`Atan2`#

Description#

Two-argument inverse tangent: the signed angle of the point (x, y) from the positive x-axis, in the range \((-\pi, \pi]\). The argument order matches numpy.arctan2: y first, x second.

This is a 2-input, 1-output function (FunctorBase<_, 2, 1>). Inputs are paired column-by-column for arrays.

Unlike Atan, Atan2 returns the correct quadrant because it sees both x and y separately. Atan(y / x) collapses two cases that Atan2(y, x) keeps distinct.

Equation:

\[ \theta[t] = \operatorname{atan2}(y[t], x[t]) \]

Parameters: Atan2 takes no parameters.

NaN handling: A NaN in either input produces a NaN output.

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np
from screamer import Atan2

Atan2()(1.0,  0.0)             # +pi/2  (point on +y axis)
Atan2()(-1.0, 0.0)             # -pi/2  (point on -y axis)
Atan2()(0.0, -1.0)             # +pi    (point on -x axis)

# Two parallel arrays - wind direction from u/v components
ux = np.random.randn(100)
uy = np.random.randn(100)
direction = Atan2()(uy, ux)

Reference#

Equivalent to numpy.arctan2. Also returned as the angular component of Cart2Polar.

Atan2#