sknano.core.math.Rz

sknano.core.math.Rz(angle, degrees=False)

Generate the $3\times3$ rotation matrix $R_z(\theta)$ for a rotation about the $z$ axis by an angle $\theta$.

Parameters:

angle : float

The rotation angle $\theta$ in radians. If the angle is given in degrees, then you must set degrees=True to correctly calculate the rotation matrix.

degrees : bool, optional

if True, then angle is converted from degrees to radians.

Returns:

ndarray

$3\times3$ rotation matrix $R_z(\theta)$ for a rotation about the $z$ axis by an angle $\theta$.

$$\begin{split}R_z = \begin{pmatrix} \cos\theta & -\sin\theta & 0\\ \sin\theta & \cos\theta & 0\\ 0 & 0 & 1 \end{pmatrix}\end{split}$$

Examples

>>> import numpy as np
>>> from sknano.core.math import Rz
>>> Rz(np.pi/4)
array([[ 0.70710678, -0.70710678,  0.        ],
       [ 0.70710678,  0.70710678,  0.        ],
       [ 0.        ,  0.        ,  1.        ]])
>>> np.alltrue(Rz(np.pi/4) == Rz(45, degrees=True))
True