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From rawkintr...@apache.org
Subject [09/51] [abbrv] [partial] mahout git commit: WEBSITE Emergency Patches for go-live closes apache/mahout#317
Date Sat, 13 May 2017 08:01:01 GMT
http://git-wip-us.apache.org/repos/asf/mahout/blob/7c0babd7/website/oldsite/_site/overview.html
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-
-
-<!DOCTYPE html>
-<html lang="en">
-<head>
-  <meta charset="utf-8">
-  <meta http-equiv="X-UA-Compatible" content="IE=edge">
-
-  <title>Downloads</title>
-  
-  <meta name="author" content="The Apache Software Foundation">
-
-  <!-- Enable responsive viewport -->
-  <meta name="viewport" content="width=device-width, initial-scale=1.0">
-
-  <!-- Bootstrap styles -->
-  <link href="/assets/themes/mahout3/css/bootstrap.min.css" rel="stylesheet">
-  <!-- Optional theme -->
-  <link href="/assets/themes/mahout3/css/bootstrap-theme.min.css" rel="stylesheet">
-  <!-- Sticky Footer -->
-  <link href="/assets/themes/mahout3/css/bs-sticky-footer.css" rel="stylesheet">
-
-  <!-- Custom styles -->
-  <link href="/assets/themes/mahout3/css/style.css" rel="stylesheet" type="text/css" media="all">
-
-  <!-- HTML5 Shim and Respond.js IE8 support of HTML5 elements and media queries -->
-  <!-- WARNING: Respond.js doesn't work if you view the page via file:// -->
-  <!--[if lt IE 9]>
-  <script src="https://oss.maxcdn.com/libs/html5shiv/3.7.0/html5shiv.js"></script>
-  <script src="https://oss.maxcdn.com/libs/respond.js/1.3.0/respond.min.js"></script>
-  <![endif]-->
-
-  <!-- Fav and touch icons -->
-  <!-- Update these with your own images
-    <link rel="shortcut icon" href="images/favicon.ico">
-    <link rel="apple-touch-icon" href="images/apple-touch-icon.png">
-    <link rel="apple-touch-icon" sizes="72x72" href="images/apple-touch-icon-72x72.png">
-    <link rel="apple-touch-icon" sizes="114x114" href="images/apple-touch-icon-114x114.png">
-  -->
-
-  <!-- atom & rss feed -->
-  <link href="/atom.xml" type="application/atom+xml" rel="alternate" title="Sitewide ATOM Feed">
-  <link href="/rss.xml" type="application/rss+xml" rel="alternate" title="Sitewide RSS Feed">
-  <script type="text/x-mathjax-config">
-  MathJax.Hub.Config({
-    tex2jax: {
-      skipTags: ['script', 'noscript', 'style', 'textarea', 'pre']
-    }
-  });
-  MathJax.Hub.Queue(function() {
-    var all = MathJax.Hub.getAllJax(), i;
-    for(i = 0; i < all.length; i += 1) {
-      all[i].SourceElement().parentNode.className += ' has-jax';
-    }
-  });
-  </script>
-  <script type="text/javascript">
-    var mathjax = document.createElement('script');
-    mathjax.type = 'text/javascript';
-    mathjax.async = true;
-
-    mathjax.src = ('https:' == document.location.protocol) ?
-        'https://c328740.ssl.cf1.rackcdn.com/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML' :
-        'http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML';
-
-      var s = document.getElementsByTagName('script')[0];
-    s.parentNode.insertBefore(mathjax, s);
-  </script>
-</head>
-
-<nav class="navbar navbar-default navbar-fixed-top">
-  <div class="container-fluid">
-    <!-- Brand and toggle get grouped for better mobile display -->
-    <div class="navbar-header">
-      <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#bs-example-navbar-collapse-1" aria-expanded="false">
-        <span class="sr-only">Toggle navigation</span>
-        <span class="icon-bar"></span>
-        <span class="icon-bar"></span>
-        <span class="icon-bar"></span>
-      </button>
-      <a class="navbar-brand" href="/">
-        <img src="/assets/img/Mahout-logo-82x100.png" height="30" alt="I'm mahout">
-      </a>
-    </div>
-
-    <!--<div class="nav-collapse collapse">-->
-<div class="collapse navbar-collapse" id="main-navbar">
-    <ul class="nav navbar-nav">
-        <!-- <li><a href="/">Home</a></li> -->
-        <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">General<b class="caret"></b></a>
-            <ul class="dropdown-menu">
-                <li><a href="/general/downloads.html">Downloads</a>
-                <li><a href="/general/who-we-are.html">Who we are</a>
-                <li><a href="/general/mailing-lists,-irc-and-archives.html">Mailing Lists</a>
-                <li><a href="/general/release-notes.html">Release Notes</a>
-                <li><a href="/general/books-tutorials-and-talks.html">Books, Tutorials, Talks</a></li>
-                <li><a href="/general/powered-by-mahout.html">Powered By Mahout</a>
-                <li><a href="/general/professional-support.html">Professional Support</a>
-                <li class="divider"></li>
-                <li class="nav-header">Resources</li>
-                <li><a href="/general/reference-reading.html">Reference Reading</a>
-                <li><a href="/general/faq.html">FAQ</a>
-                <li class="divider"></li>
-                <li class="nav-header">Legal</li>
-                <li><a href="http://www.apache.org/licenses/">License</a></li>
-                <li><a href="http://www.apache.org/security/">Security</a></li>
-                <li><a href="/general/privacy-policy.html">Privacy Policy</a>
-            </ul>
-        </li>
-        <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">Developers<b class="caret"></b></a>
-            <ul class="dropdown-menu">
-                <li><a href="/developers/developer-resources.html">Developer resources</a></li>
-                <li><a href="/developers/version-control.html">Version control</a></li>
-                <li><a href="/developers/buildingmahout.html">Build from source</a></li>
-                <li><a href="/developers/issue-tracker.html">Issue tracker</a></li>
-                <li><a href="https://builds.apache.org/job/Mahout-Quality/" target="_blank">Code quality reports</a></li>
-                <li class="divider"></li>
-                <li class="nav-header">Contributions</li>
-                <li><a href="/developers/how-to-contribute.html">How to contribute</a></li>
-                <li><a href="/developers/how-to-become-a-committer.html">How to become a committer</a></li>
-                <li><a href="/developers/gsoc.html">GSoC</a></li>
-                <li class="divider"></li>
-                <li class="nav-header">For committers</li>
-                <li><a href="/developers/how-to-update-the-website.html">How to update the website</a></li>
-                <li><a href="/developers/patch-check-list.html">Patch check list</a></li>
-                <li><a href="/developers/github.html">Handling Github PRs</a></li>
-                <li><a href="/developers/how-to-release.html">How to release</a></li>
-                <li><a href="/developers/thirdparty-dependencies.html">Third party dependencies</a></li>
-            </ul>
-        </li>
-        <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">Mahout-Samsara<b class="caret"></b></a>
-            <ul class="dropdown-menu">
-                <li><a href="/users/sparkbindings/home.html">Scala &amp; Spark Bindings Overview</a></li>
-                <li><a href="/users/sparkbindings/faq.html">FAQ</a></li>
-                <li><a href="/users/flinkbindings/playing-with-samsara-flink.html">Flink Bindings Overview</a></li>
-                <li class="nav-header">Engines</li>
-                <li><a href="/users/sparkbindings/home.html">Spark</a></li>
-                <li><a href="/users/environment/h2o-internals.html">H2O</a></li>
-                <li><a href="/users/flinkbindings/flink-internals.html">Flink</a></li>
-                <li class="nav-header">References</li>
-                <li><a href="/users/environment/in-core-reference.html">In-Core Algebraic DSL Reference</a></li>
-                <li><a href="/users/environment/out-of-core-reference.html">Distributed Algebraic DSL Reference</a></li>
-                <li class="nav-header">Tutorials</li>
-                <li><a href="/users/sparkbindings/play-with-shell.html">Playing with Mahout's Spark Shell</a></li>
-                <li><a href="/users/environment/how-to-build-an-app.html">How to build an app</a></li>
-                <li><a href="/users/environment/classify-a-doc-from-the-shell.html">Building a text classifier in Mahout's Spark Shell</a></li>
-            </ul>
-        </li>
-        <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">Algorithms<b class="caret"></b></a>
-            <ul class="dropdown-menu">
-                <li><a href="/users/basics/algorithms.html">List of algorithms</a>
-                <li class="nav-header">Distributed Matrix Decomposition</li>
-                <li><a href="/users/algorithms/d-qr.html">Cholesky QR</a></li>
-                <li><a href="/users/algorithms/d-ssvd.html">SSVD</a></li>
-                <li><a href="/users/algorithms/d-als.html">Distributed ALS</a></li>
-                <li><a href="/users/algorithms/d-spca.html">SPCA</a></li>
-                <li class="nav-header">Recommendations</li>
-                <li><a href="/users/algorithms/recommender-overview.html">Recommender Overview</a></li>
-                <li><a href="/users/algorithms/intro-cooccurrence-spark.html">Intro to cooccurrence-based<br/> recommendations with Spark</a></li>
-                <li class="nav-header">Classification</li>
-                <li><a href="/users/algorithms/spark-naive-bayes.html">Spark Naive Bayes</a></li>
-            </ul>
-        </li>
-        <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">MapReduce Basics<b class="caret"></b></a>
-            <ul class="dropdown-menu">
-                <li><a href="/users/basics/algorithms.html">List of algorithms</a>
-                <li><a href="/users/basics/quickstart.html">Overview</a>
-                <li class="divider"></li>
-                <li class="nav-header">Working with text</li>
-                <li><a href="/users/basics/creating-vectors-from-text.html">Creating vectors from text</a>
-                <li><a href="/users/basics/collocations.html">Collocations</a>
-                <li class="divider"></li>
-                <li class="nav-header">Dimensionality reduction</li>
-                <li><a href="/users/dim-reduction/dimensional-reduction.html">Singular Value Decomposition</a></li>
-                <li><a href="/users/dim-reduction/ssvd.html">Stochastic SVD</a></li>
-                <li class="divider"></li>
-                <li class="nav-header">Topic Models</li>
-                <li><a href="/users/clustering/latent-dirichlet-allocation.html">Latent Dirichlet Allocation</a></li>
-            </ul>
-        </li>
-        <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">Mahout MapReduce<b class="caret"></b></a>
-            <ul class="dropdown-menu">
-                <li class="nav-header">Classification</li>
-                <li><a href="/users/classification/bayesian.html">Naive Bayes</a></li>
-                <li><a href="/users/classification/hidden-markov-models.html">Hidden Markov Models</a></li>
-                <li><a href="/users/classification/logistic-regression.html">Logistic Regression (Single Machine)</a></li>
-                <li><a href="/users/classification/partial-implementation.html">Random Forest</a></li>
-                <li class="nav-header">Classification Examples</li>
-                <li><a href="/users/classification/breiman-example.html">Breiman example</a></li>
-                <li><a href="/users/classification/twenty-newsgroups.html">20 newsgroups example</a></li>
-                <li><a href="/users/classification/bankmarketing-example.html">SGD classifier bank marketing</a></li>
-                <li><a href="/users/classification/wikipedia-classifier-example.html">Wikipedia XML parser and classifier</a></li>
-                <li class="nav-header">Clustering</li>
-                <li><a href="/users/clustering/k-means-clustering.html">k-Means</a></li>
-                <li><a href="/users/clustering/canopy-clustering.html">Canopy</a></li>
-                <li><a href="/users/clustering/fuzzy-k-means.html">Fuzzy k-Means</a></li>
-                <li><a href="/users/clustering/streaming-k-means.html">Streaming KMeans</a></li>
-                <li><a href="/users/clustering/spectral-clustering.html">Spectral Clustering</a></li>
-                <li class="nav-header">Clustering Commandline usage</li>
-                <li><a href="/users/clustering/k-means-commandline.html">Options for k-Means</a></li>
-                <li><a href="/users/clustering/canopy-commandline.html">Options for Canopy</a></li>
-                <li><a href="/users/clustering/fuzzy-k-means-commandline.html">Options for Fuzzy k-Means</a></li>
-                <li class="nav-header">Clustering Examples</li>
-                <li><a href="/users/clustering/clustering-of-synthetic-control-data.html">Synthetic data</a></li>
-                <li class="nav-header">Cluster Post processing</li>
-                <li><a href="/users/clustering/cluster-dumper.html">Cluster Dumper tool</a></li>
-                <li><a href="/users/clustering/visualizing-sample-clusters.html">Cluster visualisation</a></li>
-                <li class="nav-header">Recommendations</li>
-                <li><a href="/users/recommender/recommender-first-timer-faq.html">First Timer FAQ</a></li>
-                <li><a href="/users/recommender/userbased-5-minutes.html">A user-based recommender <br/>in 5 minutes</a></li>
-                <li><a href="/users/recommender/matrix-factorization.html">Matrix factorization-based<br/> recommenders</a></li>
-                <li><a href="/users/recommender/recommender-documentation.html">Overview</a></li>
-                <li><a href="/users/recommender/intro-itembased-hadoop.html">Intro to item-based recommendations<br/> with Hadoop</a></li>
-                <li><a href="/users/recommender/intro-als-hadoop.html">Intro to ALS recommendations<br/> with Hadoop</a></li>
-            </ul>
-        </li>
-        <!--  <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown">Recommendations<b class="caret"></b></a>
-          <ul class="dropdown-menu">
-
-          </ul> -->
-        </li>
-    </ul>
-</div><!--/.nav-collapse -->
-  </div><!-- /.container-fluid -->
-</nav>
-
-<body>
-
-<div id="wrap">
-  <body class="">
-
-  <div class="container">
-    <hr />
-<p>layout: default
-title: Overview
-<a name="Overview-OverviewofMahout"></a></p>
-<h1 id="overview-of-mahout">Overview of Mahout</h1>
-
-<p>Mahout’s goal is to build scalable machine learning libraries. With
-scalable we mean:</p>
-<ul>
-  <li>Scalable to reasonably large data sets. Our core algorithms for
-clustering, classification and batch based collaborative filtering are
-implemented on top of Apache Hadoop using the map/reduce paradigm. However
-we do not restrict contributions to Hadoop based implementations:
-Contributions that run on a single node or on a non-Hadoop cluster are
-welcome as well. The core libraries are highly optimized to allow for good
-performance also for non-distributed algorithms.</li>
-  <li>Scalable to support your business case. Mahout is distributed under a
-commercially friendly Apache Software license.</li>
-  <li>Scalable community. The goal of Mahout is to build a vibrant, responsive,
-diverse community to facilitate discussions not only on the project itself
-but also on potential use cases. Come to the mailing lists to find out
-more.</li>
-</ul>
-
-<p>Currently Mahout supports mainly four use cases: Recommendation mining
-takes users’ behavior and from that tries to find items users might like.
-Clustering takes e.g. text documents and groups them into groups of
-topically related documents. Classification learns from exisiting
-categorized documents what documents of a specific category look like and
-is able to assign unlabelled documents to the (hopefully) correct category.
-Frequent itemset mining takes a set of item groups (terms in a query
-session, shopping cart content) and identifies, which individual items
-usually appear together.</p>
-
-<p>Interested in helping? See the <a href="http://cwiki.apache.org/confluence/display/MAHOUT">Wiki</a>
- or send us an email. Also note, we are just getting off the ground, so
-please be patient as we get the various infrastructure pieces in place.</p>
-
-  </div>
-
-
-</div>
-
-<div id="footer">
-  <div class="container">
-    <p>&copy; 2017 The Apache Software Foundation
-      with help from <a href="http://jekyllbootstrap.com" target="_blank" title="The Definitive Jekyll Blogging Framework">Jekyll Bootstrap</a>
-      and <a href="http://getbootstrap.com" target="_blank">Bootstrap</a>
-    </p>
-  </div>
-</div>
-
-
-
-
-
-
-
-<!-- Latest compiled and minified JavaScript, requires jQuery 1.x (2.x not supported in IE8) -->
-<!-- Placed at the end of the document so the pages load faster -->
-<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="/assets/themes/mahout3/js/bootstrap.min.js"></script>
-</body>
-</html>
-

http://git-wip-us.apache.org/repos/asf/mahout/blob/7c0babd7/website/oldsite/_site/release-notes/Apache-Mahout-0.10.0-Release-Notes.pdf
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http://git-wip-us.apache.org/repos/asf/mahout/blob/7c0babd7/website/oldsite/_site/robots.txt
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-Sitemap: http://localhost:4000/sitemap.xml

http://git-wip-us.apache.org/repos/asf/mahout/blob/7c0babd7/website/oldsite/_site/sitemap.xml
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-<?xml version="1.0" encoding="UTF-8"?>
-<urlset xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.sitemaps.org/schemas/sitemap/0.9 http://www.sitemaps.org/schemas/sitemap/0.9/sitemap.xsd" xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
-<url>
-<loc>http://localhost:4000/users/clustering/20newsgroups</loc>
-</url>
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-</url>
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-<loc>http://localhost:4000/users/classification/bayesian-commandline</loc>
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-</url>
-<url>
-<loc>http://localhost:4000/users/clustering/hierarchical-clustering</loc>
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-<url>
-<loc>http://localhost:4000/users/sparkbindings/home</loc>
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-<url>
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-<h1 id="distributed-cholesky-qr">Distributed Cholesky QR</h1>
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-<p>Mahout has a distributed implementation of QR decomposition for tall thin matricies<a href="[Mahout Scala and Mahout Spark Bindings for Linear Algebra Subroutines](http://mahout.apache.org/users/sparkbindings/ScalaSparkBindings.pdf)">1</a>.</p>
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-<h2 id="algorithm">Algorithm</h2>
-
-<p>For the classic QR decomposition of the form <code class="highlighter-rouge">\(\mathbf{A}=\mathbf{QR},\mathbf{A}\in\mathbb{R}^{m\times n}\)</code> a distributed version is fairly easily achieved if <code class="highlighter-rouge">\(\mathbf{A}\)</code> is tall and thin such that <code class="highlighter-rouge">\(\mathbf{A}^{\top}\mathbf{A}\)</code> fits in memory, i.e. <em>m</em> is large but <em>n</em> &lt; ~5000 Under such circumstances, only <code class="highlighter-rouge">\(\mathbf{A}\)</code> and <code class="highlighter-rouge">\(\mathbf{Q}\)</code> are distributed matricies and <code class="highlighter-rouge">\(\mathbf{A^{\top}A}\)</code> and <code class="highlighter-rouge">\(\mathbf{R}\)</code> are in-core products. We just compute the in-core version of the Cholesky decomposition in the form of <code class="highlighter-rouge">\(\mathbf{LL}^{\top}= \mathbf{A}^{\top}\mathbf{A}\)</code>.  After that we take <code class="highlighter-rouge">\(\mathbf{R}= \mathbf{L}^{\top}\)</co
 de> and <code class="highlighter-rouge">\(\mathbf{Q}=\mathbf{A}\left(\mathbf{L}^{\top}\right)^{-1}\)</code>.  The latter is easily achieved by multiplying each verticle block of <code class="highlighter-rouge">\(\mathbf{A}\)</code> by <code class="highlighter-rouge">\(\left(\mathbf{L}^{\top}\right)^{-1}\)</code>.  (There is no actual matrix inversion happening).</p>
-
-<h2 id="implementation">Implementation</h2>
-
-<p>Mahout <code class="highlighter-rouge">dqrThin(...)</code> is implemented in the mahout <code class="highlighter-rouge">math-scala</code> algebraic optimizer which translates Mahout’s R-like linear algebra operators into a physical plan for both Spark and H2O distributed engines.</p>
-
-<div class="highlighter-rouge"><pre class="highlight"><code>def dqrThin[K: ClassTag](A: DrmLike[K], checkRankDeficiency: Boolean = true): (DrmLike[K], Matrix) = {        
-    if (drmA.ncol &gt; 5000)
-        log.warn("A is too fat. A'A must fit in memory and easily broadcasted.")
-    implicit val ctx = drmA.context
-    val AtA = (drmA.t %*% drmA).checkpoint()
-    val inCoreAtA = AtA.collect
-    val ch = chol(inCoreAtA)
-    val inCoreR = (ch.getL cloned) t
-    if (checkRankDeficiency &amp;&amp; !ch.isPositiveDefinite)
-        throw new IllegalArgumentException("R is rank-deficient.")
-    val bcastAtA = sc.broadcast(inCoreAtA)
-    val Q = A.mapBlock() {
-        case (keys, block) =&gt; keys -&gt; chol(bcastAtA).solveRight(block)
-    }
-    Q -&gt; inCoreR
-}
-</code></pre>
-</div>
-
-<h2 id="usage">Usage</h2>
-
-<p>The scala <code class="highlighter-rouge">dqrThin(...)</code> method can easily be called in any Spark or H2O application built with the <code class="highlighter-rouge">math-scala</code> library and the corresponding <code class="highlighter-rouge">Spark</code> or <code class="highlighter-rouge">H2O</code> engine module as follows:</p>
-
-<div class="highlighter-rouge"><pre class="highlight"><code>import org.apache.mahout.math._
-import decompositions._
-import drm._
-
-val(drmQ, inCoreR) = dqrThin(drma)
-</code></pre>
-</div>
-
-<h2 id="references">References</h2>
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-    <h1 id="distributed-cholesky-qr">Distributed Cholesky QR</h1>
-
-<h2 id="intro">Intro</h2>
-
-<p>Mahout has a distributed implementation of QR decomposition for tall thin matrices<a href="[Mahout Scala and Mahout Spark Bindings for Linear Algebra Subroutines](http://mahout.apache.org/users/sparkbindings/ScalaSparkBindings.pdf)">1</a>.</p>
-
-<h2 id="algorithm">Algorithm</h2>
-
-<p>For the classic QR decomposition of the form <code class="highlighter-rouge">\(\mathbf{A}=\mathbf{QR},\mathbf{A}\in\mathbb{R}^{m\times n}\)</code> a distributed version is fairly easily achieved if <code class="highlighter-rouge">\(\mathbf{A}\)</code> is tall and thin such that <code class="highlighter-rouge">\(\mathbf{A}^{\top}\mathbf{A}\)</code> fits in memory, i.e. <em>m</em> is large but <em>n</em> &lt; ~5000 Under such circumstances, only <code class="highlighter-rouge">\(\mathbf{A}\)</code> and <code class="highlighter-rouge">\(\mathbf{Q}\)</code> are distributed matrices and <code class="highlighter-rouge">\(\mathbf{A^{\top}A}\)</code> and <code class="highlighter-rouge">\(\mathbf{R}\)</code> are in-core products. We just compute the in-core version of the Cholesky decomposition in the form of <code class="highlighter-rouge">\(\mathbf{LL}^{\top}= \mathbf{A}^{\top}\mathbf{A}\)</code>.  After that we take <code class="highlighter-rouge">\(\mathbf{R}= \mathbf{L}^{\top}\)</cod
 e> and <code class="highlighter-rouge">\(\mathbf{Q}=\mathbf{A}\left(\mathbf{L}^{\top}\right)^{-1}\)</code>.  The latter is easily achieved by multiplying each vertical block of <code class="highlighter-rouge">\(\mathbf{A}\)</code> by <code class="highlighter-rouge">\(\left(\mathbf{L}^{\top}\right)^{-1}\)</code>.  (There is no actual matrix inversion happening).</p>
-
-<h2 id="implementation">Implementation</h2>
-
-<p>Mahout <code class="highlighter-rouge">dqrThin(...)</code> is implemented in the mahout <code class="highlighter-rouge">math-scala</code> algebraic optimizer which translates Mahout’s R-like linear algebra operators into a physical plan for both Spark and H2O distributed engines.</p>
-
-<div class="highlighter-rouge"><pre class="highlight"><code>def dqrThin[K: ClassTag](A: DrmLike[K], checkRankDeficiency: Boolean = true): (DrmLike[K], Matrix) = {        
-    if (drmA.ncol &gt; 5000)
-        log.warn("A is too fat. A'A must fit in memory and easily broadcasted.")
-    implicit val ctx = drmA.context
-    val AtA = (drmA.t %*% drmA).checkpoint()
-    val inCoreAtA = AtA.collect
-    val ch = chol(inCoreAtA)
-    val inCoreR = (ch.getL cloned) t
-    if (checkRankDeficiency &amp;&amp; !ch.isPositiveDefinite)
-        throw new IllegalArgumentException("R is rank-deficient.")
-    val bcastAtA = sc.broadcast(inCoreAtA)
-    val Q = A.mapBlock() {
-        case (keys, block) =&gt; keys -&gt; chol(bcastAtA).solveRight(block)
-    }
-    Q -&gt; inCoreR
-}
-</code></pre>
-</div>
-
-<h2 id="usage">Usage</h2>
-
-<p>The scala <code class="highlighter-rouge">dqrThin(...)</code> method can easily be called in any Spark or H2O application built with the <code class="highlighter-rouge">math-scala</code> library and the corresponding <code class="highlighter-rouge">Spark</code> or <code class="highlighter-rouge">H2O</code> engine module as follows:</p>
-
-<div class="highlighter-rouge"><pre class="highlight"><code>import org.apache.mahout.math._
-import decompositions._
-import drm._
-
-val(drmQ, inCoreR) = dqrThin(drma)
-</code></pre>
-</div>
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-<h2 id="references">References</h2>
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