| |
| <!DOCTYPE html> |
| <!--[if lt IE 7]> <html class="no-js lt-ie9 lt-ie8 lt-ie7"> <![endif]--> |
| <!--[if IE 7]> <html class="no-js lt-ie9 lt-ie8"> <![endif]--> |
| <!--[if IE 8]> <html class="no-js lt-ie9"> <![endif]--> |
| <!--[if gt IE 8]><!--> <html class="no-js"> <!--<![endif]--> |
| <head> |
| <meta charset="utf-8"> |
| <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> |
| <title>Data sources - Spark 2.4.5 Documentation</title> |
| |
| |
| |
| |
| <link rel="stylesheet" href="css/bootstrap.min.css"> |
| <style> |
| body { |
| padding-top: 60px; |
| padding-bottom: 40px; |
| } |
| </style> |
| <meta name="viewport" content="width=device-width"> |
| <link rel="stylesheet" href="css/bootstrap-responsive.min.css"> |
| <link rel="stylesheet" href="css/main.css"> |
| |
| <script src="js/vendor/modernizr-2.6.1-respond-1.1.0.min.js"></script> |
| |
| <link rel="stylesheet" href="css/pygments-default.css"> |
| |
| |
| <!-- Google analytics script --> |
| <script type="text/javascript"> |
| var _gaq = _gaq || []; |
| _gaq.push(['_setAccount', 'UA-32518208-2']); |
| _gaq.push(['_trackPageview']); |
| |
| (function() { |
| var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; |
| ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; |
| var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); |
| })(); |
| </script> |
| |
| |
| </head> |
| <body> |
| <!--[if lt IE 7]> |
| <p class="chromeframe">You are using an outdated browser. <a href="https://browsehappy.com/">Upgrade your browser today</a> or <a href="http://www.google.com/chromeframe/?redirect=true">install Google Chrome Frame</a> to better experience this site.</p> |
| <![endif]--> |
| |
| <!-- This code is taken from http://twitter.github.com/bootstrap/examples/hero.html --> |
| |
| <div class="navbar navbar-fixed-top" id="topbar"> |
| <div class="navbar-inner"> |
| <div class="container"> |
| <div class="brand"><a href="index.html"> |
| <img src="img/spark-logo-hd.png" style="height:50px;"/></a><span class="version">2.4.5</span> |
| </div> |
| <ul class="nav"> |
| <!--TODO(andyk): Add class="active" attribute to li some how.--> |
| <li><a href="index.html">Overview</a></li> |
| |
| <li class="dropdown"> |
| <a href="#" class="dropdown-toggle" data-toggle="dropdown">Programming Guides<b class="caret"></b></a> |
| <ul class="dropdown-menu"> |
| <li><a href="quick-start.html">Quick Start</a></li> |
| <li><a href="rdd-programming-guide.html">RDDs, Accumulators, Broadcasts Vars</a></li> |
| <li><a href="sql-programming-guide.html">SQL, DataFrames, and Datasets</a></li> |
| <li><a href="structured-streaming-programming-guide.html">Structured Streaming</a></li> |
| <li><a href="streaming-programming-guide.html">Spark Streaming (DStreams)</a></li> |
| <li><a href="ml-guide.html">MLlib (Machine Learning)</a></li> |
| <li><a href="graphx-programming-guide.html">GraphX (Graph Processing)</a></li> |
| <li><a href="sparkr.html">SparkR (R on Spark)</a></li> |
| </ul> |
| </li> |
| |
| <li class="dropdown"> |
| <a href="#" class="dropdown-toggle" data-toggle="dropdown">API Docs<b class="caret"></b></a> |
| <ul class="dropdown-menu"> |
| <li><a href="api/scala/index.html#org.apache.spark.package">Scala</a></li> |
| <li><a href="api/java/index.html">Java</a></li> |
| <li><a href="api/python/index.html">Python</a></li> |
| <li><a href="api/R/index.html">R</a></li> |
| <li><a href="api/sql/index.html">SQL, Built-in Functions</a></li> |
| </ul> |
| </li> |
| |
| <li class="dropdown"> |
| <a href="#" class="dropdown-toggle" data-toggle="dropdown">Deploying<b class="caret"></b></a> |
| <ul class="dropdown-menu"> |
| <li><a href="cluster-overview.html">Overview</a></li> |
| <li><a href="submitting-applications.html">Submitting Applications</a></li> |
| <li class="divider"></li> |
| <li><a href="spark-standalone.html">Spark Standalone</a></li> |
| <li><a href="running-on-mesos.html">Mesos</a></li> |
| <li><a href="running-on-yarn.html">YARN</a></li> |
| <li><a href="running-on-kubernetes.html">Kubernetes</a></li> |
| </ul> |
| </li> |
| |
| <li class="dropdown"> |
| <a href="api.html" class="dropdown-toggle" data-toggle="dropdown">More<b class="caret"></b></a> |
| <ul class="dropdown-menu"> |
| <li><a href="configuration.html">Configuration</a></li> |
| <li><a href="monitoring.html">Monitoring</a></li> |
| <li><a href="tuning.html">Tuning Guide</a></li> |
| <li><a href="job-scheduling.html">Job Scheduling</a></li> |
| <li><a href="security.html">Security</a></li> |
| <li><a href="hardware-provisioning.html">Hardware Provisioning</a></li> |
| <li class="divider"></li> |
| <li><a href="building-spark.html">Building Spark</a></li> |
| <li><a href="https://spark.apache.org/contributing.html">Contributing to Spark</a></li> |
| <li><a href="https://spark.apache.org/third-party-projects.html">Third Party Projects</a></li> |
| </ul> |
| </li> |
| </ul> |
| <!--<p class="navbar-text pull-right"><span class="version-text">v2.4.5</span></p>--> |
| </div> |
| </div> |
| </div> |
| |
| <div class="container-wrapper"> |
| |
| |
| |
| <div class="left-menu-wrapper"> |
| <div class="left-menu"> |
| <h3><a href="ml-guide.html">MLlib: Main Guide</a></h3> |
| |
| <ul> |
| |
| <li> |
| <a href="ml-statistics.html"> |
| |
| Basic statistics |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-datasource"> |
| |
| <b>Data sources</b> |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-pipeline.html"> |
| |
| Pipelines |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-features.html"> |
| |
| Extracting, transforming and selecting features |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-classification-regression.html"> |
| |
| Classification and Regression |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-clustering.html"> |
| |
| Clustering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-collaborative-filtering.html"> |
| |
| Collaborative filtering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-frequent-pattern-mining.html"> |
| |
| Frequent Pattern Mining |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-tuning.html"> |
| |
| Model selection and tuning |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-advanced.html"> |
| |
| Advanced topics |
| |
| </a> |
| </li> |
| |
| |
| |
| </ul> |
| |
| <h3><a href="mllib-guide.html">MLlib: RDD-based API Guide</a></h3> |
| |
| <ul> |
| |
| <li> |
| <a href="mllib-data-types.html"> |
| |
| Data types |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-statistics.html"> |
| |
| Basic statistics |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-classification-regression.html"> |
| |
| Classification and regression |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-collaborative-filtering.html"> |
| |
| Collaborative filtering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-clustering.html"> |
| |
| Clustering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-dimensionality-reduction.html"> |
| |
| Dimensionality reduction |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-feature-extraction.html"> |
| |
| Feature extraction and transformation |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-frequent-pattern-mining.html"> |
| |
| Frequent pattern mining |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-evaluation-metrics.html"> |
| |
| Evaluation metrics |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-pmml-model-export.html"> |
| |
| PMML model export |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-optimization.html"> |
| |
| Optimization (developer) |
| |
| </a> |
| </li> |
| |
| |
| |
| </ul> |
| |
| </div> |
| </div> |
| |
| <input id="nav-trigger" class="nav-trigger" checked type="checkbox"> |
| <label for="nav-trigger"></label> |
| <div class="content-with-sidebar" id="content"> |
| |
| <h1 class="title">Data sources</h1> |
| |
| |
| <p>In this section, we introduce how to use data source in ML to load data. |
| Beside some general data sources such as Parquet, CSV, JSON and JDBC, we also provide some specific data sources for ML.</p> |
| |
| <p><strong>Table of Contents</strong></p> |
| |
| <ul id="markdown-toc"> |
| <li><a href="#image-data-source" id="markdown-toc-image-data-source">Image data source</a></li> |
| </ul> |
| |
| <h2 id="image-data-source">Image data source</h2> |
| |
| <p>This image data source is used to load image files from a directory, it can load compressed image (jpeg, png, etc.) into raw image representation via <code>ImageIO</code> in Java library. |
| The loaded DataFrame has one <code>StructType</code> column: “image”, containing image data stored as image schema. |
| The schema of the <code>image</code> column is:</p> |
| <ul> |
| <li>origin: <code>StringType</code> (represents the file path of the image)</li> |
| <li>height: <code>IntegerType</code> (height of the image)</li> |
| <li>width: <code>IntegerType</code> (width of the image)</li> |
| <li>nChannels: <code>IntegerType</code> (number of image channels)</li> |
| <li>mode: <code>IntegerType</code> (OpenCV-compatible type)</li> |
| <li>data: <code>BinaryType</code> (Image bytes in OpenCV-compatible order: row-wise BGR in most cases)</li> |
| </ul> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| <p><a href="api/scala/index.html#org.apache.spark.ml.source.image.ImageDataSource"><code>ImageDataSource</code></a> |
| implements a Spark SQL data source API for loading image data as a DataFrame.</p> |
| |
| <figure class="highlight"><pre><code class="language-scala" data-lang="scala"><span></span><span class="n">scala</span><span class="o">></span> <span class="k">val</span> <span class="n">df</span> <span class="k">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">"image"</span><span class="o">).</span><span class="n">option</span><span class="o">(</span><span class="s">"dropInvalid"</span><span class="o">,</span> <span class="kc">true</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">"data/mllib/images/origin/kittens"</span><span class="o">)</span> |
| <span class="n">df</span><span class="k">:</span> <span class="kt">org.apache.spark.sql.DataFrame</span> <span class="o">=</span> <span class="o">[</span><span class="kt">image:</span> <span class="kt">struct<origin:</span> <span class="kt">string</span>, <span class="kt">height:</span> <span class="kt">int</span> <span class="kt">...</span> <span class="err">4</span> <span class="kt">more</span> <span class="kt">fields></span><span class="o">]</span> |
| |
| <span class="n">scala</span><span class="o">></span> <span class="n">df</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">"image.origin"</span><span class="o">,</span> <span class="s">"image.width"</span><span class="o">,</span> <span class="s">"image.height"</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="n">truncate</span><span class="k">=</span><span class="kc">false</span><span class="o">)</span> |
| <span class="o">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="o">|</span><span class="n">origin</span> <span class="o">|</span><span class="n">width</span><span class="o">|</span><span class="n">height</span><span class="o">|</span> |
| <span class="o">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="o">|</span><span class="n">file</span><span class="o">:///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="mf">54893.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">300</span> <span class="o">|</span><span class="mi">311</span> <span class="o">|</span> |
| <span class="o">|</span><span class="n">file</span><span class="o">:///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="nc">DP802813</span><span class="o">.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">199</span> <span class="o">|</span><span class="mi">313</span> <span class="o">|</span> |
| <span class="o">|</span><span class="n">file</span><span class="o">:///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="mf">29.5</span><span class="o">.</span><span class="n">a_b_EGDP022204</span><span class="o">.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">300</span> <span class="o">|</span><span class="mi">200</span> <span class="o">|</span> |
| <span class="o">|</span><span class="n">file</span><span class="o">:///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="nc">DP153539</span><span class="o">.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">300</span> <span class="o">|</span><span class="mi">296</span> <span class="o">|</span> |
| <span class="o">+-----------------------------------------------------------------------+-----+------+</span></code></pre></figure> |
| |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/org/apache/spark/ml/source/image/ImageDataSource.html"><code>ImageDataSource</code></a> |
| implements Spark SQL data source API for loading image data as DataFrame.</p> |
| |
| <figure class="highlight"><pre><code class="language-java" data-lang="java"><span></span><span class="n">Dataset</span><span class="o"><</span><span class="n">Row</span><span class="o">></span> <span class="n">imagesDF</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">"image"</span><span class="o">).</span><span class="na">option</span><span class="o">(</span><span class="s">"dropInvalid"</span><span class="o">,</span> <span class="kc">true</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">"data/mllib/images/origin/kittens"</span><span class="o">);</span> |
| <span class="n">imageDF</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">"image.origin"</span><span class="o">,</span> <span class="s">"image.width"</span><span class="o">,</span> <span class="s">"image.height"</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="kc">false</span><span class="o">);</span> |
| <span class="cm">/*</span> |
| <span class="cm">Will output:</span> |
| <span class="cm">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="cm">|origin |width|height|</span> |
| <span class="cm">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="cm">|file:///spark/data/mllib/images/origin/kittens/54893.jpg |300 |311 |</span> |
| <span class="cm">|file:///spark/data/mllib/images/origin/kittens/DP802813.jpg |199 |313 |</span> |
| <span class="cm">|file:///spark/data/mllib/images/origin/kittens/29.5.a_b_EGDP022204.jpg |300 |200 |</span> |
| <span class="cm">|file:///spark/data/mllib/images/origin/kittens/DP153539.jpg |300 |296 |</span> |
| <span class="cm">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="cm">*/</span></code></pre></figure> |
| |
| </div> |
| |
| <div data-lang="python"> |
| <p>In PySpark we provide Spark SQL data source API for loading image data as DataFrame.</p> |
| |
| <figure class="highlight"><pre><code class="language-python" data-lang="python"><span></span><span class="o">>>></span> <span class="n">df</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s2">"image"</span><span class="p">)</span><span class="o">.</span><span class="n">option</span><span class="p">(</span><span class="s2">"dropInvalid"</span><span class="p">,</span> <span class="n">true</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s2">"data/mllib/images/origin/kittens"</span><span class="p">)</span> |
| <span class="o">>>></span> <span class="n">df</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s2">"image.origin"</span><span class="p">,</span> <span class="s2">"image.width"</span><span class="p">,</span> <span class="s2">"image.height"</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">truncate</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span> |
| <span class="o">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="o">|</span><span class="n">origin</span> <span class="o">|</span><span class="n">width</span><span class="o">|</span><span class="n">height</span><span class="o">|</span> |
| <span class="o">+-----------------------------------------------------------------------+-----+------+</span> |
| <span class="o">|</span><span class="nb">file</span><span class="p">:</span><span class="o">///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="mf">54893.j</span><span class="n">pg</span> <span class="o">|</span><span class="mi">300</span> <span class="o">|</span><span class="mi">311</span> <span class="o">|</span> |
| <span class="o">|</span><span class="nb">file</span><span class="p">:</span><span class="o">///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="n">DP802813</span><span class="o">.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">199</span> <span class="o">|</span><span class="mi">313</span> <span class="o">|</span> |
| <span class="o">|</span><span class="nb">file</span><span class="p">:</span><span class="o">///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="mf">29.5</span><span class="o">.</span><span class="n">a_b_EGDP022204</span><span class="o">.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">300</span> <span class="o">|</span><span class="mi">200</span> <span class="o">|</span> |
| <span class="o">|</span><span class="nb">file</span><span class="p">:</span><span class="o">///</span><span class="n">spark</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">mllib</span><span class="o">/</span><span class="n">images</span><span class="o">/</span><span class="n">origin</span><span class="o">/</span><span class="n">kittens</span><span class="o">/</span><span class="n">DP153539</span><span class="o">.</span><span class="n">jpg</span> <span class="o">|</span><span class="mi">300</span> <span class="o">|</span><span class="mi">296</span> <span class="o">|</span> |
| <span class="o">+-----------------------------------------------------------------------+-----+------+</span></code></pre></figure> |
| |
| </div> |
| |
| <div data-lang="r"> |
| <p>In SparkR we provide Spark SQL data source API for loading image data as DataFrame.</p> |
| |
| <figure class="highlight"><pre><code class="language-r" data-lang="r"><span></span><span class="o">></span> df <span class="o">=</span> read.df<span class="p">(</span><span class="s">"data/mllib/images/origin/kittens"</span><span class="p">,</span> <span class="s">"image"</span><span class="p">)</span> |
| <span class="o">></span> <span class="kp">head</span><span class="p">(</span>select<span class="p">(</span>df<span class="p">,</span> df<span class="o">$</span>image.origin<span class="p">,</span> df<span class="o">$</span>image.width<span class="p">,</span> df<span class="o">$</span>image.height<span class="p">))</span> |
| |
| <span class="m">1</span> <span class="kp">file</span><span class="o">:///</span>spark<span class="o">/</span>data<span class="o">/</span>mllib<span class="o">/</span>images<span class="o">/</span>origin<span class="o">/</span>kittens<span class="o">/</span><span class="m">54893.</span>jpg |
| <span class="m">2</span> <span class="kp">file</span><span class="o">:///</span>spark<span class="o">/</span>data<span class="o">/</span>mllib<span class="o">/</span>images<span class="o">/</span>origin<span class="o">/</span>kittens<span class="o">/</span>DP802813.jpg |
| <span class="m">3</span> <span class="kp">file</span><span class="o">:///</span>spark<span class="o">/</span>data<span class="o">/</span>mllib<span class="o">/</span>images<span class="o">/</span>origin<span class="o">/</span>kittens<span class="o">/</span><span class="m">29.5.</span>a_b_EGDP022204.jpg |
| <span class="m">4</span> <span class="kp">file</span><span class="o">:///</span>spark<span class="o">/</span>data<span class="o">/</span>mllib<span class="o">/</span>images<span class="o">/</span>origin<span class="o">/</span>kittens<span class="o">/</span>DP153539.jpg |
| width height |
| <span class="m">1</span> <span class="m">300</span> <span class="m">311</span> |
| <span class="m">2</span> <span class="m">199</span> <span class="m">313</span> |
| <span class="m">3</span> <span class="m">300</span> <span class="m">200</span> |
| <span class="m">4</span> <span class="m">300</span> <span class="m">296</span></code></pre></figure> |
| |
| </div> |
| |
| |
| </div> |
| |
| |
| </div> |
| |
| <!-- /container --> |
| </div> |
| |
| <script src="js/vendor/jquery-1.12.4.min.js"></script> |
| <script src="js/vendor/bootstrap.min.js"></script> |
| <script src="js/vendor/anchor.min.js"></script> |
| <script src="js/main.js"></script> |
| |
| <!-- MathJax Section --> |
| <script type="text/x-mathjax-config"> |
| MathJax.Hub.Config({ |
| TeX: { equationNumbers: { autoNumber: "AMS" } } |
| }); |
| </script> |
| <script> |
| // Note that we load MathJax this way to work with local file (file://), HTTP and HTTPS. |
| // We could use "//cdn.mathjax...", but that won't support "file://". |
| (function(d, script) { |
| script = d.createElement('script'); |
| script.type = 'text/javascript'; |
| script.async = true; |
| script.onload = function(){ |
| MathJax.Hub.Config({ |
| tex2jax: { |
| inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ], |
| displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], |
| processEscapes: true, |
| skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'] |
| } |
| }); |
| }; |
| script.src = ('https:' == document.location.protocol ? 'https://' : 'http://') + |
| 'cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js' + |
| '?config=TeX-AMS-MML_HTMLorMML'; |
| d.getElementsByTagName('head')[0].appendChild(script); |
| }(document)); |
| </script> |
| </body> |
| </html> |