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gtsam::SL4 Class Reference
Inheritance diagram for gtsam::SL4:
Matrix Lie Group | |
| using | LieAlgebra = Matrix44 |
| static Matrix44 | Hat (const Vector &xi) |
| Lie algebra coordinates for sl(4) using an orthonormal basis. | |
| static Vector | Vee (const Matrix44 &X) |
Group | |
| SL4 | inverse () const |
| inverse transformation | |
| SL4 | operator* (const SL4 &other) const |
| Group operation. | |
| static SL4 | Identity () |
| identity for group operation | |
Lie Group | |
| Matrix15x15 | AdjointMap () const |
| Adjoint representation of the tangent space. | |
| static SL4 | Expmap (const Vector &xi) |
| Exponential map at identity - create an element from canonical coordinates. | |
| static Vector | Logmap (const SL4 &p) |
| Log map at identity - return the canonical coordinates of this element. | |
Public Member Functions | |
Standard Constructors | |
| SL4 () | |
| Default constructor initializes at origin. | |
| SL4 (const Matrix44 &pose) | |
| Copy constructor. | |
| SL4 (const SL4 &pose)=default | |
| SL4 & | operator= (const SL4 &pose)=default |
| void | print (const std::string &s="") const |
| print with optional string | |
| bool | equals (const SL4 &sl4, double tol=1e-9) const |
| assert equality up to a tolerance | |
| const Matrix44 & | matrix () const |
| convert to 4*4 matrix | |
| Public Member Functions inherited from gtsam::MatrixLieGroup< SL4, 15, 4 > | |
| 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< SL4, 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 SL4 & | derived () const |
| SL4 | inverse (ChartJacobian H) const |
| SL4 | expmap (const TangentVector &v) const |
| expmap as required by manifold concept Applies exponential map to v and composes with *this | |
| TangentVector | logmap (const SL4 &g) const |
| logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g | |
| SL4 | retract (const TangentVector &v) const |
| retract as required by manifold concept: applies v at *this | |
| TangentVector | localCoordinates (const SL4 &g) const |
| localCoordinates as required by manifold concept: finds tangent vector between *this and g | |
Static Public Attributes | |
| static const size_t | dimension = 15 |
| Static Public Attributes inherited from gtsam::MatrixLieGroup< SL4, 15, 4 > | |
| static constexpr auto | dimension |
| Static Public Attributes inherited from gtsam::LieGroup< SL4, D > | |
| static constexpr auto | dimension |
Classes | |
| struct | ChartAtOrigin |
Protected Attributes | |
| Matrix44 | T_ |
Additional Inherited Members | |
| Static Public Member Functions inherited from gtsam::MatrixLieGroup< SL4, 15, 4 > | |
| 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< SL4, D > | |
| static constexpr int | Dim () |
| Static method to get the dimension (compile-time or dynamic). | |
| static SL4 | Retract (const TangentVector &v) |
| Retract at origin: possible in Lie group because it has an identity. | |
| static TangentVector | LocalCoordinates (const SL4 &g) |
| LocalCoordinates at origin: possible in Lie group because it has an identity. | |
| Public Types inherited from gtsam::MatrixLieGroup< SL4, 15, 4 > | |
| using | Base |
| using | ChartJacobian |
| using | Jacobian |
| using | TangentVector |
| using | Vectorized |
| using | VectorizedJacobian |
| Public Types inherited from gtsam::LieGroup< SL4, D > | |
| typedef OptionalJacobian< N, N > | ChartJacobian |
| typedef Eigen::Matrix< double, N, N > | Jacobian |
| typedef Eigen::Matrix< double, N, 1 > | TangentVector |
Member Function Documentation
◆ Hat()
|
static |
Lie algebra coordinates for sl(4) using an orthonormal basis.
We use the orthogonal vector-space decomposition: sl(4) = so(4) ⊕ sym_off(4) ⊕ diag_traceless(4) where so(4) is skew-symmetric rotations, sym_off is symmetric off-diagonal shears, and diag_traceless is the 3-D traceless diagonal subspace.
Ordering of xi (15x1): [r12 r13 r14 r23 r24 r34 s12 s13 s14 s23 s24 s34 h1 h2 h3]
- r_ij scale (E_ij - E_ji)/sqrt(2): skew-symmetric rotations.
- s_ij scale (E_ij + E_ji)/sqrt(2): symmetric off-diagonal shears.
- h1,h2,h3 scale orthonormal traceless diagonals: H1 = (1/sqrt(2)) diag( 1, -1, 0, 0) H2 = (1/sqrt(6)) diag( 1, 1, -2, 0) H3 = (1/sqrt(12)) diag( 1, 1, 1, -3)
The documentation for this class was generated from the following files:
