|
|
<!DOCTYPE html>
|
|
|
|
|
|
<html>
|
|
|
|
|
|
<head>
|
|
|
|
|
|
<meta charset="utf-8" />
|
|
|
<meta name="generator" content="pandoc" />
|
|
|
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
|
|
|
|
|
<meta name="author" content="Norwin Roosen" />
|
|
|
|
|
|
<meta name="date" content="2023-03-08" />
|
|
|
|
|
|
<title>Caching openSenseMap Data for Reproducibility</title>
|
|
|
|
|
|
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
|
|
|
// be compatible with the behavior of Pandoc < 2.8).
|
|
|
document.addEventListener('DOMContentLoaded', function(e) {
|
|
|
var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
|
|
|
var i, h, a;
|
|
|
for (i = 0; i < hs.length; i++) {
|
|
|
h = hs[i];
|
|
|
if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6
|
|
|
a = h.attributes;
|
|
|
while (a.length > 0) h.removeAttribute(a[0].name);
|
|
|
}
|
|
|
});
|
|
|
</script>
|
|
|
|
|
|
<style type="text/css">
|
|
|
code{white-space: pre-wrap;}
|
|
|
span.smallcaps{font-variant: small-caps;}
|
|
|
span.underline{text-decoration: underline;}
|
|
|
div.column{display: inline-block; vertical-align: top; width: 50%;}
|
|
|
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
|
|
|
ul.task-list{list-style: none;}
|
|
|
</style>
|
|
|
|
|
|
|
|
|
|
|
|
<style type="text/css">
|
|
|
code {
|
|
|
white-space: pre;
|
|
|
}
|
|
|
.sourceCode {
|
|
|
overflow: visible;
|
|
|
}
|
|
|
</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
|
|
|
{ }
|
|
|
@media screen {
|
|
|
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
|
|
|
}
|
|
|
code span.al { color: #ff0000; font-weight: bold; }
|
|
|
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; }
|
|
|
code span.at { color: #7d9029; }
|
|
|
code span.bn { color: #40a070; }
|
|
|
code span.bu { color: #008000; }
|
|
|
code span.cf { color: #007020; font-weight: bold; }
|
|
|
code span.ch { color: #4070a0; }
|
|
|
code span.cn { color: #880000; }
|
|
|
code span.co { color: #60a0b0; font-style: italic; }
|
|
|
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; }
|
|
|
code span.do { color: #ba2121; font-style: italic; }
|
|
|
code span.dt { color: #902000; }
|
|
|
code span.dv { color: #40a070; }
|
|
|
code span.er { color: #ff0000; font-weight: bold; }
|
|
|
code span.ex { }
|
|
|
code span.fl { color: #40a070; }
|
|
|
code span.fu { color: #06287e; }
|
|
|
code span.im { color: #008000; font-weight: bold; }
|
|
|
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; }
|
|
|
code span.kw { color: #007020; font-weight: bold; }
|
|
|
code span.op { color: #666666; }
|
|
|
code span.ot { color: #007020; }
|
|
|
code span.pp { color: #bc7a00; }
|
|
|
code span.sc { color: #4070a0; }
|
|
|
code span.ss { color: #bb6688; }
|
|
|
code span.st { color: #4070a0; }
|
|
|
code span.va { color: #19177c; }
|
|
|
code span.vs { color: #4070a0; }
|
|
|
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; }
|
|
|
</style>
|
|
|
<script>
|
|
|
// apply pandoc div.sourceCode style to pre.sourceCode instead
|
|
|
(function() {
|
|
|
var sheets = document.styleSheets;
|
|
|
for (var i = 0; i < sheets.length; i++) {
|
|
|
if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
|
|
|
try { var rules = sheets[i].cssRules; } catch (e) { continue; }
|
|
|
var j = 0;
|
|
|
while (j < rules.length) {
|
|
|
var rule = rules[j];
|
|
|
// check if there is a div.sourceCode rule
|
|
|
if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") {
|
|
|
j++;
|
|
|
continue;
|
|
|
}
|
|
|
var style = rule.style.cssText;
|
|
|
// check if color or background-color is set
|
|
|
if (rule.style.color === '' && rule.style.backgroundColor === '') {
|
|
|
j++;
|
|
|
continue;
|
|
|
}
|
|
|
// replace div.sourceCode by a pre.sourceCode rule
|
|
|
sheets[i].deleteRule(j);
|
|
|
sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
|
|
|
}
|
|
|
}
|
|
|
})();
|
|
|
</script>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<style type="text/css">body {
|
|
|
background-color: #fff;
|
|
|
margin: 1em auto;
|
|
|
max-width: 700px;
|
|
|
overflow: visible;
|
|
|
padding-left: 2em;
|
|
|
padding-right: 2em;
|
|
|
font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
|
|
|
font-size: 14px;
|
|
|
line-height: 1.35;
|
|
|
}
|
|
|
#TOC {
|
|
|
clear: both;
|
|
|
margin: 0 0 10px 10px;
|
|
|
padding: 4px;
|
|
|
width: 400px;
|
|
|
border: 1px solid #CCCCCC;
|
|
|
border-radius: 5px;
|
|
|
background-color: #f6f6f6;
|
|
|
font-size: 13px;
|
|
|
line-height: 1.3;
|
|
|
}
|
|
|
#TOC .toctitle {
|
|
|
font-weight: bold;
|
|
|
font-size: 15px;
|
|
|
margin-left: 5px;
|
|
|
}
|
|
|
#TOC ul {
|
|
|
padding-left: 40px;
|
|
|
margin-left: -1.5em;
|
|
|
margin-top: 5px;
|
|
|
margin-bottom: 5px;
|
|
|
}
|
|
|
#TOC ul ul {
|
|
|
margin-left: -2em;
|
|
|
}
|
|
|
#TOC li {
|
|
|
line-height: 16px;
|
|
|
}
|
|
|
table {
|
|
|
margin: 1em auto;
|
|
|
border-width: 1px;
|
|
|
border-color: #DDDDDD;
|
|
|
border-style: outset;
|
|
|
border-collapse: collapse;
|
|
|
}
|
|
|
table th {
|
|
|
border-width: 2px;
|
|
|
padding: 5px;
|
|
|
border-style: inset;
|
|
|
}
|
|
|
table td {
|
|
|
border-width: 1px;
|
|
|
border-style: inset;
|
|
|
line-height: 18px;
|
|
|
padding: 5px 5px;
|
|
|
}
|
|
|
table, table th, table td {
|
|
|
border-left-style: none;
|
|
|
border-right-style: none;
|
|
|
}
|
|
|
table thead, table tr.even {
|
|
|
background-color: #f7f7f7;
|
|
|
}
|
|
|
p {
|
|
|
margin: 0.5em 0;
|
|
|
}
|
|
|
blockquote {
|
|
|
background-color: #f6f6f6;
|
|
|
padding: 0.25em 0.75em;
|
|
|
}
|
|
|
hr {
|
|
|
border-style: solid;
|
|
|
border: none;
|
|
|
border-top: 1px solid #777;
|
|
|
margin: 28px 0;
|
|
|
}
|
|
|
dl {
|
|
|
margin-left: 0;
|
|
|
}
|
|
|
dl dd {
|
|
|
margin-bottom: 13px;
|
|
|
margin-left: 13px;
|
|
|
}
|
|
|
dl dt {
|
|
|
font-weight: bold;
|
|
|
}
|
|
|
ul {
|
|
|
margin-top: 0;
|
|
|
}
|
|
|
ul li {
|
|
|
list-style: circle outside;
|
|
|
}
|
|
|
ul ul {
|
|
|
margin-bottom: 0;
|
|
|
}
|
|
|
pre, code {
|
|
|
background-color: #f7f7f7;
|
|
|
border-radius: 3px;
|
|
|
color: #333;
|
|
|
white-space: pre-wrap;
|
|
|
}
|
|
|
pre {
|
|
|
border-radius: 3px;
|
|
|
margin: 5px 0px 10px 0px;
|
|
|
padding: 10px;
|
|
|
}
|
|
|
pre:not([class]) {
|
|
|
background-color: #f7f7f7;
|
|
|
}
|
|
|
code {
|
|
|
font-family: Consolas, Monaco, 'Courier New', monospace;
|
|
|
font-size: 85%;
|
|
|
}
|
|
|
p > code, li > code {
|
|
|
padding: 2px 0px;
|
|
|
}
|
|
|
div.figure {
|
|
|
text-align: center;
|
|
|
}
|
|
|
img {
|
|
|
background-color: #FFFFFF;
|
|
|
padding: 2px;
|
|
|
border: 1px solid #DDDDDD;
|
|
|
border-radius: 3px;
|
|
|
border: 1px solid #CCCCCC;
|
|
|
margin: 0 5px;
|
|
|
}
|
|
|
h1 {
|
|
|
margin-top: 0;
|
|
|
font-size: 35px;
|
|
|
line-height: 40px;
|
|
|
}
|
|
|
h2 {
|
|
|
border-bottom: 4px solid #f7f7f7;
|
|
|
padding-top: 10px;
|
|
|
padding-bottom: 2px;
|
|
|
font-size: 145%;
|
|
|
}
|
|
|
h3 {
|
|
|
border-bottom: 2px solid #f7f7f7;
|
|
|
padding-top: 10px;
|
|
|
font-size: 120%;
|
|
|
}
|
|
|
h4 {
|
|
|
border-bottom: 1px solid #f7f7f7;
|
|
|
margin-left: 8px;
|
|
|
font-size: 105%;
|
|
|
}
|
|
|
h5, h6 {
|
|
|
border-bottom: 1px solid #ccc;
|
|
|
font-size: 105%;
|
|
|
}
|
|
|
a {
|
|
|
color: #0033dd;
|
|
|
text-decoration: none;
|
|
|
}
|
|
|
a:hover {
|
|
|
color: #6666ff; }
|
|
|
a:visited {
|
|
|
color: #800080; }
|
|
|
a:visited:hover {
|
|
|
color: #BB00BB; }
|
|
|
a[href^="http:"] {
|
|
|
text-decoration: underline; }
|
|
|
a[href^="https:"] {
|
|
|
text-decoration: underline; }
|
|
|
|
|
|
code > span.kw { color: #555; font-weight: bold; }
|
|
|
code > span.dt { color: #902000; }
|
|
|
code > span.dv { color: #40a070; }
|
|
|
code > span.bn { color: #d14; }
|
|
|
code > span.fl { color: #d14; }
|
|
|
code > span.ch { color: #d14; }
|
|
|
code > span.st { color: #d14; }
|
|
|
code > span.co { color: #888888; font-style: italic; }
|
|
|
code > span.ot { color: #007020; }
|
|
|
code > span.al { color: #ff0000; font-weight: bold; }
|
|
|
code > span.fu { color: #900; font-weight: bold; }
|
|
|
code > span.er { color: #a61717; background-color: #e3d2d2; }
|
|
|
</style>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</head>
|
|
|
|
|
|
<body>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<h1 class="title toc-ignore">Caching openSenseMap Data for
|
|
|
Reproducibility</h1>
|
|
|
<h4 class="author">Norwin Roosen</h4>
|
|
|
<h4 class="date">2023-03-08</h4>
|
|
|
|
|
|
|
|
|
|
|
|
<p>It may be useful to download data from openSenseMap only once. For
|
|
|
reproducible results, the data should be saved to disk, and reloaded at
|
|
|
a later point.</p>
|
|
|
<p>This avoids..</p>
|
|
|
<ul>
|
|
|
<li>changed results for queries without date parameters,</li>
|
|
|
<li>unnecessary wait times,</li>
|
|
|
<li>risk of API changes / API unavailability,</li>
|
|
|
<li>stress on the openSenseMap-server.</li>
|
|
|
</ul>
|
|
|
<p>This vignette shows how to use this built in
|
|
|
<code>opensensmapr</code> feature, and how to do it yourself in case you
|
|
|
want to save to other data formats.</p>
|
|
|
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># this vignette requires:</span></span>
|
|
|
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(opensensmapr)</span>
|
|
|
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(jsonlite)</span>
|
|
|
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(readr)</span></code></pre></div>
|
|
|
<div id="using-the-opensensmapr-caching-feature" class="section level2">
|
|
|
<h2>Using the opensensmapr Caching Feature</h2>
|
|
|
<p>All data retrieval functions of <code>opensensmapr</code> have a
|
|
|
built in caching feature, which serializes an API response to disk.
|
|
|
Subsequent identical requests will then return the serialized data
|
|
|
instead of making another request.</p>
|
|
|
<p>To use this feature, just add a path to a directory to the
|
|
|
<code>cache</code> parameter:</p>
|
|
|
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>b <span class="ot">=</span> <span class="fu">osem_boxes</span>(<span class="at">grouptag =</span> <span class="st">'ifgi'</span>, <span class="at">cache =</span> <span class="fu">tempdir</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><span class="co"># the next identical request will hit the cache only!</span></span>
|
|
|
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>b <span class="ot">=</span> <span class="fu">osem_boxes</span>(<span class="at">grouptag =</span> <span class="st">'ifgi'</span>, <span class="at">cache =</span> <span class="fu">tempdir</span>())</span>
|
|
|
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a></span>
|
|
|
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="co"># requests without the cache parameter will still be performed normally</span></span>
|
|
|
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a>b <span class="ot">=</span> <span class="fu">osem_boxes</span>(<span class="at">grouptag =</span> <span class="st">'ifgi'</span>)</span></code></pre></div>
|
|
|
<p>Looking at the cache directory we can see one file for each request,
|
|
|
which is identified through a hash of the request URL:</p>
|
|
|
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">list.files</span>(<span class="fu">tempdir</span>(), <span class="at">pattern =</span> <span class="st">'osemcache</span><span class="sc">\\</span><span class="st">..*</span><span class="sc">\\</span><span class="st">.rds'</span>)</span></code></pre></div>
|
|
|
<pre><code>## [1] "osemcache.17db5c57fc6fca4d836fa2cf30345ce8767cd61a.rds"</code></pre>
|
|
|
<p>You can maintain multiple caches simultaneously which allows to only
|
|
|
store data related to a script in the same directory:</p>
|
|
|
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>cacheDir <span class="ot">=</span> <span class="fu">getwd</span>() <span class="co"># current working directory</span></span>
|
|
|
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>b <span class="ot">=</span> <span class="fu">osem_boxes</span>(<span class="at">grouptag =</span> <span class="st">'ifgi'</span>, <span class="at">cache =</span> cacheDir)</span>
|
|
|
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a></span>
|
|
|
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="co"># the next identical request will hit the cache only!</span></span>
|
|
|
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>b <span class="ot">=</span> <span class="fu">osem_boxes</span>(<span class="at">grouptag =</span> <span class="st">'ifgi'</span>, <span class="at">cache =</span> cacheDir)</span></code></pre></div>
|
|
|
<p>To get fresh results again, just call <code>osem_clear_cache()</code>
|
|
|
for the respective cache:</p>
|
|
|
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">osem_clear_cache</span>() <span class="co"># clears default cache</span></span>
|
|
|
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="fu">osem_clear_cache</span>(<span class="fu">getwd</span>()) <span class="co"># clears a custom cache</span></span></code></pre></div>
|
|
|
</div>
|
|
|
<div id="custom-de--serialization" class="section level2">
|
|
|
<h2>Custom (De-) Serialization</h2>
|
|
|
<p>If you want to roll your own serialization method to support custom
|
|
|
data formats, here’s how:</p>
|
|
|
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># first get our example data:</span></span>
|
|
|
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>measurements <span class="ot">=</span> <span class="fu">osem_measurements</span>(<span class="st">'Windgeschwindigkeit'</span>)</span></code></pre></div>
|
|
|
<p>If you are paranoid and worry about <code>.rds</code> files not being
|
|
|
decodable anymore in the (distant) future, you could serialize to a
|
|
|
plain text format such as JSON. This of course comes at the cost of
|
|
|
storage space and performance.</p>
|
|
|
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># serializing senseBoxes to JSON, and loading from file again:</span></span>
|
|
|
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="fu">write</span>(jsonlite<span class="sc">::</span><span class="fu">serializeJSON</span>(measurements), <span class="st">'measurements.json'</span>)</span>
|
|
|
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>measurements_from_file <span class="ot">=</span> jsonlite<span class="sc">::</span><span class="fu">unserializeJSON</span>(readr<span class="sc">::</span><span class="fu">read_file</span>(<span class="st">'measurements.json'</span>))</span>
|
|
|
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(measurements_from_file)</span></code></pre></div>
|
|
|
<p>This method also persists the R object metadata (classes,
|
|
|
attributes). If you were to use a serialization method that can’t
|
|
|
persist object metadata, you could re-apply it with the following
|
|
|
functions:</p>
|
|
|
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co"># note the toJSON call instead of serializeJSON</span></span>
|
|
|
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="fu">write</span>(jsonlite<span class="sc">::</span><span class="fu">toJSON</span>(measurements), <span class="st">'measurements_bad.json'</span>)</span>
|
|
|
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>measurements_without_attrs <span class="ot">=</span> jsonlite<span class="sc">::</span><span class="fu">fromJSON</span>(<span class="st">'measurements_bad.json'</span>)</span>
|
|
|
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(measurements_without_attrs)</span>
|
|
|
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a></span>
|
|
|
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a>measurements_with_attrs <span class="ot">=</span> <span class="fu">osem_as_measurements</span>(measurements_without_attrs)</span>
|
|
|
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(measurements_with_attrs)</span></code></pre></div>
|
|
|
<p>The same goes for boxes via <code>osem_as_sensebox()</code>.</p>
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
<!-- code folding -->
|
|
|
|
|
|
|
|
|
<!-- dynamically load mathjax for compatibility with self-contained -->
|
|
|
<script>
|
|
|
(function () {
|
|
|
var script = document.createElement("script");
|
|
|
script.type = "text/javascript";
|
|
|
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
|
|
|
document.getElementsByTagName("head")[0].appendChild(script);
|
|
|
})();
|
|
|
</script>
|
|
|
|
|
|
</body>
|
|
|
</html>
|