Author: buildbot
Date: Tue Apr 14 00:16:42 2015
New Revision: 947474
Log:
Staging update by buildbot for mahout
Added:
websites/staging/mahout/trunk/content/users/environment/in-core-reference.html
Modified:
websites/staging/mahout/trunk/content/ (props changed)
Propchange: websites/staging/mahout/trunk/content/
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websites/staging/mahout/trunk/content/users/environment/in-core-reference.html
==============================================================================
---
websites/staging/mahout/trunk/content/users/environment/in-core-reference.html
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websites/staging/mahout/trunk/content/users/environment/in-core-reference.html
Tue Apr 14 00:16:42 2015
@@ -0,0 +1,611 @@
+<!DOCTYPE html>
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+ <div id="main">
+ <h2
id="mahout-samsaras-in-core-linear-algebra-dsl-reference">Mahout-Samsara's
In-Core Linear Algebra DSL Reference</h2>
+<h4 id="imports">Imports</h4>
+<p>The following imports are used to enable Mahout-Samsara's Scala DSL
bindings for in-core Linear Algebra:</p>
+<div class="codehilite"><pre><span class="n">import</span> <span
class="n">org</span><span class="p">.</span><span class="n">apache</span><span
class="p">.</span><span class="n">mahout</span><span class="p">.</span><span
class="n">math</span><span class="p">.</span><span class="n">_</span>
+<span class="n">import</span> <span class="n">scalabindings</span><span
class="p">.</span><span class="n">_</span>
+<span class="n">import</span> <span class="n">RLikeOps</span><span
class="p">.</span><span class="n">_</span>
+</pre></div>
+
+
+<h4 id="inline-initalization">Inline initalization</h4>
+<p>Dense vectors:</p>
+<div class="codehilite"><pre>val densVec1: Vector = (1.0, 1.1, 1.2)
+val denseVec2 = dvec(1, 0, 1,1 ,1,2)
+</pre></div>
+
+
+<p>Sparse vectors:</p>
+<div class="codehilite"><pre>val sparseVec1: Vector = (5 -> 1.0) :: (10
-> 2.0) :: Nil
+val sparseVec1 = svec((5 -> 1.0) :: (10 -> 2.0) :: Nil)
+</pre></div>
+
+
+<p>Inline matrix initialization, either sparse or dense, is always done row
wise. </p>
+<p>Dense matrices:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">A</span> <span class="p">=</span> <span class="n">dense</span><span
class="p">((</span>1<span class="p">,</span> 2<span class="p">,</span> 3<span
class="p">),</span> <span class="p">(</span>3<span class="p">,</span> 4<span
class="p">,</span> 5<span class="p">))</span>
+</pre></div>
+
+
+<p>Sparse matrices:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">A</span> <span class="p">=</span> <span class="n">sparse</span><span
class="p">(</span>
+ <span class="p">(</span>1<span class="p">,</span> 3<span
class="p">)</span> <span class="p">::</span> <span class="n">Nil</span><span
class="p">,</span>
+ <span class="p">(</span>0<span class="p">,</span> 2<span
class="p">)</span> <span class="p">::</span> <span class="p">(</span>1<span
class="p">,</span> 2<span class="p">.</span>5<span class="p">)</span> <span
class="p">::</span> <span class="n">Nil</span>
+ <span class="p">)</span>
+</pre></div>
+
+
+<p>Diagonal matrix with constant diagonal elements:</p>
+<div class="codehilite"><pre><span class="nb">diag</span><span
class="p">(</span>10<span class="p">,</span> 3<span class="p">.</span>5<span
class="p">)</span>
+</pre></div>
+
+
+<p>Diagonal matrix with main diagonal backed by a vector:</p>
+<div class="codehilite"><pre><span class="n">diagv</span><span
class="p">((</span>1<span class="p">,</span> 2<span class="p">,</span> 3<span
class="p">,</span> 4<span class="p">,</span> 5<span class="p">))</span>
+</pre></div>
+
+
+<p>Identity matrix:</p>
+<div class="codehilite"><pre><span class="nb">eye</span><span
class="p">(</span>10<span class="p">)</span>
+</pre></div>
+
+
+<h4 id="slicing-and-assigning">Slicing and Assigning</h4>
+<p>Getting a vector element:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">d</span> <span class="p">=</span> <span class="n">vec</span><span
class="p">(</span>5<span class="p">)</span>
+</pre></div>
+
+
+<p>Setting a vector element:</p>
+<div class="codehilite"><pre><span class="n">vec</span><span
class="p">(</span>5<span class="p">)</span> <span class="p">=</span> 3<span
class="p">.</span>0
+</pre></div>
+
+
+<p>Getting a matrix element:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">d</span> <span class="p">=</span> <span class="n">m</span><span
class="p">(</span>3<span class="p">,</span>5<span class="p">)</span>
+</pre></div>
+
+
+<p>Setting a matrix element:</p>
+<div class="codehilite"><pre><span class="n">M</span><span
class="p">(</span>3<span class="p">,</span>5<span class="p">)</span> <span
class="p">=</span> 3<span class="p">.</span>0
+</pre></div>
+
+
+<p>Getting a matrix row or column:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">rowVec</span> <span class="p">=</span> <span class="n">M</span><span
class="p">(</span>3<span class="p">,</span> <span class="p">::)</span>
+<span class="n">val</span> <span class="n">colVec</span> <span
class="p">=</span> <span class="n">M</span><span class="p">(::,</span> 3<span
class="p">)</span>
+</pre></div>
+
+
+<p>Setting a matrix row or column via vector assignment:</p>
+<div class="codehilite"><pre><span class="n">M</span><span
class="p">(</span>3<span class="p">,</span> <span class="p">::)</span> <span
class="p">:=</span> <span class="p">(</span>1<span class="p">,</span> 2<span
class="p">,</span> 3<span class="p">)</span>
+<span class="n">M</span><span class="p">(::,</span> 3<span class="p">)</span>
<span class="p">:=</span> <span class="p">(</span>1<span class="p">,</span>
2<span class="p">,</span> 3<span class="p">)</span>
+</pre></div>
+
+
+<p>Setting a subslices of a matrix row or column:</p>
+<div class="codehilite"><pre><span class="n">a</span><span
class="p">(</span>0<span class="p">,</span> 0 <span class="n">to</span> 1<span
class="p">)</span> <span class="p">=</span> <span class="p">(</span>3<span
class="p">,</span> 5<span class="p">)</span>
+</pre></div>
+
+
+<p>Setting a subslices of a matrix row or column via vector assignment:</p>
+<div class="codehilite"><pre><span class="n">a</span><span
class="p">(</span>0<span class="p">,</span> 0 <span class="n">to</span> 1<span
class="p">)</span> <span class="p">:=</span> <span class="p">(</span>3<span
class="p">,</span> 5<span class="p">)</span>
+</pre></div>
+
+
+<p>Getting a matrix as from matrix contiguous block:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">B</span> <span class="p">=</span> <span class="n">A</span><span
class="p">(</span>2 <span class="n">to</span> 3<span class="p">,</span> 3 <span
class="n">to</span> 4<span class="p">)</span>
+</pre></div>
+
+
+<p>Assigning a contiguous block to a matrix:</p>
+<div class="codehilite"><pre><span class="n">A</span><span class="p">(</span>0
<span class="n">to</span> 1<span class="p">,</span> 1 <span class="n">to</span>
2<span class="p">)</span> <span class="p">=</span> <span
class="n">dense</span><span class="p">((</span>3<span class="p">,</span> 2<span
class="p">),</span> <span class="p">(</span>3 <span class="p">,</span>3<span
class="p">))</span>
+</pre></div>
+
+
+<p>Assigning a contiguous block to a matrix using the matrix assignment
operator:</p>
+<div class="codehilite"><pre><span class="n">A</span><span
class="p">(</span><span class="n">o</span> <span class="n">to</span> 1<span
class="p">,</span> 1 <span class="n">to</span> 2<span class="p">)</span> <span
class="p">:=</span> <span class="n">dense</span><span class="p">((</span>3<span
class="p">,</span> 2<span class="p">),</span> <span class="p">(</span>3<span
class="p">,</span> 3<span class="p">))</span>
+</pre></div>
+
+
+<p>Assignment operator used for copying between vectors or matrices:</p>
+<div class="codehilite"><pre><span class="n">vec1</span> <span
class="p">:=</span> <span class="n">vec2</span>
+<span class="n">M1</span> <span class="p">:=</span> <span class="n">M2</span>
+</pre></div>
+
+
+<p>Assignment operator using assignment through a functional literal for a
matrix:</p>
+<div class="codehilite"><pre><span class="n">M</span> <span
class="p">:=</span> <span class="p">((</span><span class="n">row</span><span
class="p">,</span> <span class="n">col</span><span class="p">,</span> <span
class="n">x</span><span class="p">)</span> <span class="p">=</span><span
class="o">></span> <span class="k">if</span> <span class="p">(</span><span
class="n">row</span> <span class="o">==</span> <span class="n">col</span><span
class="p">)</span> 1 <span class="k">else</span> 0
+</pre></div>
+
+
+<p>Assignment operator using assignment through a functional literal for a
vector:</p>
+<div class="codehilite"><pre><span class="n">vec</span> <span
class="p">:=</span> <span class="p">((</span><span class="n">index</span><span
class="p">,</span> <span class="n">x</span><span class="p">)</span> <span
class="p">=</span><span class="o">></span> <span class="nb">sqrt</span><span
class="p">(</span><span class="n">x</span><span class="p">)</span>
+</pre></div>
+
+
+<h4 id="blas-like-operations">BLAS-like operations</h4>
+<p>Plus/minus either vector or numeric with assignment or not:</p>
+<div class="codehilite"><pre><span class="n">a</span> <span class="o">+</span>
<span class="n">b</span>
+<span class="n">a</span> <span class="o">-</span> <span class="n">b</span>
+<span class="n">a</span> <span class="o">+</span> 5<span class="p">.</span>0
+<span class="n">a</span> <span class="o">-</span> 5<span class="p">.</span>0
+</pre></div>
+
+
+<p>Hadamard (elementwise) product, either vector or matrix or numeric
operands:</p>
+<div class="codehilite"><pre><span class="n">a</span> <span class="o">*</span>
<span class="n">b</span>
+<span class="n">a</span> <span class="o">*</span> 0<span class="p">.</span>5
+</pre></div>
+
+
+<p>Operations with assignment:</p>
+<div class="codehilite"><pre><span class="n">a</span> <span
class="o">+</span><span class="p">=</span> <span class="n">b</span>
+<span class="n">a</span> <span class="o">-</span><span class="p">=</span>
<span class="n">b</span>
+<span class="n">a</span> <span class="o">+</span><span class="p">=</span>
5<span class="p">.</span>0
+<span class="n">a</span> <span class="o">-</span><span class="p">=</span>
5<span class="p">.</span>0
+<span class="n">a</span> <span class="o">*</span><span class="p">=</span>
<span class="n">b</span>
+<span class="n">a</span> <span class="o">*</span><span class="p">=</span> 5
+</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>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">xInv</span> <span class="p">=</span> 1 <span class="o">/</span><span
class="p">:</span> <span class="n">x</span>
+</pre></div>
+
+
+<p>and R's 5.0 - x would be:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">x1</span> <span class="p">=</span> 5<span class="p">.</span>0 <span
class="o">-</span><span class="p">:</span> <span class="n">x</span>
+</pre></div>
+
+
+<p><em>note: All assignment operations, including :=, return the assignee just
like in C++</em>:</p>
+<div class="codehilite"><pre><span class="n">a</span> <span
class="o">-</span><span class="p">=</span> <span class="n">b</span>
+</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>
+<div class="codehilite"><pre><span class="n">a</span> <span
class="nb">dot</span> <span class="n">b</span>
+</pre></div>
+
+
+<p>Matrix and vector equivalency (or non-equivalency). *Dangerous, exact
equivalence is rarely useful, better to use norm comparisons with an allowance
of small errors.</p>
+<div class="codehilite"><pre><span class="n">a</span> <span
class="o">==</span><span class="p">=</span> <span class="n">b</span>
+<span class="n">a</span> !<span class="o">==</span> <span class="n">b</span>
+</pre></div>
+
+
+<p>Matrix multiply: </p>
+<div class="codehilite"><pre><span class="n">a</span> <span class="c">%*%
b</span>
+</pre></div>
+
+
+<p>Optimized Right Multiply with a diagonal matrix: </p>
+<div class="codehilite"><pre><span class="nb">diag</span><span
class="p">(</span>5<span class="p">,</span> 5<span class="p">)</span> <span
class="p">:</span><span class="c">%*% b</span>
+</pre></div>
+
+
+<p>Optimized Left Multiply with a diagonal matrix:</p>
+<div class="codehilite"><pre><span class="n">A</span> <span class="c">%*%:
diag(5, 5)</span>
+</pre></div>
+
+
+<p>Second norm, of a vector or matrix:</p>
+<div class="codehilite"><pre><span class="n">a</span><span
class="p">.</span><span class="n">norm</span>
+</pre></div>
+
+
+<p>Transpose:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">Mt</span> <span class="p">=</span> <span class="n">M</span><span
class="p">.</span><span class="n">t</span>
+</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>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">XtX</span> <span class="p">=</span> <span class="n">X</span><span
class="p">.</span><span class="n">t</span> <span class="c">%*% X</span>
+</pre></div>
+
+
+<p>will not therefore incur any additional data copying.</p>
+<h4 id="decompositions">Decompositions</h4>
+<p>All arguments in the following are matricies.</p>
+<p><strong>Cholesky decomposition</strong></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">ch</span> <span class="p">=</span> <span class="n">chol</span><span
class="p">(</span><span class="n">M</span><span class="p">)</span>
+</pre></div>
+
+
+<p><strong>SVD</strong></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="p">(</span><span class="n">U</span><span class="p">,</span> <span
class="n">V</span><span class="p">,</span> <span class="n">s</span><span
class="p">)</span> <span class="p">=</span> <span class="n">svd</span><span
class="p">(</span><span class="n">M</span><span class="p">)</span>
+</pre></div>
+
+
+<p><strong>EigenDecomposition</strong></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="p">(</span><span class="n">Q</span><span class="p">,</span> <span
class="n">R</span><span class="p">)</span> <span class="p">=</span> <span
class="n">eigen</span><span class="p">(</span><span class="n">M</span><span
class="p">)</span>
+</pre></div>
+
+
+<p><strong>QR decomposition</strong></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="p">(</span><span class="n">Q</span><span class="p">,</span> <span
class="n">R</span><span class="p">)</span> <span class="p">=</span> <span
class="n">qr</span><span class="p">(</span><span class="n">M</span><span
class="p">)</span>
+</pre></div>
+
+
+<p><strong>Rank</strong>: Check for rank deficiency (runs rank-revealing
QR)</p>
+<div class="codehilite"><pre><span class="n">M</span><span
class="p">.</span><span class="n">isFullRank</span>
+</pre></div>
+
+
+<p><strong>In-core SSVD</strong></p>
+<div class="codehilite"><pre><span class="n">Val</span> <span
class="p">(</span><span class="n">U</span><span class="p">,</span> <span
class="n">V</span><span class="p">,</span> <span class="n">s</span><span
class="p">)</span> <span class="p">=</span> <span class="n">ssvd</span><span
class="p">(</span><span class="n">A</span><span class="p">,</span> <span
class="n">k</span> <span class="p">=</span> 50<span class="p">,</span> <span
class="n">p</span> <span class="p">=</span> 15<span class="p">,</span> <span
class="n">q</span> <span class="p">=</span> 1<span class="p">)</span>
+</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>
+<div class="codehilite"><pre><span class="n">solve</span><span
class="p">(</span><span class="n">A</span><span class="p">,</span> <span
class="n">B</span><span class="p">)</span>
+</pre></div>
+
+
+<p>Solve <code>\(\mathbf{Ax}=\mathbf{b}\)</code>:</p>
+<div class="codehilite"><pre><span class="n">solve</span><span
class="p">(</span><span class="n">A</span><span class="p">,</span> <span
class="n">b</span><span class="p">)</span>
+</pre></div>
+
+
+<p>Compute <code>\(\mathbf{A^{-1}}\)</code>:</p>
+<div class="codehilite"><pre><span class="n">solve</span><span
class="p">(</span><span class="n">A</span><span class="p">)</span>
+</pre></div>
+
+
+<h4 id="misc">Misc</h4>
+<p>Vector cardinality:</p>
+<div class="codehilite"><pre><span class="n">a</span><span
class="p">.</span><span class="nb">length</span>
+</pre></div>
+
+
+<p>Matrix cardinality:</p>
+<div class="codehilite"><pre><span class="n">m</span><span
class="p">.</span><span class="n">nrow</span>
+<span class="n">m</span><span class="p">.</span><span class="n">ncol</span>
+</pre></div>
+
+
+<p>Means and sums:</p>
+<div class="codehilite"><pre><span class="n">m</span><span
class="p">.</span><span class="n">colSums</span>
+<span class="n">m</span><span class="p">.</span><span class="n">colMeans</span>
+<span class="n">m</span><span class="p">.</span><span class="n">rowSums</span>
+<span class="n">m</span><span class="p">.</span><span class="n">rowMeans</span>
+</pre></div>
+
+
+<p>Copy-By-Value:</p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">b</span> <span class="p">=</span> <span class="n">a</span> <span
class="n">cloned</span>
+</pre></div>
+
+
+<h4 id="random-matrices">Random Matrices</h4>
+<p><code>\(\mathcal{U}\)</code><em>(0,1) random matrix view</em></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">incCoreA</span> <span class="p">=</span> <span
class="n">Matrices</span><span class="p">.</span><span
class="n">uniformView</span><span class="p">(</span><span
class="n">m</span><span class="p">,</span> <span class="n">n</span><span
class="p">,</span> <span class="n">seed</span><span class="p">)</span>
+</pre></div>
+
+
+<p><code>\(\mathcal{U}\)</code><em>(-1,1) random matrix view</em></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">incCoreA</span> <span class="p">=</span> <span
class="n">Matrices</span><span class="p">.</span><span
class="n">symmetricUniformView</span><span class="p">(</span><span
class="n">m</span><span class="p">,</span> <span class="n">n</span><span
class="p">,</span> <span class="n">seed</span><span class="p">)</span>
+</pre></div>
+
+
+<p><code>\(\mathcal{N}\)</code><em>(-1,1) random matrix view</em></p>
+<div class="codehilite"><pre><span class="n">val</span> <span
class="n">incCoreA</span> <span class="p">=</span> <span
class="n">Matrices</span><span class="p">.</span><span
class="n">gaussianView</span><span class="p">(</span><span
class="n">m</span><span class="p">,</span> <span class="n">n</span><span
class="p">,</span> <span class="n">seed</span><span class="p">)</span>
+</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>
+<div class="codehilite"><pre><span class="n">import</span> <span
class="n">collection</span><span class="p">.</span><span class="n">_</span>
+<span class="n">import</span> <span class="n">JavaConversions</span><span
class="p">.</span><span class="n">_</span>
+</pre></div>
+
+
+<p>Iterating over rows in a Matrix:</p>
+<div class="codehilite"><pre><span class="kr">for</span> <span
class="p">(</span>row <span class="o"><-</span> m<span class="p">)</span>
<span class="p">{</span>
+ <span class="m">...</span> do something with row
+<span class="p">}</span>
+</pre></div>
+
+
+<p>Iterating over non-zero and all elements of a vector:
+<em>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:</em></p>
+<div class="codehilite"><pre><span class="kr">for</span> <span
class="p">(</span>row <span class="o"><-</span> m<span class="p">;</span> el
<span class="o"><-</span> row.nonZero<span class="p">)</span> el <span
class="o">=</span> <span class="m">5.0</span> <span class="o">+</span> el
+<span class="m">...</span> or
+<span class="kr">for</span> <span class="p">(</span>row <span
class="o"><-</span> m<span class="p">;</span> el <span
class="o"><-</span> row.nonZero<span class="p">)</span> el :<span
class="o">=</span> <span class="m">5.0</span> <span class="o">+</span> el
+</pre></div>
+
+
+<p>Similarly <strong>row.all</strong> produces an iterator over all elements
in a row (Vector).</p>
+<p>For more information including information on Mahout-Samsara's 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>
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