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hakyll-bootstrap/img/thumbnails/logo.png deleted 100644 → 0
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hakyll-bootstrap/img/thumbnails/palathark_logo.png

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hakyll-bootstrap/index.html deleted 100644 → 0
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<!DOCTYPE HTML>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="Homepage of Orestis Malaspinas" content="">
<meta name="Orestis Malaspinas" content="">
<title>$title$</title>
<link href="/css/bootstrap.css" rel="stylesheet">
<link href="/css/syntax.css" rel="stylesheet">
<link href="/css/carousel.css" rel="stylesheet">
<link href='http://fonts.googleapis.com/css?family=Open+Sans' rel='stylesheet' type='text/css'>
<style>
body {
font-family: 'Open Sans', sans-serif;
}
</style>
</head>
<body>
$partial("templates/nav.html")$
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================================================== -->
<div id="myCarousel" class="carousel slide" data-ride="carousel">
<ol class="carousel-indicators">
<li data-target="#myCarousel" data-slide-to="0" class="active"></li>
<li data-target="#myCarousel" data-slide-to="1"></li>
<li data-target="#myCarousel" data-slide-to="2"></li>
</ol>
<div class="carousel-inner">
<div class="item active">
<img src="img/large/q_0_5.0000.png" alt="Fluid mechanics">
<div class="container">
<div class="carousel-caption">
<!-- <h1 style="color:black;">Computational fluid mechanics</h1>
<p style="color:black;">Flow pas a sphere at Re=3900</p> -->
<p><a class="btn btn-lg btn-primary" href="https://www.palabos.org" role="button">Computational fluid dynamics</a></p>
</div>
</div>
</div>
<div class="item">
<img src="img/large/live_stream.png" alt="Live stream">
<div class="container">
<div class="carousel-caption">
<!-- <h1>Live stream</h1>
<p>Checkout if I'm live</p> -->
<p><a class="btn btn-lg btn-primary" href="https://www.twitch.tv/omhepia" role="button">Live stream: Twitch.tv</a></p>
</div>
</div>
</div>
<div class="item">
<img data-src="holder.js/900x500/vine/text: " alt="EpiCells">
<div class="container">
<div class="carousel-caption">
<h1></h1>
<p></p>
<p><a class="btn btn-lg btn-primary" href="http://www.epicells.unige.ch/index.php" role="button">EpiCells: epithelial cells simulation</a></p>
</div>
</div>
</div>
</div>
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<a class="right carousel-control" href="#myCarousel" data-slide="next"><span class="glyphicon glyphicon-chevron-right"></span></a>
</div>
<!-- Research messaging and featurettes
================================================== -->
<div class="container projects">
<div class="row">
<div class="col-lg-4">
<img class="img-square" src="img/thumbnails/boltzmann.png" alt="Palabos">
<h2>Palabos</h2>
<p>The Palabos library is a general-purpose computational fluid dynamics (CFD) library,
with a kernel based on the lattice Boltzmann (LB) method. It is used both as a research
and an engineering tool.
</p>
<p><a class="btn btn-default" href="https://www.palabos.org/" role="button">View details &raquo;</a></p>
</div>
<div class="col-lg-4">
<img class="img-square" src="img/thumbnails/palathark_logo.png" alt="Palathark">
<h2>Palathark</h2>
<p>Palathark is an open source lattice Boltzmann library written in Futhark.
Its aim if to be agnostic of the underlying hardware (single core CPU, GPU, multi-threaded CPU, ...)
while remaining very efficient numerically. It is an active research topic.
</p>
<p><a class="btn btn-default" href="https://gitedu.hesge.ch/orestis.malaspin/palathark" role="button">Gitedu repo &raquo;</a></p>
</div>
<div class="col-lg-4">
<img class="img-square" src="img/thumbnails/logo.png" alt="SimCovid">
<h2>Pandemic simulation</h2>
<p>An open source agent based pandemics simulator based on the A/B street traffic simulation game.
Currently under heavy development.
</p>
<p><a class="btn btn-default" href="https://github.com/omalaspinas/abstreet" role="button">Gthub repo &raquo;</a></p>
</div>
</div>
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/*!
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if (typeof jQuery === "undefined") { throw new Error("Bootstrap requires jQuery") }
/* ========================================================================
* Bootstrap: transition.js v3.0.2
* http://getbootstrap.com/javascript/#transitions
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// CSS TRANSITION SUPPORT (Shoutout: http://www.modernizr.com/)
// ============================================================
function transitionEnd() {
var el = document.createElement('bootstrap')
var transEndEventNames = {
'WebkitTransition' : 'webkitTransitionEnd'
, 'MozTransition' : 'transitionend'
, 'OTransition' : 'oTransitionEnd otransitionend'
, 'transition' : 'transitionend'
}
for (var name in transEndEventNames) {
if (el.style[name] !== undefined) {
return { end: transEndEventNames[name] }
}
}
}
// http://blog.alexmaccaw.com/css-transitions
$.fn.emulateTransitionEnd = function (duration) {
var called = false, $el = this
$(this).one($.support.transition.end, function () { called = true })
var callback = function () { if (!called) $($el).trigger($.support.transition.end) }
setTimeout(callback, duration)
return this
}
$(function () {
$.support.transition = transitionEnd()
})
}(jQuery);
/* ========================================================================
* Bootstrap: alert.js v3.0.2
* http://getbootstrap.com/javascript/#alerts
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// ALERT CLASS DEFINITION
// ======================
var dismiss = '[data-dismiss="alert"]'
var Alert = function (el) {
$(el).on('click', dismiss, this.close)
}
Alert.prototype.close = function (e) {
var $this = $(this)
var selector = $this.attr('data-target')
if (!selector) {
selector = $this.attr('href')
selector = selector && selector.replace(/.*(?=#[^\s]*$)/, '') // strip for ie7
}
var $parent = $(selector)
if (e) e.preventDefault()
if (!$parent.length) {
$parent = $this.hasClass('alert') ? $this : $this.parent()
}
$parent.trigger(e = $.Event('close.bs.alert'))
if (e.isDefaultPrevented()) return
$parent.removeClass('in')
function removeElement() {
$parent.trigger('closed.bs.alert').remove()
}
$.support.transition && $parent.hasClass('fade') ?
$parent
.one($.support.transition.end, removeElement)
.emulateTransitionEnd(150) :
removeElement()
}
// ALERT PLUGIN DEFINITION
// =======================
var old = $.fn.alert
$.fn.alert = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.alert')
if (!data) $this.data('bs.alert', (data = new Alert(this)))
if (typeof option == 'string') data[option].call($this)
})
}
$.fn.alert.Constructor = Alert
// ALERT NO CONFLICT
// =================
$.fn.alert.noConflict = function () {
$.fn.alert = old
return this
}
// ALERT DATA-API
// ==============
$(document).on('click.bs.alert.data-api', dismiss, Alert.prototype.close)
}(jQuery);
/* ========================================================================
* Bootstrap: button.js v3.0.2
* http://getbootstrap.com/javascript/#buttons
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// BUTTON PUBLIC CLASS DEFINITION
// ==============================
var Button = function (element, options) {
this.$element = $(element)
this.options = $.extend({}, Button.DEFAULTS, options)
}
Button.DEFAULTS = {
loadingText: 'loading...'
}
Button.prototype.setState = function (state) {
var d = 'disabled'
var $el = this.$element
var val = $el.is('input') ? 'val' : 'html'
var data = $el.data()
state = state + 'Text'
if (!data.resetText) $el.data('resetText', $el[val]())
$el[val](data[state] || this.options[state])
// push to event loop to allow forms to submit
setTimeout(function () {
state == 'loadingText' ?
$el.addClass(d).attr(d, d) :
$el.removeClass(d).removeAttr(d);
}, 0)
}
Button.prototype.toggle = function () {
var $parent = this.$element.closest('[data-toggle="buttons"]')
if ($parent.length) {
var $input = this.$element.find('input')
.prop('checked', !this.$element.hasClass('active'))
.trigger('change')
if ($input.prop('type') === 'radio') $parent.find('.active').removeClass('active')
}
this.$element.toggleClass('active')
}
// BUTTON PLUGIN DEFINITION
// ========================
var old = $.fn.button
$.fn.button = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.button')
var options = typeof option == 'object' && option
if (!data) $this.data('bs.button', (data = new Button(this, options)))
if (option == 'toggle') data.toggle()
else if (option) data.setState(option)
})
}
$.fn.button.Constructor = Button
// BUTTON NO CONFLICT
// ==================
$.fn.button.noConflict = function () {
$.fn.button = old
return this
}
// BUTTON DATA-API
// ===============
$(document).on('click.bs.button.data-api', '[data-toggle^=button]', function (e) {
var $btn = $(e.target)
if (!$btn.hasClass('btn')) $btn = $btn.closest('.btn')
$btn.button('toggle')
e.preventDefault()
})
}(jQuery);
/* ========================================================================
* Bootstrap: carousel.js v3.0.2
* http://getbootstrap.com/javascript/#carousel
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// CAROUSEL CLASS DEFINITION
// =========================
var Carousel = function (element, options) {
this.$element = $(element)
this.$indicators = this.$element.find('.carousel-indicators')
this.options = options
this.paused =
this.sliding =
this.interval =
this.$active =
this.$items = null
this.options.pause == 'hover' && this.$element
.on('mouseenter', $.proxy(this.pause, this))
.on('mouseleave', $.proxy(this.cycle, this))
}
Carousel.DEFAULTS = {
interval: 5000
, pause: 'hover'
, wrap: true
}
Carousel.prototype.cycle = function (e) {
e || (this.paused = false)
this.interval && clearInterval(this.interval)
this.options.interval
&& !this.paused
&& (this.interval = setInterval($.proxy(this.next, this), this.options.interval))
return this
}
Carousel.prototype.getActiveIndex = function () {
this.$active = this.$element.find('.item.active')
this.$items = this.$active.parent().children()
return this.$items.index(this.$active)
}
Carousel.prototype.to = function (pos) {
var that = this
var activeIndex = this.getActiveIndex()
if (pos > (this.$items.length - 1) || pos < 0) return
if (this.sliding) return this.$element.one('slid', function () { that.to(pos) })
if (activeIndex == pos) return this.pause().cycle()
return this.slide(pos > activeIndex ? 'next' : 'prev', $(this.$items[pos]))
}
Carousel.prototype.pause = function (e) {
e || (this.paused = true)
if (this.$element.find('.next, .prev').length && $.support.transition.end) {
this.$element.trigger($.support.transition.end)
this.cycle(true)
}
this.interval = clearInterval(this.interval)
return this
}
Carousel.prototype.next = function () {
if (this.sliding) return
return this.slide('next')
}
Carousel.prototype.prev = function () {
if (this.sliding) return
return this.slide('prev')
}
Carousel.prototype.slide = function (type, next) {
var $active = this.$element.find('.item.active')
var $next = next || $active[type]()
var isCycling = this.interval
var direction = type == 'next' ? 'left' : 'right'
var fallback = type == 'next' ? 'first' : 'last'
var that = this
if (!$next.length) {
if (!this.options.wrap) return
$next = this.$element.find('.item')[fallback]()
}
this.sliding = true
isCycling && this.pause()
var e = $.Event('slide.bs.carousel', { relatedTarget: $next[0], direction: direction })
if ($next.hasClass('active')) return
if (this.$indicators.length) {
this.$indicators.find('.active').removeClass('active')
this.$element.one('slid', function () {
var $nextIndicator = $(that.$indicators.children()[that.getActiveIndex()])
$nextIndicator && $nextIndicator.addClass('active')
})
}
if ($.support.transition && this.$element.hasClass('slide')) {
this.$element.trigger(e)
if (e.isDefaultPrevented()) return
$next.addClass(type)
$next[0].offsetWidth // force reflow
$active.addClass(direction)
$next.addClass(direction)
$active
.one($.support.transition.end, function () {
$next.removeClass([type, direction].join(' ')).addClass('active')
$active.removeClass(['active', direction].join(' '))
that.sliding = false
setTimeout(function () { that.$element.trigger('slid') }, 0)
})
.emulateTransitionEnd(600)
} else {
this.$element.trigger(e)
if (e.isDefaultPrevented()) return
$active.removeClass('active')
$next.addClass('active')
this.sliding = false
this.$element.trigger('slid')
}
isCycling && this.cycle()
return this
}
// CAROUSEL PLUGIN DEFINITION
// ==========================
var old = $.fn.carousel
$.fn.carousel = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.carousel')
var options = $.extend({}, Carousel.DEFAULTS, $this.data(), typeof option == 'object' && option)
var action = typeof option == 'string' ? option : options.slide
if (!data) $this.data('bs.carousel', (data = new Carousel(this, options)))
if (typeof option == 'number') data.to(option)
else if (action) data[action]()
else if (options.interval) data.pause().cycle()
})
}
$.fn.carousel.Constructor = Carousel
// CAROUSEL NO CONFLICT
// ====================
$.fn.carousel.noConflict = function () {
$.fn.carousel = old
return this
}
// CAROUSEL DATA-API
// =================
$(document).on('click.bs.carousel.data-api', '[data-slide], [data-slide-to]', function (e) {
var $this = $(this), href
var $target = $($this.attr('data-target') || (href = $this.attr('href')) && href.replace(/.*(?=#[^\s]+$)/, '')) //strip for ie7
var options = $.extend({}, $target.data(), $this.data())
var slideIndex = $this.attr('data-slide-to')
if (slideIndex) options.interval = false
$target.carousel(options)
if (slideIndex = $this.attr('data-slide-to')) {
$target.data('bs.carousel').to(slideIndex)
}
e.preventDefault()
})
$(window).on('load', function () {
$('[data-ride="carousel"]').each(function () {
var $carousel = $(this)
$carousel.carousel($carousel.data())
})
})
}(jQuery);
/* ========================================================================
* Bootstrap: collapse.js v3.0.2
* http://getbootstrap.com/javascript/#collapse
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// COLLAPSE PUBLIC CLASS DEFINITION
// ================================
var Collapse = function (element, options) {
this.$element = $(element)
this.options = $.extend({}, Collapse.DEFAULTS, options)
this.transitioning = null
if (this.options.parent) this.$parent = $(this.options.parent)
if (this.options.toggle) this.toggle()
}
Collapse.DEFAULTS = {
toggle: true
}
Collapse.prototype.dimension = function () {
var hasWidth = this.$element.hasClass('width')
return hasWidth ? 'width' : 'height'
}
Collapse.prototype.show = function () {
if (this.transitioning || this.$element.hasClass('in')) return
var startEvent = $.Event('show.bs.collapse')
this.$element.trigger(startEvent)
if (startEvent.isDefaultPrevented()) return
var actives = this.$parent && this.$parent.find('> .panel > .in')
if (actives && actives.length) {
var hasData = actives.data('bs.collapse')
if (hasData && hasData.transitioning) return
actives.collapse('hide')
hasData || actives.data('bs.collapse', null)
}
var dimension = this.dimension()
this.$element
.removeClass('collapse')
.addClass('collapsing')
[dimension](0)
this.transitioning = 1
var complete = function () {
this.$element
.removeClass('collapsing')
.addClass('in')
[dimension]('auto')
this.transitioning = 0
this.$element.trigger('shown.bs.collapse')
}
if (!$.support.transition) return complete.call(this)
var scrollSize = $.camelCase(['scroll', dimension].join('-'))
this.$element
.one($.support.transition.end, $.proxy(complete, this))
.emulateTransitionEnd(350)
[dimension](this.$element[0][scrollSize])
}
Collapse.prototype.hide = function () {
if (this.transitioning || !this.$element.hasClass('in')) return
var startEvent = $.Event('hide.bs.collapse')
this.$element.trigger(startEvent)
if (startEvent.isDefaultPrevented()) return
var dimension = this.dimension()
this.$element
[dimension](this.$element[dimension]())
[0].offsetHeight
this.$element
.addClass('collapsing')
.removeClass('collapse')
.removeClass('in')
this.transitioning = 1
var complete = function () {
this.transitioning = 0
this.$element
.trigger('hidden.bs.collapse')
.removeClass('collapsing')
.addClass('collapse')
}
if (!$.support.transition) return complete.call(this)
this.$element
[dimension](0)
.one($.support.transition.end, $.proxy(complete, this))
.emulateTransitionEnd(350)
}
Collapse.prototype.toggle = function () {
this[this.$element.hasClass('in') ? 'hide' : 'show']()
}
// COLLAPSE PLUGIN DEFINITION
// ==========================
var old = $.fn.collapse
$.fn.collapse = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.collapse')
var options = $.extend({}, Collapse.DEFAULTS, $this.data(), typeof option == 'object' && option)
if (!data) $this.data('bs.collapse', (data = new Collapse(this, options)))
if (typeof option == 'string') data[option]()
})
}
$.fn.collapse.Constructor = Collapse
// COLLAPSE NO CONFLICT
// ====================
$.fn.collapse.noConflict = function () {
$.fn.collapse = old
return this
}
// COLLAPSE DATA-API
// =================
$(document).on('click.bs.collapse.data-api', '[data-toggle=collapse]', function (e) {
var $this = $(this), href
var target = $this.attr('data-target')
|| e.preventDefault()
|| (href = $this.attr('href')) && href.replace(/.*(?=#[^\s]+$)/, '') //strip for ie7
var $target = $(target)
var data = $target.data('bs.collapse')
var option = data ? 'toggle' : $this.data()
var parent = $this.attr('data-parent')
var $parent = parent && $(parent)
if (!data || !data.transitioning) {
if ($parent) $parent.find('[data-toggle=collapse][data-parent="' + parent + '"]').not($this).addClass('collapsed')
$this[$target.hasClass('in') ? 'addClass' : 'removeClass']('collapsed')
}
$target.collapse(option)
})
}(jQuery);
/* ========================================================================
* Bootstrap: dropdown.js v3.0.2
* http://getbootstrap.com/javascript/#dropdowns
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// DROPDOWN CLASS DEFINITION
// =========================
var backdrop = '.dropdown-backdrop'
var toggle = '[data-toggle=dropdown]'
var Dropdown = function (element) {
var $el = $(element).on('click.bs.dropdown', this.toggle)
}
Dropdown.prototype.toggle = function (e) {
var $this = $(this)
if ($this.is('.disabled, :disabled')) return
var $parent = getParent($this)
var isActive = $parent.hasClass('open')
clearMenus()
if (!isActive) {
if ('ontouchstart' in document.documentElement && !$parent.closest('.navbar-nav').length) {
// if mobile we we use a backdrop because click events don't delegate
$('<div class="dropdown-backdrop"/>').insertAfter($(this)).on('click', clearMenus)
}
$parent.trigger(e = $.Event('show.bs.dropdown'))
if (e.isDefaultPrevented()) return
$parent
.toggleClass('open')
.trigger('shown.bs.dropdown')
$this.focus()
}
return false
}
Dropdown.prototype.keydown = function (e) {
if (!/(38|40|27)/.test(e.keyCode)) return
var $this = $(this)
e.preventDefault()
e.stopPropagation()
if ($this.is('.disabled, :disabled')) return
var $parent = getParent($this)
var isActive = $parent.hasClass('open')
if (!isActive || (isActive && e.keyCode == 27)) {
if (e.which == 27) $parent.find(toggle).focus()
return $this.click()
}
var $items = $('[role=menu] li:not(.divider):visible a', $parent)
if (!$items.length) return
var index = $items.index($items.filter(':focus'))
if (e.keyCode == 38 && index > 0) index-- // up
if (e.keyCode == 40 && index < $items.length - 1) index++ // down
if (!~index) index=0
$items.eq(index).focus()
}
function clearMenus() {
$(backdrop).remove()
$(toggle).each(function (e) {
var $parent = getParent($(this))
if (!$parent.hasClass('open')) return
$parent.trigger(e = $.Event('hide.bs.dropdown'))
if (e.isDefaultPrevented()) return
$parent.removeClass('open').trigger('hidden.bs.dropdown')
})
}
function getParent($this) {
var selector = $this.attr('data-target')
if (!selector) {
selector = $this.attr('href')
selector = selector && /#/.test(selector) && selector.replace(/.*(?=#[^\s]*$)/, '') //strip for ie7
}
var $parent = selector && $(selector)
return $parent && $parent.length ? $parent : $this.parent()
}
// DROPDOWN PLUGIN DEFINITION
// ==========================
var old = $.fn.dropdown
$.fn.dropdown = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('dropdown')
if (!data) $this.data('dropdown', (data = new Dropdown(this)))
if (typeof option == 'string') data[option].call($this)
})
}
$.fn.dropdown.Constructor = Dropdown
// DROPDOWN NO CONFLICT
// ====================
$.fn.dropdown.noConflict = function () {
$.fn.dropdown = old
return this
}
// APPLY TO STANDARD DROPDOWN ELEMENTS
// ===================================
$(document)
.on('click.bs.dropdown.data-api', clearMenus)
.on('click.bs.dropdown.data-api', '.dropdown form', function (e) { e.stopPropagation() })
.on('click.bs.dropdown.data-api' , toggle, Dropdown.prototype.toggle)
.on('keydown.bs.dropdown.data-api', toggle + ', [role=menu]' , Dropdown.prototype.keydown)
}(jQuery);
/* ========================================================================
* Bootstrap: modal.js v3.0.2
* http://getbootstrap.com/javascript/#modals
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// MODAL CLASS DEFINITION
// ======================
var Modal = function (element, options) {
this.options = options
this.$element = $(element)
this.$backdrop =
this.isShown = null
if (this.options.remote) this.$element.load(this.options.remote)
}
Modal.DEFAULTS = {
backdrop: true
, keyboard: true
, show: true
}
Modal.prototype.toggle = function (_relatedTarget) {
return this[!this.isShown ? 'show' : 'hide'](_relatedTarget)
}
Modal.prototype.show = function (_relatedTarget) {
var that = this
var e = $.Event('show.bs.modal', { relatedTarget: _relatedTarget })
this.$element.trigger(e)
if (this.isShown || e.isDefaultPrevented()) return
this.isShown = true
this.escape()
this.$element.on('click.dismiss.modal', '[data-dismiss="modal"]', $.proxy(this.hide, this))
this.backdrop(function () {
var transition = $.support.transition && that.$element.hasClass('fade')
if (!that.$element.parent().length) {
that.$element.appendTo(document.body) // don't move modals dom position
}
that.$element.show()
if (transition) {
that.$element[0].offsetWidth // force reflow
}
that.$element
.addClass('in')
.attr('aria-hidden', false)
that.enforceFocus()
var e = $.Event('shown.bs.modal', { relatedTarget: _relatedTarget })
transition ?
that.$element.find('.modal-dialog') // wait for modal to slide in
.one($.support.transition.end, function () {
that.$element.focus().trigger(e)
})
.emulateTransitionEnd(300) :
that.$element.focus().trigger(e)
})
}
Modal.prototype.hide = function (e) {
if (e) e.preventDefault()
e = $.Event('hide.bs.modal')
this.$element.trigger(e)
if (!this.isShown || e.isDefaultPrevented()) return
this.isShown = false
this.escape()
$(document).off('focusin.bs.modal')
this.$element
.removeClass('in')
.attr('aria-hidden', true)
.off('click.dismiss.modal')
$.support.transition && this.$element.hasClass('fade') ?
this.$element
.one($.support.transition.end, $.proxy(this.hideModal, this))
.emulateTransitionEnd(300) :
this.hideModal()
}
Modal.prototype.enforceFocus = function () {
$(document)
.off('focusin.bs.modal') // guard against infinite focus loop
.on('focusin.bs.modal', $.proxy(function (e) {
if (this.$element[0] !== e.target && !this.$element.has(e.target).length) {
this.$element.focus()
}
}, this))
}
Modal.prototype.escape = function () {
if (this.isShown && this.options.keyboard) {
this.$element.on('keyup.dismiss.bs.modal', $.proxy(function (e) {
e.which == 27 && this.hide()
}, this))
} else if (!this.isShown) {
this.$element.off('keyup.dismiss.bs.modal')
}
}
Modal.prototype.hideModal = function () {
var that = this
this.$element.hide()
this.backdrop(function () {
that.removeBackdrop()
that.$element.trigger('hidden.bs.modal')
})
}
Modal.prototype.removeBackdrop = function () {
this.$backdrop && this.$backdrop.remove()
this.$backdrop = null
}
Modal.prototype.backdrop = function (callback) {
var that = this
var animate = this.$element.hasClass('fade') ? 'fade' : ''
if (this.isShown && this.options.backdrop) {
var doAnimate = $.support.transition && animate
this.$backdrop = $('<div class="modal-backdrop ' + animate + '" />')
.appendTo(document.body)
this.$element.on('click.dismiss.modal', $.proxy(function (e) {
if (e.target !== e.currentTarget) return
this.options.backdrop == 'static'
? this.$element[0].focus.call(this.$element[0])
: this.hide.call(this)
}, this))
if (doAnimate) this.$backdrop[0].offsetWidth // force reflow
this.$backdrop.addClass('in')
if (!callback) return
doAnimate ?
this.$backdrop
.one($.support.transition.end, callback)
.emulateTransitionEnd(150) :
callback()
} else if (!this.isShown && this.$backdrop) {
this.$backdrop.removeClass('in')
$.support.transition && this.$element.hasClass('fade')?
this.$backdrop
.one($.support.transition.end, callback)
.emulateTransitionEnd(150) :
callback()
} else if (callback) {
callback()
}
}
// MODAL PLUGIN DEFINITION
// =======================
var old = $.fn.modal
$.fn.modal = function (option, _relatedTarget) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.modal')
var options = $.extend({}, Modal.DEFAULTS, $this.data(), typeof option == 'object' && option)
if (!data) $this.data('bs.modal', (data = new Modal(this, options)))
if (typeof option == 'string') data[option](_relatedTarget)
else if (options.show) data.show(_relatedTarget)
})
}
$.fn.modal.Constructor = Modal
// MODAL NO CONFLICT
// =================
$.fn.modal.noConflict = function () {
$.fn.modal = old
return this
}
// MODAL DATA-API
// ==============
$(document).on('click.bs.modal.data-api', '[data-toggle="modal"]', function (e) {
var $this = $(this)
var href = $this.attr('href')
var $target = $($this.attr('data-target') || (href && href.replace(/.*(?=#[^\s]+$)/, ''))) //strip for ie7
var option = $target.data('modal') ? 'toggle' : $.extend({ remote: !/#/.test(href) && href }, $target.data(), $this.data())
e.preventDefault()
$target
.modal(option, this)
.one('hide', function () {
$this.is(':visible') && $this.focus()
})
})
$(document)
.on('show.bs.modal', '.modal', function () { $(document.body).addClass('modal-open') })
.on('hidden.bs.modal', '.modal', function () { $(document.body).removeClass('modal-open') })
}(jQuery);
/* ========================================================================
* Bootstrap: tooltip.js v3.0.2
* http://getbootstrap.com/javascript/#tooltip
* Inspired by the original jQuery.tipsy by Jason Frame
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// TOOLTIP PUBLIC CLASS DEFINITION
// ===============================
var Tooltip = function (element, options) {
this.type =
this.options =
this.enabled =
this.timeout =
this.hoverState =
this.$element = null
this.init('tooltip', element, options)
}
Tooltip.DEFAULTS = {
animation: true
, placement: 'top'
, selector: false
, template: '<div class="tooltip"><div class="tooltip-arrow"></div><div class="tooltip-inner"></div></div>'
, trigger: 'hover focus'
, title: ''
, delay: 0
, html: false
, container: false
}
Tooltip.prototype.init = function (type, element, options) {
this.enabled = true
this.type = type
this.$element = $(element)
this.options = this.getOptions(options)
var triggers = this.options.trigger.split(' ')
for (var i = triggers.length; i--;) {
var trigger = triggers[i]
if (trigger == 'click') {
this.$element.on('click.' + this.type, this.options.selector, $.proxy(this.toggle, this))
} else if (trigger != 'manual') {
var eventIn = trigger == 'hover' ? 'mouseenter' : 'focus'
var eventOut = trigger == 'hover' ? 'mouseleave' : 'blur'
this.$element.on(eventIn + '.' + this.type, this.options.selector, $.proxy(this.enter, this))
this.$element.on(eventOut + '.' + this.type, this.options.selector, $.proxy(this.leave, this))
}
}
this.options.selector ?
(this._options = $.extend({}, this.options, { trigger: 'manual', selector: '' })) :
this.fixTitle()
}
Tooltip.prototype.getDefaults = function () {
return Tooltip.DEFAULTS
}
Tooltip.prototype.getOptions = function (options) {
options = $.extend({}, this.getDefaults(), this.$element.data(), options)
if (options.delay && typeof options.delay == 'number') {
options.delay = {
show: options.delay
, hide: options.delay
}
}
return options
}
Tooltip.prototype.getDelegateOptions = function () {
var options = {}
var defaults = this.getDefaults()
this._options && $.each(this._options, function (key, value) {
if (defaults[key] != value) options[key] = value
})
return options
}
Tooltip.prototype.enter = function (obj) {
var self = obj instanceof this.constructor ?
obj : $(obj.currentTarget)[this.type](this.getDelegateOptions()).data('bs.' + this.type)
clearTimeout(self.timeout)
self.hoverState = 'in'
if (!self.options.delay || !self.options.delay.show) return self.show()
self.timeout = setTimeout(function () {
if (self.hoverState == 'in') self.show()
}, self.options.delay.show)
}
Tooltip.prototype.leave = function (obj) {
var self = obj instanceof this.constructor ?
obj : $(obj.currentTarget)[this.type](this.getDelegateOptions()).data('bs.' + this.type)
clearTimeout(self.timeout)
self.hoverState = 'out'
if (!self.options.delay || !self.options.delay.hide) return self.hide()
self.timeout = setTimeout(function () {
if (self.hoverState == 'out') self.hide()
}, self.options.delay.hide)
}
Tooltip.prototype.show = function () {
var e = $.Event('show.bs.'+ this.type)
if (this.hasContent() && this.enabled) {
this.$element.trigger(e)
if (e.isDefaultPrevented()) return
var $tip = this.tip()
this.setContent()
if (this.options.animation) $tip.addClass('fade')
var placement = typeof this.options.placement == 'function' ?
this.options.placement.call(this, $tip[0], this.$element[0]) :
this.options.placement
var autoToken = /\s?auto?\s?/i
var autoPlace = autoToken.test(placement)
if (autoPlace) placement = placement.replace(autoToken, '') || 'top'
$tip
.detach()
.css({ top: 0, left: 0, display: 'block' })
.addClass(placement)
this.options.container ? $tip.appendTo(this.options.container) : $tip.insertAfter(this.$element)
var pos = this.getPosition()
var actualWidth = $tip[0].offsetWidth
var actualHeight = $tip[0].offsetHeight
if (autoPlace) {
var $parent = this.$element.parent()
var orgPlacement = placement
var docScroll = document.documentElement.scrollTop || document.body.scrollTop
var parentWidth = this.options.container == 'body' ? window.innerWidth : $parent.outerWidth()
var parentHeight = this.options.container == 'body' ? window.innerHeight : $parent.outerHeight()
var parentLeft = this.options.container == 'body' ? 0 : $parent.offset().left
placement = placement == 'bottom' && pos.top + pos.height + actualHeight - docScroll > parentHeight ? 'top' :
placement == 'top' && pos.top - docScroll - actualHeight < 0 ? 'bottom' :
placement == 'right' && pos.right + actualWidth > parentWidth ? 'left' :
placement == 'left' && pos.left - actualWidth < parentLeft ? 'right' :
placement
$tip
.removeClass(orgPlacement)
.addClass(placement)
}
var calculatedOffset = this.getCalculatedOffset(placement, pos, actualWidth, actualHeight)
this.applyPlacement(calculatedOffset, placement)
this.$element.trigger('shown.bs.' + this.type)
}
}
Tooltip.prototype.applyPlacement = function(offset, placement) {
var replace
var $tip = this.tip()
var width = $tip[0].offsetWidth
var height = $tip[0].offsetHeight
// manually read margins because getBoundingClientRect includes difference
var marginTop = parseInt($tip.css('margin-top'), 10)
var marginLeft = parseInt($tip.css('margin-left'), 10)
// we must check for NaN for ie 8/9
if (isNaN(marginTop)) marginTop = 0
if (isNaN(marginLeft)) marginLeft = 0
offset.top = offset.top + marginTop
offset.left = offset.left + marginLeft
$tip
.offset(offset)
.addClass('in')
// check to see if placing tip in new offset caused the tip to resize itself
var actualWidth = $tip[0].offsetWidth
var actualHeight = $tip[0].offsetHeight
if (placement == 'top' && actualHeight != height) {
replace = true
offset.top = offset.top + height - actualHeight
}
if (/bottom|top/.test(placement)) {
var delta = 0
if (offset.left < 0) {
delta = offset.left * -2
offset.left = 0
$tip.offset(offset)
actualWidth = $tip[0].offsetWidth
actualHeight = $tip[0].offsetHeight
}
this.replaceArrow(delta - width + actualWidth, actualWidth, 'left')
} else {
this.replaceArrow(actualHeight - height, actualHeight, 'top')
}
if (replace) $tip.offset(offset)
}
Tooltip.prototype.replaceArrow = function(delta, dimension, position) {
this.arrow().css(position, delta ? (50 * (1 - delta / dimension) + "%") : '')
}
Tooltip.prototype.setContent = function () {
var $tip = this.tip()
var title = this.getTitle()
$tip.find('.tooltip-inner')[this.options.html ? 'html' : 'text'](title)
$tip.removeClass('fade in top bottom left right')
}
Tooltip.prototype.hide = function () {
var that = this
var $tip = this.tip()
var e = $.Event('hide.bs.' + this.type)
function complete() {
if (that.hoverState != 'in') $tip.detach()
}
this.$element.trigger(e)
if (e.isDefaultPrevented()) return
$tip.removeClass('in')
$.support.transition && this.$tip.hasClass('fade') ?
$tip
.one($.support.transition.end, complete)
.emulateTransitionEnd(150) :
complete()
this.$element.trigger('hidden.bs.' + this.type)
return this
}
Tooltip.prototype.fixTitle = function () {
var $e = this.$element
if ($e.attr('title') || typeof($e.attr('data-original-title')) != 'string') {
$e.attr('data-original-title', $e.attr('title') || '').attr('title', '')
}
}
Tooltip.prototype.hasContent = function () {
return this.getTitle()
}
Tooltip.prototype.getPosition = function () {
var el = this.$element[0]
return $.extend({}, (typeof el.getBoundingClientRect == 'function') ? el.getBoundingClientRect() : {
width: el.offsetWidth
, height: el.offsetHeight
}, this.$element.offset())
}
Tooltip.prototype.getCalculatedOffset = function (placement, pos, actualWidth, actualHeight) {
return placement == 'bottom' ? { top: pos.top + pos.height, left: pos.left + pos.width / 2 - actualWidth / 2 } :
placement == 'top' ? { top: pos.top - actualHeight, left: pos.left + pos.width / 2 - actualWidth / 2 } :
placement == 'left' ? { top: pos.top + pos.height / 2 - actualHeight / 2, left: pos.left - actualWidth } :
/* placement == 'right' */ { top: pos.top + pos.height / 2 - actualHeight / 2, left: pos.left + pos.width }
}
Tooltip.prototype.getTitle = function () {
var title
var $e = this.$element
var o = this.options
title = $e.attr('data-original-title')
|| (typeof o.title == 'function' ? o.title.call($e[0]) : o.title)
return title
}
Tooltip.prototype.tip = function () {
return this.$tip = this.$tip || $(this.options.template)
}
Tooltip.prototype.arrow = function () {
return this.$arrow = this.$arrow || this.tip().find('.tooltip-arrow')
}
Tooltip.prototype.validate = function () {
if (!this.$element[0].parentNode) {
this.hide()
this.$element = null
this.options = null
}
}
Tooltip.prototype.enable = function () {
this.enabled = true
}
Tooltip.prototype.disable = function () {
this.enabled = false
}
Tooltip.prototype.toggleEnabled = function () {
this.enabled = !this.enabled
}
Tooltip.prototype.toggle = function (e) {
var self = e ? $(e.currentTarget)[this.type](this.getDelegateOptions()).data('bs.' + this.type) : this
self.tip().hasClass('in') ? self.leave(self) : self.enter(self)
}
Tooltip.prototype.destroy = function () {
this.hide().$element.off('.' + this.type).removeData('bs.' + this.type)
}
// TOOLTIP PLUGIN DEFINITION
// =========================
var old = $.fn.tooltip
$.fn.tooltip = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.tooltip')
var options = typeof option == 'object' && option
if (!data) $this.data('bs.tooltip', (data = new Tooltip(this, options)))
if (typeof option == 'string') data[option]()
})
}
$.fn.tooltip.Constructor = Tooltip
// TOOLTIP NO CONFLICT
// ===================
$.fn.tooltip.noConflict = function () {
$.fn.tooltip = old
return this
}
}(jQuery);
/* ========================================================================
* Bootstrap: popover.js v3.0.2
* http://getbootstrap.com/javascript/#popovers
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// POPOVER PUBLIC CLASS DEFINITION
// ===============================
var Popover = function (element, options) {
this.init('popover', element, options)
}
if (!$.fn.tooltip) throw new Error('Popover requires tooltip.js')
Popover.DEFAULTS = $.extend({} , $.fn.tooltip.Constructor.DEFAULTS, {
placement: 'right'
, trigger: 'click'
, content: ''
, template: '<div class="popover"><div class="arrow"></div><h3 class="popover-title"></h3><div class="popover-content"></div></div>'
})
// NOTE: POPOVER EXTENDS tooltip.js
// ================================
Popover.prototype = $.extend({}, $.fn.tooltip.Constructor.prototype)
Popover.prototype.constructor = Popover
Popover.prototype.getDefaults = function () {
return Popover.DEFAULTS
}
Popover.prototype.setContent = function () {
var $tip = this.tip()
var title = this.getTitle()
var content = this.getContent()
$tip.find('.popover-title')[this.options.html ? 'html' : 'text'](title)
$tip.find('.popover-content')[this.options.html ? 'html' : 'text'](content)
$tip.removeClass('fade top bottom left right in')
// IE8 doesn't accept hiding via the `:empty` pseudo selector, we have to do
// this manually by checking the contents.
if (!$tip.find('.popover-title').html()) $tip.find('.popover-title').hide()
}
Popover.prototype.hasContent = function () {
return this.getTitle() || this.getContent()
}
Popover.prototype.getContent = function () {
var $e = this.$element
var o = this.options
return $e.attr('data-content')
|| (typeof o.content == 'function' ?
o.content.call($e[0]) :
o.content)
}
Popover.prototype.arrow = function () {
return this.$arrow = this.$arrow || this.tip().find('.arrow')
}
Popover.prototype.tip = function () {
if (!this.$tip) this.$tip = $(this.options.template)
return this.$tip
}
// POPOVER PLUGIN DEFINITION
// =========================
var old = $.fn.popover
$.fn.popover = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.popover')
var options = typeof option == 'object' && option
if (!data) $this.data('bs.popover', (data = new Popover(this, options)))
if (typeof option == 'string') data[option]()
})
}
$.fn.popover.Constructor = Popover
// POPOVER NO CONFLICT
// ===================
$.fn.popover.noConflict = function () {
$.fn.popover = old
return this
}
}(jQuery);
/* ========================================================================
* Bootstrap: scrollspy.js v3.0.2
* http://getbootstrap.com/javascript/#scrollspy
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// SCROLLSPY CLASS DEFINITION
// ==========================
function ScrollSpy(element, options) {
var href
var process = $.proxy(this.process, this)
this.$element = $(element).is('body') ? $(window) : $(element)
this.$body = $('body')
this.$scrollElement = this.$element.on('scroll.bs.scroll-spy.data-api', process)
this.options = $.extend({}, ScrollSpy.DEFAULTS, options)
this.selector = (this.options.target
|| ((href = $(element).attr('href')) && href.replace(/.*(?=#[^\s]+$)/, '')) //strip for ie7
|| '') + ' .nav li > a'
this.offsets = $([])
this.targets = $([])
this.activeTarget = null
this.refresh()
this.process()
}
ScrollSpy.DEFAULTS = {
offset: 10
}
ScrollSpy.prototype.refresh = function () {
var offsetMethod = this.$element[0] == window ? 'offset' : 'position'
this.offsets = $([])
this.targets = $([])
var self = this
var $targets = this.$body
.find(this.selector)
.map(function () {
var $el = $(this)
var href = $el.data('target') || $el.attr('href')
var $href = /^#\w/.test(href) && $(href)
return ($href
&& $href.length
&& [[ $href[offsetMethod]().top + (!$.isWindow(self.$scrollElement.get(0)) && self.$scrollElement.scrollTop()), href ]]) || null
})
.sort(function (a, b) { return a[0] - b[0] })
.each(function () {
self.offsets.push(this[0])
self.targets.push(this[1])
})
}
ScrollSpy.prototype.process = function () {
var scrollTop = this.$scrollElement.scrollTop() + this.options.offset
var scrollHeight = this.$scrollElement[0].scrollHeight || this.$body[0].scrollHeight
var maxScroll = scrollHeight - this.$scrollElement.height()
var offsets = this.offsets
var targets = this.targets
var activeTarget = this.activeTarget
var i
if (scrollTop >= maxScroll) {
return activeTarget != (i = targets.last()[0]) && this.activate(i)
}
for (i = offsets.length; i--;) {
activeTarget != targets[i]
&& scrollTop >= offsets[i]
&& (!offsets[i + 1] || scrollTop <= offsets[i + 1])
&& this.activate( targets[i] )
}
}
ScrollSpy.prototype.activate = function (target) {
this.activeTarget = target
$(this.selector)
.parents('.active')
.removeClass('active')
var selector = this.selector
+ '[data-target="' + target + '"],'
+ this.selector + '[href="' + target + '"]'
var active = $(selector)
.parents('li')
.addClass('active')
if (active.parent('.dropdown-menu').length) {
active = active
.closest('li.dropdown')
.addClass('active')
}
active.trigger('activate')
}
// SCROLLSPY PLUGIN DEFINITION
// ===========================
var old = $.fn.scrollspy
$.fn.scrollspy = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.scrollspy')
var options = typeof option == 'object' && option
if (!data) $this.data('bs.scrollspy', (data = new ScrollSpy(this, options)))
if (typeof option == 'string') data[option]()
})
}
$.fn.scrollspy.Constructor = ScrollSpy
// SCROLLSPY NO CONFLICT
// =====================
$.fn.scrollspy.noConflict = function () {
$.fn.scrollspy = old
return this
}
// SCROLLSPY DATA-API
// ==================
$(window).on('load', function () {
$('[data-spy="scroll"]').each(function () {
var $spy = $(this)
$spy.scrollspy($spy.data())
})
})
}(jQuery);
/* ========================================================================
* Bootstrap: tab.js v3.0.2
* http://getbootstrap.com/javascript/#tabs
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// TAB CLASS DEFINITION
// ====================
var Tab = function (element) {
this.element = $(element)
}
Tab.prototype.show = function () {
var $this = this.element
var $ul = $this.closest('ul:not(.dropdown-menu)')
var selector = $this.data('target')
if (!selector) {
selector = $this.attr('href')
selector = selector && selector.replace(/.*(?=#[^\s]*$)/, '') //strip for ie7
}
if ($this.parent('li').hasClass('active')) return
var previous = $ul.find('.active:last a')[0]
var e = $.Event('show.bs.tab', {
relatedTarget: previous
})
$this.trigger(e)
if (e.isDefaultPrevented()) return
var $target = $(selector)
this.activate($this.parent('li'), $ul)
this.activate($target, $target.parent(), function () {
$this.trigger({
type: 'shown.bs.tab'
, relatedTarget: previous
})
})
}
Tab.prototype.activate = function (element, container, callback) {
var $active = container.find('> .active')
var transition = callback
&& $.support.transition
&& $active.hasClass('fade')
function next() {
$active
.removeClass('active')
.find('> .dropdown-menu > .active')
.removeClass('active')
element.addClass('active')
if (transition) {
element[0].offsetWidth // reflow for transition
element.addClass('in')
} else {
element.removeClass('fade')
}
if (element.parent('.dropdown-menu')) {
element.closest('li.dropdown').addClass('active')
}
callback && callback()
}
transition ?
$active
.one($.support.transition.end, next)
.emulateTransitionEnd(150) :
next()
$active.removeClass('in')
}
// TAB PLUGIN DEFINITION
// =====================
var old = $.fn.tab
$.fn.tab = function ( option ) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.tab')
if (!data) $this.data('bs.tab', (data = new Tab(this)))
if (typeof option == 'string') data[option]()
})
}
$.fn.tab.Constructor = Tab
// TAB NO CONFLICT
// ===============
$.fn.tab.noConflict = function () {
$.fn.tab = old
return this
}
// TAB DATA-API
// ============
$(document).on('click.bs.tab.data-api', '[data-toggle="tab"], [data-toggle="pill"]', function (e) {
e.preventDefault()
$(this).tab('show')
})
}(jQuery);
/* ========================================================================
* Bootstrap: affix.js v3.0.2
* http://getbootstrap.com/javascript/#affix
* ========================================================================
* Copyright 2013 Twitter, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ======================================================================== */
+function ($) { "use strict";
// AFFIX CLASS DEFINITION
// ======================
var Affix = function (element, options) {
this.options = $.extend({}, Affix.DEFAULTS, options)
this.$window = $(window)
.on('scroll.bs.affix.data-api', $.proxy(this.checkPosition, this))
.on('click.bs.affix.data-api', $.proxy(this.checkPositionWithEventLoop, this))
this.$element = $(element)
this.affixed =
this.unpin = null
this.checkPosition()
}
Affix.RESET = 'affix affix-top affix-bottom'
Affix.DEFAULTS = {
offset: 0
}
Affix.prototype.checkPositionWithEventLoop = function () {
setTimeout($.proxy(this.checkPosition, this), 1)
}
Affix.prototype.checkPosition = function () {
if (!this.$element.is(':visible')) return
var scrollHeight = $(document).height()
var scrollTop = this.$window.scrollTop()
var position = this.$element.offset()
var offset = this.options.offset
var offsetTop = offset.top
var offsetBottom = offset.bottom
if (typeof offset != 'object') offsetBottom = offsetTop = offset
if (typeof offsetTop == 'function') offsetTop = offset.top()
if (typeof offsetBottom == 'function') offsetBottom = offset.bottom()
var affix = this.unpin != null && (scrollTop + this.unpin <= position.top) ? false :
offsetBottom != null && (position.top + this.$element.height() >= scrollHeight - offsetBottom) ? 'bottom' :
offsetTop != null && (scrollTop <= offsetTop) ? 'top' : false
if (this.affixed === affix) return
if (this.unpin) this.$element.css('top', '')
this.affixed = affix
this.unpin = affix == 'bottom' ? position.top - scrollTop : null
this.$element.removeClass(Affix.RESET).addClass('affix' + (affix ? '-' + affix : ''))
if (affix == 'bottom') {
this.$element.offset({ top: document.body.offsetHeight - offsetBottom - this.$element.height() })
}
}
// AFFIX PLUGIN DEFINITION
// =======================
var old = $.fn.affix
$.fn.affix = function (option) {
return this.each(function () {
var $this = $(this)
var data = $this.data('bs.affix')
var options = typeof option == 'object' && option
if (!data) $this.data('bs.affix', (data = new Affix(this, options)))
if (typeof option == 'string') data[option]()
})
}
$.fn.affix.Constructor = Affix
// AFFIX NO CONFLICT
// =================
$.fn.affix.noConflict = function () {
$.fn.affix = old
return this
}
// AFFIX DATA-API
// ==============
$(window).on('load', function () {
$('[data-spy="affix"]').each(function () {
var $spy = $(this)
var data = $spy.data()
data.offset = data.offset || {}
if (data.offsetBottom) data.offset.bottom = data.offsetBottom
if (data.offsetTop) data.offset.top = data.offsetTop
$spy.affix(data)
})
})
}(jQuery);
hakyll-bootstrap/js/bootstrap.min.js deleted 100644 → 0
View file @ b103362d
/*!
* Bootstrap v3.0.2 by @fat and @mdo
* Copyright 2013 Twitter, Inc.
* Licensed under http://www.apache.org/licenses/LICENSE-2.0
*
* Designed and built with all the love in the world by @mdo and @fat.
*/
if("undefined"==typeof jQuery)throw new Error("Bootstrap requires jQuery");+function(a){"use strict";function b(){var a=document.createElement("bootstrap"),b={WebkitTransition:"webkitTransitionEnd",MozTransition:"transitionend",OTransition:"oTransitionEnd otransitionend",transition:"transitionend"};for(var c in b)if(void 0!==a.style[c])return{end:b[c]}}a.fn.emulateTransitionEnd=function(b){var c=!1,d=this;a(this).one(a.support.transition.end,function(){c=!0});var e=function(){c||a(d).trigger(a.support.transition.end)};return setTimeout(e,b),this},a(function(){a.support.transition=b()})}(jQuery),+function(a){"use strict";var b='[data-dismiss="alert"]',c=function(c){a(c).on("click",b,this.close)};c.prototype.close=function(b){function c(){f.trigger("closed.bs.alert").remove()}var d=a(this),e=d.attr("data-target");e||(e=d.attr("href"),e=e&&e.replace(/.*(?=#[^\s]*$)/,""));var 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b="disabled",c=this.$element,d=c.is("input")?"val":"html",e=c.data();a+="Text",e.resetText||c.data("resetText",c[d]()),c[d](e[a]||this.options[a]),setTimeout(function(){"loadingText"==a?c.addClass(b).attr(b,b):c.removeClass(b).removeAttr(b)},0)},b.prototype.toggle=function(){var a=this.$element.closest('[data-toggle="buttons"]');if(a.length){var b=this.$element.find("input").prop("checked",!this.$element.hasClass("active")).trigger("change");"radio"===b.prop("type")&&a.find(".active").removeClass("active")}this.$element.toggleClass("active")};var c=a.fn.button;a.fn.button=function(c){return this.each(function(){var d=a(this),e=d.data("bs.button"),f="object"==typeof c&&c;e||d.data("bs.button",e=new b(this,f)),"toggle"==c?e.toggle():c&&e.setState(c)})},a.fn.button.Constructor=b,a.fn.button.noConflict=function(){return a.fn.button=c,this},a(document).on("click.bs.button.data-api","[data-toggle^=button]",function(b){var 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b=function(c,d){this.$element=a(c),this.options=a.extend({},b.DEFAULTS,d),this.transitioning=null,this.options.parent&&(this.$parent=a(this.options.parent)),this.options.toggle&&this.toggle()};b.DEFAULTS={toggle:!0},b.prototype.dimension=function(){var a=this.$element.hasClass("width");return a?"width":"height"},b.prototype.show=function(){if(!this.transitioning&&!this.$element.hasClass("in")){var b=a.Event("show.bs.collapse");if(this.$element.trigger(b),!b.isDefaultPrevented()){var c=this.$parent&&this.$parent.find("> .panel > .in");if(c&&c.length){var d=c.data("bs.collapse");if(d&&d.transitioning)return;c.collapse("hide"),d||c.data("bs.collapse",null)}var e=this.dimension();this.$element.removeClass("collapse").addClass("collapsing")[e](0),this.transitioning=1;var f=function(){this.$element.removeClass("collapsing").addClass("in")[e]("auto"),this.transitioning=0,this.$element.trigger("shown.bs.collapse")};if(!a.support.transition)return f.call(this);var 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a=b.attr("data-original-title")||("function"==typeof c.title?c.title.call(b[0]):c.title)},b.prototype.tip=function(){return this.$tip=this.$tip||a(this.options.template)},b.prototype.arrow=function(){return this.$arrow=this.$arrow||this.tip().find(".tooltip-arrow")},b.prototype.validate=function(){this.$element[0].parentNode||(this.hide(),this.$element=null,this.options=null)},b.prototype.enable=function(){this.enabled=!0},b.prototype.disable=function(){this.enabled=!1},b.prototype.toggleEnabled=function(){this.enabled=!this.enabled},b.prototype.toggle=function(b){var c=b?a(b.currentTarget)[this.type](this.getDelegateOptions()).data("bs."+this.type):this;c.tip().hasClass("in")?c.leave(c):c.enter(c)},b.prototype.destroy=function(){this.hide().$element.off("."+this.type).removeData("bs."+this.type)};var c=a.fn.tooltip;a.fn.tooltip=function(c){return this.each(function(){var d=a(this),e=d.data("bs.tooltip"),f="object"==typeof c&&c;e||d.data("bs.tooltip",e=new b(this,f)),"string"==typeof c&&e[c]()})},a.fn.tooltip.Constructor=b,a.fn.tooltip.noConflict=function(){return a.fn.tooltip=c,this}}(jQuery),+function(a){"use strict";var b=function(a,b){this.init("popover",a,b)};if(!a.fn.tooltip)throw new Error("Popover requires tooltip.js");b.DEFAULTS=a.extend({},a.fn.tooltip.Constructor.DEFAULTS,{placement:"right",trigger:"click",content:"",template:'<div class="popover"><div class="arrow"></div><h3 class="popover-title"></h3><div class="popover-content"></div></div>'}),b.prototype=a.extend({},a.fn.tooltip.Constructor.prototype),b.prototype.constructor=b,b.prototype.getDefaults=function(){return b.DEFAULTS},b.prototype.setContent=function(){var a=this.tip(),b=this.getTitle(),c=this.getContent();a.find(".popover-title")[this.options.html?"html":"text"](b),a.find(".popover-content")[this.options.html?"html":"text"](c),a.removeClass("fade top bottom left right in"),a.find(".popover-title").html()||a.find(".popover-title").hide()},b.prototype.hasContent=function(){return this.getTitle()||this.getContent()},b.prototype.getContent=function(){var a=this.$element,b=this.options;return a.attr("data-content")||("function"==typeof b.content?b.content.call(a[0]):b.content)},b.prototype.arrow=function(){return this.$arrow=this.$arrow||this.tip().find(".arrow")},b.prototype.tip=function(){return this.$tip||(this.$tip=a(this.options.template)),this.$tip};var c=a.fn.popover;a.fn.popover=function(c){return this.each(function(){var d=a(this),e=d.data("bs.popover"),f="object"==typeof c&&c;e||d.data("bs.popover",e=new b(this,f)),"string"==typeof c&&e[c]()})},a.fn.popover.Constructor=b,a.fn.popover.noConflict=function(){return a.fn.popover=c,this}}(jQuery),+function(a){"use strict";function b(c,d){var e,f=a.proxy(this.process,this);this.$element=a(c).is("body")?a(window):a(c),this.$body=a("body"),this.$scrollElement=this.$element.on("scroll.bs.scroll-spy.data-api",f),this.options=a.extend({},b.DEFAULTS,d),this.selector=(this.options.target||(e=a(c).attr("href"))&&e.replace(/.*(?=#[^\s]+$)/,"")||"")+" .nav li > a",this.offsets=a([]),this.targets=a([]),this.activeTarget=null,this.refresh(),this.process()}b.DEFAULTS={offset:10},b.prototype.refresh=function(){var b=this.$element[0]==window?"offset":"position";this.offsets=a([]),this.targets=a([]);var c=this;this.$body.find(this.selector).map(function(){var d=a(this),e=d.data("target")||d.attr("href"),f=/^#\w/.test(e)&&a(e);return f&&f.length&&[[f[b]().top+(!a.isWindow(c.$scrollElement.get(0))&&c.$scrollElement.scrollTop()),e]]||null}).sort(function(a,b){return a[0]-b[0]}).each(function(){c.offsets.push(this[0]),c.targets.push(this[1])})},b.prototype.process=function(){var a,b=this.$scrollElement.scrollTop()+this.options.offset,c=this.$scrollElement[0].scrollHeight||this.$body[0].scrollHeight,d=c-this.$scrollElement.height(),e=this.offsets,f=this.targets,g=this.activeTarget;if(b>=d)return g!=(a=f.last()[0])&&this.activate(a);for(a=e.length;a--;)g!=f[a]&&b>=e[a]&&(!e[a+1]||b<=e[a+1])&&this.activate(f[a])},b.prototype.activate=function(b){this.activeTarget=b,a(this.selector).parents(".active").removeClass("active");var c=this.selector+'[data-target="'+b+'"],'+this.selector+'[href="'+b+'"]',d=a(c).parents("li").addClass("active");d.parent(".dropdown-menu").length&&(d=d.closest("li.dropdown").addClass("active")),d.trigger("activate")};var c=a.fn.scrollspy;a.fn.scrollspy=function(c){return this.each(function(){var d=a(this),e=d.data("bs.scrollspy"),f="object"==typeof c&&c;e||d.data("bs.scrollspy",e=new b(this,f)),"string"==typeof c&&e[c]()})},a.fn.scrollspy.Constructor=b,a.fn.scrollspy.noConflict=function(){return a.fn.scrollspy=c,this},a(window).on("load",function(){a('[data-spy="scroll"]').each(function(){var b=a(this);b.scrollspy(b.data())})})}(jQuery),+function(a){"use strict";var b=function(b){this.element=a(b)};b.prototype.show=function(){var b=this.element,c=b.closest("ul:not(.dropdown-menu)"),d=b.data("target");if(d||(d=b.attr("href"),d=d&&d.replace(/.*(?=#[^\s]*$)/,"")),!b.parent("li").hasClass("active")){var e=c.find(".active:last a")[0],f=a.Event("show.bs.tab",{relatedTarget:e});if(b.trigger(f),!f.isDefaultPrevented()){var g=a(d);this.activate(b.parent("li"),c),this.activate(g,g.parent(),function(){b.trigger({type:"shown.bs.tab",relatedTarget:e})})}}},b.prototype.activate=function(b,c,d){function e(){f.removeClass("active").find("> .dropdown-menu > .active").removeClass("active"),b.addClass("active"),g?(b[0].offsetWidth,b.addClass("in")):b.removeClass("fade"),b.parent(".dropdown-menu")&&b.closest("li.dropdown").addClass("active"),d&&d()}var f=c.find("> .active"),g=d&&a.support.transition&&f.hasClass("fade");g?f.one(a.support.transition.end,e).emulateTransitionEnd(150):e(),f.removeClass("in")};var c=a.fn.tab;a.fn.tab=function(c){return this.each(function(){var d=a(this),e=d.data("bs.tab");e||d.data("bs.tab",e=new b(this)),"string"==typeof c&&e[c]()})},a.fn.tab.Constructor=b,a.fn.tab.noConflict=function(){return a.fn.tab=c,this},a(document).on("click.bs.tab.data-api",'[data-toggle="tab"], [data-toggle="pill"]',function(b){b.preventDefault(),a(this).tab("show")})}(jQuery),+function(a){"use strict";var b=function(c,d){this.options=a.extend({},b.DEFAULTS,d),this.$window=a(window).on("scroll.bs.affix.data-api",a.proxy(this.checkPosition,this)).on("click.bs.affix.data-api",a.proxy(this.checkPositionWithEventLoop,this)),this.$element=a(c),this.affixed=this.unpin=null,this.checkPosition()};b.RESET="affix affix-top affix-bottom",b.DEFAULTS={offset:0},b.prototype.checkPositionWithEventLoop=function(){setTimeout(a.proxy(this.checkPosition,this),1)},b.prototype.checkPosition=function(){if(this.$element.is(":visible")){var c=a(document).height(),d=this.$window.scrollTop(),e=this.$element.offset(),f=this.options.offset,g=f.top,h=f.bottom;"object"!=typeof f&&(h=g=f),"function"==typeof g&&(g=f.top()),"function"==typeof h&&(h=f.bottom());var i=null!=this.unpin&&d+this.unpin<=e.top?!1:null!=h&&e.top+this.$element.height()>=c-h?"bottom":null!=g&&g>=d?"top":!1;this.affixed!==i&&(this.unpin&&this.$element.css("top",""),this.affixed=i,this.unpin="bottom"==i?e.top-d:null,this.$element.removeClass(b.RESET).addClass("affix"+(i?"-"+i:"")),"bottom"==i&&this.$element.offset({top:document.body.offsetHeight-h-this.$element.height()}))}};var c=a.fn.affix;a.fn.affix=function(c){return this.each(function(){var d=a(this),e=d.data("bs.affix"),f="object"==typeof c&&c;e||d.data("bs.affix",e=new b(this,f)),"string"==typeof c&&e[c]()})},a.fn.affix.Constructor=b,a.fn.affix.noConflict=function(){return a.fn.affix=c,this},a(window).on("load",function(){a('[data-spy="affix"]').each(function(){var b=a(this),c=b.data();c.offset=c.offset||{},c.offsetBottom&&(c.offset.bottom=c.offsetBottom),c.offsetTop&&(c.offset.top=c.offsetTop),b.affix(c)})})}(jQuery);
\ No newline at end of file
hakyll-bootstrap/js/holder.js deleted 100644 → 0
View file @ b103362d
/*
Holder - 2.1 - client side image placeholders
(c) 2012-2013 Ivan Malopinsky / http://imsky.co
Provided under the MIT License.
Commercial use requires attribution.
*/
var Holder = Holder || {};
(function (app, win) {
var preempted = false,
fallback = false,
canvas = document.createElement('canvas');
if (!canvas.getContext) {
fallback = true;
} else {
if (canvas.toDataURL("image/png")
.indexOf("data:image/png") < 0) {
//Android doesn't support data URI
fallback = true;
} else {
var ctx = canvas.getContext("2d");
}
}
var dpr = 1, bsr = 1;
if(!fallback){
dpr = window.devicePixelRatio || 1,
bsr = ctx.webkitBackingStorePixelRatio || ctx.mozBackingStorePixelRatio || ctx.msBackingStorePixelRatio || ctx.oBackingStorePixelRatio || ctx.backingStorePixelRatio || 1;
}
var ratio = dpr / bsr;
//getElementsByClassName polyfill
document.getElementsByClassName||(document.getElementsByClassName=function(e){var t=document,n,r,i,s=[];if(t.querySelectorAll)return t.querySelectorAll("."+e);if(t.evaluate){r=".//*[contains(concat(' ', @class, ' '), ' "+e+" ')]",n=t.evaluate(r,t,null,0,null);while(i=n.iterateNext())s.push(i)}else{n=t.getElementsByTagName("*"),r=new RegExp("(^|\\s)"+e+"(\\s|$)");for(i=0;i<n.length;i++)r.test(n[i].className)&&s.push(n[i])}return s})
//getComputedStyle polyfill
window.getComputedStyle||(window.getComputedStyle=function(e){return this.el=e,this.getPropertyValue=function(t){var n=/(\-([a-z]){1})/g;return t=="float"&&(t="styleFloat"),n.test(t)&&(t=t.replace(n,function(){return arguments[2].toUpperCase()})),e.currentStyle[t]?e.currentStyle[t]:null},this})
//http://javascript.nwbox.com/ContentLoaded by Diego Perini with modifications
function contentLoaded(n,t){var l="complete",s="readystatechange",u=!1,h=u,c=!0,i=n.document,a=i.documentElement,e=i.addEventListener?"addEventListener":"attachEvent",v=i.addEventListener?"removeEventListener":"detachEvent",f=i.addEventListener?"":"on",r=function(e){(e.type!=s||i.readyState==l)&&((e.type=="load"?n:i)[v](f+e.type,r,u),!h&&(h=!0)&&t.call(n,null))},o=function(){try{a.doScroll("left")}catch(n){setTimeout(o,50);return}r("poll")};if(i.readyState==l)t.call(n,"lazy");else{if(i.createEventObject&&a.doScroll){try{c=!n.frameElement}catch(y){}c&&o()}i[e](f+"DOMContentLoaded",r,u),i[e](f+s,r,u),n[e](f+"load",r,u)}}
//https://gist.github.com/991057 by Jed Schmidt with modifications
function selector(a){
a=a.match(/^(\W)?(.*)/);var b=document["getElement"+(a[1]?a[1]=="#"?"ById":"sByClassName":"sByTagName")](a[2]);
var ret=[]; b!==null&&(b.length?ret=b:b.length===0?ret=b:ret=[b]); return ret;
}
//shallow object property extend
function extend(a,b){var c={};for(var d in a)c[d]=a[d];for(var e in b)c[e]=b[e];return c}
//hasOwnProperty polyfill
if (!Object.prototype.hasOwnProperty)
/*jshint -W001, -W103 */
Object.prototype.hasOwnProperty = function(prop) {
var proto = this.__proto__ || this.constructor.prototype;
return (prop in this) && (!(prop in proto) || proto[prop] !== this[prop]);
}
/*jshint +W001, +W103 */
function text_size(width, height, template) {
height = parseInt(height, 10);
width = parseInt(width, 10);
var bigSide = Math.max(height, width)
var smallSide = Math.min(height, width)
var scale = 1 / 12;
var newHeight = Math.min(smallSide * 0.75, 0.75 * bigSide * scale);
return {
height: Math.round(Math.max(template.size, newHeight))
}
}
function draw(ctx, dimensions, template, ratio, literal) {
var ts = text_size(dimensions.width, dimensions.height, template);
var text_height = ts.height;
var width = dimensions.width * ratio,
height = dimensions.height * ratio;
var font = template.font ? template.font : "sans-serif";
canvas.width = width;
canvas.height = height;
ctx.textAlign = "center";
ctx.textBaseline = "middle";
ctx.fillStyle = template.background;
ctx.fillRect(0, 0, width, height);
ctx.fillStyle = template.foreground;
ctx.font = "bold " + text_height + "px " + font;
var text = template.text ? template.text : (Math.floor(dimensions.width) + "x" + Math.floor(dimensions.height));
if (literal) {
text = template.literalText;
}
var text_width = ctx.measureText(text).width;
if (text_width / width >= 0.75) {
text_height = Math.floor(text_height * 0.75 * (width / text_width));
}
//Resetting font size if necessary
ctx.font = "bold " + (text_height * ratio) + "px " + font;
ctx.fillText(text, (width / 2), (height / 2), width);
return canvas.toDataURL("image/png");
}
function render(mode, el, holder, src) {
var dimensions = holder.dimensions,
theme = holder.theme,
text = holder.text ? decodeURIComponent(holder.text) : holder.text;
var dimensions_caption = dimensions.width + "x" + dimensions.height;
theme = (text ? extend(theme, {
text: text
}) : theme);
theme = (holder.font ? extend(theme, {
font: holder.font
}) : theme);
el.setAttribute("data-src", src);
theme.literalText = dimensions_caption;
holder.originalTheme = holder.theme;
holder.theme = theme;
if (mode == "image") {
el.setAttribute("alt", text ? text : theme.text ? theme.text + " [" + dimensions_caption + "]" : dimensions_caption);
if (fallback || !holder.auto) {
el.style.width = dimensions.width + "px";
el.style.height = dimensions.height + "px";
}
if (fallback) {
el.style.backgroundColor = theme.background;
} else {
el.setAttribute("src", draw(ctx, dimensions, theme, ratio));
}
} else if (mode == "background") {
if (!fallback) {
el.style.backgroundImage = "url(" + draw(ctx, dimensions, theme, ratio) + ")";
el.style.backgroundSize = dimensions.width + "px " + dimensions.height + "px";
}
} else if (mode == "fluid") {
el.setAttribute("alt", text ? text : theme.text ? theme.text + " [" + dimensions_caption + "]" : dimensions_caption);
if (dimensions.height.slice(-1) == "%") {
el.style.height = dimensions.height
} else {
el.style.height = dimensions.height + "px"
}
if (dimensions.width.slice(-1) == "%") {
el.style.width = dimensions.width
} else {
el.style.width = dimensions.width + "px"
}
if (el.style.display == "inline" || el.style.display === "") {
el.style.display = "block";
}
if (fallback) {
el.style.backgroundColor = theme.background;
} else {
el.holderData = holder;
fluid_images.push(el);
fluid_update(el);
}
}
}
function fluid_update(element) {
var images;
if (element.nodeType == null) {
images = fluid_images;
} else {
images = [element]
}
for (var i in images) {
var el = images[i]
if (el.holderData) {
var holder = el.holderData;
el.setAttribute("src", draw(ctx, {
height: el.clientHeight,
width: el.clientWidth
}, holder.theme, ratio, !! holder.literal));
}
}
}
function parse_flags(flags, options) {
var ret = {
theme: settings.themes.gray
};
var render = false;
for (sl = flags.length, j = 0; j < sl; j++) {
var flag = flags[j];
if (app.flags.dimensions.match(flag)) {
render = true;
ret.dimensions = app.flags.dimensions.output(flag);
} else if (app.flags.fluid.match(flag)) {
render = true;
ret.dimensions = app.flags.fluid.output(flag);
ret.fluid = true;
} else if (app.flags.literal.match(flag)) {
ret.literal = true;
} else if (app.flags.colors.match(flag)) {
ret.theme = app.flags.colors.output(flag);
} else if (options.themes[flag]) {
//If a theme is specified, it will override custom colors
ret.theme = options.themes[flag];
} else if (app.flags.font.match(flag)) {
ret.font = app.flags.font.output(flag);
} else if (app.flags.auto.match(flag)) {
ret.auto = true;
} else if (app.flags.text.match(flag)) {
ret.text = app.flags.text.output(flag);
}
}
return render ? ret : false;
}
var fluid_images = [];
var settings = {
domain: "holder.js",
images: "img",
bgnodes: ".holderjs",
themes: {
"gray": {
background: "#eee",
foreground: "#aaa",
size: 12
},
"social": {
background: "#3a5a97",
foreground: "#fff",
size: 12
},
"industrial": {
background: "#434A52",
foreground: "#C2F200",
size: 12
}
},
stylesheet: ""
};
app.flags = {
dimensions: {
regex: /^(\d+)x(\d+)$/,
output: function (val) {
var exec = this.regex.exec(val);
return {
width: +exec[1],
height: +exec[2]
}
}
},
fluid: {
regex: /^([0-9%]+)x([0-9%]+)$/,
output: function (val) {
var exec = this.regex.exec(val);
return {
width: exec[1],
height: exec[2]
}
}
},
colors: {
regex: /#([0-9a-f]{3,})\:#([0-9a-f]{3,})/i,
output: function (val) {
var exec = this.regex.exec(val);
return {
size: settings.themes.gray.size,
foreground: "#" + exec[2],
background: "#" + exec[1]
}
}
},
text: {
regex: /text\:(.*)/,
output: function (val) {
return this.regex.exec(val)[1];
}
},
font: {
regex: /font\:(.*)/,
output: function (val) {
return this.regex.exec(val)[1];
}
},
auto: {
regex: /^auto$/
},
literal: {
regex: /^literal$/
}
}
for (var flag in app.flags) {
if (!app.flags.hasOwnProperty(flag)) continue;
app.flags[flag].match = function (val) {
return val.match(this.regex)
}
}
app.add_theme = function (name, theme) {
name != null && theme != null && (settings.themes[name] = theme);
return app;
};
app.add_image = function (src, el) {
var node = selector(el);
if (node.length) {
for (var i = 0, l = node.length; i < l; i++) {
var img = document.createElement("img")
img.setAttribute("data-src", src);
node[i].appendChild(img);
}
}
return app;
};
app.run = function (o) {
var options = extend(settings, o),
images = [],
imageNodes = [],
bgnodes = [];
if (typeof (options.images) == "string") {
imageNodes = selector(options.images);
} else if (window.NodeList && options.images instanceof window.NodeList) {
imageNodes = options.images;
} else if (window.Node && options.images instanceof window.Node) {
imageNodes = [options.images];
}
if (typeof (options.bgnodes) == "string") {
bgnodes = selector(options.bgnodes);
} else if (window.NodeList && options.elements instanceof window.NodeList) {
bgnodes = options.bgnodes;
} else if (window.Node && options.bgnodes instanceof window.Node) {
bgnodes = [options.bgnodes];
}
preempted = true;
for (i = 0, l = imageNodes.length; i < l; i++) images.push(imageNodes[i]);
var holdercss = document.getElementById("holderjs-style");
if (!holdercss) {
holdercss = document.createElement("style");
holdercss.setAttribute("id", "holderjs-style");
holdercss.type = "text/css";
document.getElementsByTagName("head")[0].appendChild(holdercss);
}
if (!options.nocss) {
if (holdercss.styleSheet) {
holdercss.styleSheet.cssText += options.stylesheet;
} else {
holdercss.appendChild(document.createTextNode(options.stylesheet));
}
}
var cssregex = new RegExp(options.domain + "\/(.*?)\"?\\)");
for (var l = bgnodes.length, i = 0; i < l; i++) {
var src = window.getComputedStyle(bgnodes[i], null)
.getPropertyValue("background-image");
var flags = src.match(cssregex);
var bgsrc = bgnodes[i].getAttribute("data-background-src");
if (flags) {
var holder = parse_flags(flags[1].split("/"), options);
if (holder) {
render("background", bgnodes[i], holder, src);
}
} else if (bgsrc != null) {
var holder = parse_flags(bgsrc.substr(bgsrc.lastIndexOf(options.domain) + options.domain.length + 1)
.split("/"), options);
if (holder) {
render("background", bgnodes[i], holder, src);
}
}
}
for (l = images.length, i = 0; i < l; i++) {
var attr_data_src, attr_src;
attr_src = attr_data_src = src = null;
try {
attr_src = images[i].getAttribute("src");
attr_datasrc = images[i].getAttribute("data-src");
} catch (e) {}
if (attr_datasrc == null && !! attr_src && attr_src.indexOf(options.domain) >= 0) {
src = attr_src;
} else if ( !! attr_datasrc && attr_datasrc.indexOf(options.domain) >= 0) {
src = attr_datasrc;
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hakyll-bootstrap/js/prism.js deleted 100644 → 0
View file @ b103362d
/* PrismJS 1.15.0
https://prismjs.com/download.html#themes=prism&languages=markup+css+clike+javascript+c+bash+python+rust&plugins=line-highlight+line-numbers+toolbar+highlight-keywords+copy-to-clipboard */
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Prism.languages.javascript=Prism.languages.extend("clike",{"class-name":[Prism.languages.clike["class-name"],{pattern:/(^|[^$\w\xA0-\uFFFF])[_$A-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\.(?:prototype|constructor))/,lookbehind:!0}],keyword:[{pattern:/((?:^|})\s*)(?:catch|finally)\b/,lookbehind:!0},/\b(?:as|async|await|break|case|class|const|continue|debugger|default|delete|do|else|enum|export|extends|for|from|function|get|if|implements|import|in|instanceof|interface|let|new|null|of|package|private|protected|public|return|set|static|super|switch|this|throw|try|typeof|undefined|var|void|while|with|yield)\b/],number:/\b(?:(?:0[xX][\dA-Fa-f]+|0[bB][01]+|0[oO][0-7]+)n?|\d+n|NaN|Infinity)\b|(?:\b\d+\.?\d*|\B\.\d+)(?:[Ee][+-]?\d+)?/,"function":/[_$a-zA-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\s*\(|\.(?:apply|bind|call)\()/,operator:/-[-=]?|\+[+=]?|!=?=?|<<?=?|>>?>?=?|=(?:==?|>)?|&[&=]?|\|[|=]?|\*\*?=?|\/=?|~|\^=?|%=?|\?|\.{3}/}),Prism.languages.javascript["class-name"][0].pattern=/(\b(?:class|interface|extends|implements|instanceof|new)\s+)[\w.\\]+/,Prism.languages.insertBefore("javascript","keyword",{regex:{pattern:/((?:^|[^$\w\xA0-\uFFFF."'\])\s])\s*)\/(\[(?:[^\]\\\r\n]|\\.)*]|\\.|[^\/\\\[\r\n])+\/[gimyu]{0,5}(?=\s*($|[\r\n,.;})\]]))/,lookbehind:!0,greedy:!0},"function-variable":{pattern:/[_$a-zA-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\s*[=:]\s*(?:async\s*)?(?:\bfunction\b|(?:\((?:[^()]|\([^()]*\))*\)|[_$a-zA-Z\xA0-\uFFFF][$\w\xA0-\uFFFF]*)\s*=>))/,alias:"function"},parameter:[{pattern:/(function(?:\s+[_$A-Za-z\xA0-\uFFFF][$\w\xA0-\uFFFF]*)?\s*\(\s*)(?!\s)(?:[^()]|\([^()]*\))+?(?=\s*\))/,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/[_$a-z\xA0-\uFFFF][$\w\xA0-\uFFFF]*(?=\s*=>)/i,inside:Prism.languages.javascript},{pattern:/(\(\s*)(?!\s)(?:[^()]|\([^()]*\))+?(?=\s*\)\s*=>)/,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/((?:\b|\s|^)(?!(?:as|async|await|break|case|catch|class|const|continue|debugger|default|delete|do|else|enum|export|extends|finally|for|from|function|get|if|implements|import|in|instanceof|interface|let|new|null|of|package|private|protected|public|return|set|static|super|switch|this|throw|try|typeof|undefined|var|void|while|with|yield)(?![$\w\xA0-\uFFFF]))(?:[_$A-Za-z\xA0-\uFFFF][$\w\xA0-\uFFFF]*\s*)\(\s*)(?!\s)(?:[^()]|\([^()]*\))+?(?=\s*\)\s*\{)/,lookbehind:!0,inside:Prism.languages.javascript}],constant:/\b[A-Z][A-Z\d_]*\b/}),Prism.languages.insertBefore("javascript","string",{"template-string":{pattern:/`(?:\\[\s\S]|\${[^}]+}|[^\\`])*`/,greedy:!0,inside:{interpolation:{pattern:/\${[^}]+}/,inside:{"interpolation-punctuation":{pattern:/^\${|}$/,alias:"punctuation"},rest:Prism.languages.javascript}},string:/[\s\S]+/}}}),Prism.languages.markup&&Prism.languages.insertBefore("markup","tag",{script:{pattern:/(<script[\s\S]*?>)[\s\S]*?(?=<\/script>)/i,lookbehind:!0,inside:Prism.languages.javascript,alias:"language-javascript",greedy:!0}}),Prism.languages.js=Prism.languages.javascript;
Prism.languages.c=Prism.languages.extend("clike",{"class-name":{pattern:/(\b(?:enum|struct)\s+)\w+/,lookbehind:!0},keyword:/\b(?:_Alignas|_Alignof|_Atomic|_Bool|_Complex|_Generic|_Imaginary|_Noreturn|_Static_assert|_Thread_local|asm|typeof|inline|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|int|long|register|return|short|signed|sizeof|static|struct|switch|typedef|union|unsigned|void|volatile|while)\b/,operator:/>>=?|<<=?|->|([-+&|:])\1|[?:~]|[-+*\/%&|^!=<>]=?/,number:/(?:\b0x(?:[\da-f]+\.?[\da-f]*|\.[\da-f]+)(?:p[+-]?\d+)?|(?:\b\d+\.?\d*|\B\.\d+)(?:e[+-]?\d+)?)[ful]*/i}),Prism.languages.insertBefore("c","string",{macro:{pattern:/(^\s*)#\s*[a-z]+(?:[^\r\n\\]|\\(?:\r\n|[\s\S]))*/im,lookbehind:!0,alias:"property",inside:{string:{pattern:/(#\s*include\s*)(?:<.+?>|("|')(?:\\?.)+?\2)/,lookbehind:!0},directive:{pattern:/(#\s*)\b(?:define|defined|elif|else|endif|error|ifdef|ifndef|if|import|include|line|pragma|undef|using)\b/,lookbehind:!0,alias:"keyword"}}},constant:/\b(?:__FILE__|__LINE__|__DATE__|__TIME__|__TIMESTAMP__|__func__|EOF|NULL|SEEK_CUR|SEEK_END|SEEK_SET|stdin|stdout|stderr)\b/}),delete Prism.languages.c["boolean"];
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<p>
Orestis Malaspinas<br>
Chargé d'enseignement<br>
<br>
HEPIA<br>
Rue de la Prairie 4<br>
CH-1202 Genève<br>
orestis dot malaspinas at hesge dot ch<br>
http://www.hesge.ch/hepia<br>
Tel. +41 (0)22 546 67 06<br>
<br>
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I am an HES engineer in computer science, I am currently performing a master degree at the University of Geneva.
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My main research topic is in High Performance Computing by working on a new MPI backend for the
functional language Futhark.
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---
title: Example Blog Post
author: Stephen Diehl
date: 2013-11-13
mathjax: on
---
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non est in neque luctus eleifend. Sed tincidunt vestibulum
facilisis. Aenean ut pulvinar massa.
Some math:
$$
\begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
$$
Some code:
```haskell
newtype MonadMonoid m a = MonadMonoid { unMonad :: a -> m a }
instance Monad m => Monoid (MonadMonoid m a) where
mempty = MonadMonoid return
mappend f g = MonadMonoid (f >=> g)
```
Fin.
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---
author:
- Orestis Malaspinas
title: Mathématiques en technologie de l'Information
autoSectionLabels: false
autoEqnLabels: true
eqnPrefix:
- "éq."
- "éqs."
chapters: true
numberSections: false
chaptersDepth: 1
sectionsDepth: 3
lang: fr
documentclass: book
papersize: A4
cref: false
urlcolor: blue
date: 2013-11-13
mathjax: on
---
\newcommand{\ux}{\bm{x}}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\real}{\mathbb{R}}
\newcommand{\grad}{\mathrm{grad}}
# Intégrales
## Interprétation géométrique
Dans ce chapitre nous nous intéressons au calcul d’aires sous une
fonction $f$. La fonction $f$ satisfait les hypothèses suivantes.
1. $f(x)$ est bornée dans l’intervalle $[a,b]\in{\real}$.
2. $f(x)$ est continue presque partout.
Nous définissions également l’infimum de $f$ sur un intervalle
$[x_0,x_1]$, noté $$\inf\limits_{[x_0,x_1]} f(x)$$ comme étant la plus grande valeur
bornant par dessous toutes les valeurs prises par $f(x)$ dans
l’intervalle $[x_0,x_1]$. Le suprémum sur un intervalle $[x_0,x_1]$,
noté $$\sup\limits_{[x_0,x_1]} f(x)$$ comme étant la plus petite valeur bornant par
dessus toutes les valeurs prises par $f(x)$ dans l’intervalle
$[x_0,x_1]$.
Finalement nous définissons une subdivision
$$\Delta_n=\{a=x_0<x_1<...<x_{n-1}<x_{n}=b\}$$ est une suite finie
contenant $n+1$ termes dans $[a,b]$.
On peut à présent approximer l’aire sous la fonction $f(x)$ dans
l’intervalle $[a,b]$ de plusieurs façons:
1. $A^i(n)=\sum_{i=0}^{n-1} \inf\limits_{[x_i,x_{i+1}]} f(x)\cdot (x_{i+1}-x_i)$
comme étant l’aire inférieure.
2. $A^s(n)=\sum_{i=0}^{n-1} \sup\limits_{[x_i,x_{i+1}]} f(x)\cdot (x_{i+1}-x_i)$
comme étant l’aire supérieure.
3. $A^R(n)=\sum_{i=0}^{n-1} f(\xi_i)\cdot (x_{i+1}-x_i)$, $\xi_i\in [x_i,x_{i+1}]$
1 et 2 sont les sommes de Darboux, 3 est une somme de Riemann qui, dépendant des choix des $\xi_i$, peut être égale à 1 ou à 2.
L’aire de sous la fonction $f(x)$ est donnée par la limite pour
$n\rightarrow\infty$ de $A^i$ ou $A^s$ (si elle existe). Dans ce cas $n\rightarrow\infty$ $A^R$ (pris en sandwich entre $A^i$ et $A^n$)
nous donne aussi l'aire sous la fonction.
Remarque +.#
1. Ces sommes peuvent être positives ou négatives en fonction du signe
de $f$.
2. Une implémentation informatique est immédiate, en particulier pour la somme de Riemann.
Définition (Intégrabilité au sens de Riemann) +.#
Une fonction est dite intégrable au sens de Riemann si
$$\lim\limits_{n\rightarrow\infty}A^i(n)=\lim\limits_{n\rightarrow\infty}A^s(n)=\int_a^b f(x){\mathrm{d}}x.$$
Dans la formule
$$\int_a^b f(x){\mathrm{d}}x,$$
$x$ est appelée
variable d’intégration, $a$ et $b$ sont les bornes d’intégration. Pour
des raisons de consistance dans les notations la variable d’intégration
ne peut être désignée avec le même symbole qu’une des bornes
d’intégration.
---
Exemple (Intégration de Riemann) +.#
Intégrer de $f(x)=x$ dans intervalle $[0,1]$.
---
---
Solution (Intégration de Riemann) +.#
Il est élémentaire de calculer que cette aire vaut $1/2$ (c’est l’aire d’un
triangle rectangle de côté 1). Néanmoins, évaluons également cette aire
à l’aide de $A^i$ et $A^s$. Commençons par subdiviser $[0,1]$ en $n$
intervalles égaux de longueur $\delta=1/n$. Comme $f(x)$ est strictement
croissante, on a que $\inf\limits_{[x_i,x_{i+1}]}f(x)=f(x_i)$ et que
$\sup\limits_{[x_i,x_{i+1}]}f(x)=f(x_{i+1})$. On a donc que
1. $A^i(n)=\delta\sum_{i=0}^{n-1} x_i=\delta\sum_{i=0}^{n-1}\frac{i}{n}=\frac{n(n-1)}{2n^2}=\frac{n-1}{2n}$[^2].
Et donc en prenant la limite pour $n\rightarrow\infty$ il vient
$$A^i=\lim\limits_{n\rightarrow\infty}\frac{n-1}{2n}=\frac{1}{2}.$$
2. $A^s(n)=\delta\sum_{i=0}^{n-1} x_{i+1}=\delta\sum_{i=0}^{n-1}\frac{i+1}{n}=\delta\sum_{i=0}^{n}\frac{i}{n}=\frac{n(n+1)}{2n^2}=\frac{n+1}{2n}$.
Et donc en prenant la limite pour $n\rightarrow\infty$ il vient
$$A^s=\lim\limits_{n\rightarrow\infty}\frac{n+1}{2n}=\frac{1}{2}.$$
---
---
Exemple (Intégration de Riemann de $x^2$) +.#
Calculer l’aire sous la courbe de $f(x)=x^2$ dans intervalle $[0,1]$.
Indication: $\sum_{i=0}^n i^2=\frac{1}{6}n(n+1)(2n+1).$
---
Interprétation physique
-----------------------
Supposons que nous ayons une fonction, $x(t)$, qui donne la position
d’un objet pour un intervalle de temps $t\in[a,b]$. Nous pouvons
aisément en déduire la vitesse $v(t)$ de l’objet, comme étant la
variation de $x(t)$ quand $t$ varie. Autrement dit $v(t)=x'(t)$.
Supposons à présent que nous ne connaissions que la vitesse $v(t)$ de
notre objet. Afin de déduire sa position nous prendrions un certain
nombre d’intervalles de temps $\delta t_i=t_{i+1}-t_i$ que nous
multiplierions par $v(t_i)$ afin de retrouver la distance parcourue
pendant l’intervalle $\delta t_i$ et ainsi de suite. Afin d’améliorer
l’approximation de la distance parcourue nous diminuerions la valeur de
$\delta t_i$ jusqu’à ce que $\delta t_i\rightarrow 0$.
Nous voyons ainsi que cette méthode, n’est autre qu’une façon “intuitive”
d’intégrer la vitesse afin de trouver la position. Et que
l’intégrale et la dérivée sont étroitement liées: la vitesse étant la
dérivée de la position et la position étant l’intégrale de la vitesse.
Primitive
---------
Si maintenant nous essayons de généraliser le calcul de l’intégrale
d’une fonction, il s’avère que le calcul d’une intégrale est l’inverse
du calcul d’une dérivée.
Définition (Primitive) +.#
Soit $f$ une fonction. On dit que $F$ est une primitive de $f$ sur
l’intervalle $D\subseteq{\real}$ si $F'(x)=f(x)$ $\forall x\in D$.
Si $F$ est une primitive de $f$, alors on peut définir la fonction $G$
telle que $G(x)=F(x)+C$, $C\in{\real}$ qui est aussi une
primitive de $f$. On voit que la primitive de $f$ est définie à une
constante additive près. En effet, si $F'=f$ on a
$$G'=F'+\underbrace{C'}_{=0}=F'=f.$$
Théorème (Unicité) +.#
Pour $a\in D$ et $b\in{\real}$ il existe une unique
primitive $F$ telle que $F(a)=b$.
---
Illustration (Unicité) +.#
Soit $f(x)=x$, alors l’ensemble de primitives correspondantes est
$G=x^2/2+C$. Si nous cherchons la primitive telle que $G(0)=0$, il vient
que $C=0$ et donc la primitive est unique et vaut $F(x)=x^2/2$.
---
---
Exercices (Primitives) +.#
Calculez les primitives suivantes (*indication: il s’agit de trouver les
fonctions $F(x)$ telles que $F'(x)=f(x)$*):
1. $F(x)=\int x^2{\mathrm{d}}x$.
2. $F(x)=\int x^n{\mathrm{d}}x$, $n\in {\real}\backslash\{-1\}$.
3. $F(x)=\int \sqrt{x}{\mathrm{d}}x$.
4. $F(x)=\int \frac{1}{x}{\mathrm{d}}x$.
5. $F(x)=\int \exp(x){\mathrm{d}}x$.
6. $F(x)=\int \sin(x){\mathrm{d}}x$.
---
Maintenant que vous avez calculé toutes ces primitives de base, nous
pouvons récapituler des formules qui seront importantes pour la suite:
1. $\int x^n{\mathrm{d}}x=\frac{1}{n+1}x^{n+1}+C$,
$n\in {\real}\backslash\{-1\}$.
2. $\int \frac{1}{x}{\mathrm{d}}x=\ln(x)+C$.
3. $\int \exp(x){\mathrm{d}}x=\exp(x)+C$.
4. $\int \sin(x){\mathrm{d}}x=-\cos(x)+C$.
5. $\int \cos(x){\mathrm{d}}x=\sin(x)+C$.
Théorème (Théorème fondamental du calcul intégral) +.#
En définissant à présent l’intégrale à l’aide de la notion
de primitive, nous avons que pour $a,b\in{\real}$ et $a<b$
$$\int_a^b f(x){\mathrm{d}}x=\left.F\right|_a^b=F(b)-F(a).$${#eq:thm_fond}
On dit que $x$ est la variable d’intégration. Elle est dite “muette” car
elle disparaît après que l’intégrale ait été effectuée. On peut donc
écrire l’équation ci-dessus de façon équivalente en remplaçant le
symbole $x$ par n’importe quelle autre lettre (sauf $a,b,f,F$).
---
Remarque +.#
On notera que la constante additive $C$ a disparu de cette formule. En
effet, remplaçons $F$ par $G=F+C$, il vient
$$\int_a^b f(x){\mathrm{d}}x=G(b)-G(a)=F(b)+C-F(a)-C=F(b)-F(a).$$
---
Il suit de l'@eq:thm_fond que
$$\int_a^af(x){\mathrm{d}}x=F(a)-F(a)=0$$ et que
$$\int_a^bf(x){\mathrm{d}}x= -\int_b^af(x){\mathrm{d}}x$$
Nous pouvons à présent définir la fonction $G(x)$ telle que
$$G(x)=\int_a^xf(y){\mathrm{d}}y=F(x)-F(a).$$ Il suit que $G(x)$
est la primitive de $f$ telle que $G(a)=0$.
Propriétés +.#
Soient $f$ et $g$ deux fonctions intégrables sur un intervalle
$D=[a,b]\subseteq{\real}$, $c\in[a,b]$, et $\alpha\in{\real}$.
On a
1. La dérivée et l’intégrale “s’annulent”
$$\left(\int_a^x f(x){\mathrm{d}}x\right)'=\left(F(x)-F(a)\right)'=F'(x)-\left(F(a)\right)'=F'(x)=f(x).$$
2. La fonction $h=f+g$ admet aussi une primitive sur $D$, et on a
$$\int_a^b(f(x)+g(x)){\mathrm{d}}x=\int_a^b f(x){\mathrm{d}}x+\int_a^b g(x){\mathrm{d}}x.$$
3. La fonction $h=\alpha f$ admet aussi une primitive sur $D$, et on a
$$\int_a^b\alpha f(x){\mathrm{d}}x=\alpha\int_a^b f(x){\mathrm{d}}x.$$
4. Relation de Chasles (faire la démonstration en exercice)
$$\int_a^c f(x){\mathrm{d}}x=\int_a^b f(x){\mathrm{d}}x+\int_b^c f(x){\mathrm{d}}x.$$
De cette relation on déduit qu’on peut calculer l’intégrale d’une
fonction continue par morceaux sur $[a,b]$.
5. Si $f$ est paire alors
$$\int_{-a}^a f(x){\mathrm{d}}x = 2\int_0^a f(x){\mathrm{d}}x.$$
6. Si $f$ est impaire alors $$\int_{-a}^a f(x){\mathrm{d}}x = 0.$$
### Intégrales impropres
Si une des bornes d’intégration ou si la fonction à intégrer admet une
discontinuité à des points bien définis, nous parlons intégrales
impropres.
Lorsqu’une borne d’intégration est infinie, alors nous pouvons avoir les
cas de figures suivants $$\begin{aligned}
&\int_a^\infty f(x){\mathrm{d}}x=\lim\limits_{b\rightarrow\infty}\int_a^b f(x){\mathrm{d}}x,\\
&\int_{-\infty}^b f(x){\mathrm{d}}x=\lim\limits_{a\rightarrow\infty}\int_{-a}^b f(x){\mathrm{d}}x,\\
&\int_{-\infty}^\infty f(x){\mathrm{d}}x=\lim\limits_{a\rightarrow\infty}\int_{-a}^a f(x){\mathrm{d}}x.\end{aligned}$$
---
Exemple (Intégrale impropre) +.#
Calculer l’intégrale suivante
$$\int_0^\infty e^{-ax}{\mathrm{d}}x,\quad a>0.$$
Solution (Intégrale impropre) +.#
Nous pouvons réécrire
l’intégrale ci-dessus comme
$$\int_0^\infty e^{-ax}{\mathrm{d}}x=\lim\limits_{b\rightarrow \infty}\int_0^b e^{-ax}{\mathrm{d}}x=-\frac{1}{a}\lim\limits_{b\rightarrow\infty}\left[e^{-ax}\right]_0^b=-\frac{1}{a}\left[\lim\limits_{b\rightarrow \infty}e^{-ab}-1\right]=\frac{1}{a}.$$
---
---
Exercice +.#
Calculer l’intégrale suivante
$$\int_1^\infty \frac{1}{x^2}{\mathrm{d}}x.$$
---
Lorsque nous avons une discontinuité dans la fonction $f$ au point
$c\in[a,b]$ nous avons
$$\int_a^b f(x){\mathrm{d}}x = \lim\limits_{\varepsilon\rightarrow 0}\int_a^{c-\varepsilon} f(x){\mathrm{d}}x +\int_{c+\varepsilon}^b f(x){\mathrm{d}}x.$$
Exercice +.#
Montrer que $$\int_{-1}^2\frac{1}{x}=\ln{2}.$$
Définition (Valeur moyenne) +.#
Soit une fonction $f$ admettant une primitive sur $[a,b]$ avec $a<b$,
alors la valeur moyenne $\bar{f}$ de cette fonction sur $[a,b]$, est définie par
$$\bar{f}=\frac{1}{b-a}\int_a^bf(x){\mathrm{d}}x.$$
Méthodes d’intégration
----------------------
Dans cette section, nous allons étudier différentes méthodes pour
intégrer des fonctions.
### Intégration de fonctions usuelles et cas particuliers
Le calcul d’une primitive ou d’une intégrale n’est en général pas une
chose aisée. Nous connaissons les formules d’intégration pour certaines
fonctions particulières.
#### Polynômes
Les polynômes s’intègrent terme à terme. Pour
$(\{a_i\}_{i=0}^{n}\in{\real}$ $$\begin{aligned}
&\int a_0 + a_1 x + a_2 x^2+\cdots+a_{n-1} x^{n-1}+a_{n} x^{n}{\mathrm{d}}x\\
=&\int a_0{\mathrm{d}}x + \int a_1 x{\mathrm{d}}x + \int a_2 x^2{\mathrm{d}}x+\cdots+\int a_{n-1} x^{n-1}{\mathrm{d}}x+\int a_{n} x^{n}){\mathrm{d}}x\\
=&a_0 x + \frac{a_1}{2}x^2+\frac{a_2}{3}x^3+\cdots+\frac{a_n}{n+1}x^{n+1}+c.\end{aligned}$$
---
Exercice +.#
Intégrer la fonction suivante
$$\int (x+2)(x^3+3x^2+4x-3){\mathrm{d}}x.$$
---
#### Application de la règle de chaîne pour l’intégration
Une primitive d'une fonction de la forme $f(x)f'(x)$ se calcule aisément
$$\int f(x)f'(x){\mathrm{d}}x=\frac{1}{2}f(x)^2+c.$$
Nous calculons par exemple
$$\int \sin(x)\cos(x){\mathrm{d}}x=\frac{1}{2}\sin^2(x)+c=-\frac{1}{2}\cos^2(x)+c'.$${#eq:sin_cos}
#### Inverse de la dérivation logarithmique
Une primitive de la forme
$$\int \frac{f'(x)}{f(x)}{\mathrm{d}}x=\ln(f(x))+c.$$
---
Exemple +.#
Calculer la primitive suivante
$$
\int \frac{1}{x}{\mathrm{d}}x.
$$
Solution +.#
Le calcul de la primitive de suivante
$$\int \frac{1}{x}{\mathrm{d}}x=\int \frac{(x)'}{x}{\mathrm{d}}x=\ln(x)+c.$$
---
#### Règle de chaîne
Une des façons les plus simples de calculer une primitive est
de reconnaître la règle de chaîne dans le terme à intégrer
$$\int g'(f(x))f'(x){\mathrm{d}}x=\int [g(f(x))]' {\mathrm{d}}x=g(f(x))+c.$$
Illustration +.#
Si $g$ est définie comme $g(x)=x^{-1}$ et $f(x)=3x^2+2$, alors la
primitive
$$\int \frac{f'(x)}{g'(f(x))}{\mathrm{d}}x=\int -\frac{6 x}{(3x^2+2)^2}{\mathrm{d}}x=\frac{1}{3x^2+2}+c.$$
### Intégration par parties
La dérivation d’un produit de fonctions $f\cdot g$ s’écrit
$$(f(x)g(x))'=f'(x) g(x)+f(x) g'(x).$$ En intégrant cette équation on
obtient
$$f(x)g(x)=\int f'(x) g(x){\mathrm{d}}x+\int f(x) g'(x){\mathrm{d}}x.$$
Une primitive de la forme $\int f'(x) g(x){\mathrm{d}}x$ peut ainsi se
calculer de la façon suivante
$$\int f'(x) g(x){\mathrm{d}}x=f(x)g(x)-\int f(x) g'(x){\mathrm{d}}x.$$
De façon similaire si nous nous intéressons à une intégrale définie
$$\int_a^b f'(x) g(x){\mathrm{d}}x=\left.(f(x)g(x))\right|_a^b-\int_a^b f(x) g'(x){\mathrm{d}}x.$$
Le choix des fonctions est complètement arbitraire. Néanmoins, le but de
cette transformation est de remplacer une intégrale par une autre dont
on connaîtrait la solution.
Des “règles” pour utiliser cette technique seraient que
1. $g'$ soit facile à calculer et aurait une forme plus simple que $g$.
2. $\int f'{\mathrm{d}}x$ soit facile à calculer et aurait une forme
plus simple que $f'$.
---
Exemple +.#
Calculer les primitives suivantes
1. $\int x e^x{\mathrm{d}}x$.
2. $\int \cos(x)\sin(x){\mathrm{d}}x$.
Solution +.#
1. $\int x e^x{\mathrm{d}}x$. $g(x)=x$, $f'(x)=e^x$ et donc $g'(x)=1$,
$f(x)=e^x$. Il vient
$$\int x e^x=x e^x-\int e^x{\mathrm{d}}x=x e^x-e^x+c.$$
2. $\int \cos(x)\sin(x){\mathrm{d}}x$. $g= \cos(x)$, $f'(x)=\sin(x)$ et
donc $g'(x)=-\sin(x)$, $f(x)=-\cos(x)$. Il vient $$\begin{aligned}
&\int \cos(x)\sin(x){\mathrm{d}}x=\sin^2(x)-\int \cos(x)\sin(x){\mathrm{d}}x\nonumber\\
\Rightarrow &\int \cos(x)\sin(x){\mathrm{d}}x=\frac{1}{2}\sin^2(x).
\end{aligned}$$
On voit que le résultat de l’intégration par
partie nous redonne l’intégrale de départ. Ceci nous permet
d’évaluer directement la dite intégrale pour retrouver le résultat de l'@eq:sin_cos
---
Il est également possible d’enchaîner plusieurs intégrations par
parties.
---
Exemple +.#
Calculer l’intégrale de $\int x^2 e^x{\mathrm{d}}x$.
Solution +.#
En posant $g(x)=x^2$,
$f'(x)=e^x$ et donc $g'(x)=2x$, $f(x)=e^x$. Il vient
$$\int x^2 e^x{\mathrm{d}}x=x^2e^x-2\int x e^x{\mathrm{d}}x.$$ On pose
de façon similaire $g(x)=x$, $f'(x)=e^x$ et donc $g'(x)=1$, $f(x)=e^x$
et il vient
$$\int x^2 e^x{\mathrm{d}}x=x^2e^x-2\left(x e^x -\int e^x{\mathrm{d}}x\right)=x^2e^x-2x e^x +2e^x+c.$$
---
---
Exercice +.#
Calculer les primitives suivantes
1. $\int \ln(x){\mathrm{d}}x$
2. $\int x^2 \sin(x){\mathrm{d}}x$
3. $\int e^x\sin(x){\mathrm{d}}x$
---
### Intégration par changement de variables
On observe que la dérivation de la composition de deux fonctions $F$ et
$g$ est donnée par
$$(F\circ g)'=(f\circ g)\cdot g',\mbox{ ou } [F(g(y))]'=f(g(y))\cdot g'(y),$$
où $f=F'$. Si nous intégrons cette relation on obtient $$\begin{aligned}
\int_a^b f(g(y))g'(y){\mathrm{d}}y = \int_a^b [F(g(y))]'{\mathrm{d}}y=\left.F(g(y))\right|_a^b=F(g(b))-F(g(a))=\int_{g(a)}^{g(b)}f(x){\mathrm{d}}x.\end{aligned}$$
Cette relation nous mène au théorème suivant.
Théorème (Intégration par changement de variables) +.#
Soit $f$ une fonction continue presque partout, et $g$ une fonction dont
la dérivée est continue presque partout sur un intervalle $[a,b]$. Soit
également l’image de $g$ contenue dans le domaine de définition de $f$.
Alors
$$\int_a^b f(g(x))g'(x){\mathrm{d}}x = \int_{g(a)}^{g(b)}f(z){\mathrm{d}}z.$$
Nous utilisons ce théorème de la façon suivante. L’idée est de remplacer
la fonction $g(x)$ par $z$. Puis il faut également remplacer
${\mathrm{d}}x$ par ${\mathrm{d}}z$ où nous avons que
${\mathrm{d}}x={\mathrm{d}}z/g'(x)$. Finalement, il faut changer les
bornes d’intégration par $a\rightarrow g(a)$ et $b\rightarrow g(b)$. Si
on ne calcule pas l’intégrale mais la primitive, on ne modifie
(évidemment) pas les bornes d’intégration, mais en revanche pour trouver
la primitive il faut également appliquer la transformation $x=g^{-1}(z)$
sur la solution.
---
Exemple (Changement de variable) +.#
Intégrer par changement de variables $\int_1^3 6x\ln(x^2){\mathrm{d}}x$.
Solution (Changement de variable) +.#
En définissant $z=x^2$, nous avons ${\mathrm{d}}x={\mathrm{d}}z/(2x)$.
Les bornes d’intégration deviennent $z(1)=1^2=1$ et $z(3)=3^2=9$. On
obtient donc $$\begin{aligned}
\int_1^3 6x\ln(x^2){\mathrm{d}}x&=\int_1^9 6x\ln(z)\frac{1}{2x}{\mathrm{d}}z=\int_1^9\ln(z){\mathrm{d}}z\nonumber\\
&=3\left[z\ln(z)-z\right]_1^9=3(9\ln(9)-9-\ln(1)+1)=27\ln(9)-24.
\end{aligned}$$
---
---
Exercice +.#
Calculer les primitives suivantes par changement de variable
1. $\int \frac{1}{5x-7}{\mathrm{d}}x$
2. $\int \sin(3-7x){\mathrm{d}}x$
3. $\int x e^{x^2}{\mathrm{d}}x$
---
## Le produit de convolution
Les convolutions sont très utilisées pour le traitement du signal, le traitement d'images et
les réseaux de neurones convolutifs entre autres.
### La convolution continue
La convolution de deux fonctions intégrables, $f(t)$, et $g(t)$, notée $f\ast g$ se définit comme
\begin{equation}
(f\ast g)(x)=\int_{-\infty}^\infty f(x-t)g(t)\dd t.
\end{equation}
On constate que le membre de gauche de l'équation ci-dessus n'est rien d'autre qu'une fonction de $x$.
Pour chaque valeur de $x=x_0$, on calcule l'intégrale,
\begin{equation}
\int_{-\infty}^\infty f(x_0-t)g(t)\dd t.
\end{equation}
---
Exercice (Commutativité) +.#
Démontrer que le produit de convolution est commutatif, soit
\begin{equation}
(f\ast g)(x)=(g\ast f)(x).
\end{equation}
Indication: utiliser la substitution $\tau=x-t$.
---
Afin de pouvoir interpêter un peu
ce que cela veut dire, il est intéressant de faire un calcul
"simple" pour se faire une idée.
---
Exercice +.#
Calculer la convolution du signal $f(t)$
\begin{equation}
f(t)=\left\{\begin{array}{ll}
1,&\mbox{ si }t\in[0,1]\\
0,&\mbox{ sinon.}
\end{array}\right.
\end{equation}
Indication: faites un dessin de ce que représente la convolution de ce $f$ avec lui-même.
---
#### Interprétation avec les mains
Afin d'interpréter ce que représente le produit de convolution, introduisons la fonction delta de Dirac, $\delta_a(x)$. Cette fonction est un peu particulière, elle vaut zéro partout sauf en $0$ (où elle est "infinie"), et son
intégrale vaut $1$
\begin{equation}
\int_{-\infty}^\infty\delta(x)\dd x=1.
\end{equation}
Même si cela peut sembler étrange, on peut tenter de construire une telle fonction en prenant une suite de rectangles, centrés en $0$,
dont la surface vaut 1. Puis on rend ces rectangles de plus en plus fins, en imposant que la surface vaut toujours 1 et le tour est joué.
Cette fonction est intéressante, car elle a la propriété suivante lorsqu'on l'utilise pour effectuer des convolutions.
\begin{equation}
\int_{-\infty}^\infty f(y)\delta(y-x)\dd y=f(x).
\end{equation}
En d'autre termes cette intégrale est égale à la valeur de $f$ au point où l'argument du $\delta$ est nul.
A présent, si nous considérons la convolution de $f(t)$ avec
la fonction $\delta(t-a)=\delta_a$, on obtient
\begin{equation}
(f\ast\delta_a)(x)=\int_{-\infty}^\infty f(x-t)\delta(t-a)\dd t=f(x-a).
\end{equation}
En fait la convolution d'une fonction $f$ avec le delta de Dirac centré en $a$ ne fait que translater la fonction $f$ d'une distance $a$.
En effectuant à présent la convolution avec une combinaison linéaire de $\delta$ de Dirac
\begin{equation}
(f\ast(\alpha\cdot \delta_a+\beta\cdot \delta_b))(x)=\int_{-\infty}^\infty f(x-y)(\alpha\cdot\delta(y-a)+\beta\cdot\delta(y-b))\dd y=\alpha\cdot f(x-a)+\beta\cdot f(x-b).
\end{equation}
La convolution est donc la moyenne pondérée de $f$ translatée en $a$ et en $b$ par $\alpha$ et $\beta$ respectivement.
On voit que de façon générale, qu'on peut interpréter la convolution de deux fonctions $f(t)$ et $g(t)$ comme la moyenne de $f(t)$ pondérée par la fonction $g(t)$.
#### Le lien avec les filtres
Il se trouve que dans le cas où le filtre est linéaire (filtrer la combinaison de deux signaux
est la même chose que de faire la combinaison linéaires des signaux filtrés)
et indépendant du temps (les translations temporelles n'ont aucun effet sur lui)
alors on peut lier la convolution et le filtrage.
Si on définit la réponse impulsionnelle d'un filtre, $h(t)$, le filtrage d'un signal $s(t)$,
noté $f(s)$, n'est autre que la convolution de $h(t)$ avec $s(t)$
\begin{equation}
f(s)=(s\ast h)(x)=\int_{-\infty}^\infty f(x-t)g(t)\dd t.
\end{equation}
<!-- ### La convolution discrète
En se rappelant que l'intégrale n'est rien d'autre qu'une somme un peu plus compliquée -->
Intégration numérique
---------------------
Dans certains cas, il est impossible d’évaluer analytiquement une
intégrale ou alors elle est très compliquée à calculer. Dans ce cas, on
va approximer l’intégrale et donc commettre une erreur.
Pour ce faire on subdivise l’espace d’intégration $[a,b]$ en $N$ pas
équidistants (pour simplifier) $\delta x=(b-a)/N$, et on approxime
l’intégrale par une somme finie
$$\int_a^bf(x){\mathrm{d}}x=\sum_{i=0}^{N-1} \delta x f(a+i\delta x) g_i+E(a,b,\delta x)\cong\sum_{i=0}^{N-1} \delta x f(a+i\delta x) g_i,$$
où $g_i$ est un coefficient qui va dépendre de la méthode d’intégration
que nous allons utiliser, $E$ est l’erreur commise par l’intégration
numérique et va dépendre des bornes d’intégration, de $\delta x$ (du
nombre de pas d’intégration), de la forme de $f(x)$ (combien est
“gentille”) et finalement de la méthode d’intégration.
### Erreur d’une méthode d’intégration
D’une façon générale plus $\delta x$ est petit ($N$ est grand) plus
l’erreur sera petite et donc l’intégration sera précise (et plus le
calcul sera long). Néanmoins, comme la précision des machines sur
lesquelles nous évaluons les intégrales est finie, si $\delta x$ devient
proche de la précision de la machine des erreurs d’arrondi vont dégrader
dramatiquement la précision de l’intégration.
---
Remarque +.#
De façon générale il est difficile de connaître à l’avance la valeur
exacte de $E$. En revanche on est capable de déterminer **l’ordre**
de l’erreur.
---
---
Définition (Ordre d'une méthode) +.#
On dit qu’une méthode d’intégration est d’ordre $k$, si l’erreur commise
par la méthode varie proportionnellement à $\delta x^k$. On note qu’une
erreur est d’ordre $k$ par le symbole $\mathcal{O}(\delta x^k)$.
Exemple: si une méthode est d’ordre deux, alors en diminuant $\delta x$
d’un facteur $2$, l’erreur sera elle divisée par $2^2=4$. Si une méthode
est d’ordre $3$, alors en diminuant $\delta x$ d’un facteur $2$, nous
aurons que l’erreur est divisée par un facteur $2^3=8$. Etc.
---
Comme le calcul d’une intégrale de façon numérique ne donne en général
pas un résultat exact, mais un résultat qui va dépendre d’un certain
nombre de paramètres utilisés pour l’intégration, il faut définir un
critère qui va nous dire si notre intégrale est calculée avec une
précision suffisante.
Notons $I(N,a,b,f,g)$ l’approximation du calcul de l’intégrale
entre $a$ et $b$ de la fonction $f$ avec une résolution $N$ pour la
méthode d’intégration $g$
$$I(N,a,b,f,g)=\sum_{i=0}^{N-1} \delta x f(a+i\delta x) g_i,$$ où $g_i$
est encore à préciser. Afin de déterminer si le nombre de points que
nous avons choisi est suffisant, après avoir évalué $I(N,a,b,f,g)$, nous
évaluons $I(2\cdot N,a,b,f,g)$. En d’autres termes nous évaluons
l’intégrales de la même fonction avec la même méthode mais avec un
nombre de points deux fois plus élevé. Puis, nous pouvons définir
$\varepsilon(N)$ comme étant l’erreur relative de notre intégration avec
une résolution $N$ et $2\cdot N$
$$\varepsilon(N)\equiv\left|\frac{I(2N)-I(N)}{I(2N)}\right|.$$ Si à
présent nous choisissons un $\varepsilon_0>0$ (mais plus grand que la
précision machine), nous pouvons dire que le calcul numérique de notre
intégrale a **convergé** (on parle de **convergence** du calcul
également) pour une résolution $N$ quand $\varepsilon(N)<\varepsilon_0$.
### Méthode des rectangles
Pour la méthode des rectangles, nous allons calculer l’intégrale en
approximant l’aire sous la fonction par une somme de rectangles, comme
nous l’avons fait pour la définition de l’intégration au sens de
Riemann. La différence principale est que nous ne regarderons pas les
valeurs minimales ou maximales de $f$ sur les subdivisions de l’espace,
mais uniquement les valeurs sur les bornes. Cette approximation donne
donc la formule suivante $$\begin{aligned}
\int_a^bf(x){\mathrm{d}}x&\cong\sum_{i=0}^{N-1} \delta x f(a+i\cdot\delta x)+\mathcal{O}(\delta x),\\
&\cong\sum_{i=1}^{N} \delta x f(a+i\cdot\delta x)+\mathcal{O}(\delta x)\end{aligned}$${#eq:rect_gauche}
Cette méthode est d’ordre $1$. Une exception s’applique cependant
concernant l’ordre de l’intégration. Si la fonction à intégrer est une
constante $f(x)=c$, alors l’intégration est exacte.
Dans les deux cas ci-dessus on a évalué la fonction sur une des bornes.
On peut améliorer la précision en utilisant le “point du milieu” pour
évaluer l’aire du rectangle. L’approximation devient alors
$$\begin{aligned}
\int_a^bf(x){\mathrm{d}}x&\cong\sum_{i=0}^{N-1} \delta x f(a+(i+1/2)\cdot\delta x)+\mathcal{O}(\delta x^2).\end{aligned}$$
Cette astuce permet d’améliorer la précision de la méthode à très faible
coût. En effet, la précision de la méthode des rectangles est améliorée
et devient d’ordre 2. Elle est exacte pour les fonctions linéaires $f(x)=c\cdot x + d$.
### Méthode des trapèzes
Pour la méthode des trapèzes, nous allons calculer l’intégrale en
approximant l’aire sous la fonction par une somme de trapèzes. Pour
rappel l’aire d’un trapèze, dont les côtés parallèles sont de longueurs
$c$ et $d$ et la hauteur $h$, est donnée pas $$A=(c+d)h/2.$$ Cette
approximation donne donc la formule suivante
$$\int_a^bf(x){\mathrm{d}}x\cong\sum_{i=0}^{N-1} \delta x \frac{f(a+i\cdot\delta x)+f(a+(i+1)\cdot\delta x)}{2}+\mathcal{O}(\delta x^2).$$
Cette méthode est d’ordre $2$. Cette méthode d’intégration est aussi exacte
pour les fonctions linéaires $f(x)=c\cdot x + d$.
### Méthode de Simpson
Pour cette méthode, on approxime la fonction à intégrer dans un
intervalle par une parabole.
Commençons par évaluer l’intégrale à l’aide d’une subdivision dans
l’ensemble $[a,b]$.
L’idée est la suivante. On pose $f(x)=c\cdot x^2+d\cdot x+e$ et il
faut déterminer $c$, $d$, et $e$. Il faut donc choisir 3
points dans l’intervalle $[a,b]$ pour déterminer ces constantes. On
choisit comme précédemment $f(a)$, $f(b)$, et le troisième point est
pris comme étant le point du milieu $(f(a+b)/2)$. On se retrouve ainsi
avec trois équations à trois inconnues $$\begin{aligned}
f(a)&=c\cdot a^2+d\cdot a+e,\\
f(b)&=c\cdot b^2+d\cdot b+e,\\
f((a+b)/2)&=\frac{c}{4}\cdot (a+b)^2+\frac{d}{2}\cdot (a+b)+e.\end{aligned}$$
En résolvant ce système (nous n’écrivons pas la solution ici) nous
pouvons à présent évaluer l’intégrale $$\begin{aligned}
I&=\int_a^b f(x){\mathrm{d}}x\cong\int_a^b (cx^2+dx+e){\mathrm{d}}x,\nonumber\\
&=\frac{b-a}{6}(f(a)+f(b)+4f((a+b)/2))+\mathcal{O}(\delta x^4).\end{aligned}$$
On peut généraliser et affiner cette formule en rajoutant des
intervalles comme précédemment et en répétant cette opération pour
chaque intervalle.
Il vient donc que $$\begin{aligned}
I&=\frac{\delta x}{6}\sum_{i=0}^{N-1}\left[f(a+i\cdot \delta x)+f(a+(i+1)\cdot\delta x)\right.\nonumber\\
&\left.+4f(a+(i+1/2)\cdot\delta x)\right]+\mathcal{O}(\delta x^4).\end{aligned}$$
Cette méthode permet d’évaluer exactement les intégrales des polynômes d’ordre 3,
$f(x)=ax^3+bx^2+cx+d$.
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## Contributing
Please keep the [issue tracker](http://github.com/hakimel/reveal.js/issues) limited to **bug reports**, **feature requests** and **pull requests**.
### Personal Support
If you have personal support or setup questions the best place to ask those are [StackOverflow](http://stackoverflow.com/questions/tagged/reveal.js).
### Bug Reports
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### Pull Requests
- Should follow the coding style of the file you work in, most importantly:
- Tabs to indent
- Single-quoted strings
- Should be made towards the **dev branch**
- Should be submitted from a feature/topic branch (not your master)
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Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
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