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1981 lines (1849 loc) · 432 KB
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta http-equiv="Content-Style-Type" content="text/css" />
<meta name="generator" content="pandoc" />
<meta name="author" content="Jan Verbesselt, Sytze de Bruyn, Loïc Dutrieux, Valerio Avitabile, Dainius Masiliunas, David Swinkels" />
<title>Extra: Intro to vector</title>
<style type="text/css">
html {
line-height: 1.5;
font-family: Georgia, serif;
font-size: 20px;
color: #1a1a1a;
background-color: #fdfdfd;
}
body {
margin: 0 auto;
max-width: 36em;
padding-left: 50px;
padding-right: 50px;
padding-top: 50px;
padding-bottom: 50px;
hyphens: auto;
overflow-wrap: break-word;
text-rendering: optimizeLegibility;
font-kerning: normal;
}
@media (max-width: 600px) {
body {
font-size: 0.9em;
padding: 1em;
}
h1 {
font-size: 1.8em;
}
}
@media print {
body {
background-color: transparent;
color: black;
font-size: 12pt;
}
p, h2, h3 {
orphans: 3;
widows: 3;
}
h2, h3, h4 {
page-break-after: avoid;
}
}
p {
margin: 1em 0;
}
a {
color: #1a1a1a;
}
a:visited {
color: #1a1a1a;
}
img {
max-width: 100%;
}
h1, h2, h3, h4, h5, h6 {
margin-top: 1.4em;
}
h5, h6 {
font-size: 1em;
font-style: italic;
}
h6 {
font-weight: normal;
}
ol, ul {
padding-left: 1.7em;
margin-top: 1em;
}
li > ol, li > ul {
margin-top: 0;
}
blockquote {
margin: 1em 0 1em 1.7em;
padding-left: 1em;
border-left: 2px solid #e6e6e6;
color: #606060;
}
code {
font-family: Menlo, Monaco, 'Lucida Console', Consolas, monospace;
font-size: 85%;
margin: 0;
}
pre {
margin: 1em 0;
overflow: auto;
}
pre code {
padding: 0;
overflow: visible;
overflow-wrap: normal;
}
.sourceCode {
background-color: transparent;
overflow: visible;
}
hr {
background-color: #1a1a1a;
border: none;
height: 1px;
margin: 1em 0;
}
table {
margin: 1em 0;
border-collapse: collapse;
width: 100%;
overflow-x: auto;
display: block;
font-variant-numeric: lining-nums tabular-nums;
}
table caption {
margin-bottom: 0.75em;
}
tbody {
margin-top: 0.5em;
border-top: 1px solid #1a1a1a;
border-bottom: 1px solid #1a1a1a;
}
th {
border-top: 1px solid #1a1a1a;
padding: 0.25em 0.5em 0.25em 0.5em;
}
td {
padding: 0.125em 0.5em 0.25em 0.5em;
}
header {
margin-bottom: 4em;
text-align: center;
}
#TOC li {
list-style: none;
}
#TOC ul {
padding-left: 1.3em;
}
#TOC > ul {
padding-left: 0;
}
#TOC a:not(:hover) {
text-decoration: none;
}
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 -1.6em;
vertical-align: middle;
}
.display.math{display: block; text-align: center; margin: 0.5rem auto;}
</style>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<!-- jQuery -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.10.3/jquery-ui.min.js"></script>
<!-- bootstrap -->
<!--<link href="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/css/bootstrap.min.css" rel="stylesheet" id="style">-->
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<!-- highlight.js -->
<!--<link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/7.3/styles/default.min.css" rel="stylesheet" id="code-style">-->
<script src="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/7.3/highlight.min.js"></script>
<script>
hljs.LANGUAGES.r=function(a){var b="([a-zA-Z]|\\.[a-zA-Z.])[a-zA-Z0-9._]*";return{c:[a.HCM,{b:b,l:b,k:{keyword:"function if in break next repeat else for return switch while try tryCatch|10 stop warning require library attach detach source setMethod setGeneric setGroupGeneric setClass ...|10",literal:"NULL NA TRUE FALSE T F Inf NaN NA_integer_|10 NA_real_|10 NA_character_|10 NA_complex_|10"},r:0},{cN:"number",b:"0[xX][0-9a-fA-F]+[Li]?\\b",r:0},{cN:"number",b:"\\d+(?:[eE][+\\-]?\\d*)?L\\b",r:0},{cN:"number",b:"\\d+\\.(?!\\d)(?:i\\b)?",r:0},{cN:"number",b:"\\d+(?:\\.\\d*)?(?:[eE][+\\-]?\\d*)?i?\\b",r:0},{cN:"number",b:"\\.\\d+(?:[eE][+\\-]?\\d*)?i?\\b",r:0},{b:"`",e:"`",r:0},{cN:"string",b:'"',e:'"',c:[a.BE],r:0},{cN:"string",b:"'",e:"'",c:[a.BE],r:0}]}}(hljs); </script>
<!--<script type="text/javascript", src="https://yandex.st/highlightjs/7.3/languages/r.min.js"></script>-->
<!-- Manific Popup -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/magnific-popup.js/0.8.9/jquery.magnific-popup.min.js"></script>
<script type="text/javascript"
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<script defer="defer">
// Function to generate the dynamic table of contents
jQuery.fn.generate_TOC = function () {
var base = $(this[0]);
var selectors = ['h1', 'h2', 'h3', 'h4'];
var last_ptr = [{}, {}, {}, {}];
var anchors = {};
generate_anchor = function (text) {
var test = text.replace(/\W/g, '_');
while(test in anchors){
//if no suffix, add one
if(test.match(/_\d+$/) === null){
test = test + "_2";
}
//else generate unique id for duplicates by adding one to the suffix
else {
test = test.replace(/_(\d+)$/, function(match, number){ var num=+number+1; return("_" + num) });
}
}
anchors[test]=1;
return(test);
}
$(selectors.join(',')).filter(function(index) { return $(this).parent().attr("id") != 'header'; }).each(function () {
var heading = $(this);
var idx = selectors.indexOf(heading.prop('tagName').toLowerCase());
var itr = 0;
while (itr <= idx) {
if (jQuery.isEmptyObject(last_ptr[itr])) {
last_ptr[itr] = $('<ul>').addClass('nav');
if (itr === 0) {
base.append(last_ptr[itr])
} else {
if(last_ptr[itr-1].children('li').length === 0){
last_ptr[itr-1].append(last_ptr[itr]);
}
else {
last_ptr[itr - 1].children('li').last().append(last_ptr[itr]);
}
}
}
itr++;
}
var anchor = generate_anchor(heading.text());
heading.attr('id', anchor);
var a = $('<a>')
.text(heading.text())
.attr('href', '#' + anchor);
var li = $('<li>')
.append(a);
last_ptr[idx].append(li);
for (i = idx + 1; i < last_ptr.length; i++) {
last_ptr[i] = {};
}
});
}
/* run scripts when document is ready */
$(function() {
"use strict";
var $window = $(window);
var $body = $(document.body);
/* size of thumbnails */
var hidden_types = ['source']
var output_types = ['output', 'message', 'warning', 'error']
/* style tables */
$('table').addClass('table table-striped table-bordered table-hover table-condensed');
$('pre code').each(function(i, e) {
hljs.highlightBlock(e);
});
/* Magnific Popup */
$(".thumbnail").each(function(){
$(this).magnificPopup({
disableOn: 768,
closeOnContentClick: true,
type: 'image',
items: {
src: $(this).find('img').attr('src'),
}
});
});
function toggle_block(obj, show) {
var span = obj.find('span');
if(show === true){
span.removeClass('glyphicon-chevron-up').addClass('glyphicon-chevron-down');
obj.next('pre').slideDown();
}
else {
span.removeClass('glyphicon-chevron-down').addClass('glyphicon-chevron-up');
obj.next('pre').slideUp();
}
}
function toggle_thumbnails(imgs, show){
if(show === true){
imgs.parents().show()
imgs.slideDown();
}
else {
imgs.slideUp(400, function(){ $(this).parent().hide(); });
}
}
function global_toggle(obj){
var type = obj.attr('type');
var show = !obj.parent('li').hasClass('active');
if(show === true){
obj.parent('li').addClass('active');
}
else{
obj.parent('li').removeClass('active');
}
if(type == 'figure'){
toggle_thumbnails($('.thumbnail img'), show);
}
else {
$('.toggle.' + type).each(function() { toggle_block($(this), show); });
}
}
/* onclick toggle next code block */
$('.toggle').click(function() {
var span = $(this).find('span');
toggle_block($(this), !span.hasClass('glyphicon-chevron-down'));
return false
})
// global toggles
$('.toggle-global').click(function(){
var type = $(this).attr('type');
if(type === 'all-source'){
$('li a.source').each(function() {
global_toggle($(this));
});
}
else if(type === 'all-output'){
$.each(output_types, function(i, val){
console.log(val);
global_toggle($('li a.' + val));
});
}
else {
console.log($(this));
global_toggle($(this));
}
return false;
});
/* table of contents */
if($(['h1', 'h2', 'h3', 'h4'].join(',')).length > 0){
$('body > #wrap > .container > .row').append('<div class="col-md-2"><div id="toc" class="well sidebar sidenav affix hidden-print"/></div>');
$('#toc').generate_TOC();
}
$.each(hidden_types, function(i, type) {
$('li[type=' + type + ']').each(function(){ global_toggle($(this)); });
});
/* remove paragraphs with no content */
$('p:empty').remove();
$body.scrollspy({
target: '.sidebar',
});
/* theme switch */
$('.theme-switch').click(function(){
var css = $('link[title=' + $(this).attr('title') + ']');
$('#theme[rel=stylesheet]').attr('href', css.attr('href'));
$('.theme-switch').closest('li').removeClass('active');
$(this).closest('li').addClass('active');
return false;
});
/* code style switch */ //TODO use same function for both of these?
$('.highlight-switch').click(function(){
var css = $('link[title="' + $(this).attr('title') + '"]');
$('#highlight[rel=stylesheet]').attr('href', css.attr('href'));
$('.highlight-switch').closest('li').removeClass('active');
$(this).closest('li').addClass('active');
return false;
});
//TODO refresh on show/hide
$window.on('load', function () {
$body.scrollspy('refresh');
})
});
</script>
<style>
/* Knitr_bootstrap styles */
#header {
display: none !important;
visibility: hidden !important;
}
#wrap .container-fluid {
padding: 0;
overflow: hidden;
}
.toggle{
text-transform: capitalize;
}
.toggle-global{
text-transform: capitalize;
}
/* Sticky footer styles */
* {
margin:0;
}
html,
body {
height: 100%;
padding:0 !important;
/* The html and body elements cannot have any padding or margin. */
/*overflow-x: hidden;*/
}
/* Wrapper for page content to push down footer */
#wrap {
min-height: 100%;
height: auto !important;
height: 100%;
/* Negative indent footer by it's height */
margin: 0 auto -120px;
}
/* Set the fixed height of the footer here */
#push,
#footer {
height: 120px;
}
#footer {
text-align: center;
}
/* Top level subheader elements. These are the first nested items underneath a header element. */
.header li {
font-size: 20px;
}
/* Makes the font smaller for all subheader elements. */
.sub-header li {
font-size: 12px;
}
button.thumbnails {
margin-left:0px;
}
/*
* Side navigation
*
* Scrollspy and affixed enhanced navigation to highlight sections and secondary
* sections of docs content.
*/
/* By default it's not affixed in mobile views, so undo that */
.sidebar.affix {
position: static;
}
/* First level of nav */
.sidenav {
margin-top: 30px;
margin-bottom: 30px;
padding-top: 10px;
padding-bottom: 10px;
border-radius: 5px;
}
/* All levels of nav */
.sidebar .nav > li > a {
display: block;
padding: 5px 20px;
}
.sidebar .nav > li > a:hover,
.sidebar .nav > li > a:focus {
text-decoration: none;
border-right: 1px solid;
}
.sidebar .nav > .active > a,
.sidebar .nav > .active:hover > a,
.sidebar .nav > .active:focus > a {
font-weight: bold;
background-color: transparent;
border-right: 1px solid;
}
/* Nav: second level (shown on .active) */
.sidebar .nav .nav {
display: none; /* Hide by default, but at >768px, show it */
margin-bottom: 8px;
}
.sidebar .nav .nav > li > a {
padding-top: 3px;
padding-bottom: 3px;
padding-left: 30px;
font-size: 90%;
}
.sidebar .nav .nav .nav > li > a {
padding-left: 40px;
}
.sidebar .nav .nav .nav .nav > li > a {
padding-left: 50px;
}
/* Show and affix the side nav when space allows it */
@media screen and (min-width: 992px) {
.sidebar .nav > .active > ul {
display: block;
}
/* Widen the fixed sidebar */
.sidebar.affix,
.sidebar.affix-bottom {
width: 213px;
}
.sidebar.affix-top,
.sidebar.affix {
position: fixed; /* Undo the static from mobile first approach */
top: 30px;
}
.sidebar.affix-bottom {
position: absolute; /* Undo the static from mobile first approach */
}
.sidebar.affix-bottom .sidenav,
.sidebar.affix .sidenav {
margin-top: 0;
margin-bottom: 0;
}
}
@media screen and (min-width: 1200px) {
/* Widen the fixed sidebar again */
.sidebar.affix-bottom,
.sidebar.affix {
width: 263px;
}
}
#toc {
padding: 10px 0px;
margin:0;
border:0;
}
.panel pre {
margin: 0;
padding: 0;
border: 0;
}
button + pre {
margin: 0;
padding: 0;
}
pre code {
border-radius: 0;
}
/* Magnific Popup CSS */
.mfp-bg {
top: 0;
left: 0;
width: 100%;
height: 100%;
z-index: 1042;
overflow: hidden;
position: fixed;
background: #0b0b0b;
opacity: 0.8;
filter: alpha(opacity=80); }
.mfp-wrap {
top: 0;
left: 0;
width: 100%;
height: 100%;
z-index: 1043;
position: fixed;
outline: none !important;
-webkit-backface-visibility: hidden; }
.mfp-container {
text-align: center;
position: absolute;
width: 100%;
height: 100%;
left: 0;
top: 0;
padding: 0 8px;
-webkit-box-sizing: border-box;
-moz-box-sizing: border-box;
box-sizing: border-box; }
.mfp-container:before {
content: '';
display: inline-block;
height: 100%;
vertical-align: middle; }
.mfp-align-top .mfp-container:before {
display: none; }
.mfp-content {
position: relative;
display: inline-block;
vertical-align: middle;
margin: 0 auto;
text-align: left;
z-index: 1045; }
.mfp-inline-holder .mfp-content,
.mfp-ajax-holder .mfp-content {
width: 100%;
cursor: auto; }
.mfp-ajax-cur {
cursor: progress; }
.mfp-zoom-out-cur,
.mfp-zoom-out-cur .mfp-image-holder .mfp-close {
cursor: -moz-zoom-out;
cursor: -webkit-zoom-out;
cursor: zoom-out; }
.mfp-zoom {
cursor: pointer;
cursor: -webkit-zoom-in;
cursor: -moz-zoom-in;
cursor: zoom-in; }
.mfp-auto-cursor .mfp-content {
cursor: auto; }
.mfp-close,
.mfp-arrow,
.mfp-preloader,
.mfp-counter {
-webkit-user-select: none;
-moz-user-select: none;
user-select: none; }
.mfp-loading.mfp-figure {
display: none; }
.mfp-hide {
display: none !important; }
.mfp-preloader {
color: #cccccc;
position: absolute;
top: 50%;
width: auto;
text-align: center;
margin-top: -0.8em;
left: 8px;
right: 8px;
z-index: 1044; }
.mfp-preloader a {
color: #cccccc; }
.mfp-preloader a:hover {
color: white; }
.mfp-s-ready .mfp-preloader {
display: none; }
.mfp-s-error .mfp-content {
display: none; }
button.mfp-close,
button.mfp-arrow {
overflow: visible;
cursor: pointer;
background: transparent;
border: 0;
-webkit-appearance: none;
display: block;
padding: 0;
z-index: 1046;
-webkit-box-shadow: none;
box-shadow: none; }
button::-moz-focus-inner {
padding: 0;
border: 0; }
.mfp-close {
width: 44px;
height: 44px;
line-height: 44px;
position: absolute;
right: 0;
top: 0;
text-decoration: none;
text-align: center;
opacity: 0.65;
padding: 0 0 18px 10px;
color: white;
font-style: normal;
font-size: 28px;
font-family: Arial, Baskerville, monospace; }
.mfp-close:hover, .mfp-close:focus {
opacity: 1; }
.mfp-close:active {
top: 1px; }
.mfp-close-btn-in .mfp-close {
color: #333333; }
.mfp-image-holder .mfp-close,
.mfp-iframe-holder .mfp-close {
color: white;
right: -6px;
text-align: right;
padding-right: 6px;
width: 100%; }
.mfp-counter {
position: absolute;
top: 0;
right: 0;
color: #cccccc;
font-size: 12px;
line-height: 18px; }
.mfp-arrow {
position: absolute;
opacity: 0.65;
margin: 0;
top: 50%;
margin-top: -55px;
padding: 0;
width: 90px;
height: 110px;
-webkit-tap-highlight-color: rgba(0, 0, 0, 0); }
.mfp-arrow:active {
margin-top: -54px; }
.mfp-arrow:hover,
.mfp-arrow:focus {
opacity: 1; }
.mfp-arrow:before, .mfp-arrow:after,
.mfp-arrow .mfp-b,
.mfp-arrow .mfp-a {
content: '';
display: block;
width: 0;
height: 0;
position: absolute;
left: 0;
top: 0;
margin-top: 35px;
margin-left: 35px;
border: medium inset transparent; }
.mfp-arrow:after,
.mfp-arrow .mfp-a {
border-top-width: 13px;
border-bottom-width: 13px;
top: 8px; }
.mfp-arrow:before,
.mfp-arrow .mfp-b {
border-top-width: 21px;
border-bottom-width: 21px; }
.mfp-arrow-left {
left: 0; }
.mfp-arrow-left:after,
.mfp-arrow-left .mfp-a {
border-right: 17px solid white;
margin-left: 31px; }
.mfp-arrow-left:before,
.mfp-arrow-left .mfp-b {
margin-left: 25px;
border-right: 27px solid #3f3f3f; }
.mfp-arrow-right {
right: 0; }
.mfp-arrow-right:after,
.mfp-arrow-right .mfp-a {
border-left: 17px solid white;
margin-left: 39px; }
.mfp-arrow-right:before,
.mfp-arrow-right .mfp-b {
border-left: 27px solid #3f3f3f; }
.mfp-iframe-holder {
padding-top: 40px;
padding-bottom: 40px; }
.mfp-iframe-holder .mfp-content {
line-height: 0;
width: 100%;
max-width: 900px; }
.mfp-iframe-scaler {
width: 100%;
height: 0;
overflow: hidden;
padding-top: 56.25%; }
.mfp-iframe-scaler iframe {
position: absolute;
display: block;
top: 0;
left: 0;
width: 100%;
height: 100%;
box-shadow: 0 0 8px rgba(0, 0, 0, 0.6);
background: black; }
.mfp-iframe-holder .mfp-close {
top: -40px; }
/* Main image in popup */
img.mfp-img {
width: auto;
max-width: 100%;
height: auto;
display: block;
line-height: 0;
-webkit-box-sizing: border-box;
-moz-box-sizing: border-box;
box-sizing: border-box;
padding: 40px 0 40px;
margin: 0 auto; }
/* The shadow behind the image */
.mfp-figure:after {
content: '';
position: absolute;
left: 0;
top: 40px;
bottom: 40px;
display: block;
right: 0;
width: auto;
height: auto;
z-index: -1;
box-shadow: 0 0 8px rgba(0, 0, 0, 0.6);
background: #444444; }
.mfp-figure {
line-height: 0; }
.mfp-bottom-bar {
margin-top: -36px;
position: absolute;
top: 100%;
left: 0;
width: 100%;
cursor: auto; }
.mfp-title {
text-align: left;
line-height: 18px;
color: #f3f3f3;
word-wrap: break-word;
padding-right: 36px; }
.mfp-figure small {
color: #bdbdbd;
display: block;
font-size: 12px;
line-height: 14px; }
.mfp-image-holder .mfp-content {
max-width: 100%; }
.mfp-gallery .mfp-image-holder .mfp-figure {
cursor: pointer; }
@media screen and (max-width: 800px) and (orientation: landscape), screen and (max-height: 300px) {
/**
* Remove all paddings around the image on small screen
*/
.mfp-img-mobile .mfp-image-holder {
padding-left: 0;
padding-right: 0; }
.mfp-img-mobile img.mfp-img {
padding: 0; }
/* The shadow behind the image */
.mfp-img-mobile .mfp-figure:after {
top: 0;
bottom: 0; }
.mfp-img-mobile .mfp-bottom-bar {
background: rgba(0, 0, 0, 0.6);
bottom: 0;
margin: 0;
top: auto;
padding: 3px 5px;
position: fixed;
-webkit-box-sizing: border-box;
-moz-box-sizing: border-box;
box-sizing: border-box; }
.mfp-img-mobile .mfp-bottom-bar:empty {
padding: 0; }
.mfp-img-mobile .mfp-counter {
right: 5px;
top: 3px; }
.mfp-img-mobile .mfp-close {
top: 0;
right: 0;
width: 35px;
height: 35px;
line-height: 35px;
background: rgba(0, 0, 0, 0.6);
position: fixed;
text-align: center;
padding: 0; }
.mfp-img-mobile .mfp-figure small {
display: inline;
margin-left: 5px; } }
@media all and (max-width: 900px) {
.mfp-arrow {
-webkit-transform: scale(0.75);
transform: scale(0.75); }
.mfp-arrow-left {
-webkit-transform-origin: 0;
transform-origin: 0; }
.mfp-arrow-right {
-webkit-transform-origin: 100%;
transform-origin: 100%; }
.mfp-container {
padding-left: 6px;
padding-right: 6px; } }
.mfp-ie7 .mfp-img {
padding: 0; }
.mfp-ie7 .mfp-bottom-bar {
width: 600px;
left: 50%;
margin-left: -300px;
margin-top: 5px;
padding-bottom: 5px; }
.mfp-ie7 .mfp-container {
padding: 0; }
.mfp-ie7 .mfp-content {
padding-top: 44px; }
.mfp-ie7 .mfp-close {
top: 0;
right: 0;
padding-top: 0; }
//Magnific overrides
.mfp-image img{
background: white;
}
.mfp-figure:after {
background: white;
}
/*
* Off Canvas navbar toggle right
* --------------------------------------------------
*/
@media screen and (max-width: 768px) {
.row-offcanvas .collapsing {
-webkit-transition: none 0;
-moz-transition: none 0;
transition: none 0;
}
.row-offcanvas .navbar {
position: absolute;
z-index: 2;
right:0;
height:100%;
width:55px;
border:0;
background-color:transparent;
}
.row-offcanvas .navbar-toggle {
margin-right: 5px;
margin-left: 5px;
}
.row-offcanvas {
position: relative;
}
.row-offcanvas-right.active .navbar {
position: absolute;
z-index: 2;
right: -28.4%;
width:40%;
background-color:#eee;