jaxlie.manifold
¶
Package Contents¶
Functions¶
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Manifold right minus. |
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Manifold right plus. |
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Analytical Jacobians for |
-
jaxlie.manifold.
rminus
(a: T, b: T) → types.TangentVector[source]¶ Manifold right minus.
Computes
delta = (T_wa.inverse() @ T_wb).log()
.- Parameters
a (T) –
T_wa
b (T) –
T_wb
- Returns
types.TangentVector –
T_ab.log()
-
jaxlie.manifold.
rplus
(transform: T, delta: types.TangentVector) → T[source]¶ Manifold right plus.
Computes
T_wb = T_wa @ exp(delta)
.- Parameters
transform (T) –
T_wa
delta (types.TangentVector) –
T_ab.log()
- Returns
T –
T_wb
-
jaxlie.manifold.
rplus_jacobian_parameters_wrt_delta
(transform: MatrixLieGroup) → jnp.ndarray[source]¶ Analytical Jacobians for
jaxlie.manifold.rplus()
, linearized around a zero local delta.Useful for on-manifold optimization.
Equivalent to –
def rplus_jacobian_parameters_wrt_delta(transform: MatrixLieGroup) -> jnp.ndarray: # Since transform objects are PyTree containers, note that `jacfwd` returns a # transformation object itself and that the Jacobian terms corresponding to the # parameters are grabbed explicitly. return jax.jacfwd( jaxlie.manifold.rplus, # Args are (transform, delta) argnums=1, # Jacobian wrt delta )(transform, onp.zeros(transform.tangent_dim)).parameters
- Parameters
transform (T) – transform
- Returns
jnp.ndarray – Jacobian. Shape should be
(Group.parameters_dim, Group.tangent_dim)
.