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<div class="section" id="torch-logsumexp">
<h1>torch.logsumexp<a class="headerlink" href="#torch-logsumexp" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.logsumexp">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">logsumexp</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">dim</em>, <em class="sig-param">keepdim=False</em>, <em class="sig-param">*</em>, <em class="sig-param">out=None</em><span class="sig-paren">)</span><a class="headerlink" href="#torch.logsumexp" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the log of summed exponentials of each row of the <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>
tensor in the given dimension <code class="xref py py-attr docutils literal notranslate"><span class="pre">dim</span></code>. The computation is numerically
stabilized.</p>
<p>For summation index <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span>
</span> given by <cite>dim</cite> and other indices <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>
</span>, the result is</p>
<blockquote>
<div><div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>logsumexp</mtext><mo stretchy="false">(</mo><mi>x</mi><msub><mo stretchy="false">)</mo><mi>i</mi></msub><mo>=</mo><mi>log</mi><mo></mo><munder><mo>∑</mo><mi>j</mi></munder><mi>exp</mi><mo></mo><mo stretchy="false">(</mo><msub><mi>x</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\text{logsumexp}(x)_{i} = \log \sum_j \exp(x_{ij})
</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="mord text"><span class="mord">logsumexp</span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></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:2.463782em;vertical-align:-1.413777em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8723309999999997em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.413777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">exp</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span>
</div></div></blockquote>
<p>If <code class="xref py py-attr docutils literal notranslate"><span class="pre">keepdim</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, the output tensor is of the same size
as <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> except in the dimension(s) <code class="xref py py-attr docutils literal notranslate"><span class="pre">dim</span></code> where it is of size 1.
Otherwise, <code class="xref py py-attr docutils literal notranslate"><span class="pre">dim</span></code> is squeezed (see <a class="reference internal" href="torch.squeeze.html#torch.squeeze" title="torch.squeeze"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.squeeze()</span></code></a>), resulting in the
output tensor having 1 (or <code class="docutils literal notranslate"><span class="pre">len(dim)</span></code>) fewer dimension(s).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em> or </em><em>tuple of python:ints</em>) – the dimension or dimensions to reduce.</p></li>
<li><p><strong>keepdim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.9)"><em>bool</em></a>) – whether the output tensor has <code class="xref py py-attr docutils literal notranslate"><span class="pre">dim</span></code> retained or not.</p></li>
</ul>
</dd>
<dt class="field-even">Keyword Arguments</dt>
<dd class="field-even"><p><strong>out</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em>, </em><em>optional</em>) – the output tensor.</p>
</dd>
</dl>
<dl>
<dt>Example::</dt><dd><div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">logsumexp</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="go">tensor([ 0.8442, 1.4322, 0.8711])</span>
</pre></div>
</div>
</dd>
</dl>
</dd></dl>
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