gtsam::MatrixLieGroup< Class, D, N > Struct Template Reference

Detailed Description

template<class Class, int D, int N>
struct gtsam::MatrixLieGroup< Class, D, N >

A CRTP helper class that implements matrix Lie group methods.

To use, derive from MatrixLieGroup<Class,D,N> instead of LieGroup<Class,D>. Your class must implement a matrix() method and static Hat()/Vee() methods.

Inheritance diagram for gtsam::MatrixLieGroup< Class, D, N >:

Matrix Lie Group
Eigen::Matrix< double, internal::product(N, N), 1 >	vec (OptionalJacobian< internal::product(N, N), D > H={}) const
	Vectorize the matrix representation of a Lie group element.
Jacobian	AdjointMap () const
	A generic implementation of AdjointMap for matrix Lie groups.
TangentVector	Adjoint (const TangentVector &xi, ChartJacobian H_this={}, ChartJacobian H_xi={}) const
	Adjoint action on a tangent vector.
TangentVector	AdjointTranspose (const TangentVector &x, ChartJacobian H_this={}, ChartJacobian H_x={}) const
	Dual Adjoint action on a tangent covector.
static Jacobian	adjointMap (const TangentVector &xi)
	Lie algebra adjoint map ad_xi, with optional specialization in derived classes.
static TangentVector	adjoint (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={})
	Lie algebra action ad_xi(y), with optional Jacobians.
static TangentVector	adjointTranspose (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={})
	Dual Lie algebra action ad_xi^T(y), with optional Jacobians.

Public Member Functions
std::enable_if_t< M !=Eigen::Dynamic, int >	dim () const
	Provided fixed dimension in dim() if needed.
Public Member Functions inherited from gtsam::LieGroup< Class, D >
std::enable_if_t< M !=Eigen::Dynamic, int >	dim () const
	Provided fixed dimension in dim() if needed.
const Class &	derived () const
Class	compose (const Class &g) const
Class	between (const Class &g) const
Class	compose (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const
Class	between (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const
Class	inverse (ChartJacobian H) const
Class	expmap (const TangentVector &v) const
	expmap as required by manifold concept Applies exponential map to v and composes with *this
TangentVector	logmap (const Class &g) const
	logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
Class	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives, when the class provides them
TangentVector	logmap (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives, when the class provides them
Class	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this
TangentVector	localCoordinates (const Class &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g
Class	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives, when the chart provides them
TangentVector	localCoordinates (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives, when the chart provides them
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

Static Public Member Functions
static constexpr int	Dim ()
	Static method to get the dimension (compile-time or dynamic).
Static Public Member Functions inherited from gtsam::LieGroup< Class, D >
static constexpr int	Dim ()
	Static method to get the dimension (compile-time or dynamic).
static Class	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity.
static TangentVector	LocalCoordinates (const Class &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity.
static Class	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative, when the chart provides it.
static TangentVector	LocalCoordinates (const Class &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative, when provided.

Static Public Attributes
static constexpr auto	dimension
Static Public Attributes inherited from gtsam::LieGroup< Class, D >
static constexpr auto	dimension

Public Types
using	Base = LieGroup<Class, D>
using	ChartJacobian = typename Base::ChartJacobian
using	Jacobian = typename Base::Jacobian
using	TangentVector = typename Base::TangentVector
using	Vectorized = Eigen::Matrix<double, internal::product(N, N), 1>
using	VectorizedJacobian
Public Types inherited from gtsam::LieGroup< Class, D >
typedef OptionalJacobian< N, N >	ChartJacobian
typedef Eigen::Matrix< double, N, N >	Jacobian
typedef Eigen::Matrix< double, N, 1 >	TangentVector

Member Typedef Documentation

VectorizedJacobian

template<class Class, int D, int N>

using gtsam::MatrixLieGroup< Class, D, N >::VectorizedJacobian

Initial value:

 
OptionalJacobian<internal::product(N, N), D>

Member Function Documentation

Adjoint()

template<class Class, int D, int N>

TangentVector gtsam::MatrixLieGroup< Class, D, N >::Adjoint ( const TangentVector & xi, ChartJacobian H_this = {}, ChartJacobian H_xi = {} ) const

inline

Adjoint action on a tangent vector.

Returns Ad_g * xi with optional Jacobians with respect to g and xi.

AdjointMap()

template<class Class, int D, int N>

Jacobian gtsam::MatrixLieGroup< Class, D, N >::AdjointMap ( ) const

inline

A generic implementation of AdjointMap for matrix Lie groups.

The Adjoint map Ad_g is the tangent map of the conjugation C_g(x) = g*x*g.inverse() at the identity. For matrix Lie groups, Ad_g(v) = g*v*g.inverse() where v is an element of the Lie algebra. The columns of the Adjoint matrix are vee(g * Hat(e_i) * g.inverse()) for each basis vector e_i. This method can be overridden by derived classes with a more efficient, closed-form solution.

AdjointTranspose()

template<class Class, int D, int N>

TangentVector gtsam::MatrixLieGroup< Class, D, N >::AdjointTranspose ( const TangentVector & x, ChartJacobian H_this = {}, ChartJacobian H_x = {} ) const

inline

Dual Adjoint action on a tangent covector.

Returns Ad_g^T * x with optional Jacobians with respect to g and x.

vec()

template<class Class, int D, int N>

Eigen::Matrix< double, internal::product(N, N), 1 > gtsam::MatrixLieGroup< Class, D, N >::vec ( OptionalJacobian< internal::product(N, N), D > H = {} ) const

inline

Vectorize the matrix representation of a Lie group element.

The derivative H is the (N*N) x D Jacobian of this vectorization map. It is given by the formula H = (I_N ⊗ T) * P, where T is the N x N matrix of this group element, ⊗ is the Kronecker product, and P is the (N*N) x D matrix whose columns are the vectorized Lie algebra generators vec(Hat(e_j)). This can be computed efficiently via block-wise multiplication.

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The documentation for this struct was generated from the following file:

• /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/base/MatrixLieGroup.h