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<div class="section" id="rowmatrix">
<h1>RowMatrix<a class="headerlink" href="#rowmatrix" title="Permalink to this headline"></a></h1>
<dl class="py class">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix">
<em class="property">class </em><code class="sig-prename descclassname">pyspark.mllib.linalg.distributed.</code><code class="sig-name descname">RowMatrix</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">rows</span><span class="p">:</span> <span class="n">Union<span class="p">[</span>pyspark.rdd.RDD<span class="p">[</span><a class="reference internal" href="pyspark.mllib.linalg.Vector.html#pyspark.mllib.linalg.Vector" title="pyspark.mllib.linalg.Vector">pyspark.mllib.linalg.Vector</a><span class="p">]</span><span class="p">, </span>pyspark.sql.dataframe.DataFrame<span class="p">]</span></span></em>, <em class="sig-param"><span class="n">numRows</span><span class="p">:</span> <span class="n">int</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">numCols</span><span class="p">:</span> <span class="n">int</span> <span class="o">=</span> <span class="default_value">0</span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix" title="Permalink to this definition"></a></dt>
<dd><p>Represents a row-oriented distributed Matrix with no meaningful
row indices.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>rows</strong><span class="classifier"><a class="reference internal" href="pyspark.RDD.html#pyspark.RDD" title="pyspark.RDD"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.RDD</span></code></a> or <a class="reference internal" href="../pyspark.sql/api/pyspark.sql.DataFrame.html#pyspark.sql.DataFrame" title="pyspark.sql.DataFrame"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.sql.DataFrame</span></code></a></span></dt><dd><p>An RDD or DataFrame of vectors. If a DataFrame is provided, it must have a single
vector typed column.</p>
</dd>
<dt><strong>numRows</strong><span class="classifier">int, optional</span></dt><dd><p>Number of rows in the matrix. A non-positive
value means unknown, at which point the number
of rows will be determined by the number of
records in the <cite>rows</cite> RDD.</p>
</dd>
<dt><strong>numCols</strong><span class="classifier">int, optional</span></dt><dd><p>Number of columns in the matrix. A non-positive
value means unknown, at which point the number
of columns will be determined by the size of
the first row.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Methods</p>
<table class="longtable table autosummary">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.columnSimilarities" title="pyspark.mllib.linalg.distributed.RowMatrix.columnSimilarities"><code class="xref py py-obj docutils literal notranslate"><span class="pre">columnSimilarities</span></code></a>([threshold])</p></td>
<td><p>Compute similarities between columns of this matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeColumnSummaryStatistics" title="pyspark.mllib.linalg.distributed.RowMatrix.computeColumnSummaryStatistics"><code class="xref py py-obj docutils literal notranslate"><span class="pre">computeColumnSummaryStatistics</span></code></a>()</p></td>
<td><p>Computes column-wise summary statistics.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeCovariance" title="pyspark.mllib.linalg.distributed.RowMatrix.computeCovariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">computeCovariance</span></code></a>()</p></td>
<td><p>Computes the covariance matrix, treating each row as an observation.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeGramianMatrix" title="pyspark.mllib.linalg.distributed.RowMatrix.computeGramianMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">computeGramianMatrix</span></code></a>()</p></td>
<td><p>Computes the Gramian matrix <cite>A^T A</cite>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.computePrincipalComponents" title="pyspark.mllib.linalg.distributed.RowMatrix.computePrincipalComponents"><code class="xref py py-obj docutils literal notranslate"><span class="pre">computePrincipalComponents</span></code></a>(k)</p></td>
<td><p>Computes the k principal components of the given row matrix</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeSVD" title="pyspark.mllib.linalg.distributed.RowMatrix.computeSVD"><code class="xref py py-obj docutils literal notranslate"><span class="pre">computeSVD</span></code></a>(k[, computeU, rCond])</p></td>
<td><p>Computes the singular value decomposition of the RowMatrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.multiply" title="pyspark.mllib.linalg.distributed.RowMatrix.multiply"><code class="xref py py-obj docutils literal notranslate"><span class="pre">multiply</span></code></a>(matrix)</p></td>
<td><p>Multiply this matrix by a local dense matrix on the right.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.numCols" title="pyspark.mllib.linalg.distributed.RowMatrix.numCols"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numCols</span></code></a>()</p></td>
<td><p>Get or compute the number of cols.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.numRows" title="pyspark.mllib.linalg.distributed.RowMatrix.numRows"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numRows</span></code></a>()</p></td>
<td><p>Get or compute the number of rows.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.tallSkinnyQR" title="pyspark.mllib.linalg.distributed.RowMatrix.tallSkinnyQR"><code class="xref py py-obj docutils literal notranslate"><span class="pre">tallSkinnyQR</span></code></a>([computeQ])</p></td>
<td><p>Compute the QR decomposition of this RowMatrix.</p></td>
</tr>
</tbody>
</table>
<p class="rubric">Attributes</p>
<table class="longtable table autosummary">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix.rows" title="pyspark.mllib.linalg.distributed.RowMatrix.rows"><code class="xref py py-obj docutils literal notranslate"><span class="pre">rows</span></code></a></p></td>
<td><p>Rows of the RowMatrix stored as an RDD of vectors.</p></td>
</tr>
</tbody>
</table>
<p class="rubric">Methods Documentation</p>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.columnSimilarities">
<code class="sig-name descname">columnSimilarities</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">threshold</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.0</span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="pyspark.mllib.linalg.distributed.CoordinateMatrix.html#pyspark.mllib.linalg.distributed.CoordinateMatrix" title="pyspark.mllib.linalg.distributed.CoordinateMatrix">pyspark.mllib.linalg.distributed.CoordinateMatrix</a><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.columnSimilarities"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.columnSimilarities" title="Permalink to this definition"></a></dt>
<dd><p>Compute similarities between columns of this matrix.</p>
<p>The threshold parameter is a trade-off knob between estimate
quality and computational cost.</p>
<p>The default threshold setting of 0 guarantees deterministically
correct results, but uses the brute-force approach of computing
normalized dot products.</p>
<p>Setting the threshold to positive values uses a sampling
approach and incurs strictly less computational cost than the
brute-force approach. However the similarities computed will
be estimates.</p>
<p>The sampling guarantees relative-error correctness for those
pairs of columns that have similarity greater than the given
similarity threshold.</p>
<p>To describe the guarantee, we set some notation:</p>
<ul class="simple">
<li><p>Let A be the smallest in magnitude non-zero element of
this matrix.</p></li>
<li><p>Let B be the largest in magnitude non-zero element of
this matrix.</p></li>
<li><p>Let L be the maximum number of non-zeros per row.</p></li>
</ul>
<p>For example, for {0,1} matrices: A=B=1.
Another example, for the Netflix matrix: A=1, B=5</p>
<p>For those column pairs that are above the threshold, the
computed similarity is correct to within 20% relative error
with probability at least 1 - (0.981)^10/B^</p>
<p>The shuffle size is bounded by the <em>smaller</em> of the following
two expressions:</p>
<ul class="simple">
<li><p>O(n log(n) L / (threshold * A))</p></li>
<li><p>O(m L^2^)</p></li>
</ul>
<p>The latter is the cost of the brute-force approach, so for
non-zero thresholds, the cost is always cheaper than the
brute-force approach.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.0.0.</span></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>threshold</strong><span class="classifier">float, optional</span></dt><dd><p>Set to 0 for deterministic guaranteed
correctness. Similarities above this
threshold are estimated with the cost vs
estimate quality trade-off described above.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><a class="reference internal" href="pyspark.mllib.linalg.distributed.CoordinateMatrix.html#pyspark.mllib.linalg.distributed.CoordinateMatrix" title="pyspark.mllib.linalg.distributed.CoordinateMatrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">CoordinateMatrix</span></code></a></dt><dd><p>An n x n sparse upper-triangular CoordinateMatrix of
cosine similarities between columns of this matrix.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">sims</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">columnSimilarities</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">sims</span><span class="o">.</span><span class="n">entries</span><span class="o">.</span><span class="n">first</span><span class="p">()</span><span class="o">.</span><span class="n">value</span>
<span class="go">0.91914503...</span>
</pre></div>
</div>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.0.0.</span></p>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.computeColumnSummaryStatistics">
<code class="sig-name descname">computeColumnSummaryStatistics</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; pyspark.mllib.stat._statistics.MultivariateStatisticalSummary<a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.computeColumnSummaryStatistics"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeColumnSummaryStatistics" title="Permalink to this definition"></a></dt>
<dd><p>Computes column-wise summary statistics.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.0.0.</span></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><dl class="simple">
<dt><code class="xref py py-class docutils literal notranslate"><span class="pre">MultivariateStatisticalSummary</span></code></dt><dd><p>object containing column-wise summary statistics.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">colStats</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">computeColumnSummaryStatistics</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">colStats</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
<span class="go">array([ 2.5, 3.5, 4.5])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.computeCovariance">
<code class="sig-name descname">computeCovariance</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix">pyspark.mllib.linalg.Matrix</a><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.computeCovariance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeCovariance" title="Permalink to this definition"></a></dt>
<dd><p>Computes the covariance matrix, treating each row as an
observation.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.0.0.</span></p>
</div>
<p class="rubric">Notes</p>
<p>This cannot be computed on matrices with more than 65535 columns.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">computeCovariance</span><span class="p">()</span>
<span class="go">DenseMatrix(2, 2, [0.5, -0.5, -0.5, 0.5], 0)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.computeGramianMatrix">
<code class="sig-name descname">computeGramianMatrix</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix">pyspark.mllib.linalg.Matrix</a><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.computeGramianMatrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeGramianMatrix" title="Permalink to this definition"></a></dt>
<dd><p>Computes the Gramian matrix <cite>A^T A</cite>.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.0.0.</span></p>
</div>
<p class="rubric">Notes</p>
<p>This cannot be computed on matrices with more than 65535 columns.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">computeGramianMatrix</span><span class="p">()</span>
<span class="go">DenseMatrix(3, 3, [17.0, 22.0, 27.0, 22.0, 29.0, 36.0, 27.0, 36.0, 45.0], 0)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.computePrincipalComponents">
<code class="sig-name descname">computePrincipalComponents</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">k</span><span class="p">:</span> <span class="n">int</span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix">pyspark.mllib.linalg.Matrix</a><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.computePrincipalComponents"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.computePrincipalComponents" title="Permalink to this definition"></a></dt>
<dd><p>Computes the k principal components of the given row matrix</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.2.0.</span></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>k</strong><span class="classifier">int</span></dt><dd><p>Number of principal components to keep.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><a class="reference internal" href="pyspark.mllib.linalg.DenseMatrix.html#pyspark.mllib.linalg.DenseMatrix" title="pyspark.mllib.linalg.DenseMatrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.DenseMatrix</span></code></a></dt><dd></dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>This cannot be computed on matrices with more than 65535 columns.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rm</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Returns the two principal components of rm</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">pca</span> <span class="o">=</span> <span class="n">rm</span><span class="o">.</span><span class="n">computePrincipalComponents</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">pca</span>
<span class="go">DenseMatrix(3, 2, [-0.349, -0.6981, 0.6252, -0.2796, -0.5592, -0.7805], 0)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Transform into new dimensions with the greatest variance.</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rm</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">pca</span><span class="p">)</span><span class="o">.</span><span class="n">rows</span><span class="o">.</span><span class="n">collect</span><span class="p">()</span>
<span class="go">[DenseVector([0.1305, -3.7394]), DenseVector([-0.3642, -6.6983]), DenseVector([-4.6102, -4.9745])]</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.computeSVD">
<code class="sig-name descname">computeSVD</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">k</span><span class="p">:</span> <span class="n">int</span></em>, <em class="sig-param"><span class="n">computeU</span><span class="p">:</span> <span class="n">bool</span> <span class="o">=</span> <span class="default_value">False</span></em>, <em class="sig-param"><span class="n">rCond</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">1e-09</span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="pyspark.mllib.linalg.distributed.SingularValueDecomposition.html#pyspark.mllib.linalg.distributed.SingularValueDecomposition" title="pyspark.mllib.linalg.distributed.SingularValueDecomposition">pyspark.mllib.linalg.distributed.SingularValueDecomposition</a><span class="p">[</span><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix" title="pyspark.mllib.linalg.distributed.RowMatrix">pyspark.mllib.linalg.distributed.RowMatrix</a><span class="p">, </span><a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix">pyspark.mllib.linalg.Matrix</a><span class="p">]</span><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.computeSVD"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.computeSVD" title="Permalink to this definition"></a></dt>
<dd><p>Computes the singular value decomposition of the RowMatrix.</p>
<p>The given row matrix A of dimension (m X n) is decomposed into
U * s * V’T where</p>
<ul class="simple">
<li><p>U: (m X k) (left singular vectors) is a RowMatrix whose
columns are the eigenvectors of (A X A’)</p></li>
<li><p>s: DenseVector consisting of square root of the eigenvalues
(singular values) in descending order.</p></li>
<li><p>v: (n X k) (right singular vectors) is a Matrix whose columns
are the eigenvectors of (A’ X A)</p></li>
</ul>
<p>For more specific details on implementation, please refer
the Scala documentation.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.2.0.</span></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>k</strong><span class="classifier">int</span></dt><dd><p>Number of leading singular values to keep (<cite>0 &lt; k &lt;= n</cite>).
It might return less than k if there are numerically zero singular values
or there are not enough Ritz values converged before the maximum number of
Arnoldi update iterations is reached (in case that matrix A is ill-conditioned).</p>
</dd>
<dt><strong>computeU</strong><span class="classifier">bool, optional</span></dt><dd><p>Whether or not to compute U. If set to be
True, then U is computed by A * V * s^-1</p>
</dd>
<dt><strong>rCond</strong><span class="classifier">float, optional</span></dt><dd><p>Reciprocal condition number. All singular values
smaller than rCond * s[0] are treated as zero
where s[0] is the largest singular value.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><a class="reference internal" href="pyspark.mllib.linalg.distributed.SingularValueDecomposition.html#pyspark.mllib.linalg.distributed.SingularValueDecomposition" title="pyspark.mllib.linalg.distributed.SingularValueDecomposition"><code class="xref py py-class docutils literal notranslate"><span class="pre">SingularValueDecomposition</span></code></a></dt><dd></dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rm</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">svd_model</span> <span class="o">=</span> <span class="n">rm</span><span class="o">.</span><span class="n">computeSVD</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">svd_model</span><span class="o">.</span><span class="n">U</span><span class="o">.</span><span class="n">rows</span><span class="o">.</span><span class="n">collect</span><span class="p">()</span>
<span class="go">[DenseVector([-0.7071, 0.7071]), DenseVector([-0.7071, -0.7071])]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">svd_model</span><span class="o">.</span><span class="n">s</span>
<span class="go">DenseVector([3.4641, 3.1623])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">svd_model</span><span class="o">.</span><span class="n">V</span>
<span class="go">DenseMatrix(3, 2, [-0.4082, -0.8165, -0.4082, 0.8944, -0.4472, 0.0], 0)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.multiply">
<code class="sig-name descname">multiply</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">matrix</span><span class="p">:</span> <span class="n"><a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix">pyspark.mllib.linalg.Matrix</a></span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix" title="pyspark.mllib.linalg.distributed.RowMatrix">pyspark.mllib.linalg.distributed.RowMatrix</a><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.multiply"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.multiply" title="Permalink to this definition"></a></dt>
<dd><p>Multiply this matrix by a local dense matrix on the right.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.2.0.</span></p>
</div>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>matrix</strong><span class="classifier"><a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.Matrix</span></code></a></span></dt><dd><p>a local dense matrix whose number of rows must match the number of columns
of this matrix</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix" title="pyspark.mllib.linalg.distributed.RowMatrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">RowMatrix</span></code></a></dt><dd></dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rm</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]]))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rm</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">DenseMatrix</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</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="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">]))</span><span class="o">.</span><span class="n">rows</span><span class="o">.</span><span class="n">collect</span><span class="p">()</span>
<span class="go">[DenseVector([2.0, 3.0]), DenseVector([6.0, 11.0])]</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.numCols">
<code class="sig-name descname">numCols</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; int<a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.numCols"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.numCols" title="Permalink to this definition"></a></dt>
<dd><p>Get or compute the number of cols.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="p">())</span>
<span class="go">3</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="p">())</span>
<span class="go">6</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.numRows">
<code class="sig-name descname">numRows</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; int<a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.numRows"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.numRows" title="Permalink to this definition"></a></dt>
<dd><p>Get or compute the number of rows.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="p">())</span>
<span class="go">4</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="p">())</span>
<span class="go">7</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.tallSkinnyQR">
<code class="sig-name descname">tallSkinnyQR</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">computeQ</span><span class="p">:</span> <span class="n">bool</span> <span class="o">=</span> <span class="default_value">False</span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="pyspark.mllib.linalg.QRDecomposition.html#pyspark.mllib.linalg.QRDecomposition" title="pyspark.mllib.linalg.QRDecomposition">pyspark.mllib.linalg.QRDecomposition</a><span class="p">[</span>Optional<span class="p">[</span><a class="reference internal" href="#pyspark.mllib.linalg.distributed.RowMatrix" title="pyspark.mllib.linalg.distributed.RowMatrix">pyspark.mllib.linalg.distributed.RowMatrix</a><span class="p">]</span><span class="p">, </span><a class="reference internal" href="pyspark.mllib.linalg.Matrix.html#pyspark.mllib.linalg.Matrix" title="pyspark.mllib.linalg.Matrix">pyspark.mllib.linalg.Matrix</a><span class="p">]</span><a class="reference internal" href="../../_modules/pyspark/mllib/linalg/distributed.html#RowMatrix.tallSkinnyQR"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.tallSkinnyQR" title="Permalink to this definition"></a></dt>
<dd><p>Compute the QR decomposition of this RowMatrix.</p>
<p>The implementation is designed to optimize the QR decomposition
(factorization) for the RowMatrix of a tall and skinny shape <a class="reference internal" href="#r0c40050f2c2e-1" id="id1">[1]</a>.</p>
<dl class="citation">
<dt class="label" id="r0c40050f2c2e-1"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
<dd><p>Paul G. Constantine, David F. Gleich. “Tall and skinny QR
factorizations in MapReduce architectures”
<a class="reference external" href="https://doi.org/10.1145/1996092.1996103">https://doi.org/10.1145/1996092.1996103</a></p>
</dd>
</dl>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.0.0.</span></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>computeQ</strong><span class="classifier">bool, optional</span></dt><dd><p>whether to computeQ</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><a class="reference internal" href="pyspark.mllib.linalg.QRDecomposition.html#pyspark.mllib.linalg.QRDecomposition" title="pyspark.mllib.linalg.QRDecomposition"><code class="xref py py-class docutils literal notranslate"><span class="pre">pyspark.mllib.linalg.QRDecomposition</span></code></a></dt><dd><p>QRDecomposition(Q: RowMatrix, R: Matrix), where
Q = None if computeQ = false.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="o">-</span><span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">decomp</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">tallSkinnyQR</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Q</span> <span class="o">=</span> <span class="n">decomp</span><span class="o">.</span><span class="n">Q</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">R</span> <span class="o">=</span> <span class="n">decomp</span><span class="o">.</span><span class="n">R</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Test with absolute values</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">absQRows</span> <span class="o">=</span> <span class="n">Q</span><span class="o">.</span><span class="n">rows</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">row</span><span class="p">:</span> <span class="nb">abs</span><span class="p">(</span><span class="n">row</span><span class="o">.</span><span class="n">toArray</span><span class="p">())</span><span class="o">.</span><span class="n">tolist</span><span class="p">())</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">absQRows</span><span class="o">.</span><span class="n">collect</span><span class="p">()</span>
<span class="go">[[0.6..., 0.0], [0.8..., 0.0], [0.0, 1.0]]</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Test with absolute values</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">abs</span><span class="p">(</span><span class="n">R</span><span class="o">.</span><span class="n">toArray</span><span class="p">())</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="go">[[5.0, 10.0], [0.0, 1.0]]</span>
</pre></div>
</div>
</dd></dl>
<p class="rubric">Attributes Documentation</p>
<dl class="py attribute">
<dt id="pyspark.mllib.linalg.distributed.RowMatrix.rows">
<code class="sig-name descname">rows</code><a class="headerlink" href="#pyspark.mllib.linalg.distributed.RowMatrix.rows" title="Permalink to this definition"></a></dt>
<dd><p>Rows of the RowMatrix stored as an RDD of vectors.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]]))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">rows</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rows</span><span class="o">.</span><span class="n">first</span><span class="p">()</span>
<span class="go">DenseVector([1.0, 2.0, 3.0])</span>
</pre></div>
</div>
</dd></dl>
</dd></dl>
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