Standard Euclidean vector space. More...

#include <aligator/core/vector-space.hpp>

Inheritance diagram for aligator::VectorSpaceTpl< _Scalar, _Dim >:

Collaboration diagram for aligator::VectorSpaceTpl< _Scalar, _Dim >:

Public Types
using	Scalar = _Scalar

using	Base = ManifoldAbstractTpl<Scalar>

Public Types inherited from aligator::ManifoldAbstractTpl< _Scalar >
using	Scalar = _Scalar

using	TangentSpaceType = VectorSpaceTpl<Scalar, Eigen::Dynamic>
	Typedef for the tangent space, as a manifold.

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	VectorSpaceTpl (const int dim)
	Default constructor where the dimension is supplied.

int	dim () const

template<int N = Dim, typename = typename std::enable_if_t<N != Eigen::Dynamic>>
	VectorSpaceTpl ()
	Default constructor without arguments.

template<int OtherDim>
	VectorSpaceTpl (const VectorSpaceTpl< Scalar, OtherDim > &other)
	Build from VectorSpaceTpl of different dimension.

int	ndx () const
	Get manifold tangent space dimension.

int	nx () const
	Get manifold representation dimension.

Public Member Functions inherited from aligator::ManifoldAbstractTpl< _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.

virtual bool	isNormalized (const ConstVectorRef &) const
	Check if the input vector `x` is a viable element of 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	Dim = _Dim

Protected Member Functions
implementations
void	integrate_impl (const ConstVectorRef &x, const ConstVectorRef &v, VectorRef out) const
	Perform the manifold integration operation.

void	Jintegrate_impl (const ConstVectorRef &, const ConstVectorRef &, MatrixRef Jout, int) const

void	JintegrateTransport_impl (const ConstVectorRef &, const ConstVectorRef &, MatrixRef, int) const

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

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

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

Protected Member Functions inherited from aligator::ManifoldAbstractTpl< _Scalar >
virtual void	neutral_impl (VectorRef out) const

virtual void	rand_impl (VectorRef out) const

Additional Inherited Members
Protected Attributes inherited from aligator::ManifoldAbstractTpl< _Scalar >
int	nx_

int	ndx_

Detailed Description

template<typename _Scalar, int _Dim>
struct aligator::VectorSpaceTpl< _Scalar, _Dim >

Standard Euclidean vector space.

Definition at line 13 of file vector-space.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar, int _Dim>

using aligator::VectorSpaceTpl< _Scalar, _Dim >::Scalar = _Scalar

Definition at line 14 of file vector-space.hpp.

◆ Base

template<typename _Scalar, int _Dim>

using aligator::VectorSpaceTpl< _Scalar, _Dim >::Base = ManifoldAbstractTpl<Scalar>

Definition at line 16 of file vector-space.hpp.

Constructor & Destructor Documentation

◆ VectorSpaceTpl() [1/3]

template<typename _Scalar, int _Dim>

aligator::VectorSpaceTpl< _Scalar, _Dim >::VectorSpaceTpl ( const int dim )

inlineexplicit

Default constructor where the dimension is supplied.

Definition at line 22 of file vector-space.hpp.

◆ VectorSpaceTpl() [2/3]

template<typename _Scalar, int _Dim>

template<int N = Dim, typename = typename std::enable_if_t<N != Eigen::Dynamic>>

aligator::VectorSpaceTpl< _Scalar, _Dim >::VectorSpaceTpl ( )

inlineexplicit

Default constructor without arguments.

This constructor is disabled if the dimension is not known at compile time.

Definition at line 37 of file vector-space.hpp.

◆ VectorSpaceTpl() [3/3]

template<typename _Scalar, int _Dim>

template<int OtherDim>

aligator::VectorSpaceTpl< _Scalar, _Dim >::VectorSpaceTpl ( const VectorSpaceTpl< Scalar, OtherDim > & other )

inline

Build from VectorSpaceTpl of different dimension.

Definition at line 42 of file vector-space.hpp.

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

template<typename _Scalar, int _Dim>

aligator::VectorSpaceTpl< _Scalar, _Dim >::ALIGATOR_DYNAMIC_TYPEDEFS ( Scalar )

◆ dim()

template<typename _Scalar, int _Dim>

int aligator::VectorSpaceTpl< _Scalar, _Dim >::dim ( ) const

inline

Definition at line 29 of file vector-space.hpp.

◆ integrate_impl()

template<typename _Scalar, int _Dim>

void aligator::VectorSpaceTpl< _Scalar, _Dim >::integrate_impl	(	const ConstVectorRef &	x,
		const ConstVectorRef &	v,
		VectorRef	out ) const

inlineprotectedvirtual

Perform the manifold integration operation.

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 52 of file vector-space.hpp.

◆ Jintegrate_impl()

template<typename _Scalar, int _Dim>

void aligator::VectorSpaceTpl< _Scalar, _Dim >::Jintegrate_impl	(	const ConstVectorRef &	,
		const ConstVectorRef &	,
		MatrixRef	Jout,
		int	) const

inlineprotectedvirtual

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 57 of file vector-space.hpp.

◆ JintegrateTransport_impl()

template<typename _Scalar, int _Dim>

void aligator::VectorSpaceTpl< _Scalar, _Dim >::JintegrateTransport_impl	(	const ConstVectorRef &	,
		const ConstVectorRef &	,
		MatrixRef	,
		int	) const

inlineprotectedvirtual

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 62 of file vector-space.hpp.

◆ difference_impl()

template<typename _Scalar, int _Dim>

void aligator::VectorSpaceTpl< _Scalar, _Dim >::difference_impl	(	const ConstVectorRef &	x0,
		const ConstVectorRef &	x1,
		VectorRef	out ) const

inlineprotectedvirtual

Implementation of the manifold retraction operation.

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 67 of file vector-space.hpp.

◆ Jdifference_impl()

template<typename _Scalar, int _Dim>

void aligator::VectorSpaceTpl< _Scalar, _Dim >::Jdifference_impl	(	const ConstVectorRef &	,
		const ConstVectorRef &	,
		MatrixRef	Jout,
		int	arg ) const

inlineprotectedvirtual

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 72 of file vector-space.hpp.

◆ interpolate_impl()

template<typename _Scalar, int _Dim>

void aligator::VectorSpaceTpl< _Scalar, _Dim >::interpolate_impl	(	const ConstVectorRef &	x0,
		const ConstVectorRef &	x1,
		const Scalar &	u,
		VectorRef	out ) const

inlineprotectedvirtual

Interpolation operation.

Reimplemented from aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 86 of file vector-space.hpp.

◆ ndx()

template<typename _Scalar, int _Dim>

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

inline

Get manifold tangent space dimension.

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

◆ nx()

template<typename _Scalar, int _Dim>

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

inline

Get manifold representation dimension.

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

Member Data Documentation

◆ Dim

template<typename _Scalar, int _Dim>

int aligator::VectorSpaceTpl< _Scalar, _Dim >::Dim = _Dim

staticconstexpr

Definition at line 15 of file vector-space.hpp.

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

include/aligator/core/vector-space.hpp

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ Base

Constructor & Destructor Documentation

◆ VectorSpaceTpl() [1/3]

◆ VectorSpaceTpl() [2/3]

◆ VectorSpaceTpl() [3/3]

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

◆ dim()

◆ integrate_impl()

◆ Jintegrate_impl()

◆ JintegrateTransport_impl()

◆ difference_impl()

◆ Jdifference_impl()

◆ interpolate_impl()

◆ ndx()

◆ nx()

Member Data Documentation

◆ Dim