The cartesian product of two or more manifolds. More...

#include <aligator/modelling/spaces/cartesian-product.hpp>

Inheritance diagram for aligator::CartesianProductTpl< _Scalar >:

Collaboration diagram for aligator::CartesianProductTpl< _Scalar >:

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)

const Base &	getComponent (std::size_t i) const

std::size_t	numComponents () const

template<class Concrete>
void	addComponent (const Concrete &c)

void	addComponent (const CartesianProductTpl &other)

	CartesianProductTpl ()=default

	CartesianProductTpl (const CartesianProductTpl &)=default

CartesianProductTpl &	operator= (const CartesianProductTpl &)=default

	CartesianProductTpl (CartesianProductTpl &&)=default

CartesianProductTpl &	operator= (CartesianProductTpl &&)=default

	CartesianProductTpl (const std::vector< xyz::polymorphic< Base > > &components)

	CartesianProductTpl (std::vector< xyz::polymorphic< Base > > &&components)

	CartesianProductTpl (std::initializer_list< xyz::polymorphic< Base > > components)

	CartesianProductTpl (const xyz::polymorphic< Base > &left, const xyz::polymorphic< Base > &right)

int	nx () const
	Get manifold representation dimension.

int	ndx () const
	Get manifold tangent space dimension.

void	neutral_impl (VectorRef out) const

void	rand_impl (VectorRef out) const

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

template<class VectorType, class U = std::remove_const_t<VectorType>>
std::vector< U >	split_impl (VectorType &x) const

template<class VectorType, class U = std::remove_const_t<VectorType>>
std::vector< U >	split_vector_impl (VectorType &v) const

std::vector< VectorRef >	split (VectorRef x) const

std::vector< ConstVectorRef >	split (const ConstVectorRef &x) const

std::vector< VectorRef >	split_vector (VectorRef v) const

std::vector< ConstVectorRef >	split_vector (const ConstVectorRef &v) const

VectorXs	merge (const std::vector< VectorXs > &xs) const

VectorXs	merge_vector (const std::vector< VectorXs > &vs) const

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

virtual	~ManifoldAbstractTpl ()=default

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.

Protected Member Functions
void	integrate_impl (const ConstVectorRef &x, const ConstVectorRef &v, 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

Protected Member Functions inherited from aligator::ManifoldAbstractTpl< _Scalar >
virtual void	interpolate_impl (const ConstVectorRef &x0, const ConstVectorRef &x1, const Scalar &u, VectorRef out) const
	Interpolation operation.

Protected Attributes
std::vector< xyz::polymorphic< Base > >	m_components

Detailed Description

template<typename _Scalar>
struct aligator::CartesianProductTpl< _Scalar >

The cartesian product of two or more manifolds.

Definition at line 13 of file cartesian-product.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar>

using aligator::CartesianProductTpl< _Scalar >::Scalar = _Scalar

Definition at line 15 of file cartesian-product.hpp.

◆ Base

template<typename _Scalar>

using aligator::CartesianProductTpl< _Scalar >::Base = ManifoldAbstractTpl<Scalar>

Definition at line 17 of file cartesian-product.hpp.

Constructor & Destructor Documentation

◆ CartesianProductTpl() [1/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl ( )

explicitdefault

◆ CartesianProductTpl() [2/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl ( const CartesianProductTpl< _Scalar > & )

default

◆ CartesianProductTpl() [3/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl ( CartesianProductTpl< _Scalar > && )

default

◆ CartesianProductTpl() [4/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl ( const std::vector< xyz::polymorphic< Base > > & components )

inline

Definition at line 45 of file cartesian-product.hpp.

◆ CartesianProductTpl() [5/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl ( std::vector< xyz::polymorphic< Base > > && components )

inline

Definition at line 48 of file cartesian-product.hpp.

◆ CartesianProductTpl() [6/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl ( std::initializer_list< xyz::polymorphic< Base > > components )

inline

Definition at line 51 of file cartesian-product.hpp.

◆ CartesianProductTpl() [7/7]

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::CartesianProductTpl	(	const xyz::polymorphic< Base > &	left,
		const xyz::polymorphic< Base > &	right )

inline

Definition at line 54 of file cartesian-product.hpp.

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

template<typename _Scalar>

aligator::CartesianProductTpl< _Scalar >::ALIGATOR_DYNAMIC_TYPEDEFS ( Scalar )

◆ getComponent()

template<typename _Scalar>

const Base & aligator::CartesianProductTpl< _Scalar >::getComponent ( std::size_t i ) const

inline

Definition at line 20 of file cartesian-product.hpp.

◆ numComponents()

template<typename _Scalar>

std::size_t aligator::CartesianProductTpl< _Scalar >::numComponents ( ) const

inline

Definition at line 22 of file cartesian-product.hpp.

◆ addComponent() [1/2]

template<typename _Scalar>

template<class Concrete>

void aligator::CartesianProductTpl< _Scalar >::addComponent ( const Concrete & c )

inline

Definition at line 24 of file cartesian-product.hpp.

◆ addComponent() [2/2]

template<typename _Scalar>

void aligator::CartesianProductTpl< _Scalar >::addComponent ( const CartesianProductTpl< _Scalar > & other )

inline

Definition at line 33 of file cartesian-product.hpp.

◆ operator=() [1/2]

template<typename _Scalar>

CartesianProductTpl & aligator::CartesianProductTpl< _Scalar >::operator= ( const CartesianProductTpl< _Scalar > & )

default

◆ operator=() [2/2]

template<typename _Scalar>

CartesianProductTpl & aligator::CartesianProductTpl< _Scalar >::operator= ( CartesianProductTpl< _Scalar > && )

default

◆ nx()

template<typename _Scalar>

int aligator::CartesianProductTpl< _Scalar >::nx ( ) const

inlinevirtual

Get manifold representation dimension.

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 58 of file cartesian-product.hpp.

◆ ndx()

template<typename _Scalar>

int aligator::CartesianProductTpl< _Scalar >::ndx ( ) const

inlinevirtual

Get manifold tangent space dimension.

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Definition at line 66 of file cartesian-product.hpp.

◆ neutral_impl()

template<typename _Scalar>

void aligator::CartesianProductTpl< _Scalar >::neutral_impl ( VectorRef out ) const

virtual

Reimplemented from aligator::ManifoldAbstractTpl< _Scalar >.

◆ rand_impl()

template<typename _Scalar>

void aligator::CartesianProductTpl< _Scalar >::rand_impl ( VectorRef out ) const

virtual

Reimplemented from aligator::ManifoldAbstractTpl< _Scalar >.

◆ isNormalized()

template<typename _Scalar>

bool aligator::CartesianProductTpl< _Scalar >::isNormalized ( const ConstVectorRef & ) const

virtual

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

Reimplemented from aligator::ManifoldAbstractTpl< _Scalar >.

◆ split_impl()

template<typename _Scalar>

template<class VectorType, class U = std::remove_const_t<VectorType>>

std::vector< U > aligator::CartesianProductTpl< _Scalar >::split_impl ( VectorType & x ) const

◆ split_vector_impl()

template<typename _Scalar>

template<class VectorType, class U = std::remove_const_t<VectorType>>

std::vector< U > aligator::CartesianProductTpl< _Scalar >::split_vector_impl ( VectorType & v ) const

◆ split() [1/2]

template<typename _Scalar>

std::vector< VectorRef > aligator::CartesianProductTpl< _Scalar >::split ( VectorRef x ) const

inline

Definition at line 84 of file cartesian-product.hpp.

◆ split() [2/2]

template<typename _Scalar>

std::vector< ConstVectorRef > aligator::CartesianProductTpl< _Scalar >::split ( const ConstVectorRef & x ) const

inline

Definition at line 88 of file cartesian-product.hpp.

◆ split_vector() [1/2]

template<typename _Scalar>

std::vector< VectorRef > aligator::CartesianProductTpl< _Scalar >::split_vector ( VectorRef v ) const

inline

Definition at line 92 of file cartesian-product.hpp.

◆ split_vector() [2/2]

template<typename _Scalar>

std::vector< ConstVectorRef > aligator::CartesianProductTpl< _Scalar >::split_vector ( const ConstVectorRef & v ) const

inline

Definition at line 96 of file cartesian-product.hpp.

◆ merge()

template<typename _Scalar>

VectorXs aligator::CartesianProductTpl< _Scalar >::merge ( const std::vector< VectorXs > & xs ) const

◆ merge_vector()

template<typename _Scalar>

VectorXs aligator::CartesianProductTpl< _Scalar >::merge_vector ( const std::vector< VectorXs > & vs ) const

◆ integrate_impl()

template<typename _Scalar>

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

protectedvirtual

Perform the manifold integration operation.

Implements aligator::ManifoldAbstractTpl< _Scalar >.

◆ difference_impl()

template<typename _Scalar>

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

protectedvirtual

Implementation of the manifold retraction operation.

Implements aligator::ManifoldAbstractTpl< _Scalar >.

◆ Jintegrate_impl()

template<typename _Scalar>

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

protectedvirtual

Implements aligator::ManifoldAbstractTpl< _Scalar >.

◆ JintegrateTransport_impl()

template<typename _Scalar>

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

protectedvirtual

Implements aligator::ManifoldAbstractTpl< _Scalar >.

◆ Jdifference_impl()

template<typename _Scalar>

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

protectedvirtual

Implements aligator::ManifoldAbstractTpl< _Scalar >.

Member Data Documentation

◆ m_components

template<typename _Scalar>

std::vector<xyz::polymorphic<Base> > aligator::CartesianProductTpl< _Scalar >::m_components

protected

Definition at line 105 of file cartesian-product.hpp.

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

include/aligator/modelling/spaces/cartesian-product.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ Base

Constructor & Destructor Documentation

◆ CartesianProductTpl() [1/7]

◆ CartesianProductTpl() [2/7]

◆ CartesianProductTpl() [3/7]

◆ CartesianProductTpl() [4/7]

◆ CartesianProductTpl() [5/7]

◆ CartesianProductTpl() [6/7]

◆ CartesianProductTpl() [7/7]

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

◆ getComponent()

◆ numComponents()

◆ addComponent() [1/2]

◆ addComponent() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ nx()

◆ ndx()

◆ neutral_impl()

◆ rand_impl()

◆ isNormalized()

◆ split_impl()

◆ split_vector_impl()

◆ split() [1/2]

◆ split() [2/2]

◆ split_vector() [1/2]

◆ split_vector() [2/2]

◆ merge()

◆ merge_vector()

◆ integrate_impl()

◆ difference_impl()

◆ Jintegrate_impl()

◆ JintegrateTransport_impl()

◆ Jdifference_impl()

Member Data Documentation

◆ m_components