Ry

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

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

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

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:

$3\times3$ rotation matrix $R_y(\theta)$ for a rotation about the $y$ axis by an angle $\theta$:

Return type:

ndarray

Examples

>>>

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