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class="col-xs-12"> - <h1 id="faq-for-using-mahout-with-spark">FAQ for using Mahout with Spark</h1> + <div class="col-lg-8"> + <h1 id="faq-for-using-mahout-with-spark">FAQ for using Mahout with Spark</h1> <p><strong>Q: Mahout Spark shell doesnât start; âClassNotFoundâ problems or various classpath problems.</strong></p> @@ -228,10 +180,10 @@ the classpath is sane and is made available to Mahout:</p> <ol> <li>Check Spark is of correct version (same as in Mahoutâs poms), is compiled and SPARK_HOME is set.</li> <li>Check Mahout is compiled and MAHOUT_HOME is set.</li> - <li>Run <code>$SPARK_HOME/bin/compute-classpath.sh</code> and make sure it produces sane result with no errors. + <li>Run <code class="highlighter-rouge">$SPARK_HOME/bin/compute-classpath.sh</code> and make sure it produces sane result with no errors. If it outputs something other than a straightforward classpath string, most likely Spark is not compiled/set correctly (later spark versions require -<code>sbt/sbt assembly</code> to be run, simply runnig <code>sbt/sbt publish-local</code> is not enough any longer).</li> - <li>Run <code>$MAHOUT_HOME/bin/mahout -spark classpath</code> and check that path reported in step (3) is included.</li> +<code class="highlighter-rouge">sbt/sbt assembly</code> to be run, simply runnig <code class="highlighter-rouge">sbt/sbt publish-local</code> is not enough any longer).</li> + <li>Run <code class="highlighter-rouge">$MAHOUT_HOME/bin/mahout -spark classpath</code> and check that path reported in step (3) is included.</li> </ol> <p><strong>Q: I am using the command line Mahout jobs that run on Spark or am writing my own application that uses @@ -258,34 +210,26 @@ or mis-identified classes.</li> <p><strong>A:</strong> In the Mahout spark-shell the SparkContext is called âsdcâ, where the âdâ stands for distributed.</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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class="container"> - + <div class="container mt-5 pb-4"> -<div class="page-header"> - <h1>Mahout Samsara In Core </h1> -</div> + <div class="row"> -<div class="row"> - <div class="col-xs-12"> - <h2 id="mahout-samsaras-in-core-linear-algebra-dsl-reference">Mahout-Samsaraâs In-Core Linear Algebra DSL Reference</h2> + <div class="col-lg-8"> + <h2 id="mahout-samsaras-in-core-linear-algebra-dsl-reference">Mahout-Samsaraâs In-Core Linear Algebra DSL Reference</h2> <h4 id="imports">Imports</h4> <p>The following imports are used to enable Mahout-Samsaraâs Scala DSL bindings for in-core Linear Algebra:</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._ </code></pre> +</div> <h4 id="inline-initalization">Inline initalization</h4> <p>Dense vectors:</p> -<pre><code>val densVec1: Vector = (1.0, 1.1, 1.2) +<div class="highlighter-rouge"><pre class="highlight"><code>val densVec1: Vector = (1.0, 1.1, 1.2) val denseVec2 = dvec(1, 0, 1,1 ,1,2) </code></pre> +</div> <p>Sparse vectors:</p> -<pre><code>val sparseVec1: Vector = (5 -> 1.0) :: (10 -> 2.0) :: Nil +<div class="highlighter-rouge"><pre class="highlight"><code>val sparseVec1: Vector = (5 -> 1.0) :: (10 -> 2.0) :: Nil val sparseVec1 = svec((5 -> 1.0) :: (10 -> 2.0) :: Nil) // to create a vector with specific cardinality val sparseVec1 = svec((5 -> 1.0) :: (10 -> 2.0) :: Nil, cardinality = 20) </code></pre> +</div> <p>Inline matrix initialization, either sparse or dense, is always done row wise.</p> <p>Dense matrices:</p> -<pre><code>val A = dense((1, 2, 3), (3, 4, 5)) +<div class="highlighter-rouge"><pre class="highlight"><code>val A = dense((1, 2, 3), (3, 4, 5)) </code></pre> +</div> <p>Sparse matrices:</p> -<pre><code>val A = sparse( +<div class="highlighter-rouge"><pre class="highlight"><code>val A = sparse( (1, 3) :: Nil, (0, 2) :: (1, 2.5) :: Nil ) </code></pre> +</div> <p>Diagonal matrix with constant diagonal elements:</p> -<pre><code>diag(3.5, 10) +<div class="highlighter-rouge"><pre class="highlight"><code>diag(3.5, 10) </code></pre> +</div> <p>Diagonal matrix with main diagonal backed by a vector:</p> -<pre><code>diagv((1, 2, 3, 4, 5)) +<div class="highlighter-rouge"><pre class="highlight"><code>diagv((1, 2, 3, 4, 5)) </code></pre> +</div> <p>Identity matrix:</p> -<pre><code>eye(10) +<div class="highlighter-rouge"><pre class="highlight"><code>eye(10) </code></pre> +</div> <p>####Slicing and Assigning</p> <p>Getting a vector element:</p> -<pre><code>val d = vec(5) +<div class="highlighter-rouge"><pre class="highlight"><code>val d = vec(5) </code></pre> +</div> <p>Setting a vector element:</p> -<pre><code>vec(5) = 3.0 +<div class="highlighter-rouge"><pre class="highlight"><code>vec(5) = 3.0 </code></pre> +</div> <p>Getting a matrix element:</p> -<pre><code>val d = m(3,5) +<div class="highlighter-rouge"><pre class="highlight"><code>val d = m(3,5) </code></pre> +</div> <p>Setting a matrix element:</p> -<pre><code>M(3,5) = 3.0 +<div class="highlighter-rouge"><pre class="highlight"><code>M(3,5) = 3.0 </code></pre> +</div> <p>Getting a matrix row or column:</p> -<pre><code>val rowVec = M(3, ::) +<div class="highlighter-rouge"><pre class="highlight"><code>val rowVec = M(3, ::) val colVec = M(::, 3) </code></pre> +</div> <p>Setting a matrix row or column via vector assignment:</p> -<pre><code>M(3, ::) := (1, 2, 3) +<div class="highlighter-rouge"><pre class="highlight"><code>M(3, ::) := (1, 2, 3) M(::, 3) := (1, 2, 3) </code></pre> +</div> <p>Setting a subslices of a matrix row or column:</p> -<pre><code>a(0, 0 to 1) = (3, 5) +<div class="highlighter-rouge"><pre class="highlight"><code>a(0, 0 to 1) = (3, 5) </code></pre> +</div> <p>Setting a subslices of a matrix row or column via vector assignment:</p> -<pre><code>a(0, 0 to 1) := (3, 5) +<div class="highlighter-rouge"><pre class="highlight"><code>a(0, 0 to 1) := (3, 5) </code></pre> +</div> <p>Getting a matrix as from matrix contiguous block:</p> -<pre><code>val B = A(2 to 3, 3 to 4) +<div class="highlighter-rouge"><pre class="highlight"><code>val B = A(2 to 3, 3 to 4) </code></pre> +</div> <p>Assigning a contiguous block to a matrix:</p> -<pre><code>A(0 to 1, 1 to 2) = dense((3, 2), (3 ,3)) +<div class="highlighter-rouge"><pre class="highlight"><code>A(0 to 1, 1 to 2) = dense((3, 2), (3 ,3)) </code></pre> +</div> <p>Assigning a contiguous block to a matrix using the matrix assignment operator:</p> -<pre><code>A(o to 1, 1 to 2) := dense((3, 2), (3, 3)) +<div class="highlighter-rouge"><pre class="highlight"><code>A(o to 1, 1 to 2) := dense((3, 2), (3, 3)) </code></pre> +</div> <p>Assignment operator used for copying between vectors or matrices:</p> -<pre><code>vec1 := vec2 +<div class="highlighter-rouge"><pre class="highlight"><code>vec1 := vec2 M1 := M2 </code></pre> +</div> <p>Assignment operator using assignment through a functional literal for a matrix:</p> -<pre><code>M := ((row, col, x) => if (row == col) 1 else 0 +<div class="highlighter-rouge"><pre class="highlight"><code>M := ((row, col, x) => if (row == col) 1 else 0 </code></pre> +</div> <p>Assignment operator using assignment through a functional literal for a vector:</p> -<pre><code>vec := ((index, x) => sqrt(x) +<div class="highlighter-rouge"><pre class="highlight"><code>vec := ((index, x) => sqrt(x) </code></pre> +</div> <h4 id="blas-like-operations">BLAS-like operations</h4> <p>Plus/minus either vector or numeric with assignment or not:</p> -<pre><code>a + b +<div class="highlighter-rouge"><pre class="highlight"><code>a + b a - b a + 5.0 a - 5.0 </code></pre> +</div> <p>Hadamard (elementwise) product, either vector or matrix or numeric operands:</p> -<pre><code>a * b +<div class="highlighter-rouge"><pre class="highlight"><code>a * b a * 0.5 </code></pre> +</div> <p>Operations with assignment:</p> -<pre><code>a += b +<div class="highlighter-rouge"><pre class="highlight"><code>a += b a -= b a += 5.0 a -= 5.0 a *= b a *= 5 </code></pre> +</div> <p><em>Some nuanced rules</em>:</p> <p>1/x in R (where x is a vector or a matrix) is elementwise inverse. In scala it would be expressed as:</p> -<pre><code>val xInv = 1 /: x +<div class="highlighter-rouge"><pre class="highlight"><code>val xInv = 1 /: x </code></pre> +</div> <p>and Râs 5.0 - x would be:</p> -<pre><code>val x1 = 5.0 -: x +<div class="highlighter-rouge"><pre class="highlight"><code>val x1 = 5.0 -: x </code></pre> +</div> <p><em>note: All assignment operations, including :=, return the assignee just like in C++</em>:</p> -<pre><code>a -= b +<div class="highlighter-rouge"><pre class="highlight"><code>a -= b </code></pre> +</div> <p>assigns <strong>a - b</strong> to <strong>b</strong> (in-place) and returns <strong>b</strong>. Similarly for <strong>a /=: b</strong> or <strong>1 /=: v</strong></p> <p>Dot product:</p> -<pre><code>a dot b +<div class="highlighter-rouge"><pre class="highlight"><code>a dot b </code></pre> +</div> <p>Matrix and vector equivalency (or non-equivalency). <strong>Dangerous, exact equivalence is rarely useful, better to use norm comparisons with an allowance of small errors.</strong></p> -<pre><code>a === b +<div class="highlighter-rouge"><pre class="highlight"><code>a === b a !== b </code></pre> +</div> <p>Matrix multiply:</p> -<pre><code>a %*% b +<div class="highlighter-rouge"><pre class="highlight"><code>a %*% b </code></pre> +</div> <p>Optimized Right Multiply with a diagonal matrix:</p> -<pre><code>diag(5, 5) :%*% b +<div class="highlighter-rouge"><pre class="highlight"><code>diag(5, 5) :%*% b </code></pre> +</div> <p>Optimized Left Multiply with a diagonal matrix:</p> -<pre><code>A %*%: diag(5, 5) +<div class="highlighter-rouge"><pre class="highlight"><code>A %*%: diag(5, 5) </code></pre> +</div> <p>Second norm, of a vector or matrix:</p> -<pre><code>a.norm +<div class="highlighter-rouge"><pre class="highlight"><code>a.norm </code></pre> +</div> <p>Transpose:</p> -<pre><code>val Mt = M.t +<div class="highlighter-rouge"><pre class="highlight"><code>val Mt = M.t </code></pre> +</div> -<p><em>note: Transposition is currently handled via view, i.e. updating a transposed matrix will be updating the original.</em> Also computing something like <code>\(\mathbf{X^\top}\mathbf{X}\)</code>:</p> +<p><em>note: Transposition is currently handled via view, i.e. updating a transposed matrix will be updating the original.</em> Also computing something like <code class="highlighter-rouge">\(\mathbf{X^\top}\mathbf{X}\)</code>:</p> -<pre><code>val XtX = X.t %*% X +<div class="highlighter-rouge"><pre class="highlight"><code>val XtX = X.t %*% X </code></pre> +</div> <p>will not therefore incur any additional data copying.</p> @@ -436,115 +424,134 @@ a !== b <p>Matrix decompositions require an additional import:</p> -<pre><code>import org.apache.mahout.math.decompositions._ +<div class="highlighter-rouge"><pre class="highlight"><code>import org.apache.mahout.math.decompositions._ </code></pre> +</div> <p>All arguments in the following are matricies.</p> <p><strong>Cholesky decomposition</strong></p> -<pre><code>val ch = chol(M) +<div class="highlighter-rouge"><pre class="highlight"><code>val ch = chol(M) </code></pre> +</div> <p><strong>SVD</strong></p> -<pre><code>val (U, V, s) = svd(M) +<div class="highlighter-rouge"><pre class="highlight"><code>val (U, V, s) = svd(M) </code></pre> +</div> <p><strong>EigenDecomposition</strong></p> -<pre><code>val (V, d) = eigen(M) +<div class="highlighter-rouge"><pre class="highlight"><code>val (V, d) = eigen(M) </code></pre> +</div> <p><strong>QR decomposition</strong></p> -<pre><code>val (Q, R) = qr(M) +<div class="highlighter-rouge"><pre class="highlight"><code>val (Q, R) = qr(M) </code></pre> +</div> <p><strong>Rank</strong>: Check for rank deficiency (runs rank-revealing QR)</p> -<pre><code>M.isFullRank +<div class="highlighter-rouge"><pre class="highlight"><code>M.isFullRank </code></pre> +</div> <p><strong>In-core SSVD</strong></p> -<pre><code>Val (U, V, s) = ssvd(A, k = 50, p = 15, q = 1) +<div class="highlighter-rouge"><pre class="highlight"><code>Val (U, V, s) = ssvd(A, k = 50, p = 15, q = 1) </code></pre> +</div> <p><strong>Solving linear equation systems and matrix inversion:</strong> fully similar to R semantics; there are three forms of invocation:</p> -<p>Solve <code>\(\mathbf{AX}=\mathbf{B}\)</code>:</p> +<p>Solve <code class="highlighter-rouge">\(\mathbf{AX}=\mathbf{B}\)</code>:</p> -<pre><code>solve(A, B) +<div class="highlighter-rouge"><pre class="highlight"><code>solve(A, B) </code></pre> +</div> -<p>Solve <code>\(\mathbf{Ax}=\mathbf{b}\)</code>:</p> +<p>Solve <code class="highlighter-rouge">\(\mathbf{Ax}=\mathbf{b}\)</code>:</p> -<pre><code>solve(A, b) +<div class="highlighter-rouge"><pre class="highlight"><code>solve(A, b) </code></pre> +</div> -<p>Compute <code>\(\mathbf{A^{-1}}\)</code>:</p> +<p>Compute <code class="highlighter-rouge">\(\mathbf{A^{-1}}\)</code>:</p> -<pre><code>solve(A) +<div class="highlighter-rouge"><pre class="highlight"><code>solve(A) </code></pre> +</div> <h4 id="misc">Misc</h4> <p>Vector cardinality:</p> -<pre><code>a.length +<div class="highlighter-rouge"><pre class="highlight"><code>a.length </code></pre> +</div> <p>Matrix cardinality:</p> -<pre><code>m.nrow +<div class="highlighter-rouge"><pre class="highlight"><code>m.nrow m.ncol </code></pre> +</div> <p>Means and sums:</p> -<pre><code>m.colSums +<div class="highlighter-rouge"><pre class="highlight"><code>m.colSums m.colMeans m.rowSums m.rowMeans </code></pre> +</div> <p>Copy-By-Value:</p> -<pre><code>val b = a cloned +<div class="highlighter-rouge"><pre class="highlight"><code>val b = a cloned </code></pre> +</div> <h4 id="random-matrices">Random Matrices</h4> -<p><code>\(\mathcal{U}\)</code>(0,1) random matrix view:</p> +<p><code class="highlighter-rouge">\(\mathcal{U}\)</code>(0,1) random matrix view:</p> -<pre><code>val incCoreA = Matrices.uniformView(m, n, seed) +<div class="highlighter-rouge"><pre class="highlight"><code>val incCoreA = Matrices.uniformView(m, n, seed) </code></pre> +</div> -<p><code>\(\mathcal{U}\)</code>(-1,1) random matrix view:</p> +<p><code class="highlighter-rouge">\(\mathcal{U}\)</code>(-1,1) random matrix view:</p> -<pre><code>val incCoreA = Matrices.symmetricUniformView(m, n, seed) +<div class="highlighter-rouge"><pre class="highlight"><code>val incCoreA = Matrices.symmetricUniformView(m, n, seed) </code></pre> +</div> -<p><code>\(\mathcal{N}\)</code>(-1,1) random matrix view:</p> +<p><code class="highlighter-rouge">\(\mathcal{N}\)</code>(-1,1) random matrix view:</p> -<pre><code>val incCoreA = Matrices.gaussianView(m, n, seed) +<div class="highlighter-rouge"><pre class="highlight"><code>val incCoreA = Matrices.gaussianView(m, n, seed) </code></pre> +</div> <h4 id="iterators">Iterators</h4> <p>Mahout-Math already exposes a number of iterators. Scala code just needs the following imports to enable implicit conversions to scala iterators.</p> -<pre><code>import collection._ +<div class="highlighter-rouge"><pre class="highlight"><code>import collection._ import JavaConversions._ </code></pre> +</div> <p>Iterating over rows in a Matrix:</p> -<pre><code>for (row <- m) { +<div class="highlighter-rouge"><pre class="highlight"><code>for (row <- m) { ... do something with row } </code></pre> +</div> <!--Iterating over non-zero and all elements of a vector: *Note that Vector.Element also has some implicit syntatic sugar, e.g to add 5.0 to every non-zero element of a matrix, the following code may be used:* @@ -559,34 +566,26 @@ Similarly **row.all** produces an iterator over all elements in a row (Vector). <p>For more information including information on Mahout-Samsaraâs out-of-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>
