Tangent bundle of a base manifold M. More...

#include <aligator/modelling/spaces/tangent-bundle.hpp>

Inheritance diagram for aligator::TangentBundleTpl< Base >:

Collaboration diagram for aligator::TangentBundleTpl< Base >:

Public Types
using	Self = TangentBundleTpl<Base>

using	Scalar = typename Base::Scalar

using	ManifoldBase = ManifoldAbstractTpl<Scalar>

Public Types inherited from aligator::ManifoldAbstractTpl< Base::Scalar >
using	Scalar

using	TangentSpaceType
	Typedef for the tangent space, as a manifold.

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	TangentBundleTpl (const Base &base)
	Constructor using base space instance.

template<typename... BaseCtorArgs>
	TangentBundleTpl (BaseCtorArgs... args)
	Constructor using base space constructor.

bool	isNormalized (const ConstVectorRef &x) const
	Check if the input vector `x` is a viable element of the manifold.

const Base &	getBaseSpace () const

template<typename Point>
Point::ConstSegmentReturnType	getBasePoint (const Eigen::MatrixBase< Point > &x) const

template<typename Point>
Point::SegmentReturnType	getBasePointWrite (const Eigen::MatrixBase< Point > &x) const

template<typename Tangent>
Tangent::ConstSegmentReturnType	getBaseTangent (const Tangent &v) const

template<typename Tangent>
Tangent::SegmentReturnType	getTangentHeadWrite (const Eigen::MatrixBase< Tangent > &v) const

template<typename Jac>
Eigen::Block< Jac, Eigen::Dynamic, Eigen::Dynamic >	getBaseJacobian (const Eigen::MatrixBase< Jac > &J) const

int	ndx () const
	Get manifold tangent space dimension.

int	nx () const
	Get manifold representation dimension.

Public Member Functions inherited from aligator::ManifoldAbstractTpl< Base::Scalar >
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)
	Scalar type.

	ManifoldAbstractTpl (int nx, int ndx)

virtual	~ManifoldAbstractTpl ()=default

int	nx () const
	Get manifold representation dimension.

int	ndx () const
	Get manifold tangent space dimension.

VectorXs	neutral () const
	Get the neutral element \(e \in M\) from the manifold (if this makes sense).

void	neutral (VectorRef out) const
	Get the neutral element \(e \in M\) from the manifold (if this makes sense).

VectorXs	rand () const
	Sample a random point \(x \in M\) on the manifold.

void	rand (VectorRef out) const
	Sample a random point \(x \in M\) on the manifold.

TangentSpaceType	tangentSpace () const
	Return an object representing the tangent space as a manifold.

void	integrate (const ConstVectorRef &x, const ConstVectorRef &v, VectorRef out) const
	Manifold integration operation \(x \oplus v\).

void	Jintegrate (const ConstVectorRef &x, const ConstVectorRef &v, MatrixRef Jout, int arg) const
	Jacobian of the integation operation.

void	JintegrateTransport (const ConstVectorRef &x, const ConstVectorRef &v, MatrixRef Jout, int arg) const
	Perform the parallel transport operation.

void	difference (const ConstVectorRef &x0, const ConstVectorRef &x1, VectorRef out) const
	Manifold difference/retraction operation \(x_1 \ominus x_0\).

void	Jdifference (const ConstVectorRef &x0, const ConstVectorRef &x1, MatrixRef Jout, int arg) const
	Jacobian of the retraction operation.

void	interpolate (const ConstVectorRef &x0, const ConstVectorRef &x1, const Scalar &u, VectorRef out) const

VectorXs	integrate (const ConstVectorRef &x, const ConstVectorRef &v) const
	Manifold integration operation \(x \oplus v\).

VectorXs	difference (const ConstVectorRef &x0, const ConstVectorRef &x1) const
	Manifold difference/retraction operation \(x_1 \ominus x_0\).

VectorXs	interpolate (const ConstVectorRef &x0, const ConstVectorRef &x1, const Scalar &u) const
	Interpolation operation.

Static Public Attributes
static constexpr int	Options = Base::Options

Protected Member Functions
Implementations of operators
void	neutral_impl (VectorRef out) const

void	rand_impl (VectorRef out) const

void	integrate_impl (const ConstVectorRef &x, const ConstVectorRef &dx, VectorRef out) const
	Perform the manifold integration operation.

void	difference_impl (const ConstVectorRef &x0, const ConstVectorRef &x1, VectorRef out) const
	Implementation of the manifold retraction operation.

void	Jintegrate_impl (const ConstVectorRef &x, const ConstVectorRef &v, MatrixRef Jout, int arg) const

void	JintegrateTransport_impl (const ConstVectorRef &x, const ConstVectorRef &v, MatrixRef Jout, int arg) const

void	Jdifference_impl (const ConstVectorRef &x0, const ConstVectorRef &x1, MatrixRef Jout, int arg) const

void	interpolate_impl (const ConstVectorRef &x0, const ConstVectorRef &x1, const Scalar &u, VectorRef out) const
	Interpolation operation.

Protected Attributes
Base	base_

Protected Attributes inherited from aligator::ManifoldAbstractTpl< Base::Scalar >
int	nx_

int	ndx_

Detailed Description

template<class Base>
struct aligator::TangentBundleTpl< Base >

Tangent bundle of a base manifold M.

Definition at line 9 of file tangent-bundle.hpp.

Member Typedef Documentation

◆ Self

template<class Base>

using aligator::TangentBundleTpl< Base >::Self = TangentBundleTpl<Base>

Definition at line 14 of file tangent-bundle.hpp.

◆ Scalar

template<class Base>

using aligator::TangentBundleTpl< Base >::Scalar = typename Base::Scalar

Definition at line 15 of file tangent-bundle.hpp.

◆ ManifoldBase

template<class Base>

using aligator::TangentBundleTpl< Base >::ManifoldBase = ManifoldAbstractTpl<Scalar>

Definition at line 18 of file tangent-bundle.hpp.

Constructor & Destructor Documentation

◆ TangentBundleTpl() [1/2]

template<class Base>

aligator::TangentBundleTpl< Base >::TangentBundleTpl ( const Base & base )

inline

Constructor using base space instance.

Definition at line 23 of file tangent-bundle.hpp.

◆ TangentBundleTpl() [2/2]

template<class Base>

template<typename... BaseCtorArgs>

aligator::TangentBundleTpl< Base >::TangentBundleTpl ( BaseCtorArgs... args )

inline

Constructor using base space constructor.

Definition at line 29 of file tangent-bundle.hpp.

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

template<class Base>

aligator::TangentBundleTpl< Base >::ALIGATOR_DYNAMIC_TYPEDEFS ( Scalar )

◆ isNormalized()

template<class Base>

bool aligator::TangentBundleTpl< Base >::isNormalized ( const ConstVectorRef & ) const

inlinevirtual

Check if the input vector x is a viable element of the manifold.

Reimplemented from aligator::ManifoldAbstractTpl< Base::Scalar >.

Definition at line 36 of file tangent-bundle.hpp.

◆ getBaseSpace()

template<class Base>

const Base & aligator::TangentBundleTpl< Base >::getBaseSpace ( ) const

inline

Definition at line 41 of file tangent-bundle.hpp.

◆ getBasePoint()

template<class Base>

template<typename Point>

Point::ConstSegmentReturnType aligator::TangentBundleTpl< Base >::getBasePoint ( const Eigen::MatrixBase< Point > & x ) const

inline

Get base point of an element of the tangent bundle. This map is exactly the natural projection.

Definition at line 47 of file tangent-bundle.hpp.

◆ getBasePointWrite()

template<class Base>

template<typename Point>

Point::SegmentReturnType aligator::TangentBundleTpl< Base >::getBasePointWrite ( const Eigen::MatrixBase< Point > & x ) const

inline

Definition at line 53 of file tangent-bundle.hpp.

◆ getBaseTangent()

template<class Base>

template<typename Tangent>

Tangent::ConstSegmentReturnType aligator::TangentBundleTpl< Base >::getBaseTangent ( const Tangent & v ) const

inline

Definition at line 59 of file tangent-bundle.hpp.

◆ getTangentHeadWrite()

template<class Base>

template<typename Tangent>

Tangent::SegmentReturnType aligator::TangentBundleTpl< Base >::getTangentHeadWrite ( const Eigen::MatrixBase< Tangent > & v ) const

inline

Definition at line 65 of file tangent-bundle.hpp.

◆ getBaseJacobian()

template<class Base>

template<typename Jac>

Eigen::Block< Jac, Eigen::Dynamic, Eigen::Dynamic > aligator::TangentBundleTpl< Base >::getBaseJacobian ( const Eigen::MatrixBase< Jac > & J ) const

inline

Definition at line 71 of file tangent-bundle.hpp.

◆ neutral_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::neutral_impl ( VectorRef out ) const

protectedvirtual

Reimplemented from aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ rand_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::rand_impl ( VectorRef out ) const

protectedvirtual

Reimplemented from aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ integrate_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::integrate_impl	(	const ConstVectorRef &	x,
		const ConstVectorRef &	v,
		VectorRef	out ) const

protectedvirtual

Perform the manifold integration operation.

Implements aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ difference_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::difference_impl	(	const ConstVectorRef &	x0,
		const ConstVectorRef &	x1,
		VectorRef	out ) const

protectedvirtual

Implementation of the manifold retraction operation.

Implements aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ Jintegrate_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::Jintegrate_impl	(	const ConstVectorRef &	x,
		const ConstVectorRef &	v,
		MatrixRef	Jout,
		int	arg ) const

protectedvirtual

Implements aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ JintegrateTransport_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::JintegrateTransport_impl	(	const ConstVectorRef &	x,
		const ConstVectorRef &	v,
		MatrixRef	Jout,
		int	arg ) const

protectedvirtual

Implements aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ Jdifference_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::Jdifference_impl	(	const ConstVectorRef &	x0,
		const ConstVectorRef &	x1,
		MatrixRef	Jout,
		int	arg ) const

protectedvirtual

Implements aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ interpolate_impl()

template<class Base>

void aligator::TangentBundleTpl< Base >::interpolate_impl	(	const ConstVectorRef &	x0,
		const ConstVectorRef &	x1,
		const Scalar &	u,
		VectorRef	out ) const

protectedvirtual

Interpolation operation.

Reimplemented from aligator::ManifoldAbstractTpl< Base::Scalar >.

◆ ndx()

template<class Base>

int aligator::ManifoldAbstractTpl< Scalar >::ndx ( ) const

inline

Get manifold tangent space dimension.

Definition at line 27 of file manifold-base.hpp.

◆ nx()

template<class Base>

int aligator::ManifoldAbstractTpl< Scalar >::nx ( ) const

inline

Get manifold representation dimension.

Definition at line 25 of file manifold-base.hpp.

Member Data Documentation

◆ base_

template<class Base>

Base aligator::TangentBundleTpl< Base >::base_

protected

Definition at line 11 of file tangent-bundle.hpp.

◆ Options

template<class Base>

int aligator::TangentBundleTpl< Base >::Options = Base::Options

staticconstexpr

Definition at line 16 of file tangent-bundle.hpp.

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

include/aligator/modelling/spaces/tangent-bundle.hpp

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Self

◆ Scalar

◆ ManifoldBase

Constructor & Destructor Documentation

◆ TangentBundleTpl() [1/2]

◆ TangentBundleTpl() [2/2]

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

◆ isNormalized()

◆ getBaseSpace()

◆ getBasePoint()

◆ getBasePointWrite()

◆ getBaseTangent()

◆ getTangentHeadWrite()

◆ getBaseJacobian()

◆ neutral_impl()

◆ rand_impl()

◆ integrate_impl()

◆ difference_impl()

◆ Jintegrate_impl()

◆ JintegrateTransport_impl()

◆ Jdifference_impl()

◆ interpolate_impl()

◆ ndx()

◆ nx()

Member Data Documentation

◆ base_

◆ Options