#include <utility>
#include <Eigen/Core>
#include "manifold.hpp"

Include dependency graph for lie_group.hpp:

This graph shows which files directly or indirectly include this file:

Classes
struct	traits::man< G >
	Manifold interface for LieGroup types (all LieGroups are also Manifolds). More...

Concepts
concept	LieGroup
	Class-external Lie group interface defined through the traits::lie trait class.

Functions
template<LieGroup G>
PlainObject< G >	Identity (Eigen::Index dof)
	Identity in Lie group.

template<LieGroup G> requires (Dof<G> > 0)
PlainObject< G >	Identity ()
	Identity in Lie group with static Dof.

template<LieGroup G>
PlainObject< G >	Random (Eigen::Index dof)
	Random element in Lie group.

template<LieGroup G> requires (Dof<G> > 0)
PlainObject< G >	Random ()
	Random element in Lie group with static Dof.

template<LieGroup G>
TangentMap< G >	Ad (const G &g)
	Group adjoint \( Ad_g a \coloneq (G * \hat(a) * G^{-1})^{\wedge} \).

template<LieGroup G, typename Arg >
PlainObject< G >	composition (const G &g, Arg &&a)
	Group binary composition.

template<LieGroup G, typename Arg , typename... Args>
PlainObject< G >	composition (const G &g, Arg &&a, Args &&... as)
	Group multinary composition.

template<LieGroup G>
PlainObject< G >	inverse (const G &g)
	Group inverse.

template<LieGroup G, typename Arg >
bool	isApprox (const G &g, Arg &&a, typename traits::lie< G >::Scalar eps=Eigen::NumTraits< typename traits::lie< G >::Scalar >::dummy_precision())
	Check if two group elements are approximately equal.

template<LieGroup G>
Tangent< G >	log (const G &g)
	Group logarithm.

template<LieGroup G, typename Arg >
TangentMap< G >	ad (Arg &&a)
	Lie algebra adjoint \( ad_a b = [a, b] \).

template<LieGroup G, typename Arg >
PlainObject< G >	exp (Arg &&a)
	Lie algebra exponential.

template<LieGroup G, typename Arg >
TangentMap< G >	dr_exp (Arg &&a)
	Right Jacobian of exponential map.

template<LieGroup G, typename Arg >
TangentMap< G >	dr_expinv (Arg &&a)
	Right Jacobian of exponential map inverse.

template<LieGroup G, typename Arg >
Hessian< G >	d2r_exp (Arg &&a)
	Right Hessian of exponential map.

template<LieGroup G, typename Arg >
Hessian< G >	d2r_expinv (Arg &&a)
	Right Hessian of exponential map inverse.

template<LieGroup G, typename Derived >
PlainObject< G >	lplus (const G &g, const Eigen::MatrixBase< Derived > &a)
	Left-plus.

template<LieGroup G, LieGroup Go>
Tangent< G >	lminus (const G &g1, const Go &g2)
	Left-minus.

template<LieGroup G, typename Derived >
TangentMap< G >	dl_exp (const Eigen::MatrixBase< Derived > &a)
	Left Jacobian of exponential map.

template<LieGroup G, typename Derived >
TangentMap< G >	dl_expinv (const Eigen::MatrixBase< Derived > &a)
	Left Jacobian of exponential map inverse.

template<LieGroup G, typename Derived >
Hessian< G >	d2l_exp (const Eigen::MatrixBase< Derived > &a)
	Left Hessian of exponential map.

template<LieGroup G, typename Derived >
Hessian< G >	d2l_expinv (const Eigen::MatrixBase< Derived > &a)
	Left Hessian of exponential map inverse.

Detailed Description

Internal and external LieGroup interfaces and free LieGroup functions.

Definition in file lie_group.hpp.

Function Documentation

◆ ad()

template<LieGroup G, typename Arg >

TangentMap< G > ad ( Arg && a )

inline

Lie algebra adjoint \( ad_a b = [a, b] \).

Definition at line 247 of file lie_group.hpp.

◆ Ad()

template<LieGroup G>

TangentMap< G > Ad ( const G & g )

inline

Group adjoint \( Ad_g a \coloneq (G * \hat(a) * G^{-1})^{\wedge} \).

Definition at line 186 of file lie_group.hpp.

◆ composition() [1/2]

template<LieGroup G, typename Arg >

PlainObject< G > composition	(	const G &	g,
		Arg &&	a
	)

inline

Group binary composition.

Definition at line 195 of file lie_group.hpp.

◆ composition() [2/2]

template<LieGroup G, typename Arg , typename... Args>

PlainObject< G > composition	(	const G &	g,
		Arg &&	a,
		Args &&...	as
	)

inline

Group multinary composition.

Definition at line 204 of file lie_group.hpp.

◆ d2l_exp()

template<LieGroup G, typename Derived >

Hessian< G > d2l_exp ( const Eigen::MatrixBase< Derived > & a )

inline

Left Hessian of exponential map.

Definition at line 341 of file lie_group.hpp.

◆ d2l_expinv()

template<LieGroup G, typename Derived >

Hessian< G > d2l_expinv ( const Eigen::MatrixBase< Derived > & a )

inline

Left Hessian of exponential map inverse.

Definition at line 350 of file lie_group.hpp.

◆ d2r_exp()

template<LieGroup G, typename Arg >

Hessian< G > d2r_exp ( Arg && a )

inline

Right Hessian of exponential map.

Definition at line 285 of file lie_group.hpp.

◆ d2r_expinv()

template<LieGroup G, typename Arg >

Hessian< G > d2r_expinv ( Arg && a )

inline

Right Hessian of exponential map inverse.

Definition at line 294 of file lie_group.hpp.

◆ dl_exp()

template<LieGroup G, typename Derived >

TangentMap< G > dl_exp ( const Eigen::MatrixBase< Derived > & a )

inline

Left Jacobian of exponential map.

Definition at line 323 of file lie_group.hpp.

◆ dl_expinv()

template<LieGroup G, typename Derived >

TangentMap< G > dl_expinv ( const Eigen::MatrixBase< Derived > & a )

inline

Left Jacobian of exponential map inverse.

Definition at line 332 of file lie_group.hpp.

◆ dr_exp()

template<LieGroup G, typename Arg >

TangentMap< G > dr_exp ( Arg && a )

inline

Right Jacobian of exponential map.

Definition at line 267 of file lie_group.hpp.

◆ dr_expinv()

template<LieGroup G, typename Arg >

TangentMap< G > dr_expinv ( Arg && a )

inline

Right Jacobian of exponential map inverse.

Definition at line 276 of file lie_group.hpp.

◆ exp()

template<LieGroup G, typename Arg >

PlainObject< G > exp ( Arg && a )

inline

Lie algebra exponential.

See also: log()

Definition at line 258 of file lie_group.hpp.

◆ Identity() [1/2]

template<LieGroup G>
requires (Dof<G> > 0)

PlainObject< G > Identity ( )

inline

Identity in Lie group with static Dof.

Definition at line 162 of file lie_group.hpp.

◆ Identity() [2/2]

template<LieGroup G>

PlainObject< G > Identity ( Eigen::Index dof )

inline

Identity in Lie group.

Parameters

dof	degrees of freedom

Definition at line 152 of file lie_group.hpp.

◆ inverse()

template<LieGroup G>

PlainObject< G > inverse ( const G & g )

inline

Group inverse.

Definition at line 213 of file lie_group.hpp.

◆ isApprox()

template<LieGroup G, typename Arg >

bool isApprox	(	const G &	g,
		Arg &&	a,
		typename traits::lie< G >::Scalar	eps = `Eigen::NumTraits<typename traits::lie<G>::Scalar>::dummy_precision()`
	)

inline

Check if two group elements are approximately equal.

Definition at line 222 of file lie_group.hpp.

◆ lminus()

template<LieGroup G, LieGroup Go>

Tangent< G > lminus	(	const G &	g1,
		const Go &	g2
	)

inline

Left-minus.

Definition at line 314 of file lie_group.hpp.

◆ log()

template<LieGroup G>

Tangent< G > log ( const G & g )

inline

Group logarithm.

See also: exp()

Definition at line 236 of file lie_group.hpp.

◆ lplus()

template<LieGroup G, typename Derived >

PlainObject< G > lplus	(	const G &	g,
		const Eigen::MatrixBase< Derived > &	a
	)

inline

Left-plus.

Definition at line 305 of file lie_group.hpp.

◆ Random() [1/2]

template<LieGroup G>
requires (Dof<G> > 0)

PlainObject< G > Random ( )

inline

Random element in Lie group with static Dof.

Definition at line 180 of file lie_group.hpp.

◆ Random() [2/2]

template<LieGroup G>

PlainObject< G > Random ( Eigen::Index dof )

inline

Random element in Lie group.

Parameters

dof	degrees of freedom

Definition at line 170 of file lie_group.hpp.

Classes

Concepts

Functions

Detailed Description

Function Documentation

◆ ad()

◆ Ad()

◆ composition() [1/2]

◆ composition() [2/2]

◆ d2l_exp()

◆ d2l_expinv()

◆ d2r_exp()

◆ d2r_expinv()

◆ dl_exp()

◆ dl_expinv()

◆ dr_exp()

◆ dr_expinv()

◆ exp()

◆ Identity() [1/2]

◆ Identity() [2/2]

◆ inverse()

◆ isApprox()

◆ lminus()

◆ log()

◆ lplus()

◆ Random() [1/2]

◆ Random() [2/2]