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<div class="section" id="torch-digamma">
<h1>torch.digamma<a class="headerlink" href="#torch-digamma" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.digamma">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">digamma</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">out=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.digamma" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the logarithmic derivative of the gamma function on <cite>input</cite>.</p>
<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><mi>ψ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mi>d</mi><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mi>ln</mi><mo></mo><mrow><mo fence="true">(</mo><mi mathvariant="normal">Γ</mi><mrow><mo fence="true">(</mo><mi>x</mi><mo fence="true">)</mo></mrow><mo fence="true">)</mo></mrow><mo>=</mo><mfrac><mrow><msup><mi mathvariant="normal">Γ</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\psi(x) = \frac{d}{dx} \ln\left(\Gamma\left(x\right)\right) = \frac{\Gamma'(x)}{\Gamma(x)}
</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 mathnormal" style="margin-right:0.03588em;">ψ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</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:2.05744em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">ln</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">Γ</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord mathnormal">x</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="mclose delimcenter" style="top:0em;">)</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:2.364892em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">Γ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord">Γ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><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 mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>
</div><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>input</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the tensor to compute the digamma function on</p>
</dd>
</dl>
<p>Example:</p>
<div class="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">tensor</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">digamma</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">tensor([-0.5772, -1.9635])</span>
</pre></div>
</div>
</dd></dl>
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