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gtsam::SO< N > Class Template Reference
Detailed Description
template<int N>
class gtsam::SO< N >
class gtsam::SO< N >
Manifold of special orthogonal rotation matrices SO<N>.
Template paramater N can be a fixed integer or can be Eigen::Dynamic
Inheritance diagram for gtsam::SO< N >:
Manifold | |
| using | TangentVector = Eigen::Matrix<double, dimension, 1> |
| using | ChartJacobian = OptionalJacobian<dimension, dimension> |
| size_t | dim () const |
| static size_t | Dimension (size_t n) |
| static size_t | AmbientDim (size_t d) |
| static MatrixNN | Hat (const TangentVector &xi) |
| Hat operator creates Lie algebra element corresponding to d-vector, where d is the dimensionality of the manifold. | |
| static void | Hat (const Vector &xi, Eigen::Ref< MatrixNN > X) |
| In-place version of Hat (see details there), implements recursion. | |
| static TangentVector | Vee (const MatrixNN &X) |
| Inverse of Hat. See note about xi element order in Hat. | |
| template<int N_ = N, typename = IsDynamic<N_>> | |
| static MatrixDD | IdentityJacobian (size_t n) |
Constructors | |
| template<int N_ = N, typename = IsFixed<N_>> | |
| SO () | |
| Construct SO<N> identity for N >= 2. | |
| template<int N_ = N, typename = IsDynamic<N_>> | |
| SO (size_t n=0) | |
| Construct SO<N> identity for N == Eigen::Dynamic. | |
| template<typename Derived> | |
| SO (const Eigen::MatrixBase< Derived > &R) | |
| Constructor from Eigen Matrix, dynamic version. | |
| template<int M, int N_ = N, typename = IsDynamic<N_>> | |
| SO (const SO< M > &R) | |
| Construct dynamic SO(n) from Fixed SO<M>. | |
| template<int N_ = N, typename = IsSO3<N_>> | |
| SO (const Eigen::AngleAxisd &angleAxis) | |
| Constructor from AngleAxisd. | |
| template<typename Derived> | |
| static SO | FromMatrix (const Eigen::MatrixBase< Derived > &R) |
| Named constructor from Eigen Matrix. | |
| template<typename Derived, int N_ = N, typename = IsDynamic<N_>> | |
| static SO | Lift (size_t n, const Eigen::MatrixBase< Derived > &R) |
| Named constructor from lower dimensional matrix. | |
| static SO | AxisAngle (const Vector3 &axis, double theta) |
| Constructor from axis and angle. Only defined for SO3. | |
| static SO | ClosestTo (const MatrixNN &M) |
| Named constructor that finds SO(n) matrix closest to M in Frobenius norm, currently only defined for SO3. | |
| static SO | ChordalMean (const std::vector< SO > &rotations) |
| Named constructor that finds chordal mean \( mu = argmin_R \sum sqr(|R-R_i|_F) \), currently only defined for SO3. | |
| template<int N_ = N, typename = IsDynamic<N_>> | |
| static SO | Random (std::mt19937 &rng, size_t n=0) |
| Random SO(n) element (no big claims about uniformity). SO(3) is specialized in SO3.cpp. | |
| template<int N_ = N, typename = IsFixed<N_>> | |
| static SO | Random (std::mt19937 &rng) |
| Random SO(N) element (no big claims about uniformity). | |
Group | |
| SO | operator* (const SO &other) const |
| Multiplication. | |
| SO | inverse () const |
| inverse of a rotation = transpose | |
| template<int N_ = N, typename = IsFixed<N_>> | |
| static SO | Identity () |
| SO<N> identity for N >= 2. | |
| template<int N_ = N, typename = IsDynamic<N_>> | |
| static SO | Identity (size_t n=0) |
| SO<N> identity for N == Eigen::Dynamic. | |
Lie Group | |
| MatrixDD | AdjointMap () const |
| Adjoint map. | |
| static SO | Expmap (const TangentVector &omega) |
| Exponential map at identity - create a rotation from canonical coordinates. | |
| static SO | Expmap (const TangentVector &omega, ChartJacobian H)=delete |
| Exponential map with a Jacobian, specialized when supported. | |
| static MatrixDD | ExpmapDerivative (const TangentVector &omega)=delete |
| Derivative of Expmap, specialized when supported. | |
| static TangentVector | Logmap (const SO &R) |
| Log map at identity - returns the canonical coordinates of this rotation. | |
| static TangentVector | Logmap (const SO &R, ChartJacobian H)=delete |
| Logarithm map with a Jacobian, specialized when supported. | |
| static MatrixDD | LogmapDerivative (const TangentVector &omega)=delete |
| Derivative of Logmap, specialized when supported. | |
Other methods | |
| VectorN2 | vec (OptionalJacobian< internal::NSquaredSO(N), dimension > H={}) const |
| Return vectorized rotation matrix in column order. | |
| template<int N_ = N, typename = IsFixed<N_>> | |
| static Matrix | VectorizedGenerators () |
| Calculate N^2 x dim matrix of vectorized Lie algebra generators for SO(N). | |
| template<int N_ = N, typename = IsDynamic<N_>> | |
| static Matrix | VectorizedGenerators (size_t n=0) |
| Calculate n^2 x dim matrix of vectorized Lie algebra generators for SO(n). | |
Public Member Functions | |
Standard methods | |
| const MatrixNN & | matrix () const |
| Return matrix. | |
| size_t | rows () const |
| size_t | cols () const |
Testable | |
| void | print (const std::string &s=std::string()) const |
| bool | equals (const SO &other, double tol) const |
| Public Member Functions inherited from gtsam::MatrixLieGroup< SO< N >, internal::DimensionSO(N), N > | |
| std::enable_if_t< M !=Eigen::Dynamic, int > | dim () const |
| Provided fixed dimension in dim() if needed. | |
| Eigen::Matrix< double, internal::product(N, N), 1 > | vec (OptionalJacobian< internal::product(N, N), D > H={}) const |
| Vectorize the matrix representation of a Lie group element. | |
| Jacobian | AdjointMap () const |
| A generic implementation of AdjointMap for matrix Lie groups. | |
| TangentVector | Adjoint (const TangentVector &xi, ChartJacobian H_this={}, ChartJacobian H_xi={}) const |
| Adjoint action on a tangent vector. | |
| TangentVector | AdjointTranspose (const TangentVector &x, ChartJacobian H_this={}, ChartJacobian H_x={}) const |
| Dual Adjoint action on a tangent covector. | |
| Public Member Functions inherited from gtsam::LieGroup< SO< N >, D > | |
| 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 SO< N > & | derived () const |
| SO< N > | inverse (ChartJacobian H) const |
| SO< N > | expmap (const TangentVector &v) const |
| expmap as required by manifold concept Applies exponential map to v and composes with *this | |
| TangentVector | logmap (const SO< N > &g) const |
| logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g | |
| SO< N > | retract (const TangentVector &v) const |
| retract as required by manifold concept: applies v at *this | |
| TangentVector | localCoordinates (const SO< N > &g) const |
| localCoordinates as required by manifold concept: finds tangent vector between *this and g | |
Static Public Attributes | |
| static constexpr auto | dimension = internal::DimensionSO(N) |
| Static Public Attributes inherited from gtsam::MatrixLieGroup< SO< N >, internal::DimensionSO(N), N > | |
| static constexpr auto | dimension |
| Static Public Attributes inherited from gtsam::LieGroup< SO< N >, D > | |
| static constexpr auto | dimension |
Public Types | |
| using | MatrixNN = Eigen::Matrix<double, N, N> |
| using | VectorN2 = Eigen::Matrix<double, internal::NSquaredSO(N), 1> |
| using | MatrixDD = Eigen::Matrix<double, dimension, dimension> |
| using | LieAlgebra = MatrixNN |
| LieGroup Concept requirements. | |
| Public Types inherited from gtsam::MatrixLieGroup< SO< N >, internal::DimensionSO(N), N > | |
| using | Base |
| using | ChartJacobian |
| using | Jacobian |
| using | TangentVector |
| using | Vectorized |
| using | VectorizedJacobian |
| Public Types inherited from gtsam::LieGroup< SO< N >, D > | |
| typedef OptionalJacobian< N, N > | ChartJacobian |
| typedef Eigen::Matrix< double, N, N > | Jacobian |
| typedef Eigen::Matrix< double, N, 1 > | TangentVector |
Classes | |
| struct | ChartAtOrigin |
Protected Attributes | |
| MatrixNN | matrix_ |
| Rotation matrix. | |
Additional Inherited Members | |
| Static Public Member Functions inherited from gtsam::MatrixLieGroup< SO< N >, internal::DimensionSO(N), N > | |
| static constexpr int | Dim () |
| Static method to get the dimension (compile-time or dynamic). | |
| static Jacobian | adjointMap (const TangentVector &xi) |
| Lie algebra adjoint map ad_xi, with optional specialization in derived classes. | |
| static TangentVector | adjoint (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={}) |
| Lie algebra action ad_xi(y), with optional Jacobians. | |
| static TangentVector | adjointTranspose (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={}) |
| Dual Lie algebra action ad_xi^T(y), with optional Jacobians. | |
| Static Public Member Functions inherited from gtsam::LieGroup< SO< N >, D > | |
| static constexpr int | Dim () |
| Static method to get the dimension (compile-time or dynamic). | |
| static SO< N > | Retract (const TangentVector &v) |
| Retract at origin: possible in Lie group because it has an identity. | |
| static TangentVector | LocalCoordinates (const SO< N > &g) |
| LocalCoordinates at origin: possible in Lie group because it has an identity. | |
Member Function Documentation
◆ Hat()
Hat operator creates Lie algebra element corresponding to d-vector, where d is the dimensionality of the manifold.
This function is implemented recursively, and the d-vector is assumed to laid out such that the last element corresponds to so(2), the last 3 to so(3), the last 6 to so(4) etc... For example, the vector-space isomorphic to so(5) is laid out as: a b c d | u v w | x y | z where the latter elements correspond to "telescoping" sub-algebras: 0 -z y w -d z 0 -x -v c -y x 0 u -b -w v -u 0 a d -c b -a 0 This scheme behaves exactly as expected for SO(2) and SO(3).
The documentation for this class was generated from the following files:
