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1203 lines
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<article itemscope itemtype="http://schema.org/Article"><div class="article__header"><header><h1>EDDL: How do we train neural networks on limited edge devices - PART 2</h1></header></div><meta itemprop="headline" content="EDDL: How do we train neural networks on limited edge devices - PART 2"><div class="article__info clearfix"><ul class="left-col menu"><li>
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<a class="button button--secondary button--pill button--sm"
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href="/archive.html?tag=Edge+computing">Edge computing</a>
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</li></ul><ul class="right-col menu"><li><i class="fas fa-user"></i> <span>Pengzhan Hao</span></li><li><i class="far fa-calendar-alt"></i> <span>Oct 31, 2021</span>
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</li></ul></div><meta itemprop="author" content="Pengzhan Hao"/><meta itemprop="datePublished" content="2021-10-31T13:01:14-04:00">
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<div class="article__content" itemprop="articleBody"><p>In the last post, part1, our idea of distributed learning on edge environment was generally addressed.
|
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I introduced the reason why edge distributed learning is needed and what improvements it can achieve.
|
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In this post, I will talk about our motivation study and how our framework works.</p>
|
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|
||
<h2 id="how-does-data-support-us-training-on-edge">How does data support us training on edge?</h2>
|
||
|
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<p>Before designing and implementing our framework, we first need confirmation that training on edge resource-limited devices is worthwhile.
|
||
We were using a malware detection neural network to show why a small, customized neural network is better.</p>
|
||
|
||
<p>We collected 32000+ mobile apps feature as global data.
|
||
With these data records, we trained a multilayer perceptron called “PerNet” to determine whether a given feature belongs to a benign or malware app.
|
||
We called this <strong>detection</strong>.
|
||
As well, PerNet can also classify malware apps into different types of attacks.
|
||
We called this <strong>classification</strong>.
|
||
The global model can achieve 93% above recall rate and 96.93% above accuracy.</p>
|
||
|
||
<p>With all these data, we selected two community app usage sub-dataset for local model generations.</p>
|
||
|
||
<ul>
|
||
<li>
|
||
<p>Large categories (Scenario 1)
|
||
We chose the 5 largest categories of apps, including entertainment, tools, brain&Puzzle, Lifestyle, and Education, as well as the 5 largest malware categories.
|
||
All together, 12000+ apps were included in this sub-dataset, almost 50 to 50 between benign and malware.</p>
|
||
</li>
|
||
<li>
|
||
<p>Campus-community categories (Scenario 2)
|
||
We chose the 5 most downloaded categories from college students as benign groups, as well as a similar amount of 5 malware categories.
|
||
To ensure that malware apps are included in 5 benign categories, we also considered synthesizing some other malware apps within categories of 5 most downloaded(benign) categories.</p>
|
||
</li>
|
||
</ul>
|
||
|
||
<p>With these two types of sub-dataset, we used the same PerNet to generate multiple local models.
|
||
Under each scenarios experiment, we compared global and local models on the preserved test dataset.
|
||
In all classification performances, local beat global in every scenario.
|
||
In detection performances, local also share the same accuracy as global does.</p>
|
||
|
||
<p><img src="/static/2021-10/t.3_inference_result.png" alt="Inference results" /></p>
|
||
|
||
<p>In summary, local models were trained on special occasions.
|
||
Under the same circumstance, a global model can achieve no better accuracy than local models.
|
||
The reason why local is better might be because of overfitting.
|
||
I believe this issue also be considered in the machine learning communities that they brought <a href="https://en.wikipedia.org/wiki/Transfer_learning">transfer learning</a>,
|
||
a technique to optimize global models to special scenarios but performing more training to a global model once it’s shipped to local.</p>
|
||
|
||
<h2 id="design-and-implementation">Design and Implementation</h2>
|
||
|
||
<h3 id="overall-design">Overall design</h3>
|
||
|
||
<p>The basic EDDL distributed training setup consists of 3 parts.
|
||
<strong>EDDL training cluster</strong>, a device cluster that consists of edge or mobile devices that are participating in training.
|
||
<strong>EDDL manager</strong>, the initial driver program that works as collect training data, relay data to training devices and initial training clusters.
|
||
<strong>Training data entry (TDE)</strong>, a data storage for all training data.</p>
|
||
|
||
<h3 id="dynamic-training-data-distribution">Dynamic training data distribution</h3>
|
||
|
||
<p>Existing distributed DNN training solutions usually statically partition training data among workers.
|
||
It can be a problem when the training node joins and exits.
|
||
We designed our framework that can dynamically distribute training data during learning.
|
||
Before every training batch started, a batch of TDE will be sent to devices.</p>
|
||
|
||
<p>In our experiments, we found that by applying this design, overall training time was shortened by doing.
|
||
Especially in large amount devices cases, this optimization can be 50% less than statically divided.</p>
|
||
|
||
<h3 id="scaling-up-cluster-size">Scaling up cluster size</h3>
|
||
|
||
<p>Our framework was designed to have both sync and async parameter aggregation.
|
||
Asynchronous aggregation can allow a high outcome of training batch but with a sacrifice or converge time.
|
||
Synchronous aggregation allows a quick converge time in epochs, however can’t ensure performance when there’s a struggler worker.</p>
|
||
|
||
<p>As showed in experiments, we chose sync as default because the converging time is dominant in overall training time.
|
||
But, we also considered the possibilities of that async with more workers can achieve similar overall training time.</p>
|
||
|
||
<p>We introduced a formula to determine whether adding more training nodes can help or not.
|
||
Here we used bandwidth usage coefficient (BUC) as</p>
|
||
|
||
\[BUC = \dfrac{n}{T_{sync}}\]
|
||
|
||
<p>In this formula, \(n\) is the number of devices, and \(T_{sync}\) is the transmission time of parameters.
|
||
With an increasing number of workers, n increase linearly but transmission time does not.
|
||
When \(BUC\) increases, the cluster can speed up training time by adding workers.
|
||
Otherwise, adding more workers won’t help with overall training time.</p>
|
||
|
||
<h3 id="adaptive-leader-role-splitting">Adaptive leader role splitting</h3>
|
||
|
||
<p>The idea of role splitting is simple that a device can work as a worker as well leader.
|
||
The advantage of doing this is straightforward that we can transfer 1 less parameter and training time will be shortened.</p>
|
||
|
||
<p>However, in our current settings, it can’t perform much better help since only 1 leader role is in a cluster.
|
||
We can benefit from this in our future works.</p>
|
||
|
||
<h3 id="overall-architecture">Overall architecture</h3>
|
||
|
||
<p><img src="/static/2021-10/f.5_Impl_leader_worker.png" alt="Implementation" /></p>
|
||
|
||
<p>Details were given in the image.</p>
|
||
|
||
<h3 id="prototype-hardware-and-software">Prototype hardware and software</h3>
|
||
|
||
<p>EDDL was designed to be run on two single-board computer embedded platforms.
|
||
One such platform is <a href="https://www.hardkernel.com/shop/odroid-xu4-special-price/">ODROID-XU4</a>, which is equipped with a 2.1/1.4 GHz 32-bit ARM processor and 2GB memory.
|
||
The other platform is the <a href="https://www.raspberrypi.com/products/raspberry-pi-3-model-b/">Raspberry Pi 3 Model B board</a>, which comes with an ARM 1.2 GHz 64-bit quad-core processor and 1GB memory.</p>
|
||
|
||
<p>The operating system running on the above platforms is Ubuntu 18.04 with Linux kernel 4.14.
|
||
We used <a href="http://dlib.net/">Dlib</a>, a C++ library that provides implementations for a wide range of machine learning algorithms.
|
||
We chose the Dlib library because it is written in C/C++, and can be easily and natively used in embedded devices.</p>
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<div class="article__section-navigator clearfix"><div class="previous"><span>PREVIOUS</span><a href="/posts/eddl-how-do-we-train-on-limited-edge-devices">EDDL: How do we train neural networks on limited edge devices - PART 1</a></div><div class="next"><span>NEXT</span><a href="/posts/cs350-labs">Labs of CS350</a></div></div></div>
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}
|
||
function init() {
|
||
setState(visible);
|
||
}
|
||
function setState(isShow) {
|
||
if (isShow === visible) {
|
||
return;
|
||
}
|
||
visible = isShow;
|
||
if (visible) {
|
||
activeCount++;
|
||
scrollTop = $(window).scrollTop() || $pageMain.scrollTop();
|
||
$root.addClass('modal--show');
|
||
$pageMain.scrollTop(scrollTop);
|
||
activeCount === 1 && ($pageRoot.addClass('show-modal'), $body.addClass('of-hidden'));
|
||
hideWhenWindowScroll && window.hasEvent('touchstart') && $window.on('scroll', hide);
|
||
$window.on('keyup', handleKeyup);
|
||
} else {
|
||
activeCount > 0 && activeCount--;
|
||
$root.removeClass('modal--show');
|
||
$window.scrollTop(scrollTop);
|
||
activeCount === 0 && ($pageRoot.removeClass('show-modal'), $body.removeClass('of-hidden'));
|
||
hideWhenWindowScroll && window.hasEvent('touchstart') && $window.off('scroll', hide);
|
||
$window.off('keyup', handleKeyup);
|
||
}
|
||
onChange && onChange(visible);
|
||
}
|
||
function show() {
|
||
setState(true);
|
||
}
|
||
function hide() {
|
||
setState(false);
|
||
}
|
||
function handleKeyup(e) {
|
||
// Char Code: 27 ESC
|
||
if (e.which === 27) {
|
||
hide();
|
||
}
|
||
}
|
||
setOptions(options);
|
||
init();
|
||
return {
|
||
show: show,
|
||
hide: hide,
|
||
$el: $root
|
||
};
|
||
}
|
||
$.fn.modal = modal;
|
||
});
|
||
})();
|
||
</script><div class="modal modal--overflow page__search-modal d-print-none js-page-search-modal"><script>
|
||
(function () {
|
||
var SOURCES = window.TEXT_VARIABLES.sources;
|
||
window.Lazyload.js(SOURCES.jquery, function() {
|
||
// search panel
|
||
var search = (window.search || (window.search = {}));
|
||
var useDefaultSearchBox = window.useDefaultSearchBox === undefined ?
|
||
true : window.useDefaultSearchBox ;
|
||
|
||
var $searchModal = $('.js-page-search-modal');
|
||
var $searchToggle = $('.js-search-toggle');
|
||
var searchModal = $searchModal.modal({ onChange: handleModalChange, hideWhenWindowScroll: true });
|
||
var modalVisible = false;
|
||
search.searchModal = searchModal;
|
||
|
||
var $searchBox = null;
|
||
var $searchInput = null;
|
||
var $searchClear = null;
|
||
|
||
function getModalVisible() {
|
||
return modalVisible;
|
||
}
|
||
search.getModalVisible = getModalVisible;
|
||
|
||
function handleModalChange(visible) {
|
||
modalVisible = visible;
|
||
if (visible) {
|
||
search.onShow && search.onShow();
|
||
useDefaultSearchBox && $searchInput[0] && $searchInput[0].focus();
|
||
} else {
|
||
search.onShow && search.onHide();
|
||
useDefaultSearchBox && $searchInput[0] && $searchInput[0].blur();
|
||
setTimeout(function() {
|
||
useDefaultSearchBox && ($searchInput.val(''), $searchBox.removeClass('not-empty'));
|
||
search.clear && search.clear();
|
||
window.pageAsideAffix && window.pageAsideAffix.refresh();
|
||
}, 400);
|
||
}
|
||
}
|
||
|
||
$searchToggle.on('click', function() {
|
||
modalVisible ? searchModal.hide() : searchModal.show();
|
||
});
|
||
// Char Code: 83 S, 191 /
|
||
$(window).on('keyup', function(e) {
|
||
if (!modalVisible && !window.isFormElement(e.target || e.srcElement) && (e.which === 83 || e.which === 191)) {
|
||
modalVisible || searchModal.show();
|
||
}
|
||
});
|
||
|
||
if (useDefaultSearchBox) {
|
||
$searchBox = $('.js-search-box');
|
||
$searchInput = $searchBox.children('input');
|
||
$searchClear = $searchBox.children('.js-icon-clear');
|
||
search.getSearchInput = function() {
|
||
return $searchInput.get(0);
|
||
};
|
||
search.getVal = function() {
|
||
return $searchInput.val();
|
||
};
|
||
search.setVal = function(val) {
|
||
$searchInput.val(val);
|
||
};
|
||
|
||
$searchInput.on('focus', function() {
|
||
$(this).addClass('focus');
|
||
});
|
||
$searchInput.on('blur', function() {
|
||
$(this).removeClass('focus');
|
||
});
|
||
$searchInput.on('input', window.throttle(function() {
|
||
var val = $(this).val();
|
||
if (val === '' || typeof val !== 'string') {
|
||
search.clear && search.clear();
|
||
} else {
|
||
$searchBox.addClass('not-empty');
|
||
search.onInputNotEmpty && search.onInputNotEmpty(val);
|
||
}
|
||
}, 400));
|
||
$searchClear.on('click', function() {
|
||
$searchInput.val(''); $searchBox.removeClass('not-empty');
|
||
search.clear && search.clear();
|
||
});
|
||
}
|
||
});
|
||
})();
|
||
</script><div class="search search--dark">
|
||
<div class="main">
|
||
<div class="search__header">Search</div>
|
||
<div class="search-bar">
|
||
<div class="search-box js-search-box">
|
||
<div class="search-box__icon-search"><i class="fas fa-search"></i></div>
|
||
<input type="text" />
|
||
<div class="search-box__icon-clear js-icon-clear">
|
||
<a><i class="fas fa-times"></i></a>
|
||
</div>
|
||
</div>
|
||
<button class="button button--theme-dark button--pill search__cancel js-search-toggle">
|
||
Cancel</button>
|
||
</div>
|
||
<div class="search-result js-search-result"></div>
|
||
</div>
|
||
</div>
|
||
<script>var SOURCES = window.TEXT_VARIABLES.sources;
|
||
var PAHTS = window.TEXT_VARIABLES.paths;
|
||
window.Lazyload.js([SOURCES.jquery, PAHTS.search_js], function() {
|
||
var search = (window.search || (window.search = {}));
|
||
var searchData = window.TEXT_SEARCH_DATA || {};
|
||
|
||
function memorize(f) {
|
||
var cache = {};
|
||
return function () {
|
||
var key = Array.prototype.join.call(arguments, ',');
|
||
if (key in cache) return cache[key];
|
||
else return cache[key] = f.apply(this, arguments);
|
||
};
|
||
}
|
||
|
||
/// search
|
||
function searchByQuery(query) {
|
||
var i, j, key, keys, cur, _title, result = {};
|
||
keys = Object.keys(searchData);
|
||
for (i = 0; i < keys.length; i++) {
|
||
key = keys[i];
|
||
for (j = 0; j < searchData[key].length; j++) {
|
||
cur = searchData[key][j], _title = cur.title;
|
||
if ((result[key] === undefined || result[key] && result[key].length < 4 )
|
||
&& _title.toLowerCase().indexOf(query.toLowerCase()) >= 0) {
|
||
if (result[key] === undefined) {
|
||
result[key] = [];
|
||
}
|
||
result[key].push(cur);
|
||
}
|
||
}
|
||
}
|
||
return result;
|
||
}
|
||
|
||
var renderHeader = memorize(function(header) {
|
||
return $('<p class="search-result__header">' + header + '</p>');
|
||
});
|
||
|
||
var renderItem = function(index, title, url) {
|
||
return $('<li class="search-result__item" data-index="' + index + '"><a class="button" href="' + url + '">' + title + '</a></li>');
|
||
};
|
||
|
||
function render(data) {
|
||
if (!data) { return null; }
|
||
var $root = $('<ul></ul>'), i, j, key, keys, cur, itemIndex = 0;
|
||
keys = Object.keys(data);
|
||
for (i = 0; i < keys.length; i++) {
|
||
key = keys[i];
|
||
$root.append(renderHeader(key));
|
||
for (j = 0; j < data[key].length; j++) {
|
||
cur = data[key][j];
|
||
$root.append(renderItem(itemIndex++, cur.title, cur.url));
|
||
}
|
||
}
|
||
return $root;
|
||
}
|
||
|
||
// search box
|
||
var $result = $('.js-search-result'), $resultItems;
|
||
var lastActiveIndex, activeIndex;
|
||
|
||
function clear() {
|
||
$result.html(null);
|
||
$resultItems = $('.search-result__item'); activeIndex = 0;
|
||
}
|
||
function onInputNotEmpty(val) {
|
||
$result.html(render(searchByQuery(val)));
|
||
$resultItems = $('.search-result__item'); activeIndex = 0;
|
||
$resultItems.eq(0).addClass('active');
|
||
}
|
||
|
||
search.clear = clear;
|
||
search.onInputNotEmpty = onInputNotEmpty;
|
||
|
||
function updateResultItems() {
|
||
lastActiveIndex >= 0 && $resultItems.eq(lastActiveIndex).removeClass('active');
|
||
activeIndex >= 0 && $resultItems.eq(activeIndex).addClass('active');
|
||
}
|
||
|
||
function moveActiveIndex(direction) {
|
||
var itemsCount = $resultItems ? $resultItems.length : 0;
|
||
if (itemsCount > 1) {
|
||
lastActiveIndex = activeIndex;
|
||
if (direction === 'up') {
|
||
activeIndex = (activeIndex - 1 + itemsCount) % itemsCount;
|
||
} else if (direction === 'down') {
|
||
activeIndex = (activeIndex + 1 + itemsCount) % itemsCount;
|
||
}
|
||
updateResultItems();
|
||
}
|
||
}
|
||
|
||
// Char Code: 13 Enter, 37 ⬅, 38 ⬆, 39 ➡, 40 ⬇
|
||
$(window).on('keyup', function(e) {
|
||
var modalVisible = search.getModalVisible && search.getModalVisible();
|
||
if (modalVisible) {
|
||
if (e.which === 38) {
|
||
modalVisible && moveActiveIndex('up');
|
||
} else if (e.which === 40) {
|
||
modalVisible && moveActiveIndex('down');
|
||
} else if (e.which === 13) {
|
||
modalVisible && $resultItems && activeIndex >= 0 && $resultItems.eq(activeIndex).children('a')[0].click();
|
||
}
|
||
}
|
||
});
|
||
|
||
$result.on('mouseover', '.search-result__item > a', function() {
|
||
var itemIndex = $(this).parent().data('index');
|
||
itemIndex >= 0 && (lastActiveIndex = activeIndex, activeIndex = itemIndex, updateResultItems());
|
||
});
|
||
});
|
||
</script>
|
||
</div></div>
|
||
|
||
|
||
<script>(function() {
|
||
var SOURCES = window.TEXT_VARIABLES.sources;
|
||
window.Lazyload.js(SOURCES.jquery, function() {
|
||
function scrollToAnchor(anchor, duration, callback) {
|
||
var $root = this;
|
||
$root.animate({ scrollTop: $(anchor).position().top }, duration, function() {
|
||
window.history.replaceState(null, '', window.location.href.split('#')[0] + anchor);
|
||
callback && callback();
|
||
});
|
||
}
|
||
$.fn.scrollToAnchor = scrollToAnchor;
|
||
});
|
||
})();
|
||
(function() {
|
||
var SOURCES = window.TEXT_VARIABLES.sources;
|
||
window.Lazyload.js(SOURCES.jquery, function() {
|
||
function affix(options) {
|
||
var $root = this, $window = $(window), $scrollTarget, $scroll,
|
||
offsetBottom = 0, scrollTarget = window, scroll = window.document, disabled = false, isOverallScroller = true,
|
||
rootTop, rootLeft, rootHeight, scrollBottom, rootBottomTop,
|
||
hasInit = false, curState;
|
||
|
||
function setOptions(options) {
|
||
var _options = options || {};
|
||
_options.offsetBottom && (offsetBottom = _options.offsetBottom);
|
||
_options.scrollTarget && (scrollTarget = _options.scrollTarget);
|
||
_options.scroll && (scroll = _options.scroll);
|
||
_options.disabled !== undefined && (disabled = _options.disabled);
|
||
$scrollTarget = $(scrollTarget);
|
||
isOverallScroller = window.isOverallScroller($scrollTarget[0]);
|
||
$scroll = $(scroll);
|
||
}
|
||
function preCalc() {
|
||
top();
|
||
rootHeight = $root.outerHeight();
|
||
rootTop = $root.offset().top + (isOverallScroller ? 0 : $scrollTarget.scrollTop());
|
||
rootLeft = $root.offset().left;
|
||
}
|
||
function calc(needPreCalc) {
|
||
needPreCalc && preCalc();
|
||
scrollBottom = $scroll.outerHeight() - offsetBottom - rootHeight;
|
||
rootBottomTop = scrollBottom - rootTop;
|
||
}
|
||
function top() {
|
||
if (curState !== 'top') {
|
||
$root.removeClass('fixed').css({
|
||
left: 0,
|
||
top: 0
|
||
});
|
||
curState = 'top';
|
||
}
|
||
}
|
||
function fixed() {
|
||
if (curState !== 'fixed') {
|
||
$root.addClass('fixed').css({
|
||
left: rootLeft + 'px',
|
||
top: 0
|
||
});
|
||
curState = 'fixed';
|
||
}
|
||
}
|
||
function bottom() {
|
||
if (curState !== 'bottom') {
|
||
$root.removeClass('fixed').css({
|
||
left: 0,
|
||
top: rootBottomTop + 'px'
|
||
});
|
||
curState = 'bottom';
|
||
}
|
||
}
|
||
function setState() {
|
||
var scrollTop = $scrollTarget.scrollTop();
|
||
if (scrollTop >= rootTop && scrollTop <= scrollBottom) {
|
||
fixed();
|
||
} else if (scrollTop < rootTop) {
|
||
top();
|
||
} else {
|
||
bottom();
|
||
}
|
||
}
|
||
function init() {
|
||
if(!hasInit) {
|
||
var interval, timeout;
|
||
calc(true); setState();
|
||
// run calc every 100 millisecond
|
||
interval = setInterval(function() {
|
||
calc();
|
||
}, 100);
|
||
timeout = setTimeout(function() {
|
||
clearInterval(interval);
|
||
}, 45000);
|
||
window.pageLoad.then(function() {
|
||
setTimeout(function() {
|
||
clearInterval(interval);
|
||
clearTimeout(timeout);
|
||
}, 3000);
|
||
});
|
||
$scrollTarget.on('scroll', function() {
|
||
disabled || setState();
|
||
});
|
||
$window.on('resize', function() {
|
||
disabled || (calc(true), setState());
|
||
});
|
||
hasInit = true;
|
||
}
|
||
}
|
||
|
||
setOptions(options);
|
||
if (!disabled) {
|
||
init();
|
||
}
|
||
$window.on('resize', window.throttle(function() {
|
||
init();
|
||
}, 200));
|
||
return {
|
||
setOptions: setOptions,
|
||
refresh: function() {
|
||
calc(true, { animation: false }); setState();
|
||
}
|
||
};
|
||
}
|
||
$.fn.affix = affix;
|
||
});
|
||
})();
|
||
(function() {
|
||
var SOURCES = window.TEXT_VARIABLES.sources;
|
||
window.Lazyload.js(SOURCES.jquery, function() {
|
||
function toc(options) {
|
||
var $root = this, $window = $(window), $scrollTarget, $scroller, $tocUl = $('<ul class="toc toc--ellipsis"></ul>'), $tocLi, $headings, $activeLast, $activeCur,
|
||
selectors = 'h1,h2,h3', container = 'body', scrollTarget = window, scroller = 'html, body', disabled = false,
|
||
headingsPos, scrolling = false, hasRendered = false, hasInit = false;
|
||
|
||
function setOptions(options) {
|
||
var _options = options || {};
|
||
_options.selectors && (selectors = _options.selectors);
|
||
_options.container && (container = _options.container);
|
||
_options.scrollTarget && (scrollTarget = _options.scrollTarget);
|
||
_options.scroller && (scroller = _options.scroller);
|
||
_options.disabled !== undefined && (disabled = _options.disabled);
|
||
$headings = $(container).find(selectors).filter('[id]');
|
||
$scrollTarget = $(scrollTarget);
|
||
$scroller = $(scroller);
|
||
}
|
||
function calc() {
|
||
headingsPos = [];
|
||
$headings.each(function() {
|
||
headingsPos.push(Math.floor($(this).position().top));
|
||
});
|
||
}
|
||
function setState(element, disabled) {
|
||
var scrollTop = $scrollTarget.scrollTop(), i;
|
||
if (disabled || !headingsPos || headingsPos.length < 1) { return; }
|
||
if (element) {
|
||
$activeCur = element;
|
||
} else {
|
||
for (i = 0; i < headingsPos.length; i++) {
|
||
if (scrollTop >= headingsPos[i]) {
|
||
$activeCur = $tocLi.eq(i);
|
||
} else {
|
||
$activeCur || ($activeCur = $tocLi.eq(i));
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
$activeLast && $activeLast.removeClass('active');
|
||
($activeLast = $activeCur).addClass('active');
|
||
}
|
||
function render() {
|
||
if(!hasRendered) {
|
||
$root.append($tocUl);
|
||
$headings.each(function() {
|
||
var $this = $(this);
|
||
$tocUl.append($('<li></li>').addClass('toc-' + $this.prop('tagName').toLowerCase())
|
||
.append($('<a></a>').text($this.text()).attr('href', '#' + $this.prop('id'))));
|
||
});
|
||
$tocLi = $tocUl.children('li');
|
||
$tocUl.on('click', 'a', function(e) {
|
||
e.preventDefault();
|
||
var $this = $(this);
|
||
scrolling = true;
|
||
setState($this.parent());
|
||
$scroller.scrollToAnchor($this.attr('href'), 400, function() {
|
||
scrolling = false;
|
||
});
|
||
});
|
||
}
|
||
hasRendered = true;
|
||
}
|
||
function init() {
|
||
var interval, timeout;
|
||
if(!hasInit) {
|
||
render(); calc(); setState(null, scrolling);
|
||
// run calc every 100 millisecond
|
||
interval = setInterval(function() {
|
||
calc();
|
||
}, 100);
|
||
timeout = setTimeout(function() {
|
||
clearInterval(interval);
|
||
}, 45000);
|
||
window.pageLoad.then(function() {
|
||
setTimeout(function() {
|
||
clearInterval(interval);
|
||
clearTimeout(timeout);
|
||
}, 3000);
|
||
});
|
||
$scrollTarget.on('scroll', function() {
|
||
disabled || setState(null, scrolling);
|
||
});
|
||
$window.on('resize', window.throttle(function() {
|
||
if (!disabled) {
|
||
render(); calc(); setState(null, scrolling);
|
||
}
|
||
}, 100));
|
||
}
|
||
hasInit = true;
|
||
}
|
||
|
||
setOptions(options);
|
||
if (!disabled) {
|
||
init();
|
||
}
|
||
$window.on('resize', window.throttle(function() {
|
||
init();
|
||
}, 200));
|
||
return {
|
||
setOptions: setOptions
|
||
};
|
||
}
|
||
$.fn.toc = toc;
|
||
});
|
||
})();
|
||
/*(function () {
|
||
|
||
})();*/
|
||
</script><script>
|
||
/* toc must before affix, since affix need to konw toc' height. */(function() {
|
||
var SOURCES = window.TEXT_VARIABLES.sources;
|
||
var TOC_SELECTOR = window.TEXT_VARIABLES.site.toc.selectors;
|
||
window.Lazyload.js(SOURCES.jquery, function() {
|
||
var $window = $(window);
|
||
var $articleContent = $('.js-article-content');
|
||
var $tocRoot = $('.js-toc-root'), $col2 = $('.js-col-aside');
|
||
var toc;
|
||
var tocDisabled = false;
|
||
var hasSidebar = $('.js-page-root').hasClass('layout--page--sidebar');
|
||
var hasToc = $articleContent.find(TOC_SELECTOR).length > 0;
|
||
|
||
function disabled() {
|
||
return $col2.css('display') === 'none' || !hasToc;
|
||
}
|
||
|
||
tocDisabled = disabled();
|
||
|
||
toc = $tocRoot.toc({
|
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selectors: TOC_SELECTOR,
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||
container: $articleContent,
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scrollTarget: hasSidebar ? '.js-page-main' : null,
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scroller: hasSidebar ? '.js-page-main' : null,
|
||
disabled: tocDisabled
|
||
});
|
||
|
||
$window.on('resize', window.throttle(function() {
|
||
tocDisabled = disabled();
|
||
toc && toc.setOptions({
|
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disabled: tocDisabled
|
||
});
|
||
}, 100));
|
||
|
||
});
|
||
})();
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(function() {
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var SOURCES = window.TEXT_VARIABLES.sources;
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window.Lazyload.js(SOURCES.jquery, function() {
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var $window = $(window), $pageFooter = $('.js-page-footer');
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var $pageAside = $('.js-page-aside');
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var affix;
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var tocDisabled = false;
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var hasSidebar = $('.js-page-root').hasClass('layout--page--sidebar');
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||
|
||
affix = $pageAside.affix({
|
||
offsetBottom: $pageFooter.outerHeight(),
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scrollTarget: hasSidebar ? '.js-page-main' : null,
|
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scroller: hasSidebar ? '.js-page-main' : null,
|
||
scroll: hasSidebar ? $('.js-page-main').children() : null,
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disabled: tocDisabled
|
||
});
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||
|
||
$window.on('resize', window.throttle(function() {
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affix && affix.setOptions({
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disabled: tocDisabled
|
||
});
|
||
}, 100));
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||
|
||
window.pageAsideAffix = affix;
|
||
});
|
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})();
|
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</script><script type="text/x-mathjax-config">
|
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var _config = { tex2jax: {
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inlineMath: [['$','$'], ['\\(','\\)']]
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}};MathJax.Hub.Config(_config);
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</script>
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<script type="text/javascript" src="/static/2022-09/MathJax.js?config=TeX-MML-AM_CHTML" async></script>
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</div>
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<script>(function () {
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var $root = document.getElementsByClassName('root')[0];
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if (window.hasEvent('touchstart')) {
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$root.dataset.isTouch = true;
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document.addEventListener('touchstart', function(){}, false);
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}
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})();
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</script>
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</body>
|
||
</html>
|
||
|