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<div class="title">ATAN2 Inverse Trigonometric 4-Quadrant Arctangent Function </div> </div>
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<div class="textblock"><p>Section: <a class="el" href="sec_mathfunctions.html">Mathematical Functions</a> </p>
<h1><a class="anchor" id="Usage"></a>
Usage</h1>
<p>Computes the <code>atan2</code> function for its argument. The general syntax for its use is </p>
<pre class="fragment"> z = atan2(y,x)
</pre><p> where <code>x</code> and <code>y</code> are <code>n</code>-dimensional arrays of numerical type. Integer types are promoted to the <code>double</code> type prior to calculation of the <code>atan2</code> function. The size of the output depends on the size of <code>x</code> and <code>y</code>. If <code>x</code> is a scalar, then <code>z</code> is the same size as <code>y</code>, and if <code>y</code> is a scalar, then <code>z</code> is the same size as <code>x</code>. The type of the output is equal to the type of |y/x|. </p>
<h1><a class="anchor" id="Function"></a>
Internals</h1>
<p>The function is defined (for real values) to return an angle between <code>-pi</code> and <code>pi</code>. The signs of <code>x</code> and <code>y</code> are used to find the correct quadrant for the solution. For complex arguments, the two-argument arctangent is computed via </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathrm{atan2}(y,x) \equiv -i \log\left(\frac{x+i y}{\sqrt{x^2+y^2}} \right) \]" src="form_55.png"/>
</p>
<p> For real valued arguments <code>x,y</code>, the function is computed directly using the standard C library's numerical <code>atan2</code> function. For both real and complex arguments <code>x</code>, note that generally </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathrm{atan2}(\sin(x),\cos(x)) \neq x, \]" src="form_56.png"/>
</p>
<p> due to the periodicities of <code>cos(x)</code> and <code>sin(x)</code>. </p>
<h1><a class="anchor" id="Example"></a>
Example</h1>
<p>The following code demonstates the difference between the <code>atan2</code> function and the <code>atan</code> function over the range <code>[-pi,pi]</code>.</p>
<pre class="fragment">--> x = linspace(-pi,pi);
--> sx = sin(x); cx = cos(x);
--> plot(x,atan(sx./cx),x,atan2(sx,cx))
</pre><div class="image">
<img src="atan2plot.png" alt="atan2plot.png"/>
</div>
Note how the two-argument <code>atan2</code> function (green line) correctly ``unwraps'' the phase of the angle, while the <code>atan</code> function (red line) wraps the angle to the interval <img class="formulaInl" alt="$[-\pi/2,\pi/2]$" src="form_57.png"/>. </p>
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