#include <SOn.h>

Inheritance diagram for gtsam::SO< N >:

Classes
struct	ChartAtOrigin

Public Types
enum	{ dimension = internal::DimensionSO(N) }

using	MatrixDD = Eigen::Matrix< double, dimension, dimension >

using	MatrixNN = Eigen::Matrix< double, N, N >

using	VectorN2 = Eigen::Matrix< double, internal::NSquaredSO(N), 1 >

Public Types inherited from gtsam::LieGroup< SO< N >, internal::DimensionSO(N)>
enum

typedef OptionalJacobian< N, N >	ChartJacobian

typedef Eigen::Matrix< double, N, N >	Jacobian

typedef Eigen::Matrix< double, N, 1 >	TangentVector

Public Member Functions
Standard methods
const MatrixNN &	matrix () const
	Return matrix. More...

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::LieGroup< SO< N >, internal::DimensionSO(N)>
SO< N >	between (const SO< N > &g) const

SO< N >	between (const SO< N > &g, ChartJacobian H1, ChartJacobian H2={}) const

SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

GTSAM_EXPORT SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

SO< N >	compose (const SO< N > &g) const

SO< N >	compose (const SO< N > &g, ChartJacobian H1, ChartJacobian H2={}) const

SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

GTSAM_EXPORT SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

const SO< N > &	derived () const

SO< N >	expmap (const TangentVector &v) const

SO< N >	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

SO< N >	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const SO< N > &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const SO< N > &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const SO< N > &g) const

TangentVector	logmap (const SO< N > &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

SO< N >	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

SO< N >	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Protected Types
template<int N_>
using	IsDynamic = typename std::enable_if< N_==Eigen::Dynamic, void >::type

template<int N_>
using	IsFixed = typename std::enable_if< N_ >=2, void >::type

template<int N_>
using	IsSO3 = typename std::enable_if< N_==3, void >::type

Protected Attributes
MatrixNN	matrix_
	Rotation matrix. More...

Constructors
template<int N_ = N, typename = IsFixed<N_>>
	SO ()
	Construct SO<N> identity for N >= 2. More...

template<int N_ = N, typename = IsDynamic<N_>>
	SO (size_t n=0)
	Construct SO<N> identity for N == Eigen::Dynamic. More...

template<typename Derived >
	SO (const Eigen::MatrixBase< Derived > &R)
	Constructor from Eigen Matrix, dynamic version. More...

template<int M, int N_ = N, typename = IsDynamic<N_>>
	SO (const SO< M > &R)
	Construct dynamic SO(n) from Fixed SO<M> More...

template<int N_ = N, typename = IsSO3<N_>>
	SO (const Eigen::AngleAxisd &angleAxis)
	Constructor from AngleAxisd. More...

template<typename Derived >
static SO	FromMatrix (const Eigen::MatrixBase< Derived > &R)
	Named constructor from Eigen Matrix. More...

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. More...

static SO	AxisAngle (const Vector3 &axis, double theta)
	Constructor from axis and angle. Only defined for SO3. More...

static SO	ClosestTo (const MatrixNN &M)

static SO	ChordalMean (const std::vector< SO > &rotations)

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. More...

template<int N_ = N, typename = IsFixed<N_>>
static SO	Random (std::mt19937 &rng)
	Random SO(N) element (no big claims about uniformity) More...

Group
SO	operator* (const SO &other) const
	Multiplication. More...

SO	inverse () const
	inverse of a rotation = transpose More...

template<int N_ = N, typename = IsFixed<N_>>
static SO	Identity ()
	SO<N> identity for N >= 2. More...

template<int N_ = N, typename = IsDynamic<N_>>
static SO	Identity (size_t n=0)
	SO<N> identity for N == Eigen::Dynamic. More...

Manifold
using	TangentVector = Eigen::Matrix< double, dimension, 1 >

using	ChartJacobian = OptionalJacobian< dimension, dimension >

size_t	dim () const

static int	Dim ()
	Return compile-time dimensionality: fixed size N or Eigen::Dynamic. More...

static size_t	Dimension (size_t n)

static size_t	AmbientDim (size_t d)

static MatrixNN	Hat (const TangentVector &xi)

static void	Hat (const Vector &xi, Eigen::Ref< MatrixNN > X)
	In-place version of Hat (see details there), implements recursion. More...

static TangentVector	Vee (const MatrixNN &X)
	Inverse of Hat. See note about xi element order in Hat. More...

template<int N_ = N, typename = IsDynamic<N_>>
static MatrixDD	IdentityJacobian (size_t n)

Lie Group
MatrixDD	AdjointMap () const
	Adjoint map. More...

static SO	Expmap (const TangentVector &omega, ChartJacobian H={})

static MatrixDD	ExpmapDerivative (const TangentVector &omega)
	Derivative of Expmap, currently only defined for SO3. More...

static TangentVector	Logmap (const SO &R, ChartJacobian H={})

static MatrixDD	LogmapDerivative (const TangentVector &omega)
	Derivative of Logmap, currently only defined for SO3. More...

Other methods
VectorN2	vec (OptionalJacobian< internal::NSquaredSO(N), dimension > H={}) const

template<int N_ = N, typename = IsFixed<N_>>
static Matrix	VectorizedGenerators ()
	Calculate N^2 x dim matrix of vectorized Lie algebra generators for SO(N) More...

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) More...

Additional Inherited Members
Static Public Member Functions inherited from gtsam::LieGroup< SO< N >, internal::DimensionSO(N)>
static TangentVector	LocalCoordinates (const SO< N > &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const SO< N > &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static SO< N >	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static SO< N >	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

template<int 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

Definition at line 54 of file SOn.h.

Member Typedef Documentation

◆ ChartJacobian

template<int N>

using gtsam::SO< N >::ChartJacobian = OptionalJacobian<dimension, dimension>

Definition at line 202 of file SOn.h.

◆ IsDynamic

template<int N>

template<int N_>

using gtsam::SO< N >::IsDynamic = typename std::enable_if<N_ == Eigen::Dynamic, void>::type

protected

Definition at line 69 of file SOn.h.

◆ IsFixed

template<int N>

template<int N_>

using gtsam::SO< N >::IsFixed = typename std::enable_if<N_ >= 2, void>::type

protected

Definition at line 71 of file SOn.h.

◆ IsSO3

template<int N>

template<int N_>

using gtsam::SO< N >::IsSO3 = typename std::enable_if<N_ == 3, void>::type

protected

Definition at line 73 of file SOn.h.

◆ MatrixDD

template<int N>

using gtsam::SO< N >::MatrixDD = Eigen::Matrix<double, dimension, dimension>

Definition at line 59 of file SOn.h.

◆ MatrixNN

template<int N>

using gtsam::SO< N >::MatrixNN = Eigen::Matrix<double, N, N>

Definition at line 57 of file SOn.h.

◆ TangentVector

template<int N>

using gtsam::SO< N >::TangentVector = Eigen::Matrix<double, dimension, 1>

Definition at line 201 of file SOn.h.

◆ VectorN2

template<int N>

using gtsam::SO< N >::VectorN2 = Eigen::Matrix<double, internal::NSquaredSO(N), 1>

Definition at line 58 of file SOn.h.

Member Enumeration Documentation

◆ anonymous enum

template<int N>

anonymous enum

Enumerator
dimension

Definition at line 56 of file SOn.h.

Constructor & Destructor Documentation

◆ SO() [1/5]

template<int N>

template<int N_ = N, typename = IsFixed<N_>>

gtsam::SO< N >::SO ( )

inline

Construct SO<N> identity for N >= 2.

Definition at line 81 of file SOn.h.

◆ SO() [2/5]

template<int N>

template<int N_ = N, typename = IsDynamic<N_>>

gtsam::SO< N >::SO ( size_t n = 0 )

inlineexplicit

Construct SO<N> identity for N == Eigen::Dynamic.

Definition at line 85 of file SOn.h.

◆ SO() [3/5]

template<int N>

template<typename Derived >

gtsam::SO< N >::SO ( const Eigen::MatrixBase< Derived > & R )

inlineexplicit

Constructor from Eigen Matrix, dynamic version.

Definition at line 93 of file SOn.h.

◆ SO() [4/5]

template<int N>

template<int M, int N_ = N, typename = IsDynamic<N_>>

gtsam::SO< N >::SO ( const SO< M > & R )

inlineexplicit

Construct dynamic SO(n) from Fixed SO<M>

Definition at line 113 of file SOn.h.

◆ SO() [5/5]

template<int N>

template<int N_ = N, typename = IsSO3<N_>>

gtsam::SO< N >::SO ( const Eigen::AngleAxisd & angleAxis )

inlineexplicit

Constructor from AngleAxisd.

Definition at line 117 of file SOn.h.

Member Function Documentation

◆ AdjointMap()

template<int N>

SO< N >::MatrixDD gtsam::SO< N >::AdjointMap

Adjoint map.

Definition at line 159 of file SO4.cpp.

◆ AmbientDim()

template<int N>

static size_t gtsam::SO< N >::AmbientDim ( size_t d )

inlinestatic

Definition at line 212 of file SOn.h.

◆ AxisAngle()

template<int N>

static SO gtsam::SO< N >::AxisAngle	(	const Vector3 &	axis,
		double	theta
	)

static

Constructor from axis and angle. Only defined for SO3.

◆ ChordalMean()

template<int N>

static SO gtsam::SO< N >::ChordalMean ( const std::vector< SO< N > > & rotations )

static

Named constructor that finds chordal mean $mu = argmin_R \sum sqr(|R-R_i|_F)$ , currently only defined for SO3.

◆ ClosestTo()

template<int N>

static SO gtsam::SO< N >::ClosestTo ( const MatrixNN & M )

static

Named constructor that finds SO(n) matrix closest to M in Frobenius norm, currently only defined for SO3.

◆ cols()

template<int N>

size_t gtsam::SO< N >::cols ( ) const

inline

Definition at line 160 of file SOn.h.

◆ Dim()

template<int N>

static int gtsam::SO< N >::Dim ( )

inlinestatic

Return compile-time dimensionality: fixed size N or Eigen::Dynamic.

Definition at line 205 of file SOn.h.

◆ dim()

template<int N>

size_t gtsam::SO< N >::dim ( ) const

inline

Definition at line 216 of file SOn.h.

◆ Dimension()

template<int N>

static size_t gtsam::SO< N >::Dimension ( size_t n )

inlinestatic

Definition at line 209 of file SOn.h.

◆ equals()

template<int N>

bool gtsam::SO< N >::equals	(	const SO< N > &	other,
		double	tol
	)		const

inline

Definition at line 168 of file SOn.h.

◆ Expmap()

template<int N>

SO< N > gtsam::SO< N >::Expmap	(	const TangentVector &	omega,
		ChartJacobian	H = `{}`
	)

static

Exponential map at identity - create a rotation from canonical coordinates

Definition at line 67 of file SOn-inl.h.

◆ ExpmapDerivative()

template<int N>

SO< N >::MatrixDD gtsam::SO< N >::ExpmapDerivative ( const TangentVector & omega )

static

Derivative of Expmap, currently only defined for SO3.

Definition at line 72 of file SOn-inl.h.

◆ FromMatrix()

template<int N>

template<typename Derived >

static SO gtsam::SO< N >::FromMatrix ( const Eigen::MatrixBase< Derived > & R )

inlinestatic

Named constructor from Eigen Matrix.

Definition at line 97 of file SOn.h.

◆ Hat() [1/2]

template<int N>

SO< N >::MatrixNN gtsam::SO< N >::Hat ( const TangentVector & xi )

static

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).

Definition at line 29 of file SOn-inl.h.

◆ Hat() [2/2]

template<int N>

static void gtsam::SO< N >::Hat	(	const Vector &	xi,
		Eigen::Ref< MatrixNN >	X
	)

static

In-place version of Hat (see details there), implements recursion.

◆ Identity() [1/2]

template<int N>

template<int N_ = N, typename = IsFixed<N_>>

static SO gtsam::SO< N >::Identity ( )

inlinestatic

SO<N> identity for N >= 2.

Definition at line 184 of file SOn.h.

◆ Identity() [2/2]

template<int N>

template<int N_ = N, typename = IsDynamic<N_>>

static SO gtsam::SO< N >::Identity ( size_t n = 0 )

inlinestatic

SO<N> identity for N == Eigen::Dynamic.

Definition at line 190 of file SOn.h.

◆ IdentityJacobian()

template<int N>

template<int N_ = N, typename = IsDynamic<N_>>

static MatrixDD gtsam::SO< N >::IdentityJacobian ( size_t n )

inlinestatic

Definition at line 257 of file SOn.h.

◆ inverse()

template<int N>

SO gtsam::SO< N >::inverse ( ) const

inline

inverse of a rotation = transpose

Definition at line 195 of file SOn.h.

◆ Lift()

template<int N>

template<typename Derived , int N_ = N, typename = IsDynamic<N_>>

static SO gtsam::SO< N >::Lift	(	size_t	n,
		const Eigen::MatrixBase< Derived > &	R
	)

inlinestatic

Named constructor from lower dimensional matrix.

Definition at line 103 of file SOn.h.

◆ Logmap()

template<int N>

SO< N >::TangentVector gtsam::SO< N >::Logmap	(	const SO< N > &	R,
		ChartJacobian	H = `{}`
	)

static

Log map at identity - returns the canonical coordinates of this rotation

Definition at line 77 of file SOn-inl.h.

◆ LogmapDerivative()

template<int N>

SO< N >::MatrixDD gtsam::SO< N >::LogmapDerivative ( const TangentVector & omega )

static

Derivative of Logmap, currently only defined for SO3.

Definition at line 82 of file SOn-inl.h.

◆ matrix()

template<int N>

const MatrixNN& gtsam::SO< N >::matrix ( ) const

inline

Return matrix.

Definition at line 157 of file SOn.h.

◆ operator*()

template<int N>

SO gtsam::SO< N >::operator* ( const SO< N > & other ) const

inline

Multiplication.

Definition at line 177 of file SOn.h.

◆ print()

template<int N>

void gtsam::SO< N >::print ( const std::string & s = std::string() ) const

Definition at line 108 of file SOn-inl.h.

◆ Random() [1/2]

template<int N>

template<int N_ = N, typename = IsFixed<N_>>

static SO gtsam::SO< N >::Random ( std::mt19937 & rng )

inlinestatic

Random SO(N) element (no big claims about uniformity)

Definition at line 147 of file SOn.h.

◆ Random() [2/2]

template<int N>

template<int N_ = N, typename = IsDynamic<N_>>

static SO gtsam::SO< N >::Random	(	std::mt19937 &	rng,
		size_t	n = `0`
	)

inlinestatic

Random SO(n) element (no big claims about uniformity). SO(3) is specialized in SO3.cpp.

Definition at line 133 of file SOn.h.

◆ rows()

template<int N>

size_t gtsam::SO< N >::rows ( ) const

inline

Definition at line 159 of file SOn.h.

◆ vec()

template<int N>

SO< N >::VectorN2 gtsam::SO< N >::vec ( OptionalJacobian< internal::NSquaredSO< N >(N), dimension > H = {} ) const

Return vectorized rotation matrix in column order. Will use dynamic matrices as intermediate results, but returns a fixed size X and fixed-size Jacobian if dimension is known at compile time.

Definition at line 88 of file SOn-inl.h.

◆ VectorizedGenerators() [1/2]

template<int N>

template<int N_ = N, typename = IsFixed<N_>>

static Matrix gtsam::SO< N >::VectorizedGenerators ( )

inlinestatic

Calculate N^2 x dim matrix of vectorized Lie algebra generators for SO(N)

Definition at line 302 of file SOn.h.

◆ VectorizedGenerators() [2/2]

template<int N>

template<int N_ = N, typename = IsDynamic<N_>>

static Matrix gtsam::SO< N >::VectorizedGenerators ( size_t n = 0 )

inlinestatic

Calculate n^2 x dim matrix of vectorized Lie algebra generators for SO(n)

Definition at line 314 of file SOn.h.

◆ Vee()

template<int N>

SO< N >::TangentVector gtsam::SO< N >::Vee ( const MatrixNN & X )

static

Inverse of Hat. See note about xi element order in Hat.

Definition at line 35 of file SOn-inl.h.

Member Data Documentation

◆ matrix_

template<int N>

MatrixNN gtsam::SO< N >::matrix_

protected

Rotation matrix.

Definition at line 64 of file SOn.h.

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

Classes

Public Types

Public Member Functions

Protected Types

Protected Attributes

Constructors

Group

Manifold

Lie Group

Other methods

Additional Inherited Members

Detailed Description

template<int N> class gtsam::SO< N >

Member Typedef Documentation

◆ ChartJacobian

◆ IsDynamic

◆ IsFixed

◆ IsSO3

◆ MatrixDD

◆ MatrixNN

◆ TangentVector

◆ VectorN2

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ SO() [1/5]

◆ SO() [2/5]

◆ SO() [3/5]

◆ SO() [4/5]

◆ SO() [5/5]

Member Function Documentation

◆ AdjointMap()

◆ AmbientDim()

◆ AxisAngle()

◆ ChordalMean()

◆ ClosestTo()

◆ cols()

◆ Dim()

◆ dim()

◆ Dimension()

◆ equals()

◆ Expmap()

◆ ExpmapDerivative()

◆ FromMatrix()

◆ Hat() [1/2]

◆ Hat() [2/2]

◆ Identity() [1/2]

◆ Identity() [2/2]

◆ IdentityJacobian()

◆ inverse()

◆ Lift()

◆ Logmap()

◆ LogmapDerivative()

◆ matrix()

◆ operator*()

◆ print()

◆ Random() [1/2]

◆ Random() [2/2]

◆ rows()

◆ vec()

◆ VectorizedGenerators() [1/2]

◆ VectorizedGenerators() [2/2]

◆ Vee()

Member Data Documentation

◆ matrix_

template<int N>
class gtsam::SO< N >