jaxlie.manifold._deltas

Helpers for recursively applying tangent-space deltas.

Module Contents

Functions

rplus(…)	Manifold right plus. Computes T' = T @ exp(delta).
rminus(…)	Manifold right minus. Computes
rplus_jacobian_parameters_wrt_delta(transform)	Analytical Jacobians for jaxlie.manifold.rplus(), linearized around a zero

Attributes

PytreeType
GroupType

jaxlie.manifold._deltas.PytreeType

jaxlie.manifold._deltas.GroupType

jaxlie.manifold._deltas.rplus(transform: GroupType, delta: jaxlie.hints.Array) → GroupType

jaxlie.manifold._deltas.rplus(transform: PytreeType, delta: jaxlie.manifold._tree_utils.TangentPytree) → PytreeType

Manifold right plus. Computes T' = T @ exp(delta).

Supports pytrees containing Lie group instances recursively; simple Euclidean addition will be performed for all other arrays.

jaxlie.manifold._deltas.rminus(a: GroupType, b: GroupType) → jax.Array

jaxlie.manifold._deltas.rminus(a: PytreeType, b: PytreeType) → jaxlie.manifold._tree_utils.TangentPytree

Manifold right minus. Computes delta = T_ab.log() = (T_wa.inverse() @ T_wb).log().

Supports pytrees containing Lie group instances recursively; simple Euclidean subtraction will be performed for all other arrays.

jaxlie.manifold._deltas.rplus_jacobian_parameters_wrt_delta(transform)

Analytical Jacobians for jaxlie.manifold.rplus(), linearized around a zero local delta.

Mostly useful for reducing JIT compile times for tangent-space optimization.

Equivalent to –

def rplus_jacobian_parameters_wrt_delta(transform: MatrixLieGroup) -> jax.Array:
    # 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 (jaxlie.MatrixLieGroup) – Transform to linearize around.

Returns:

Jacobian. Shape should be (Group.parameters_dim, Group.tangent_dim).

Return type:

jax.Array