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<section id="numpy-atan2">
<h1>numpy.atan2<a class="headerlink" href="#numpy-atan2" title="Link to this heading">#</a></h1>
<dl class="py data">
<dt class="sig sig-object py" id="numpy.atan2">
<span class="sig-prename descclassname"><span class="pre">numpy.</span></span><span class="sig-name descname"><span class="pre">atan2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x2</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">'arctan2'></span></em><a class="headerlink" href="#numpy.atan2" title="Link to this definition">#</a></dt>
<dd><p>Element-wise arc tangent of <code class="docutils literal notranslate"><span class="pre">x1/x2</span></code> choosing the quadrant correctly.</p>
<p>The quadrant (i.e., branch) is chosen so that <code class="docutils literal notranslate"><span class="pre">arctan2(x1,</span> <span class="pre">x2)</span></code> is
the signed angle in radians between the ray ending at the origin and
passing through the point (1,0), and the ray ending at the origin and
passing through the point (<em class="xref py py-obj">x2</em>, <em class="xref py py-obj">x1</em>). (Note the role reversal: the
“<em class="xref py py-obj">y</em>-coordinate” is the first function parameter, the “<em class="xref py py-obj">x</em>-coordinate”
is the second.) By IEEE convention, this function is defined for
<em class="xref py py-obj">x2</em> = +/-0 and for either or both of <em class="xref py py-obj">x1</em> and <em class="xref py py-obj">x2</em> = +/-inf (see
Notes for specific values).</p>
<p>This function is not defined for complex-valued arguments; for the
so-called argument of complex values, use <a class="reference internal" href="numpy.angle.html#numpy.angle" title="numpy.angle"><code class="xref py py-obj docutils literal notranslate"><span class="pre">angle</span></code></a>.</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>x1</strong><span class="classifier">array_like, real-valued</span></dt><dd><p><em class="xref py py-obj">y</em>-coordinates.</p>
</dd>
<dt><strong>x2</strong><span class="classifier">array_like, real-valued</span></dt><dd><p><em class="xref py py-obj">x</em>-coordinates.
If <code class="docutils literal notranslate"><span class="pre">x1.shape</span> <span class="pre">!=</span> <span class="pre">x2.shape</span></code>, they must be broadcastable to a common
shape (which becomes the shape of the output).</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>angle</strong><span class="classifier">ndarray</span></dt><dd><p>Array of angles in radians, in the range <code class="docutils literal notranslate"><span class="pre">[-pi,</span> <span class="pre">pi]</span></code>.
This is a scalar if both <em class="xref py py-obj">x1</em> and <em class="xref py py-obj">x2</em> are scalars.</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.arctan.html#numpy.arctan" title="numpy.arctan"><code class="xref py py-obj docutils literal notranslate"><span class="pre">arctan</span></code></a>, <a class="reference internal" href="numpy.tan.html#numpy.tan" title="numpy.tan"><code class="xref py py-obj docutils literal notranslate"><span class="pre">tan</span></code></a>, <a class="reference internal" href="numpy.angle.html#numpy.angle" title="numpy.angle"><code class="xref py py-obj docutils literal notranslate"><span class="pre">angle</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p><em>arctan2</em> is identical to the <a class="reference internal" href="#numpy.atan2" title="numpy.atan2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">atan2</span></code></a> function of the underlying
C library. The following special values are defined in the C
standard: <a class="reference internal" href="#r20c8bad59052-1" id="id1">[1]</a></p>
<div class="pst-scrollable-table-container"><table class="table">
<thead>
<tr class="row-odd"><th class="head"><p><em class="xref py py-obj">x1</em></p></th>
<th class="head"><p><em class="xref py py-obj">x2</em></p></th>
<th class="head"><p><em class="xref py py-obj">arctan2(x1,x2)</em></p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>+/- 0</p></td>
<td><p>+0</p></td>
<td><p>+/- 0</p></td>
</tr>
<tr class="row-odd"><td><p>+/- 0</p></td>
<td><p>-0</p></td>
<td><p>+/- pi</p></td>
</tr>
<tr class="row-even"><td><p>> 0</p></td>
<td><p>+/-inf</p></td>
<td><p>+0 / +pi</p></td>
</tr>
<tr class="row-odd"><td><p>< 0</p></td>
<td><p>+/-inf</p></td>
<td><p>-0 / -pi</p></td>
</tr>
<tr class="row-even"><td><p>+/-inf</p></td>
<td><p>+inf</p></td>
<td><p>+/- (pi/4)</p></td>
</tr>
<tr class="row-odd"><td><p>+/-inf</p></td>
<td><p>-inf</p></td>
<td><p>+/- (3*pi/4)</p></td>
</tr>
</tbody>
</table>
</div>
<p>Note that +0 and -0 are distinct floating point numbers, as are +inf
and -inf.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r20c8bad59052-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>ISO/IEC standard 9899:1999, “Programming language C.”</p>
</div>
</div>
<p class="rubric">Examples</p>
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<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('db01b574-9899-42ca-b3a5-4f3d5b1a8618','09b3bd3d-50b2-4f29-8f79-7e6023e832b2','58290312-7859-4266-b54d-8ba6c32f543d','../../lite/tree/../notebooks/index.html?path=25587a03_53c9_407e_8a27_ad9b8a45af36.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<p>Consider four points in different quadrants:</p>
<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">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="o">+</span><span class="mi">1</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">*</span> <span class="mi">180</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
<span class="go">array([-135., -45., 45., 135.])</span>
</pre></div>
</div>
<p>Note the order of the parameters. <a class="reference internal" href="numpy.arctan2.html#numpy.arctan2" title="numpy.arctan2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">arctan2</span></code></a> is defined also when <em class="xref py py-obj">x2</em> = 0
and at several other special points, obtaining values in
the range <code class="docutils literal notranslate"><span class="pre">[-pi,</span> <span class="pre">pi]</span></code>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">])</span>
<span class="go">array([ 1.57079633, -1.57079633])</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">([</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">],</span> <span class="p">[</span><span class="o">+</span><span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">])</span>
<span class="go">array([0. , 3.14159265, 0.78539816])</span>
</pre></div>
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