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<h1>torch.svd_lowrank<a class="headerlink" href="#torch-svd-lowrank" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.svd_lowrank">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">svd_lowrank</code><span class="sig-paren">(</span><em class="sig-param">A</em>, <em class="sig-param">q=6</em>, <em class="sig-param">niter=2</em>, <em class="sig-param">M=None</em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/torch/_lowrank.html#svd_lowrank"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.svd_lowrank" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the singular value decomposition <code class="docutils literal notranslate"><span class="pre">(U,</span> <span class="pre">S,</span> <span class="pre">V)</span></code> of a matrix,
batches of matrices, or a sparse matrix <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span></span></span></span>
</span> such that
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>≈</mo><mi>U</mi><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo><msup><mi>V</mi><mi>T</mi></msup></mrow><annotation encoding="application/x-tex">A \approx U diag(S) V^T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mord mathnormal">d</span><span class="mord mathnormal">i</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mclose">)</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span></span></span></span>
</span>. In case <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span>
</span> is given, then
SVD is computed for the matrix <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>−</mo><mi>M</mi></mrow><annotation encoding="application/x-tex">A - M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span>
</span>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The implementation is based on the Algorithm 5.1 from
Halko et al, 2009.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>To obtain repeatable results, reset the seed for the
pseudorandom number generator</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The input is assumed to be a low-rank matrix.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>In general, use the full-rank SVD implementation
<code class="docutils literal notranslate"><span class="pre">torch.svd</span></code> for dense matrices due to its 10-fold
higher performance characteristics. The low-rank SVD
will be useful for huge sparse matrices that
<code class="docutils literal notranslate"><span class="pre">torch.svd</span></code> cannot handle.</p>
</div>
<dl>
<dt>Arguments::</dt><dd><p>A (Tensor): the input tensor of size <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>∗</mo><mo separator="true">,</mo><mi>m</mi><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(*, m, n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">∗</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>
</span></p>
<p>q (int, optional): a slightly overestimated rank of A.</p>
<dl class="simple">
<dt>niter (int, optional): the number of subspace iterations to</dt><dd><p>conduct; niter must be a nonnegative
integer, and defaults to 2</p>
</dd>
<dt>M (Tensor, optional): the input tensor’s mean of size</dt><dd><p><span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>∗</mo><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(*, 1, n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">∗</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>
</span>.</p>
</dd>
</dl>
</dd>
<dt>References::</dt><dd><ul class="simple">
<li><p>Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp, Finding
structure with randomness: probabilistic algorithms for
constructing approximate matrix decompositions,
arXiv:0909.4061 [math.NA; math.PR], 2009 (available at
<a class="reference external" href="https://arxiv.org/abs/0909.4061">arXiv</a>).</p></li>
</ul>
</dd>
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