FreeMat: ATAN2 Inverse Trigonometric 4-Quadrant Arctangent Function

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ATAN2 Inverse Trigonometric 4-Quadrant Arctangent Function

Section: Mathematical Functions

# Usage

Computes the `atan2` function for its argument. The general syntax for its use is

      z = atan2(y,x)

where `x` and `y` are `n`-dimensional arrays of numerical type. Integer types are promoted to the `double` type prior to calculation of the `atan2` function. The size of the output depends on the size of `x` and `y`. If `x` is a scalar, then `z` is the same size as `y`, and if `y` is a scalar, then `z` is the same size as `x`. The type of the output is equal to the type of |y/x|.

# Internals

The function is defined (for real values) to return an angle between `-pi` and `pi`. The signs of `x` and `y` are used to find the correct quadrant for the solution. For complex arguments, the two-argument arctangent is computed via

For real valued arguments `x,y`, the function is computed directly using the standard C library's numerical `atan2` function. For both real and complex arguments `x`, note that generally

due to the periodicities of `cos(x)` and `sin(x)`.

# Example

The following code demonstates the difference between the `atan2` function and the `atan` function over the range `[-pi,pi]`.

    --> x = linspace(-pi,pi);
    --> sx = sin(x); cx = cos(x);
    --> plot(x,atan(sx./cx),x,atan2(sx,cx))

Note how the two-argument `atan2` function (green line) correctly ``unwraps'' the phase of the angle, while the `atan` function (red line) wraps the angle to the interval .