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<li class="toctree-l3"><a class="reference internal" href="#riecovest.covariance_estimation.est_covariance_manifold"><code class="docutils literal notranslate"><span class="pre">est_covariance_manifold()</span></code></a></li>
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<section id="riecovest-covariance-estimation-est-covariance-manifold">
<h1>riecovest.covariance_estimation.est_covariance_manifold<a class="headerlink" href="#riecovest-covariance-estimation-est-covariance-manifold" title="Link to this heading"></a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="riecovest.covariance_estimation.est_covariance_manifold">
<span class="sig-prename descclassname"><span class="pre">riecovest.covariance_estimation.</span></span><span class="sig-name descname"><span class="pre">est_covariance_manifold</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ambient_dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cost</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">manifold</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start_value</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#riecovest.covariance_estimation.est_covariance_manifold" title="Link to this definition"></a></dt>
<dd><p>Generic function for estimating a signal and noise covariance matrix on a Riemannian manifold.</p>
<p>Assumes that the signal covariance matrix is low-rank and the noise covariance matrix is full-rank. Specifically that
the signal covariance matrix is returned in the form of X, where R_x = X &#64; X^H.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>ambient_dim</strong> (<em>int</em>) – Dimension of the covariance matrices.</p></li>
<li><p><strong>rank</strong> (<em>int</em>) – Rank of the signal covariance matrix.</p></li>
<li><p><strong>cost</strong> (<em>function</em>) – Cost function to minimize. Must be compatible with pymanopt.function.jax.</p></li>
<li><p><strong>manifold</strong> – Riemannian manifold to optimize over. Must be compatible with pymanopt.manifolds.</p></li>
<li><p><strong>start_value</strong> (<em>tuple</em><em> of </em><em>ndarrays</em><em>, </em><em>optional</em>) – Initial value for the optimization. If None, the optimization starts from a random point.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>Rx</strong> (<em>ndarray of shape (ambient_dim, ambient_dim)</em>) – Estimated signal covariance matrix.</p></li>
<li><p><strong>Rv</strong> (<em>ndarray of shape (ambient_dim, ambient_dim)</em>) – Estimated noise covariance matrix.</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>

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