Base class for Bundle lie groups. More...

#include <bundle.hpp>

Inheritance diagram for BundleBase< _Derived >:

Public Types
template<std::size_t Idx>
using	PartType = typename liebase_info< _Derived >::template PartPlainObject< Idx >
	Part type.

Public Types inherited from LieGroupBase< _Derived >
using	Scalar = typename traits::Scalar
	Scalar type.

using	Matrix = Eigen::Matrix< Scalar, Dim, Dim >
	Lie group matrix type.

using	Tangent = Eigen::Matrix< Scalar, Dof, 1 >
	Lie group parameterized tangent type.

using	TangentMap = Eigen::Matrix< Scalar, Dof, Dof >
	Matrix representing map between tangent elements.

using	Hessian = Eigen::Matrix< Scalar, Dof, Dof *Dof >
	Plain return type with different scalar.

using	CastT = typename traits::template PlainObject< NewScalar >
	Plain return type with different scalar.

using	PlainObject = CastT< Scalar >
	Plain return type.

Public Member Functions
template<std::size_t Idx> requires is_mutable
MapDispatch< PartType< Idx > >	part ()
	Access part no Idx of Bundle.

template<std::size_t Idx>
MapDispatch< const PartType< Idx > >	part () const
	Const access part no Idx of Bundle.

Public Member Functions inherited from LieGroupBase< _Derived >
auto &	coeffs () const
	Access underlying storages.

const auto &	coeffs () const
	Const access underlying storages.

auto *	data () const
	Access raw pointer.

const auto *	data () const
	Const access raw pointer.

_Derived &	operator= (const LieGroupBase< OtherDerived > &o) noexcept

Eigen::Index	dof () const noexcept
	Dynamic size (degrees of freedom).

void	setIdentity () noexcept
	Set to group identity element.

void	setRandom () noexcept
	Set to a random element.

Matrix	matrix () const noexcept
	Return as matrix Lie group element in \( \mathbb{R}^{\mathtt{dim} \times \mathtt{dim}} \).

bool	isApprox (const LieGroupBase< OtherDerived > &o, const Scalar &eps=Eigen::NumTraits< Scalar >::dummy_precision()) const noexcept
	Check if (approximately) equal to other element `o`.

CastT< NewScalar >	cast () const noexcept
	Cast to different scalar type.

PlainObject	operator* (const LieGroupBase< OtherDerived > &o) const noexcept
	Group binary composition operation.

_Derived &	operator*= (const LieGroupBase< OtherDerived > &o) noexcept
	Inplace group binary composition operation.

PlainObject	inverse () const noexcept
	Group inverse operation.

Tangent	log () const noexcept
	Lie group logarithm.

TangentMap	Ad () const noexcept
	Lie group adjoint.

PlainObject	operator+ (const Eigen::MatrixBase< TangentDerived > &a) const noexcept
	Right-plus.

_Derived &	operator+= (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Inplace right-plus: \( \mathbf{x} \leftarrow \mathbf{x} \circ \exp(\mathbf{a}) \).

Tangent	operator- (const LieGroupBase< OtherDerived > &xo) const noexcept
	Right-minus.

Public Attributes
	SMOOTH_INHERIT_TYPEDEFS

Static Public Attributes
static constexpr auto	BundleSize = Impl::BundleSize
	Number of elements in Bundle.

template<std::size_t Idx>
static constexpr auto	PartStart = Impl::DofsPsum[Idx]
	Part starting index (degrees of freedom).

template<std::size_t Idx>
static constexpr auto	PartDof = Impl::Dofs[Idx]
	Part degrees of freedom.

Static Public Attributes inherited from LieGroupBase< _Derived >
static constexpr int	RepSize
	Number of scalars in internal representation.

static constexpr int	Dof
	Degrees of freedom of manifold (equal to tangent space dimension).

static constexpr int	Dim
	Side of Lie group matrix representation.

static constexpr bool	IsCommutative
	Commutativity of group. A commutative group has a zero Lie bracket.

Additional Inherited Members
Static Public Member Functions inherited from LieGroupBase< _Derived >
static PlainObject	Identity () noexcept
	Construct the identity element.

static PlainObject	Random () noexcept
	Construct a random element.

static PlainObject	exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Lie group exponential map.

static Matrix	hat (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Lie algebra hat map.

static Tangent	vee (const Eigen::MatrixBase< MatrixDerived > &A) noexcept
	Lie alebra vee map.

static TangentMap	ad (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Lie algebra adjoint.

static Tangent	lie_bracket (const Eigen::MatrixBase< TangentDerived1 > &a, const Eigen::MatrixBase< TangentDerived2 > &b) noexcept
	Lie algebra bracket.

static TangentMap	dr_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Right jacobian of the exponential map.

static TangentMap	dr_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Inverse of right jacobian of the exponential map.

static TangentMap	dl_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Left jacobian of the exponential map.

static TangentMap	dl_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Inverse of left jacobian of the exponential map.

static Hessian	d2r_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Right Hessian of the exponential map.

static Hessian	d2r_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Right Hessian of the log map.

static Hessian	d2l_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Left Hessian of the exponential map.

static Hessian	d2l_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Left Hessian of the log map.

Protected Types inherited from LieGroupBase< _Derived >
using	traits = liebase_info< _Derived >
	CRTP traits.

using	Impl = typename traits::Impl
	Group-specific Lie group implementation.

Static Protected Attributes inherited from LieGroupBase< _Derived >
static constexpr bool	is_mutable
	True if underlying storage supports modification.

Detailed Description

template<typename _Derived>
class BundleBase< _Derived >

Base class for Bundle lie groups.

Represents a direct product \(G_1 \times \ldots G_n \) between a collection \(G_1, \ldots, G_n \) of Lie groups.

Elements of the Bundle are of the form \( (g_1, \ldots g_n) \), and operations are performed element-wise, i.e. group composition is

\[ (g_1, \ldots, g_n) \circ (g_1', \ldots, g_n') = (g_1 \circ g_1', \ldots, g_n \circ g_n'). \]

The tangent space dimension is the sum of the tangent space dimension of the member types, and similary for the reprenstation size and the matrix dimension.

Definition at line 48 of file bundle.hpp.

Member Typedef Documentation

◆ PartType

template<typename _Derived >

template<std::size_t Idx>

using BundleBase< _Derived >::PartType = typename liebase_info<_Derived>::template PartPlainObject<Idx>

Part type.

Definition at line 68 of file bundle.hpp.

Member Function Documentation

◆ part() [1/2]

template<typename _Derived >

template<std::size_t Idx>
requires is_mutable

MapDispatch< PartType< Idx > > BundleBase< _Derived >::part ( )

inline

Access part no Idx of Bundle.

Definition at line 86 of file bundle.hpp.

◆ part() [2/2]

template<typename _Derived >

template<std::size_t Idx>

MapDispatch< const PartType< Idx > > BundleBase< _Derived >::part ( ) const

inline

Const access part no Idx of Bundle.

Definition at line 96 of file bundle.hpp.

Member Data Documentation

◆ BundleSize

template<typename _Derived >

constexpr auto BundleBase< _Derived >::BundleSize = Impl::BundleSize

staticconstexpr

Number of elements in Bundle.

Definition at line 62 of file bundle.hpp.

◆ PartDof

template<typename _Derived >

template<std::size_t Idx>

constexpr auto BundleBase< _Derived >::PartDof = Impl::Dofs[Idx]

staticconstexpr

Part degrees of freedom.

Definition at line 80 of file bundle.hpp.

◆ PartStart

template<typename _Derived >

template<std::size_t Idx>

constexpr auto BundleBase< _Derived >::PartStart = Impl::DofsPsum[Idx]

staticconstexpr

Part starting index (degrees of freedom).

Definition at line 74 of file bundle.hpp.

◆ SMOOTH_INHERIT_TYPEDEFS

template<typename _Derived >

BundleBase< _Derived >::SMOOTH_INHERIT_TYPEDEFS

Definition at line 57 of file bundle.hpp.

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

include/smooth/bundle.hpp

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ PartType

Member Function Documentation

◆ part() [1/2]

◆ part() [2/2]

Member Data Documentation

◆ BundleSize

◆ PartDof

◆ PartStart

◆ SMOOTH_INHERIT_TYPEDEFS