qops.multiply()#
- RotationalDiffusion.quaternions.multiply(q1, q2)[source]#
Compute the Hamilton product (of arrays) of quaternions \(q_1\) and \(q_2\).
- Parameters:
- q1, q2(…, 4)
ndarray Input arrays to be multiplied, must be broadcastable to a common shape.
- q1, q2(…, 4)
- Returns:
- q_prod(…, 4)
ndarray The pairwise Hamilton products of quaternions in \(q_1\) and \(q_2\).
- q_prod(…, 4)
Notes
The Hamilton product[1] of two quaternions \(q_1 = w_1 + x_1 \cdot i + y_1 \cdot j + z_1 \cdot k\) and \(q_2 = w_2 + x_2 \cdot i + y_2 \cdot j + z_2 \cdot k\) is
\[\begin{split}q_1 \cdot q_2 \quad = \quad &(w_1 \cdot w_2 - x_1 \cdot x_2 - y_1 \cdot y_2 - z_1 \cdot z_2) \\ + &(w_1 \cdot x_2 + x_1 \cdot w_2 + y_1 \cdot z_2 - z_1 \cdot y_2) \cdot i \\ + &(w_1 \cdot y_2 - x_1 \cdot z_2 + y_1 \cdot w_2 + z_1 \cdot x_2) \cdot j \\ + &(w_1 \cdot z_2 + x_1 \cdot y_2 - y_1 \cdot x_2 + z_1 \cdot w_2) \cdot k .\end{split}\]References