angle

→Tensor

angle(input: Tensor)

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Phase angle (argument) of each element.

Computes the polar-coordinate angle of each complex element: $\arg(z) = \arctan2(\Im(z), \Re(z))$ , in radians on the interval $[-\pi, \pi]$ . A real element is a complex number on the real axis: its angle is $\pi$ when it is negative and 0 otherwise, and NaN stays NaN.

Parameters

inputTensor

Complex or real tensor. A bool or integer one is taken at the default floating dtype.

Returns

Tensor

Real tensor with the same shape as input: float32 for complex64, float64 for complex128, a real input's own floating dtype.

Notes

Mathematical definition:

\text{out}_i = \arg(z_i) = \arctan2(\Im(z_i), \Re(z_i))

Uses quadrant-correct lucid.atan2 internally — unlike a naive arctan(imag / real), this returns the proper four-quadrant angle. Zero complex inputs yield 0.0 (not NaN).

Examples

>>> import lucid
>>> z = lucid.tensor([1+0j, 1+1j, 0+1j, -1+0j])
>>> lucid.angle(z)
tensor([0., 0.7854, 1.571, 3.142])
>>> lucid.angle(lucid.tensor([-2, 3]))
tensor([3.142, 0.])