Detailed Description

template<typename G>
class gtsam::TangentLieGroup< G >

Tangent Lie group TG = G ⋉ 𝔤, with dimension 2 dim(G).

Elements are pairs (g,v), with product (g1,v1)(g2,v2) = (g1 g2, v1 + Ad_g1 v2). This dedicated class exposes the tangent structure directly, allowing its repeated-block Jacobians and adjoints to be assembled without a generic semidirect-action layer. Standard Lie-group operations and their Jacobians are inherited from LieGroup; this class supplies the tangent-group law, charts, adjoints, and specialized kernels.

Inheritance diagram for gtsam::TangentLieGroup< G >:

Public Member Functions
	TangentLieGroup (const G &g, const BaseTangent &v)
	TangentLieGroup (const Base &base)
constexpr size_t	dim () const
TangentLieGroup	operator* (const TangentLieGroup &other) const
TangentLieGroup	inverse () const
TangentLieGroup	retract (const TangentVector &xi, ChartJacobian H1={}, ChartJacobian H2={}) const
TangentVector	localCoordinates (const TangentLieGroup &other, ChartJacobian H1={}, ChartJacobian H2={}) const
Jacobian	AdjointMap () const
void	print (const std::string &s="") const
bool	equals (const TangentLieGroup &other, double tol=1e-9) const
This	between (const This &g) const
This	between (const This &g, ChartJacobian H1, ChartJacobian H2={}) const
SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
This	compose (const This &g) const
This	compose (const This &g, ChartJacobian H1, ChartJacobian H2={}) const
SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
This	expmap (const TangentVector &v) const
	expmap as required by manifold concept Applies exponential map to v and composes with *this
This	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives, when the class provides them
This	inverse (ChartJacobian H) const
TangentVector	logmap (const This &g) const
	logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
TangentVector	logmap (const This &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives, when the class provides them
Public Member Functions inherited from gtsam::LieGroup< TangentLieGroup< G >, internal::dimensionProduct(2, traits< G >::dimension)>
SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
GTSAM_EXPORT SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
GTSAM_EXPORT SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
std::enable_if_t< M !=Eigen::Dynamic, int >	dim () const
	Provided fixed dimension in dim() if needed.
const TangentLieGroup< G > &	derived () const
TangentLieGroup< G >	inverse (ChartJacobian H) const
TangentLieGroup< G >	expmap (const TangentVector &v) const
	expmap as required by manifold concept Applies exponential map to v and composes with *this
TangentVector	logmap (const TangentLieGroup< G > &g) const
	logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
TangentLieGroup< G >	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this
TangentVector	localCoordinates (const TangentLieGroup< G > &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g

Static Public Member Functions
static TangentLieGroup	Identity ()
static TangentLieGroup	Expmap (const TangentVector &xi, ChartJacobian H={})
static TangentLieGroup	Expmap (const Eigen::Ref< const BaseTangent > &u, const Eigen::Ref< const BaseTangent > &v, SplitJacobian H1={}, SplitJacobian H2={})
static TangentVector	Logmap (const TangentLieGroup &p, ChartJacobian H={})
static TangentVector	LocalCoordinates (const TangentLieGroup &p, ChartJacobian H={})
static Jacobian	adjointMap (const TangentVector &xi)
static constexpr int	Dim ()
	Static method to get the dimension (compile-time or dynamic).
Static Public Member Functions inherited from gtsam::LieGroup< TangentLieGroup< G >, internal::dimensionProduct(2, traits< G >::dimension)>
static constexpr int	Dim ()
	Static method to get the dimension (compile-time or dynamic).
static TangentLieGroup< G >	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity.
static TangentVector	LocalCoordinates (const TangentLieGroup< G > &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity.

Static Public Attributes
static constexpr auto	dimension
Static Public Attributes inherited from gtsam::LieGroup< TangentLieGroup< G >, internal::dimensionProduct(2, traits< G >::dimension)>
static constexpr auto	dimension

Public Types
using	This = TangentLieGroup<G>
using	Base = std::pair<G, typename traits<G>::TangentVector>
using	LieBase = LieGroup<This, internal::dimensionProduct(2, n)>
using	BaseTangent = typename traits<G>::TangentVector
using	BaseJacobian = typename traits<G>::Jacobian
using	TangentVector = typename LieBase::TangentVector
using	Jacobian = typename LieBase::Jacobian
using	ChartJacobian = typename LieBase::ChartJacobian
using	ChartAtOrigin = internal::ChartAtIdentity<This, dimension>
using	SplitJacobian = OptionalJacobian<Eigen::Dynamic, Eigen::Dynamic>
using	group_flavor = multiplicative_group_tag
Public Types inherited from gtsam::LieGroup< TangentLieGroup< G >, internal::dimensionProduct(2, traits< G >::dimension)>
typedef OptionalJacobian< N, N >	ChartJacobian
typedef Eigen::Matrix< double, N, N >	Jacobian
typedef Eigen::Matrix< double, N, 1 >	TangentVector

The documentation for this class was generated from the following files:

/tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/base/TangentLieGroup.h
/tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/base/TangentLieGroup-inl.h

Detailed Description

Public Member Functions

Static Public Member Functions

Static Public Attributes

Public Types