atan2

→Tensor

atan2(other: Tensor | Scalar, input: Tensor)

source

Element-wise quadrant-aware inverse tangent.

Computes $\arctan(y / x)$ while using the signs of y and x to pick the correct quadrant, returning a result in $(-\pi, \pi]$ . Unlike arctan, this handles all four quadrants of the plane and the special cases at the axes.

Parameters

otherTensor or scalar

The x (denominator) coordinate.

inputTensor

The y (numerator) coordinate. Broadcasts against other.

Returns

Tensor

Angles in radians in the range $(-\pi, \pi]$ , with shape broadcast(input.shape, other.shape).

Notes

Definition by cases:

\mathrm{atan2}(y, x) = \begin{cases} \arctan(y/x) & x > 0 \\ \arctan(y/x) + \pi & x < 0,\, y \ge 0 \\ \arctan(y/x) - \pi & x < 0,\, y < 0 \\ +\pi/2 & x = 0,\, y > 0 \\ -\pi/2 & x = 0,\, y < 0 \end{cases}

Useful for polar / spherical coordinate conversions. The argument order is the mathematical convention atan2(y, x).

Examples

>>> import lucid
>>> y = lucid.tensor([1.0, -1.0])
>>> x = lucid.tensor([1.0, -1.0])
>>> lucid.atan2(x, y)
Tensor([0.7854, -2.3562])