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Link Jacobians
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AlexanderFabisch committed Sep 28, 2023
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24 changes: 24 additions & 0 deletions pytransform3d/rotations/_jacobians.py
Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,14 @@ def left_jacobian_SO3(omega):
-------
J : array, shape (3, 3)
Left Jacobian of SO(3).
See also
--------
left_jacobian_SO3_series :
Left Jacobian of SO(3) at theta from Taylor series.
left_jacobian_SO3_inv :
Inverse left Jacobian of SO(3) at theta (angle of rotation).
"""
omega = np.asarray(omega)
theta = np.linalg.norm(omega)
Expand Down Expand Up @@ -54,6 +62,10 @@ def left_jacobian_SO3_series(omega, n_terms):
-------
J : array, shape (3, 3)
Left Jacobian of SO(3).
See Also
--------
left_jacobian_SO3 : Left Jacobian of SO(3) at theta (angle of rotation).
"""
omega = np.asarray(omega)
J = np.eye(3)
Expand Down Expand Up @@ -86,6 +98,13 @@ def left_jacobian_SO3_inv(omega):
-------
J_inv : array, shape (3, 3)
Inverse left Jacobian of SO(3).
See Also
--------
left_jacobian_SO3 : Left Jacobian of SO(3) at theta (angle of rotation).
left_jacobian_SO3_inv_series :
Inverse left Jacobian of SO(3) at theta from Taylor series.
"""
omega = np.asarray(omega)
theta = np.linalg.norm(omega)
Expand Down Expand Up @@ -116,6 +135,11 @@ def left_jacobian_SO3_inv_series(omega, n_terms):
-------
J_inv : array, shape (3, 3)
Inverse left Jacobian of SO(3).
See Also
--------
left_jacobian_SO3_inv :
Inverse left Jacobian of SO(3) at theta (angle of rotation).
"""
from scipy.special import bernoulli

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22 changes: 22 additions & 0 deletions pytransform3d/transformations/_jacobians.py
Original file line number Diff line number Diff line change
Expand Up @@ -38,6 +38,13 @@ def left_jacobian_SE3(Stheta):
J : array, shape (6, 6)
Jacobian of SE(3).
See Also
--------
left_jacobian_SE3_series :
Left Jacobian of SE(3) at theta from Taylor series.
left_jacobian_SE3_inv : Left inverse Jacobian of SE(3).
References
----------
Barfoot, Furgale: Associating Uncertainty With Three-Dimensional Poses for
Expand Down Expand Up @@ -77,6 +84,10 @@ def left_jacobian_SE3_series(Stheta, n_terms):
-------
J : array, shape (3, 3)
Left Jacobian of SE(3).
See Also
--------
left_jacobian_SE3 : Left Jacobian of SE(3).
"""
Stheta = check_exponential_coordinates(Stheta)
J = np.eye(6)
Expand Down Expand Up @@ -120,6 +131,13 @@ def left_jacobian_SE3_inv(Stheta):
-------
J_inv : array, shape (6, 6)
Inverse Jacobian of SE(3).
See Also
--------
left_jacobian_SE3 : Left Jacobian of SE(3).
left_jacobian_SE3_inv_series :
Left inverse Jacobian of SE(3) at theta from Taylor series.
"""
Stheta = check_exponential_coordinates(Stheta)

Expand Down Expand Up @@ -185,6 +203,10 @@ def left_jacobian_SE3_inv_series(Stheta, n_terms):
-------
J_inv : array, shape (3, 3)
Inverse left Jacobian of SE(3).
See Also
--------
left_jacobian_SE3_inv : Left inverse Jacobian of SE(3).
"""
from scipy.special import bernoulli

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