Spark 1.3.0 docs

author: Patrick Wendell <pwendell@apache.org> 2015-03-13 02:30:55 +0000
committer: Patrick Wendell <pwendell@apache.org> 2015-03-13 02:30:55 +0000
commit: aaf670598f15d47784d8b91b34dd614d0f8162af (patch)
tree: d86a329b056b3e9e9e79591d5b5bc3ee1781386b /site/docs/1.3.0/mllib-data-types.html
parent: 0d484ac791630a4f0ca7e82002113d94c931a1e7 (diff)
download: spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.gz
spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.bz2
spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.zip
1 files changed, 668 insertions, 0 deletions
diff --git a/site/docs/1.3.0/mllib-data-types.html b/site/docs/1.3.0/mllib-data-types.html
new file mode 100644
index 000000000..8b7f7c0e9
--- /dev/null
+++ b/site/docs/1.3.0/mllib-data-types.html
@@ -0,0 +1,668 @@
+<!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 Types - MLlib - Spark 1.3.0 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">
+
+        
+
+    </head>
+    <body>
+        <!--[if lt IE 7]>
+            <p class="chromeframe">You are using an outdated browser. <a href="http://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">1.3.0</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="programming-guide.html">Spark Programming Guide</a></li>
+                                <li class="divider"></li>
+                                <li><a href="streaming-programming-guide.html">Spark Streaming</a></li>
+                                <li><a href="sql-programming-guide.html">DataFrames and SQL</a></li>
+                                <li><a href="mllib-guide.html">MLlib (Machine Learning)</a></li>
+                                <li><a href="graphx-programming-guide.html">GraphX (Graph Processing)</a></li>
+                                <li><a href="bagel-programming-guide.html">Bagel (Pregel 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>
+                            </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 class="divider"></li>
+                                <li><a href="ec2-scripts.html">Amazon EC2</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><a href="hadoop-third-party-distributions.html">3<sup>rd</sup>-Party Hadoop Distros</a></li>
+                                <li class="divider"></li>
+                                <li><a href="building-spark.html">Building Spark</a></li>
+                                <li><a href="https://cwiki.apache.org/confluence/display/SPARK/Contributing+to+Spark">Contributing to Spark</a></li>
+                                <li><a href="https://cwiki.apache.org/confluence/display/SPARK/Supplemental+Spark+Projects">Supplemental Projects</a></li>
+                            </ul>
+                        </li>
+                    </ul>
+                    <!--<p class="navbar-text pull-right"><span class="version-text">v1.3.0</span></p>-->
+                </div>
+            </div>
+        </div>
+
+        <div class="container" id="content">
+          
+            <h1 class="title"><a href="mllib-guide.html">MLlib</a> - Data Types</h1>
+          
+
+          <ul id="markdown-toc">
+  <li><a href="#local-vector">Local vector</a></li>
+  <li><a href="#labeled-point">Labeled point</a></li>
+  <li><a href="#local-matrix">Local matrix</a></li>
+  <li><a href="#distributed-matrix">Distributed matrix</a>    <ul>
+      <li><a href="#blockmatrix">BlockMatrix</a></li>
+      <li><a href="#rowmatrix">RowMatrix</a></li>
+      <li><a href="#indexedrowmatrix">IndexedRowMatrix</a></li>
+      <li><a href="#coordinatematrix">CoordinateMatrix</a></li>
+    </ul>
+  </li>
+</ul>
+
+<p>MLlib supports local vectors and matrices stored on a single machine, 
+as well as distributed matrices backed by one or more RDDs.
+Local vectors and local matrices are simple data models 
+that serve as public interfaces. The underlying linear algebra operations are provided by
+<a href="http://www.scalanlp.org/">Breeze</a> and <a href="http://jblas.org/">jblas</a>.
+A training example used in supervised learning is called a &#8220;labeled point&#8221; in MLlib.</p>
+
+<h2 id="local-vector">Local vector</h2>
+
+<p>A local vector has integer-typed and 0-based indices and double-typed values, stored on a single
+machine.  MLlib supports two types of local vectors: dense and sparse.  A dense vector is backed by
+a double array representing its entry values, while a sparse vector is backed by two parallel
+arrays: indices and values.  For example, a vector <code>(1.0, 0.0, 3.0)</code> can be represented in dense
+format as <code>[1.0, 0.0, 3.0]</code> or in sparse format as <code>(3, [0, 2], [1.0, 3.0])</code>, where <code>3</code> is the size
+of the vector.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>The base class of local vectors is
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vector"><code>Vector</code></a>, and we provide two
+implementations: <a href="api/scala/index.html#org.apache.spark.mllib.linalg.DenseVector"><code>DenseVector</code></a> and
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.SparseVector"><code>SparseVector</code></a>.  We recommend
+using the factory methods implemented in
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vector"><code>Vectors</code></a> to create local vectors.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="o">{</span><span class="nc">Vector</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">}</span>
+
+<span class="c1">// Create a dense vector (1.0, 0.0, 3.0).</span>
+<span class="k">val</span> <span class="n">dv</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)</span>
+<span class="c1">// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.</span>
+<span class="k">val</span> <span class="n">sv1</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">))</span>
+<span class="c1">// Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries.</span>
+<span class="k">val</span> <span class="n">sv2</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="nc">Seq</span><span class="o">((</span><span class="mi">0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">),</span> <span class="o">(</span><span class="mi">2</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)))</span></code></pre></div>
+
+    <p><strong><em>Note:</em></strong>
+Scala imports <code>scala.collection.immutable.Vector</code> by default, so you have to import
+<code>org.apache.spark.mllib.linalg.Vector</code> explicitly to use MLlib&#8217;s <code>Vector</code>.</p>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>The base class of local vectors is
+<a href="api/java/org/apache/spark/mllib/linalg/Vector.html"><code>Vector</code></a>, and we provide two
+implementations: <a href="api/java/org/apache/spark/mllib/linalg/DenseVector.html"><code>DenseVector</code></a> and
+<a href="api/java/org/apache/spark/mllib/linalg/SparseVector.html"><code>SparseVector</code></a>.  We recommend
+using the factory methods implemented in
+<a href="api/java/org/apache/spark/mllib/linalg/Vector.html"><code>Vectors</code></a> to create local vectors.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span>
+
+<span class="c1">// Create a dense vector (1.0, 0.0, 3.0).</span>
+<span class="n">Vector</span> <span class="n">dv</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">);</span>
+<span class="c1">// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.</span>
+<span class="n">Vector</span> <span class="n">sv</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">},</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">});</span></code></pre></div>
+
+  </div>
+
+<div data-lang="python">
+    <p>MLlib recognizes the following types as dense vectors:</p>
+
+    <ul>
+      <li>NumPy&#8217;s <a href="http://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html"><code>array</code></a></li>
+      <li>Python&#8217;s list, e.g., <code>[1, 2, 3]</code></li>
+    </ul>
+
+    <p>and the following as sparse vectors:</p>
+
+    <ul>
+      <li>MLlib&#8217;s <a href="api/python/pyspark.mllib.linalg.SparseVector-class.html"><code>SparseVector</code></a>.</li>
+      <li>SciPy&#8217;s
+<a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csc_matrix.html#scipy.sparse.csc_matrix"><code>csc_matrix</code></a>
+with a single column</li>
+    </ul>
+
+    <p>We recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented
+in <a href="api/python/pyspark.mllib.linalg.Vectors-class.html"><code>Vectors</code></a> to create sparse vectors.</p>
+
+    <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">scipy.sparse</span> <span class="kn">as</span> <span class="nn">sps</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span>
+
+<span class="c"># Use a NumPy array as a dense vector.</span>
+<span class="n">dv1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>
+<span class="c"># Use a Python list as a dense vector.</span>
+<span class="n">dv2</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]</span>
+<span class="c"># Create a SparseVector.</span>
+<span class="n">sv1</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>
+<span class="c"># Use a single-column SciPy csc_matrix as a sparse vector.</span>
+<span class="n">sv2</span> <span class="o">=</span> <span class="n">sps</span><span class="o">.</span><span class="n">csc_matrix</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])),</span> <span class="n">shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span></code></pre></div>
+
+  </div>
+</div>
+
+<h2 id="labeled-point">Labeled point</h2>
+
+<p>A labeled point is a local vector, either dense or sparse, associated with a label/response.
+In MLlib, labeled points are used in supervised learning algorithms.
+We use a double to store a label, so we can use labeled points in both regression and classification.
+For binary classification, a label should be either <code>0</code> (negative) or <code>1</code> (positive).
+For multiclass classification, labels should be class indices starting from zero: <code>0, 1, 2, ...</code>.</p>
+
+<div class="codetabs">
+
+<div data-lang="scala">
+
+    <p>A labeled point is represented by the case class
+<a href="api/scala/index.html#org.apache.spark.mllib.regression.LabeledPoint"><code>LabeledPoint</code></a>.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span>
+
+<span class="c1">// Create a labeled point with a positive label and a dense feature vector.</span>
+<span class="k">val</span> <span class="n">pos</span> <span class="k">=</span> <span class="nc">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">))</span>
+
+<span class="c1">// Create a labeled point with a negative label and a sparse feature vector.</span>
+<span class="k">val</span> <span class="n">neg</span> <span class="k">=</span> <span class="nc">LabeledPoint</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)))</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>A labeled point is represented by
+<a href="api/java/org/apache/spark/mllib/regression/LabeledPoint.html"><code>LabeledPoint</code></a>.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span>
+
+<span class="c1">// Create a labeled point with a positive label and a dense feature vector.</span>
+<span class="n">LabeledPoint</span> <span class="n">pos</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">));</span>
+
+<span class="c1">// Create a labeled point with a negative label and a sparse feature vector.</span>
+<span class="n">LabeledPoint</span> <span class="n">neg</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">},</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">}));</span></code></pre></div>
+
+  </div>
+
+<div data-lang="python">
+
+    <p>A labeled point is represented by
+<a href="api/python/pyspark.mllib.regression.LabeledPoint-class.html"><code>LabeledPoint</code></a>.</p>
+
+    <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">SparseVector</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span>
+
+<span class="c"># Create a labeled point with a positive label and a dense feature vector.</span>
+<span class="n">pos</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>
+
+<span class="c"># Create a labeled point with a negative label and a sparse feature vector.</span>
+<span class="n">neg</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">SparseVector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]))</span></code></pre></div>
+
+  </div>
+</div>
+
+<p><strong><em>Sparse data</em></strong></p>
+
+<p>It is very common in practice to have sparse training data.  MLlib supports reading training
+examples stored in <code>LIBSVM</code> format, which is the default format used by
+<a href="http://www.csie.ntu.edu.tw/~cjlin/libsvm/"><code>LIBSVM</code></a> and
+<a href="http://www.csie.ntu.edu.tw/~cjlin/liblinear/"><code>LIBLINEAR</code></a>.  It is a text format in which each line
+represents a labeled sparse feature vector using the following format:</p>
+
+<pre><code>label index1:value1 index2:value2 ...
+</code></pre>
+
+<p>where the indices are one-based and in ascending order. 
+After loading, the feature indices are converted to zero-based.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p><a href="api/scala/index.html#org.apache.spark.mllib.util.MLUtils$"><code>MLUtils.loadLibSVMFile</code></a> reads training
+examples stored in LIBSVM format.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span>
+
+<span class="k">val</span> <span class="n">examples</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">LabeledPoint</span><span class="o">]</span> <span class="k">=</span> <span class="nc">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+    <p><a href="api/java/org/apache/spark/mllib/util/MLUtils.html"><code>MLUtils.loadLibSVMFile</code></a> reads training
+examples stored in LIBSVM format.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
+
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">LabeledPoint</span><span class="o">&gt;</span> <span class="n">examples</span> <span class="o">=</span> 
+  <span class="n">MLUtils</span><span class="o">.</span><span class="na">loadLibSVMFile</span><span class="o">(</span><span class="n">jsc</span><span class="o">.</span><span class="na">sc</span><span class="o">(),</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">();</span></code></pre></div>
+
+  </div>
+
+<div data-lang="python">
+    <p><a href="api/python/pyspark.mllib.util.MLUtils-class.html"><code>MLUtils.loadLibSVMFile</code></a> reads training
+examples stored in LIBSVM format.</p>
+
+    <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.util</span> <span class="kn">import</span> <span class="n">MLUtils</span>
+
+<span class="n">examples</span> <span class="o">=</span> <span class="n">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span></code></pre></div>
+
+  </div>
+</div>
+
+<h2 id="local-matrix">Local matrix</h2>
+
+<p>A local matrix has integer-typed row and column indices and double-typed values, stored on a single
+machine.  MLlib supports dense matrices, whose entry values are stored in a single double array in
+column major.  For example, the following matrix <code>\[ \begin{pmatrix}
+1.0 &amp; 2.0 \\
+3.0 &amp; 4.0 \\
+5.0 &amp; 6.0
+\end{pmatrix}
+\]</code>
+is stored in a one-dimensional array <code>[1.0, 3.0, 5.0, 2.0, 4.0, 6.0]</code> with the matrix size <code>(3, 2)</code>.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>The base class of local matrices is
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.Matrix"><code>Matrix</code></a>, and we provide one
+implementation: <a href="api/scala/index.html#org.apache.spark.mllib.linalg.DenseMatrix"><code>DenseMatrix</code></a>.
+We recommend using the factory methods implemented
+in <a href="api/scala/index.html#org.apache.spark.mllib.linalg.Matrices"><code>Matrices</code></a> to create local
+matrices.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="o">{</span><span class="nc">Matrix</span><span class="o">,</span> <span class="nc">Matrices</span><span class="o">}</span>
+
+<span class="c1">// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))</span>
+<span class="k">val</span> <span class="n">dm</span><span class="k">:</span> <span class="kt">Matrix</span> <span class="o">=</span> <span class="nc">Matrices</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">))</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>The base class of local matrices is
+<a href="api/java/org/apache/spark/mllib/linalg/Matrix.html"><code>Matrix</code></a>, and we provide one
+implementation: <a href="api/java/org/apache/spark/mllib/linalg/DenseMatrix.html"><code>DenseMatrix</code></a>.
+We recommend using the factory methods implemented
+in <a href="api/java/org/apache/spark/mllib/linalg/Matrices.html"><code>Matrices</code></a> to create local
+matrices.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrices</span><span class="o">;</span>
+
+<span class="c1">// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))</span>
+<span class="n">Matrix</span> <span class="n">dm</span> <span class="o">=</span> <span class="n">Matrices</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">});</span></code></pre></div>
+
+  </div>
+
+</div>
+
+<h2 id="distributed-matrix">Distributed matrix</h2>
+
+<p>A distributed matrix has long-typed row and column indices and double-typed values, stored
+distributively in one or more RDDs.  It is very important to choose the right format to store large
+and distributed matrices.  Converting a distributed matrix to a different format may require a
+global shuffle, which is quite expensive.  Three types of distributed matrices have been implemented
+so far.</p>
+
+<p>The basic type is called <code>RowMatrix</code>. A <code>RowMatrix</code> is a row-oriented distributed
+matrix without meaningful row indices, e.g., a collection of feature vectors.
+It is backed by an RDD of its rows, where each row is a local vector.
+We assume that the number of columns is not huge for a <code>RowMatrix</code> so that a single
+local vector can be reasonably communicated to the driver and can also be stored /
+operated on using a single node. 
+An <code>IndexedRowMatrix</code> is similar to a <code>RowMatrix</code> but with row indices,
+which can be used for identifying rows and executing joins.
+A <code>CoordinateMatrix</code> is a distributed matrix stored in <a href="https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_.28COO.29">coordinate list (COO)</a> format,
+backed by an RDD of its entries.</p>
+
+<p><strong><em>Note</em></strong></p>
+
+<p>The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size.
+In general the use of non-deterministic RDDs can lead to errors.</p>
+
+<h3 id="blockmatrix">BlockMatrix</h3>
+
+<p>A <code>BlockMatrix</code> is a distributed matrix backed by an RDD of <code>MatrixBlock</code>s, where a <code>MatrixBlock</code> is
+a tuple of <code>((Int, Int), Matrix)</code>, where the <code>(Int, Int)</code> is the index of the block, and <code>Matrix</code> is
+the sub-matrix at the given index with size <code>rowsPerBlock</code> x <code>colsPerBlock</code>.
+<code>BlockMatrix</code> supports methods such as <code>add</code> and <code>multiply</code> with another <code>BlockMatrix</code>.
+<code>BlockMatrix</code> also has a helper function <code>validate</code> which can be used to check whether the
+<code>BlockMatrix</code> is set up properly.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>A <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.BlockMatrix"><code>BlockMatrix</code></a> can be
+most easily created from an <code>IndexedRowMatrix</code> or <code>CoordinateMatrix</code> by calling <code>toBlockMatrix</code>.
+<code>toBlockMatrix</code> creates blocks of size 1024 x 1024 by default.
+Users may change the block size by supplying the values through <code>toBlockMatrix(rowsPerBlock, colsPerBlock)</code>.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.</span><span class="o">{</span><span class="nc">BlockMatrix</span><span class="o">,</span> <span class="nc">CoordinateMatrix</span><span class="o">,</span> <span class="nc">MatrixEntry</span><span class="o">}</span>
+
+<span class="k">val</span> <span class="n">entries</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">MatrixEntry</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of (i, j, v) matrix entries</span>
+<span class="c1">// Create a CoordinateMatrix from an RDD[MatrixEntry].</span>
+<span class="k">val</span> <span class="n">coordMat</span><span class="k">:</span> <span class="kt">CoordinateMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">)</span>
+<span class="c1">// Transform the CoordinateMatrix to a BlockMatrix</span>
+<span class="k">val</span> <span class="n">matA</span><span class="k">:</span> <span class="kt">BlockMatrix</span> <span class="o">=</span> <span class="n">coordMat</span><span class="o">.</span><span class="n">toBlockMatrix</span><span class="o">().</span><span class="n">cache</span><span class="o">()</span>
+
+<span class="c1">// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.</span>
+<span class="c1">// Nothing happens if it is valid.</span>
+<span class="n">matA</span><span class="o">.</span><span class="n">validate</span><span class="o">()</span>
+
+<span class="c1">// Calculate A^T A.</span>
+<span class="k">val</span> <span class="n">ata</span> <span class="k">=</span> <span class="n">matA</span><span class="o">.</span><span class="n">transpose</span><span class="o">.</span><span class="n">multiply</span><span class="o">(</span><span class="n">matA</span><span class="o">)</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>A <a href="api/java/org/apache/spark/mllib/linalg/distributed/BlockMatrix.html"><code>BlockMatrix</code></a> can be
+most easily created from an <code>IndexedRowMatrix</code> or <code>CoordinateMatrix</code> by calling <code>toBlockMatrix</code>.
+<code>toBlockMatrix</code> creates blocks of size 1024 x 1024 by default.
+Users may change the block size by supplying the values through <code>toBlockMatrix(rowsPerBlock, colsPerBlock)</code>.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.BlockMatrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.CoordinateMatrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix</span><span class="o">;</span>
+
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">MatrixEntry</span><span class="o">&gt;</span> <span class="n">entries</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of (i, j, v) Matrix Entries</span>
+<span class="c1">// Create a CoordinateMatrix from a JavaRDD&lt;MatrixEntry&gt;.</span>
+<span class="n">CoordinateMatrix</span> <span class="n">coordMat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span>
+<span class="c1">// Transform the CoordinateMatrix to a BlockMatrix</span>
+<span class="n">BlockMatrix</span> <span class="n">matA</span> <span class="o">=</span> <span class="n">coordMat</span><span class="o">.</span><span class="na">toBlockMatrix</span><span class="o">().</span><span class="na">cache</span><span class="o">();</span>
+
+<span class="c1">// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.</span>
+<span class="c1">// Nothing happens if it is valid.</span>
+<span class="n">matA</span><span class="o">.</span><span class="na">validate</span><span class="o">();</span>
+
+<span class="c1">// Calculate A^T A.</span>
+<span class="n">BlockMatrix</span> <span class="n">ata</span> <span class="o">=</span> <span class="n">matA</span><span class="o">.</span><span class="na">transpose</span><span class="o">().</span><span class="na">multiply</span><span class="o">(</span><span class="n">matA</span><span class="o">);</span></code></pre></div>
+
+  </div>
+</div>
+
+<h3 id="rowmatrix">RowMatrix</h3>
+
+<p>A <code>RowMatrix</code> is a row-oriented distributed matrix without meaningful row indices, backed by an RDD
+of its rows, where each row is a local vector.
+Since each row is represented by a local vector, the number of columns is
+limited by the integer range but it should be much smaller in practice.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>A <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.RowMatrix"><code>RowMatrix</code></a> can be
+created from an <code>RDD[Vector]</code> instance.  Then we can compute its column summary statistics.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.RowMatrix</span>
+
+<span class="k">val</span> <span class="n">rows</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Vector</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of local vectors</span>
+<span class="c1">// Create a RowMatrix from an RDD[Vector].</span>
+<span class="k">val</span> <span class="n">mat</span><span class="k">:</span> <span class="kt">RowMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">RowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">)</span>
+
+<span class="c1">// Get its size.</span>
+<span class="k">val</span> <span class="n">m</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="o">()</span>
+<span class="k">val</span> <span class="n">n</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="o">()</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>A <a href="api/java/org/apache/spark/mllib/linalg/distributed/RowMatrix.html"><code>RowMatrix</code></a> can be
+created from a <code>JavaRDD&lt;Vector&gt;</code> instance.  Then we can compute its column summary statistics.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.RowMatrix</span><span class="o">;</span>
+
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">Vector</span><span class="o">&gt;</span> <span class="n">rows</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of local vectors</span>
+<span class="c1">// Create a RowMatrix from an JavaRDD&lt;Vector&gt;.</span>
+<span class="n">RowMatrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span>
+
+<span class="c1">// Get its size.</span>
+<span class="kt">long</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numRows</span><span class="o">();</span>
+<span class="kt">long</span> <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numCols</span><span class="o">();</span></code></pre></div>
+
+  </div>
+</div>
+
+<h3 id="indexedrowmatrix">IndexedRowMatrix</h3>
+
+<p>An <code>IndexedRowMatrix</code> is similar to a <code>RowMatrix</code> but with meaningful row indices.  It is backed by
+an RDD of indexed rows, so that each row is represented by its index (long-typed) and a local vector.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>An
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix"><code>IndexedRowMatrix</code></a>
+can be created from an <code>RDD[IndexedRow]</code> instance, where
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.IndexedRow"><code>IndexedRow</code></a> is a
+wrapper over <code>(Long, Vector)</code>.  An <code>IndexedRowMatrix</code> can be converted to a <code>RowMatrix</code> by dropping
+its row indices.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.</span><span class="o">{</span><span class="nc">IndexedRow</span><span class="o">,</span> <span class="nc">IndexedRowMatrix</span><span class="o">,</span> <span class="nc">RowMatrix</span><span class="o">}</span>
+
+<span class="k">val</span> <span class="n">rows</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">IndexedRow</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of indexed rows</span>
+<span class="c1">// Create an IndexedRowMatrix from an RDD[IndexedRow].</span>
+<span class="k">val</span> <span class="n">mat</span><span class="k">:</span> <span class="kt">IndexedRowMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">IndexedRowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">)</span>
+
+<span class="c1">// Get its size.</span>
+<span class="k">val</span> <span class="n">m</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="o">()</span>
+<span class="k">val</span> <span class="n">n</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="o">()</span>
+
+<span class="c1">// Drop its row indices.</span>
+<span class="k">val</span> <span class="n">rowMat</span><span class="k">:</span> <span class="kt">RowMatrix</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toRowMatrix</span><span class="o">()</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>An
+<a href="api/java/org/apache/spark/mllib/linalg/distributed/IndexedRowMatrix.html"><code>IndexedRowMatrix</code></a>
+can be created from an <code>JavaRDD&lt;IndexedRow&gt;</code> instance, where
+<a href="api/java/org/apache/spark/mllib/linalg/distributed/IndexedRow.html"><code>IndexedRow</code></a> is a
+wrapper over <code>(long, Vector)</code>.  An <code>IndexedRowMatrix</code> can be converted to a <code>RowMatrix</code> by dropping
+its row indices.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRow</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.RowMatrix</span><span class="o">;</span>
+
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">IndexedRow</span><span class="o">&gt;</span> <span class="n">rows</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of indexed rows</span>
+<span class="c1">// Create an IndexedRowMatrix from a JavaRDD&lt;IndexedRow&gt;.</span>
+<span class="n">IndexedRowMatrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IndexedRowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span>
+
+<span class="c1">// Get its size.</span>
+<span class="kt">long</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numRows</span><span class="o">();</span>
+<span class="kt">long</span> <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numCols</span><span class="o">();</span>
+
+<span class="c1">// Drop its row indices.</span>
+<span class="n">RowMatrix</span> <span class="n">rowMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">toRowMatrix</span><span class="o">();</span></code></pre></div>
+
+  </div></div>
+
+<h3 id="coordinatematrix">CoordinateMatrix</h3>
+
+<p>A <code>CoordinateMatrix</code> is a distributed matrix backed by an RDD of its entries.  Each entry is a tuple
+of <code>(i: Long, j: Long, value: Double)</code>, where <code>i</code> is the row index, <code>j</code> is the column index, and
+<code>value</code> is the entry value.  A <code>CoordinateMatrix</code> should be used only when both
+dimensions of the matrix are huge and the matrix is very sparse.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>A
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.CoordinateMatrix"><code>CoordinateMatrix</code></a>
+can be created from an <code>RDD[MatrixEntry]</code> instance, where
+<a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.MatrixEntry"><code>MatrixEntry</code></a> is a
+wrapper over <code>(Long, Long, Double)</code>.  A <code>CoordinateMatrix</code> can be converted to an <code>IndexedRowMatrix</code>
+with sparse rows by calling <code>toIndexedRowMatrix</code>.  Other computations for 
+<code>CoordinateMatrix</code> are not currently supported.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.</span><span class="o">{</span><span class="nc">CoordinateMatrix</span><span class="o">,</span> <span class="nc">MatrixEntry</span><span class="o">}</span>
+
+<span class="k">val</span> <span class="n">entries</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">MatrixEntry</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of matrix entries</span>
+<span class="c1">// Create a CoordinateMatrix from an RDD[MatrixEntry].</span>
+<span class="k">val</span> <span class="n">mat</span><span class="k">:</span> <span class="kt">CoordinateMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">)</span>
+
+<span class="c1">// Get its size.</span>
+<span class="k">val</span> <span class="n">m</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="o">()</span>
+<span class="k">val</span> <span class="n">n</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="o">()</span>
+
+<span class="c1">// Convert it to an IndexRowMatrix whose rows are sparse vectors.</span>
+<span class="k">val</span> <span class="n">indexedRowMatrix</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toIndexedRowMatrix</span><span class="o">()</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>A
+<a href="api/java/org/apache/spark/mllib/linalg/distributed/CoordinateMatrix.html"><code>CoordinateMatrix</code></a>
+can be created from a <code>JavaRDD&lt;MatrixEntry&gt;</code> instance, where
+<a href="api/java/org/apache/spark/mllib/linalg/distributed/MatrixEntry.html"><code>MatrixEntry</code></a> is a
+wrapper over <code>(long, long, double)</code>.  A <code>CoordinateMatrix</code> can be converted to an <code>IndexedRowMatrix</code>
+with sparse rows by calling <code>toIndexedRowMatrix</code>. Other computations for 
+<code>CoordinateMatrix</code> are not currently supported.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.CoordinateMatrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.MatrixEntry</span><span class="o">;</span>
+
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">MatrixEntry</span><span class="o">&gt;</span> <span class="n">entries</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of matrix entries</span>
+<span class="c1">// Create a CoordinateMatrix from a JavaRDD&lt;MatrixEntry&gt;.</span>
+<span class="n">CoordinateMatrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span>
+
+<span class="c1">// Get its size.</span>
+<span class="kt">long</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numRows</span><span class="o">();</span>
+<span class="kt">long</span> <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numCols</span><span class="o">();</span>
+
+<span class="c1">// Convert it to an IndexRowMatrix whose rows are sparse vectors.</span>
+<span class="n">IndexedRowMatrix</span> <span class="n">indexedRowMatrix</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">toIndexedRowMatrix</span><span class="o">();</span></code></pre></div>
+
+  </div>
+</div>
+
+
+        </div> <!-- /container -->
+
+        <script src="js/vendor/jquery-1.8.0.min.js"></script>
+        <script src="js/vendor/bootstrap.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://') +
+                    'cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML';
+                d.getElementsByTagName('head')[0].appendChild(script);
+            }(document));
+        </script>
+    </body>
+</html>
author	Patrick Wendell <pwendell@apache.org>	2015-03-13 02:30:55 +0000
committer	Patrick Wendell <pwendell@apache.org>	2015-03-13 02:30:55 +0000
commit	aaf670598f15d47784d8b91b34dd614d0f8162af (patch)
tree	d86a329b056b3e9e9e79591d5b5bc3ee1781386b /site/docs/1.3.0/mllib-data-types.html
parent	0d484ac791630a4f0ca7e82002113d94c931a1e7 (diff)
download	spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.gz spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.bz2 spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.zip