > ul {
padding-left: 0;
}
.d-contents ul {
padding-left: 1em
}
.d-contents nav ul li {
margin-top: 0.6em;
margin-bottom: 0.2em;
}
.d-contents nav a {
font-size: 13px;
border-bottom: none;
text-decoration: none
color: rgba(0, 0, 0, 0.8);