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<section id="numpy-atanh">
<h1>numpy.atanh<a class="headerlink" href="#numpy-atanh" title="Link to this heading">#</a></h1>
<dl class="py data">
<dt class="sig sig-object py" id="numpy.atanh">
<span class="sig-prename descclassname"><span class="pre">numpy.</span></span><span class="sig-name descname"><span class="pre">atanh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">/</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">where=True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">casting='same_kind'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order='K'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">subok=True</span></span></em><span class="optional">[</span>, <em class="sig-param"><span class="n"><span class="pre">signature</span></span></em><span class="optional">]</span><span class="sig-paren">)</span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre"><ufunc</span> <span class="pre">'arctanh'></span></em><a class="headerlink" href="#numpy.atanh" title="Link to this definition">#</a></dt>
<dd><p>Inverse hyperbolic tangent element-wise.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>x</strong><span class="classifier">array_like</span></dt><dd><p>Input array.</p>
</dd>
<dt><strong>out</strong><span class="classifier">ndarray, None, or tuple of ndarray and None, optional</span></dt><dd><p>A location into which the result is stored. If provided, it must have
a shape that the inputs broadcast to. If not provided or None,
a freshly-allocated array is returned. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.</p>
</dd>
<dt><strong>where</strong><span class="classifier">array_like, optional</span></dt><dd><p>This condition is broadcast over the input. At locations where the
condition is True, the <em class="xref py py-obj">out</em> array will be set to the ufunc result.
Elsewhere, the <em class="xref py py-obj">out</em> array will retain its original value.
Note that if an uninitialized <em class="xref py py-obj">out</em> array is created via the default
<code class="docutils literal notranslate"><span class="pre">out=None</span></code>, locations within it where the condition is False will
remain uninitialized.</p>
</dd>
<dt><strong>**kwargs</strong></dt><dd><p>For other keyword-only arguments, see the
<a class="reference internal" href="../ufuncs.html#ufuncs-kwargs"><span class="std std-ref">ufunc docs</span></a>.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Array of the same shape as <em class="xref py py-obj">x</em>.
This is a scalar if <em class="xref py py-obj">x</em> is a scalar.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.emath.arctanh.html#numpy.emath.arctanh" title="numpy.emath.arctanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">emath.arctanh</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p><a class="reference internal" href="numpy.arctanh.html#numpy.arctanh" title="numpy.arctanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">arctanh</span></code></a> is a multivalued function: for each <em class="xref py py-obj">x</em> there are infinitely
many numbers <em class="xref py py-obj">z</em> such that <code class="docutils literal notranslate"><span class="pre">tanh(z)</span> <span class="pre">=</span> <span class="pre">x</span></code>. The convention is to return
the <em class="xref py py-obj">z</em> whose imaginary part lies in <em class="xref py py-obj">[-pi/2, pi/2]</em>.</p>
<p>For real-valued input data types, <a class="reference internal" href="numpy.arctanh.html#numpy.arctanh" title="numpy.arctanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">arctanh</span></code></a> always returns real output.
For each value that cannot be expressed as a real number or infinity,
it yields <code class="docutils literal notranslate"><span class="pre">nan</span></code> and sets the <em class="xref py py-obj">invalid</em> floating point error flag.</p>
<p>For complex-valued input, <a class="reference internal" href="numpy.arctanh.html#numpy.arctanh" title="numpy.arctanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">arctanh</span></code></a> is a complex analytical function
that has branch cuts <em class="xref py py-obj">[-1, -inf]</em> and <em class="xref py py-obj">[1, inf]</em> and is continuous from
above on the former and from below on the latter.</p>
<p>The inverse hyperbolic tangent is also known as <a class="reference internal" href="#numpy.atanh" title="numpy.atanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">atanh</span></code></a> or <code class="docutils literal notranslate"><span class="pre">tanh^-1</span></code>.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="rf5e3e797e6cd-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”,
10th printing, 1964, pp. 86.
<a class="reference external" href="https://personal.math.ubc.ca/~cbm/aands/page_86.htm">https://personal.math.ubc.ca/~cbm/aands/page_86.htm</a></p>
</div>
<div class="citation" id="rf5e3e797e6cd-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Inverse hyperbolic function”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Arctanh">https://en.wikipedia.org/wiki/Arctanh</a></p>
</div>
</div>
<p class="rubric">Examples</p>
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<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">arctanh</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">])</span>
<span class="go">array([ 0. , -0.54930614])</span>
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