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For more information, including information on Mahout-Samsaraâs Algebraic Optimizer please see: <a href="http://mahout.apache.org/users/sparkbindings/ScalaSparkBindings.pdf";>Mahout Scala Bindings and Mahout Spark Bindings for Linear Algebra Subroutines</a>.</strong></p> <p>The subjects of this reference are solely applicable to Mahout-Samsaraâs <strong>DRM</strong> (distributed row matrix).</p> -<p>In this reference, DRMs will be denoted as e.g. <code>A</code>, and in-core matrices as e.g. <code>inCoreA</code>.</p> +<p>In this reference, DRMs will be denoted as e.g. <code class="highlighter-rouge">A</code>, and in-core matrices as e.g. <code class="highlighter-rouge">inCoreA</code>.</p> <h4 id="imports">Imports</h4> <p>The following imports are used to enable seamless in-core and distributed algebraic DSL operations:</p> -<pre><code>import org.apache.mahout.math._ +<div class="highlighter-rouge"><pre class="highlight"><code>import org.apache.mahout.math._ import scalabindings._ import RLikeOps._ import drm._ import RLikeDRMOps._ </code></pre> +</div> <p>If working with mixed scala/java code:</p> -<pre><code>import collection._ +<div class="highlighter-rouge"><pre class="highlight"><code>import collection._ import JavaConversions._ </code></pre> +</div> <p>If you are working with Mahout-Samsaraâs Spark-specific operations e.g. for context creation:</p> -<pre><code>import org.apache.mahout.sparkbindings._ +<div class="highlighter-rouge"><pre class="highlight"><code>import org.apache.mahout.sparkbindings._ </code></pre> +</div> <p>The Mahout shell does all of these imports automatically.</p> @@ -249,38 +204,44 @@ import JavaConversions._ <p>Loading a DRM from (HD)FS:</p> -<pre><code>drmDfsRead(path = hdfsPath) +<div class="highlighter-rouge"><pre class="highlight"><code>drmDfsRead(path = hdfsPath) </code></pre> +</div> <p>Parallelizing from an in-core matrix:</p> -<pre><code>val inCoreA = (dense(1, 2, 3), (3, 4, 5)) +<div class="highlighter-rouge"><pre class="highlight"><code>val inCoreA = (dense(1, 2, 3), (3, 4, 5)) val A = drmParallelize(inCoreA) </code></pre> +</div> <p>Creating an empty DRM:</p> -<pre><code>val A = drmParallelizeEmpty(100, 50) +<div class="highlighter-rouge"><pre class="highlight"><code>val A = drmParallelizeEmpty(100, 50) </code></pre> +</div> <p>Collecting to driverâs jvm in-core:</p> -<pre><code>val inCoreA = A.collect +<div class="highlighter-rouge"><pre class="highlight"><code>val inCoreA = A.collect </code></pre> +</div> <p><strong>Warning: The collection of distributed matrices happens implicitly whenever conversion to an in-core (o.a.m.math.Matrix) type is required. E.g.:</strong></p> -<pre><code>val inCoreA: Matrix = ... +<div class="highlighter-rouge"><pre class="highlight"><code>val inCoreA: Matrix = ... val drmB: DrmLike[Int] =... val inCoreC: Matrix = inCoreA %*%: drmB </code></pre> +</div> <p><strong>implies (incoreA %*%: drmB).collect</strong></p> <p>Collecting to (HD)FS as a Mahoutâs DRM formatted file:</p> -<pre><code>A.dfsWrite(path = hdfsPath) +<div class="highlighter-rouge"><pre class="highlight"><code>A.dfsWrite(path = hdfsPath) </code></pre> +</div> <h4 id="logical-algebraic-operators-on-drm-matrices">Logical algebraic operators on DRM matrices:</h4> @@ -289,12 +250,13 @@ val inCoreC: Matrix = inCoreA %*%: drmB <p>Cache a DRM and trigger an optimized physical plan:</p> -<pre><code>drmA.checkpoint(CacheHint.MEMORY_AND_DISK) +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.checkpoint(CacheHint.MEMORY_AND_DISK) </code></pre> +</div> <p>Other valid caching Instructions:</p> -<pre><code>drmA.checkpoint(CacheHint.NONE) +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.checkpoint(CacheHint.NONE) drmA.checkpoint(CacheHint.DISK_ONLY) drmA.checkpoint(CacheHint.DISK_ONLY_2) drmA.checkpoint(CacheHint.MEMORY_ONLY) @@ -305,37 +267,43 @@ drmA.checkpoint(CacheHint.MEMORY_AND_DISK_2) drmA.checkpoint(CacheHint.MEMORY_AND_DISK_SER) drmA.checkpoint(CacheHint.MEMORY_AND_DISK_SER_2) </code></pre> +</div> <p><em>Note: Logical DRM operations are lazily computed. Currently the actual computations and optional caching will be triggered by dfsWrite(â¦), collect(â¦) and blockify(â¦).</em></p> <p>Transposition:</p> -<pre><code>A.t +<div class="highlighter-rouge"><pre class="highlight"><code>A.t </code></pre> +</div> <p>Elementwise addition <em>(Matrices of identical geometry and row key types)</em>:</p> -<pre><code>A + B +<div class="highlighter-rouge"><pre class="highlight"><code>A + B </code></pre> +</div> <p>Elementwise subtraction <em>(Matrices of identical geometry and row key types)</em>:</p> -<pre><code>A - B +<div class="highlighter-rouge"><pre class="highlight"><code>A - B </code></pre> +</div> <p>Elementwise multiplication (Hadamard) <em>(Matrices of identical geometry and row key types)</em>:</p> -<pre><code>A * B +<div class="highlighter-rouge"><pre class="highlight"><code>A * B </code></pre> +</div> <p>Elementwise division <em>(Matrices of identical geometry and row key types)</em>:</p> -<pre><code>A / B +<div class="highlighter-rouge"><pre class="highlight"><code>A / B </code></pre> +</div> <p><strong>Elementwise operations involving one in-core argument (int-keyed DRMs only)</strong>:</p> -<pre><code>A + inCoreB +<div class="highlighter-rouge"><pre class="highlight"><code>A + inCoreB A - inCoreB A * inCoreB A / inCoreB @@ -348,32 +316,35 @@ inCoreA -: B inCoreA *: B inCoreA /: B </code></pre> +</div> -<p>Note the Spark associativity change (e.g. <code>A *: inCoreB</code> means <code>B.leftMultiply(A</code>), same as when both arguments are in core). Whenever operator arguments include both in-core and out-of-core arguments, the operator can only be associated with the out-of-core (DRM) argument to support the distributed implementation.</p> +<p>Note the Spark associativity change (e.g. <code class="highlighter-rouge">A *: inCoreB</code> means <code class="highlighter-rouge">B.leftMultiply(A</code>), same as when both arguments are in core). Whenever operator arguments include both in-core and out-of-core arguments, the operator can only be associated with the out-of-core (DRM) argument to support the distributed implementation.</p> <p><strong>Matrix-matrix multiplication %*%</strong>:</p> -<p><code>\(\mathbf{M}=\mathbf{AB}\)</code></p> +<p><code class="highlighter-rouge">\(\mathbf{M}=\mathbf{AB}\)</code></p> -<pre><code>A %*% B +<div class="highlighter-rouge"><pre class="highlight"><code>A %*% B A %*% inCoreB A %*% inCoreDiagonal A %*%: B </code></pre> +</div> <p><em>Note: same as above, whenever operator arguments include both in-core and out-of-core arguments, the operator can only be associated with the out-of-core (DRM) argument to support the distributed implementation.</em></p> <p><strong>Matrix-vector multiplication %*%</strong> -Currently we support a right multiply product of a DRM and an in-core Vector(<code>\(\mathbf{Ax}\)</code>) resulting in a single column DRM, which then can be collected in front (usually the desired outcome):</p> +Currently we support a right multiply product of a DRM and an in-core Vector(<code class="highlighter-rouge">\(\mathbf{Ax}\)</code>) resulting in a single column DRM, which then can be collected in front (usually the desired outcome):</p> -<pre><code>val Ax = A %*% x +<div class="highlighter-rouge"><pre class="highlight"><code>val Ax = A %*% x val inCoreX = Ax.collect(::, 0) </code></pre> +</div> <p><strong>Matrix-scalar +,-,*,/</strong> Elementwise operations of every matrix element and a scalar:</p> -<pre><code>A + 5.0 +<div class="highlighter-rouge"><pre class="highlight"><code>A + 5.0 A - 5.0 A :- 5.0 5.0 -: A @@ -381,39 +352,45 @@ A * 5.0 A / 5.0 5.0 /: a </code></pre> +</div> -<p>Note that <code>5.0 -: A</code> means <code>\(m_{ij} = 5 - a_{ij}\)</code> and <code>5.0 /: A</code> means <code>\(m_{ij} = \frac{5}{a{ij}}\)</code> for all elements of the result.</p> +<p>Note that <code class="highlighter-rouge">5.0 -: A</code> means <code class="highlighter-rouge">\(m_{ij} = 5 - a_{ij}\)</code> and <code class="highlighter-rouge">5.0 /: A</code> means <code class="highlighter-rouge">\(m_{ij} = \frac{5}{a{ij}}\)</code> for all elements of the result.</p> <h4 id="slicing">Slicing</h4> <p>General slice:</p> -<pre><code>A(100 to 200, 100 to 200) +<div class="highlighter-rouge"><pre class="highlight"><code>A(100 to 200, 100 to 200) </code></pre> +</div> <p>Horizontal Block:</p> -<pre><code>A(::, 100 to 200) +<div class="highlighter-rouge"><pre class="highlight"><code>A(::, 100 to 200) </code></pre> +</div> <p>Vertical Block:</p> -<pre><code>A(100 to 200, ::) +<div class="highlighter-rouge"><pre class="highlight"><code>A(100 to 200, ::) </code></pre> +</div> -<p><em>Note: if row range is not all-range (::) the the DRM must be <code>Int</code>-keyed. General case row slicing is not supported by DRMs with key types other than <code>Int</code></em>.</p> +<p><em>Note: if row range is not all-range (::) the the DRM must be <code class="highlighter-rouge">Int</code>-keyed. General case row slicing is not supported by DRMs with key types other than <code class="highlighter-rouge">Int</code></em>.</p> <h4 id="stitching">Stitching</h4> <p>Stitch side by side (cbind R semantics):</p> -<pre><code>val drmAnextToB = drmA cbind drmB +<div class="highlighter-rouge"><pre class="highlight"><code>val drmAnextToB = drmA cbind drmB </code></pre> +</div> <p>Stitch side by side (Scala):</p> -<pre><code>val drmAnextToB = drmA.cbind(drmB) +<div class="highlighter-rouge"><pre class="highlight"><code>val drmAnextToB = drmA.cbind(drmB) </code></pre> +</div> <p>Analogously, vertical concatenation is available via <strong>rbind</strong></p> @@ -422,32 +399,34 @@ A / 5.0 <p><strong>drm.mapBlock(â¦)</strong>:</p> -<p>The DRM operator <code>mapBlock</code> provides transformational access to the distributed vertical blockified tuples of a matrix (Row-Keys, Vertical-Matrix-Block).</p> +<p>The DRM operator <code class="highlighter-rouge">mapBlock</code> provides transformational access to the distributed vertical blockified tuples of a matrix (Row-Keys, Vertical-Matrix-Block).</p> -<p>Using <code>mapBlock</code> to add 1.0 to a DRM:</p> +<p>Using <code class="highlighter-rouge">mapBlock</code> to add 1.0 to a DRM:</p> -<pre><code>val inCoreA = dense((1, 2, 3), (2, 3 , 4), (3, 4, 5)) +<div class="highlighter-rouge"><pre class="highlight"><code>val inCoreA = dense((1, 2, 3), (2, 3 , 4), (3, 4, 5)) val drmA = drmParallelize(inCoreA) val B = A.mapBlock() { case (keys, block) => keys -> (block += 1.0) } </code></pre> +</div> <h4 id="broadcasting-vectors-and-matrices-to-closures">Broadcasting Vectors and matrices to closures</h4> <p>Generally we can create and use one-way closure attributes to be used on the back end.</p> <p>Scalar matrix multiplication:</p> -<pre><code>val factor: Int = 15 +<div class="highlighter-rouge"><pre class="highlight"><code>val factor: Int = 15 val drm2 = drm1.mapBlock() { case (keys, block) => block *= factor keys -> block } </code></pre> +</div> -<p><strong>Closure attributes must be java-serializable. Currently Mahoutâs in-core Vectors and Matrices are not java-serializable, and must be broadcast to the closure using <code>drmBroadcast(...)</code></strong>:</p> +<p><strong>Closure attributes must be java-serializable. Currently Mahoutâs in-core Vectors and Matrices are not java-serializable, and must be broadcast to the closure using <code class="highlighter-rouge">drmBroadcast(...)</code></strong>:</p> -<pre><code>val v: Vector ... +<div class="highlighter-rouge"><pre class="highlight"><code>val v: Vector ... val bcastV = drmBroadcast(v) val drm2 = drm1.mapBlock() { case (keys, block) => @@ -455,125 +434,131 @@ val drm2 = drm1.mapBlock() { keys -> block } </code></pre> +</div> <h4 id="computations-providing-ad-hoc-summaries">Computations providing ad-hoc summaries</h4> <p>Matrix cardinality:</p> -<pre><code>drmA.nrow +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.nrow drmA.ncol </code></pre> +</div> -<p><em>Note: depending on the stage of optimization, these may trigger a computational action. I.e. if one calls <code>nrow()</code> n times, then the back end will actually recompute <code>nrow</code> n times.</em></p> +<p><em>Note: depending on the stage of optimization, these may trigger a computational action. I.e. if one calls <code class="highlighter-rouge">nrow()</code> n times, then the back end will actually recompute <code class="highlighter-rouge">nrow</code> n times.</em></p> <p>Means and sums:</p> -<pre><code>drmA.colSums +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.colSums drmA.colMeans drmA.rowSums drmA.rowMeans </code></pre> +</div> -<p><em>Note: These will always trigger a computational action. I.e. if one calls <code>colSums()</code> n times, then the back end will actually recompute <code>colSums</code> n times.</em></p> +<p><em>Note: These will always trigger a computational action. I.e. if one calls <code class="highlighter-rouge">colSums()</code> n times, then the back end will actually recompute <code class="highlighter-rouge">colSums</code> n times.</em></p> <h4 id="distributed-matrix-decompositions">Distributed Matrix Decompositions</h4> <p>To import the decomposition package:</p> -<pre><code>import org.apache.mahout.math._ +<div class="highlighter-rouge"><pre class="highlight"><code>import org.apache.mahout.math._ import decompositions._ </code></pre> +</div> <p>Distributed thin QR:</p> -<pre><code>val (drmQ, incoreR) = dqrThin(drmA) +<div class="highlighter-rouge"><pre class="highlight"><code>val (drmQ, incoreR) = dqrThin(drmA) </code></pre> +</div> <p>Distributed SSVD:</p> -<pre><code>val (drmU, drmV, s) = dssvd(drmA, k = 40, q = 1) +<div class="highlighter-rouge"><pre class="highlight"><code>val (drmU, drmV, s) = dssvd(drmA, k = 40, q = 1) </code></pre> +</div> <p>Distributed SPCA:</p> -<pre><code>val (drmU, drmV, s) = dspca(drmA, k = 30, q = 1) +<div class="highlighter-rouge"><pre class="highlight"><code>val (drmU, drmV, s) = dspca(drmA, k = 30, q = 1) </code></pre> +</div> <p>Distributed regularized ALS:</p> -<pre><code>val (drmU, drmV, i) = dals(drmA, +<div class="highlighter-rouge"><pre class="highlight"><code>val (drmU, drmV, i) = dals(drmA, k = 50, lambda = 0.0, maxIterations = 10, convergenceThreshold = 0.10)) </code></pre> +</div> <h4 id="adjusting-parallelism-of-computations">Adjusting parallelism of computations</h4> -<p>Set the minimum parallelism to 100 for computations on <code>drmA</code>:</p> +<p>Set the minimum parallelism to 100 for computations on <code class="highlighter-rouge">drmA</code>:</p> -<pre><code>drmA.par(min = 100) +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.par(min = 100) </code></pre> +</div> -<p>Set the exact parallelism to 100 for computations on <code>drmA</code>:</p> +<p>Set the exact parallelism to 100 for computations on <code class="highlighter-rouge">drmA</code>:</p> -<pre><code>drmA.par(exact = 100) +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.par(exact = 100) </code></pre> +</div> -<p>Set the engine specific automatic parallelism adjustment for computations on <code>drmA</code>:</p> +<p>Set the engine specific automatic parallelism adjustment for computations on <code class="highlighter-rouge">drmA</code>:</p> -<pre><code>drmA.par(auto = true) +<div class="highlighter-rouge"><pre class="highlight"><code>drmA.par(auto = true) </code></pre> +</div> <h4 id="retrieving-the-engine-specific-data-structure-backing-the-drm">Retrieving the engine specific data structure backing the DRM:</h4> <p><strong>A Spark RDD:</strong></p> -<pre><code>val myRDD = drmA.checkpoint().rdd +<div class="highlighter-rouge"><pre class="highlight"><code>val myRDD = drmA.checkpoint().rdd </code></pre> +</div> <p><strong>An H2O Frame and Key Vec:</strong></p> -<pre><code>val myFrame = drmA.frame +<div class="highlighter-rouge"><pre class="highlight"><code>val myFrame = drmA.frame val myKeys = drmA.keys </code></pre> +</div> <p><strong>A Flink DataSet:</strong></p> -<pre><code>val myDataSet = drmA.ds +<div class="highlighter-rouge"><pre class="highlight"><code>val myDataSet = drmA.ds </code></pre> +</div> <p>For more information including information on Mahout-Samsaraâs Algebraic Optimizer and in-core Linear algebra bindings see: <a href="http://mahout.apache.org/users/sparkbindings/ScalaSparkBindings.pdf";>Mahout Scala Bindings and Mahout Spark Bindings for Linear Algebra Subroutines</a></p> - </div> -</div> + </div> </div> - </div> -<div id="footer"> - <div class="container"> - <p>© 2017 Apache Mahout - 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> - - - - + <footer class="footer bg-light"> + <div class="container text-center small"> + Copyright © 2014-2017 The Apache Software Foundation, Licensed under the Apache License, Version 2.0. + </div> +</footer> + <script src="/assets/vendor/jquery/jquery-slim.min.js"></script> + <script src="/assets/vendor/popper/popper.min.js"></script> + <script src="/assets/vendor/bootstrap/js/bootstrap.min.js"></script> + <script src="/assets/header.js"></script> + <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; type="text/javascript"></script> -<!-- 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> +</html>
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