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gtsam::ProductLieGroup< G, H > Class Template Reference
Detailed Description
template<typename G, typename H>
class gtsam::ProductLieGroup< G, H >
class gtsam::ProductLieGroup< G, H >
Direct product Lie group G × H.
Operations are componentwise and tangent vectors concatenate the G and H coordinates. Use SemidirectLieGroup when the first factor acts on the second, and TangentLieGroup for the adjoint-action tangent construction. Standard Lie-group operations and their Jacobians are inherited from LieGroup; this class supplies the direct-product law, component charts, adjoints, and exponential/logarithmic kernels.
Inheritance diagram for gtsam::ProductLieGroup< G, H >:
Group Operations | |
| typedef multiplicative_group_tag | group_flavor |
| ProductLieGroup | operator* (const ProductLieGroup &other) const |
| Group multiplication. | |
| ProductLieGroup | inverse () const |
| Group inverse. | |
| Class | between (const Class &g) const |
| Class | between (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const |
| SOn | between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const |
| Class | compose (const Class &g) const |
| Class | compose (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const |
| SOn | compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const |
| Class | expmap (const TangentVector &v) const |
| expmap as required by manifold concept Applies exponential map to v and composes with *this | |
| template<class C = Class, class = internal::ExpmapWithJacobian<C, TangentVector, ChartJacobian>> | |
| Class | expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const |
| expmap with optional derivatives, when the class provides them | |
| Class | inverse (ChartJacobian H) const |
| TangentVector | logmap (const Class &g) const |
| logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g | |
| template<class C = Class, class = internal::LogmapWithJacobian<C, ChartJacobian>> | |
| TangentVector | logmap (const Class &g, ChartJacobian H1, ChartJacobian H2={}) const |
| logmap with optional derivatives, when the class provides them | |
| static ProductLieGroup | Identity () |
| Identity element. | |
Lie Group Operations | |
| Jacobian | AdjointMap () const |
| Adjoint map. | |
| static ProductLieGroup | Expmap (const TangentVector &v, ChartJacobian Hv={}) |
| Exponential map. | |
| static ProductLieGroup | Expmap (const Eigen::Ref< const typename traits< G >::TangentVector > &v1, const Eigen::Ref< const typename traits< H >::TangentVector > &v2, OptionalJacobian< Eigen::Dynamic, Eigen::Dynamic > H1={}, OptionalJacobian< Eigen::Dynamic, Eigen::Dynamic > H2={}) |
| Exponential map from subgroup tangent vectors. | |
| static TangentVector | Logmap (const ProductLieGroup &p, ChartJacobian Hp={}) |
| Logarithmic map. | |
| static TangentVector | LocalCoordinates (const ProductLieGroup &p, ChartJacobian Hp={}) |
| Local coordinates (same as Logmap). | |
| static Jacobian | adjointMap (const TangentVector &xi) |
| Static Lie-algebra adjoint ad_xi. | |
Public Member Functions | |
Standard Constructors | |
| ProductLieGroup () | |
| Default constructor yields identity. | |
| ProductLieGroup (const G &g, const H &h) | |
| Construct from two subgroup elements. | |
| ProductLieGroup (const Base &base) | |
| Construct from base pair. | |
Manifold Operations | |
| size_t | dim () const |
| Return manifold dimension. | |
| ProductLieGroup | retract (const TangentVector &v, ChartJacobian H1={}, ChartJacobian H2={}) const |
| Retract to manifold. | |
| TangentVector | localCoordinates (const ProductLieGroup &g, ChartJacobian H1={}, ChartJacobian H2={}) const |
| Local coordinates on manifold. | |
Testable interface | |
| void | print (const std::string &s="") const |
| bool | equals (const ProductLieGroup &other, double tol=1e-9) const |
| Public Member Functions inherited from gtsam::LieGroup< ProductLieGroup< G, H >, internal::dimensionSum(traits< G >::dimension, traits< H >::dimension)> | |
| 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 |
| std::enable_if_t< M !=Eigen::Dynamic, int > | dim () const |
| Provided fixed dimension in dim() if needed. | |
| const ProductLieGroup< G, H > & | derived () const |
| ProductLieGroup< G, H > | inverse (ChartJacobian H) const |
| ProductLieGroup< G, H > | expmap (const TangentVector &v) const |
| expmap as required by manifold concept Applies exponential map to v and composes with *this | |
| TangentVector | logmap (const ProductLieGroup< G, H > &g) const |
| logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g | |
| ProductLieGroup< G, H > | retract (const TangentVector &v) const |
| retract as required by manifold concept: applies v at *this | |
| TangentVector | localCoordinates (const ProductLieGroup< G, H > &g) const |
| localCoordinates as required by manifold concept: finds tangent vector between *this and g | |
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< ProductLieGroup< G, H >, internal::dimensionSum(traits< G >::dimension, traits< H >::dimension)> | |
| static constexpr int | Dim () |
| Static method to get the dimension (compile-time or dynamic). | |
| static ProductLieGroup< G, H > | Retract (const TangentVector &v) |
| Retract at origin: possible in Lie group because it has an identity. | |
| static TangentVector | LocalCoordinates (const ProductLieGroup< G, H > &g) |
| LocalCoordinates at origin: possible in Lie group because it has an identity. | |
Static Public Attributes | |
| static constexpr auto | dimension |
| Static Public Attributes inherited from gtsam::LieGroup< ProductLieGroup< G, H >, internal::dimensionSum(traits< G >::dimension, traits< H >::dimension)> | |
| static constexpr auto | dimension |
Public Types | |
| using | This = ProductLieGroup<G, H> |
| using | Base = std::pair<G, H> |
| Base pair type. | |
| using | LieBase |
| using | TangentVector = typename LieBase::TangentVector |
| using | ChartJacobian = typename LieBase::ChartJacobian |
| using | Jacobian = typename LieBase::Jacobian |
| using | Jacobian1 = typename traits<G>::Jacobian |
| using | Jacobian2 = typename traits<H>::Jacobian |
| Public Types inherited from gtsam::LieGroup< ProductLieGroup< G, H >, internal::dimensionSum(traits< G >::dimension, traits< H >::dimension)> | |
| typedef OptionalJacobian< N, N > | ChartJacobian |
| typedef Eigen::Matrix< double, N, N > | Jacobian |
| typedef Eigen::Matrix< double, N, 1 > | TangentVector |
Classes | |
| struct | ChartAtOrigin |
| Component-wise chart at the product identity. More... | |
Protected Member Functions | |
| size_t | firstDim () const |
| size_t | secondDim () const |
| void | checkMatchingDimensions (const ProductLieGroup &other, const char *operation) const |
| Check that another product has matching runtime dimensions. | |
Static Protected Member Functions | |
| template<typename T> | |
| static T | defaultIdentity () |
| Return default identity for fixed-size factors and a placeholder for dynamic ones. | |
| template<typename T, int ComponentDimension = traits<T>::dimension> | |
| static traits< T >::TangentVector | tangentSegment (const TangentVector &v, size_t start, size_t d) |
| Extract a tangent segment for one factor. | |
| template<typename T> | |
| static traits< T >::Jacobian | componentAdjointMap (const typename traits< T >::TangentVector &xi) |
| Compute one factor's static algebra adjoint, including vector spaces. | |
| static TangentVector | makeTangentVector (const typename traits< G >::TangentVector &v1, const typename traits< H >::TangentVector &v2, size_t d1, size_t d2) |
| Concatenate subgroup tangent vectors into the product tangent. | |
| static Jacobian | zeroJacobian (size_t d) |
| Create a zero Jacobian with the requested runtime size. | |
Static Protected Attributes | |
| static constexpr int | n = traits<G>::dimension |
| Dimensions of the two subgroups. | |
| static constexpr int | m = traits<H>::dimension |
| static constexpr bool | firstDynamic = n == Eigen::Dynamic |
| static constexpr bool | secondDynamic = m == Eigen::Dynamic |
Member Typedef Documentation
◆ LieBase
template<typename G, typename H>
| using gtsam::ProductLieGroup< G, H >::LieBase |
Initial value:
constexpr int dimensionSum(int n, int m)
Sum compile-time dimensions, propagating Eigen::Dynamic.
Definition Lie.h:46
A manifold defines a space in which there is a notion of a linear tangent space that can be centered ...
Definition Group.h:37
A CRTP helper class that implements Lie group methods Prerequisites: methods operator*,...
Definition Lie.h:114
Member Function Documentation
◆ adjointMap()
template<typename G, typename H>
|
static |
Static Lie-algebra adjoint ad_xi.
Vector-space factors are treated as abelian; other factors must provide a static adjointMap().
The documentation for this class was generated from the following files:
- /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/base/ProductLieGroup.h
- /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/base/ProductLieGroup-inl.h
