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<span class="k">def</span><span class="w"> </span><span class="nf">trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
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<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s2">&quot;...ii&quot;</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span></div>
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<span class="k">def</span><span class="w"> </span><span class="nf">exp_bures</span><span class="p">(</span><span class="n">Sigma</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">nx</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
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<span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
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<span class="sd"> Exponential map in Bures-Wasserstein space at Sigma:</span>
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<span class="sd"> .. math::</span>
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<span class="sd"> \exp_\Sigma(S) = (I_d+S)\Sigma(I_d+S).</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> Sigma : array-like (d,d)</span>
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<span class="sd"> SPD matrix</span>
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<span class="sd"> Symmetric matrix</span>
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<span class="sd"> The numerical backend module to use. If not provided, the backend will</span>
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<span class="sd"> be fetched from the input matrices `Sigma, S`.</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> P : array-like (d,d)</span>
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<span class="sd"> SPD matrix obtained as the exponential map of S at Sigma</span>
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<span class="sd"> &quot;&quot;&quot;</span>
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<span class="n">d</span> <span class="o">=</span> <span class="n">S</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<span class="n">Id</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">type_as</span><span class="o">=</span><span class="n">S</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">nx</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s2">&quot;ij,jk,kl -&gt; il&quot;</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">Sigma</span><span class="p">,</span> <span class="n">C</span><span class="p">)</span></div>
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<div class="viewcode-block" id="check_number_threads">
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<a class="viewcode-back" href="../../gen_modules/ot.utils.html#ot.check_number_threads">[docs]</a>
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<span class="k">def</span><span class="w"> </span><span class="nf">check_number_threads</span><span class="p">(</span><span class="n">numThreads</span><span class="p">):</span>

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