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updated doc to 0.1.1
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
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const DOCUMENTATION_OPTIONS = {
VERSION: '0.1.0',
VERSION: '0.1.1',
LANGUAGE: 'en',
COLLAPSE_INDEX: false,
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<head>
<meta charset="utf-8" />
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<title>Index &#8212; Dyson Equalizer 0.1.0 documentation</title>
<title>Index &#8212; Dyson Equalizer 0.1.1 documentation</title>



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<p class="title logo__title">Dyson Equalizer 0.1.0 documentation</p>
<p class="title logo__title">Dyson Equalizer 0.1.1 documentation</p>

</a></div>

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<meta charset="utf-8" />
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<title>Dyson Equalizer &#8212; Dyson Equalizer 0.1.0 documentation</title>
<title>Dyson Equalizer &#8212; Dyson Equalizer 0.1.1 documentation</title>



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<p class="title logo__title">Dyson Equalizer 0.1.0 documentation</p>
<p class="title logo__title">Dyson Equalizer 0.1.1 documentation</p>

</a></div>

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<p>This package is a Python implementation of the Dyson Equalizer.
The method is described in detail in the article <a class="reference external" href="https://doi.org/10.48550/arXiv.2306.11263">The Dyson Equalizer: Adaptive Noise Stabilization for Low-Rank Signal Detection and Recovery
</a></p>
<p>The documentation is available at <a class="reference external" href="https://klugerlab.github.io/DysonEqualizer">https://klugerlab.github.io/DysonEqualizer</a>.</p>
<section id="installation">
<h2>Installation<a class="headerlink" href="#installation" title="Link to this heading">#</a></h2>
<p>The main version of the package can be installed as</p>
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<head>
<meta charset="utf-8" />
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<title>Python Module Index &#8212; Dyson Equalizer 0.1.0 documentation</title>
<title>Python Module Index &#8212; Dyson Equalizer 0.1.1 documentation</title>



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<p class="title logo__title">Dyson Equalizer 0.1.0 documentation</p>
<p class="title logo__title">Dyson Equalizer 0.1.1 documentation</p>

</a></div>

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<title>dyson_equalizer.algorithm module &#8212; Dyson Equalizer 0.1.1 documentation</title>



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<p class="title logo__title">Dyson Equalizer 0.1.0 documentation</p>
<p class="title logo__title">Dyson Equalizer 0.1.1 documentation</p>

</a></div>

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<li class="nav-item current active">
<a class="nav-link nav-internal" href="dyson_equalizer.html">
API and modules
dyson_equalizer package
</a>
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<a class="nav-link nav-internal" href="dyson_equalizer.html">
API and modules
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<li class="breadcrumb-item"><a href="dyson_equalizer.html" class="nav-link">API and modules</a></li>
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<span class="sig-prename descclassname"><span class="pre">dyson_equalizer.algorithm.</span></span><span class="sig-name descname"><span class="pre">compute_low_rank_approximation_mp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">svd</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.12)"><span class="pre">tuple</span></a><span class="p"><span class="pre">[</span></span><span class="pre">array</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><span class="pre">int</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#dyson_equalizer.algorithm.compute_low_rank_approximation_mp" title="Link to this definition">#</a></dt>
<dd><p>Computes the low rank approximation by keeping all eigeinvalues above the maximum
of the Marchenko-Pastur distribution.
Details, derivation and convergence analysis are provided in <a href="#id3"><span class="problematic" id="id1">[1]_</span></a>, in particular Algorithms 2 and 3.</p>
Details, derivation and convergence analysis are provided in <a class="reference internal" href="#rab46b60d179e-1" id="id1">[1]</a>, in particular Algorithms 2 and 3.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
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<p class="rubric">Notes</p>
<p>The threshold for significance is based on the Marchenko-Pastur distribution
and is estimated as <span class="math notranslate nohighlight">\(\sqrt{m} + \sqrt{m}\)</span>, where <span class="math notranslate nohighlight">\(m \le n\)</span> are the matrix’s dimensions.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="rab46b60d179e-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>Landa B., Kluger Y., “The Dyson Equalizer: Adaptive Noise Stabilization for Low-Rank Signal
Detection and Recovery,” arXiv, <a class="reference external" href="https://arxiv.org/abs/2306.11263">https://arxiv.org/abs/2306.11263</a></p>
</div>
</div>
</dd></dl>

<dl class="py function">
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</div>
<p class="rubric">Notes</p>
<p>This function computes the normalizing factors for the Dyson equalizer.
Details, derivation and convergence analysis are provided in <a href="#id4"><span class="problematic" id="id2">[1]_</span></a>, in particular Algorithm 1.</p>
Details, derivation and convergence analysis are provided in <a class="reference internal" href="#r493b555ec528-1" id="id3">[1]</a>, in particular Algorithm 1.</p>
<p>First, it computes the solutions to the Dyson equation as</p>
<div class="math notranslate nohighlight">
\[\hat{g}_{i}^{(1)} = \sum_{k=1}^{m} \frac{\eta^2}{\sigma^2_k + \eta^2} U^2_{ik}\]</div>
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</ul>
</dd>
</dl>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r493b555ec528-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">1</a><span class="fn-bracket">]</span></span>
<p>Landa B., Kluger Y., “The Dyson Equalizer: Adaptive Noise Stabilization for Low-Rank Signal
Detection and Recovery,” arXiv, <a class="reference external" href="https://arxiv.org/abs/2306.11263">https://arxiv.org/abs/2306.11263</a></p>
</div>
</div>
</dd></dl>

<dl class="py function">
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<p class="title logo__title">Dyson Equalizer 0.1.0 documentation</p>
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<p class="title logo__title">Dyson Equalizer 0.1.0 documentation</p>
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