jaxtransform3d.rotations.matrix_inverse#

Invert rotation matrix.

The inverse of a rotation matrix \(\boldsymbol{R} \in SO(3)\) is its transpose \(\boldsymbol{R}^{-1} = \boldsymbol{R}^T\) because of the orthonormality constraint \(\boldsymbol{R}\boldsymbol{R}^T = \boldsymbol{I}\) (see norm_matrix()).

Parameters:

Rarray-like, shape (…, 3, 3): Rotation matrix.

Returns:

R_invarray, shape (…, 3, 3): Inverted rotation matrix.

See also

quaternion_conjugate: Inverts the rotation represented by a unit quaternion.

Examples

>>> import jax.numpy as jnp
>>> from jaxtransform3d.rotations import matrix_inverse

Inverting a single rotation matrix:

>>> matrix_inverse(jnp.eye(3))
Array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]], dtype=float32)

Inversion is inhenrently vectorized. You can easily apply it to any number of dimensions, e.g., a 1D list of rotation matrices:

>>> import jax
>>> from jaxtransform3d.rotations import matrix_from_compact_axis_angle
>>> key = jax.random.PRNGKey(42)
>>> a = jax.random.normal(key, shape=(20, 3))
>>> R = matrix_from_compact_axis_angle(a)
>>> R_inv = matrix_inverse(R)
>>> R_inv
Array([[[...]]], dtype=float32)
>>> R_inv.shape
(20, 3, 3)
>>> from jaxtransform3d.rotations import compose_matrices
>>> I = compose_matrices(R, R_inv)
>>> I[0].round(5)
Array([[...1., ...0., ...0.],
       [...0., ...1., ...0.],
       [...0., ...0., ...1.]], ...)

Or a 2D list of rotation matrices:

>>> R = R.reshape(5, 4, 3, 3)
>>> R_inv = matrix_inverse(R)
>>> R_inv
Array([[[[...]]]], dtype=float32)
>>> R_inv.shape
(5, 4, 3, 3)
>>> I = compose_matrices(R, R_inv)
>>> I[0, 0].round(5)
Array([[...1., ...0., ...0.],
       [...0., ...1., ...0.],
       [...0., ...0., ...1.]], ...)