Detailed Description

A chordal Wahba factor relating two directions through an unknown rotation.

For a rotation aRb that maps frame-b coordinates into frame a, the unwhitened residual is

e(aRb) = aRb * bDirection - measured_aDirection.

The directions are stored as Unit3 values, while the residual is the three-dimensional difference between their unit vectors. This is the classical chordal Wahba objective and is affine in the entries of aRb, so it supports an exact D=1 QCQP conversion. RotateDirectionsFactor instead uses a two-dimensional Unit3 tangent-space error and a different nonlinear model.

See gtsam/slam/doc/WahbaFactor.ipynb for a comparison of the two residuals and a runnable QCQP objective check.

Inheritance diagram for gtsam::WahbaFactor:

Public Member Functions
	WahbaFactor (Key key, const Unit3 &bDirection, const Unit3 &measured_aDirection, const SharedNoiseModel &model)
	Construct from a key, two directions, and a three-dimensional noise model.
NonlinearFactor::shared_ptr	clone () const override
	Creates a shared_ptr clone of the factor - needs to be specialized to allow for subclasses.
bool	equals (const NonlinearFactor &expected, double tol=1e-9) const override
	Check if two factors are equal.
Vector	evaluateError (const Rot3 &aRb, OptionalMatrixType H) const override
	Evaluate the rotated frame-b direction minus measured_aDirection.
void	qcqpFactors (NonlinearFactorGraph costs, NonlinearEqualityConstraints constraints, size_t columnDimension=1) const override
	Add the exact D=1 chordal Wahba cost to a QCQP.
virtual Vector	evaluateError (const ValueTypes &... x, OptionalMatrixTypeT< ValueTypes >... H) const =0
	Override evaluateError to finish implementing an n-way factor.
Vector	evaluateError (const ValueTypes &... x, MatrixTypeT< ValueTypes > &... H) const
	If all the optional arguments are matrices then redirect the call to the one which takes pointers.
Vector	evaluateError (const ValueTypes &... x) const
	No-Jacobians requested function overload.
AreAllMatrixRefs< Vector, OptionalJacArgs... >	evaluateError (const ValueTypes &... x, OptionalJacArgs &&... H) const
	Some (but not all) optional Jacobians are omitted (function overload) and the jacobians are l-value references to matrices.
Public Member Functions inherited from gtsam::NoiseModelFactorT< Vector, ValueTypes... >
Key	key () const
	Returns a key.
Vector	unwhitenedError (const Values &x, std::vector< Matrix > &H) const
	support taking in the actual vector instead of the pointer as well to get access to this version of the function from derived classes one will need to use the "using" keyword and specify that like this: public: using NoiseModelFactor::unwhitenedError;
	NoiseModelFactorT ()
	Default Constructor for I/O.
	NoiseModelFactorT (const SharedNoiseModel &noiseModel, KeyType< ValueTypes >... keys)
	Constructor.
	NoiseModelFactorT (const SharedNoiseModel &noiseModel, CONTAINER keys)
	Constructor.
virtual Vector	evaluateError (const ValueTypes &... x, OptionalMatrixTypeT< ValueTypes >... H) const=0
	Override evaluateError to finish implementing an n-way factor.
Vector	evaluateError (const ValueTypes &... x, MatrixTypeT< ValueTypes > &... H) const
	If all the optional arguments are matrices then redirect the call to the one which takes pointers.
Vector	evaluateError (const ValueTypes &... x) const
	No-Jacobians requested function overload.
AreAllMatrixRefs< Vector, OptionalJacArgs... >	evaluateError (const ValueTypes &... x, OptionalJacArgs &&... H) const
	Some (but not all) optional Jacobians are omitted (function overload) and the jacobians are l-value references to matrices.
AreAllMatrixPtrs< Vector, OptionalJacArgs... >	evaluateError (const ValueTypes &... x, OptionalJacArgs &&... H) const
	Some (but not all) optional Jacobians are omitted (function overload) and the jacobians are pointers to matrices.
Key	key1 () const
Key	key2 () const
Key	key3 () const
Key	key4 () const
Key	key5 () const
Key	key6 () const
std::shared_ptr< GaussianFactor >	linearize (const Values &values) const override
	Linearize factors whose error and argument dimensions are all fixed to an arbitrary-arity FixedJacobianFactor.
Vector	unwhitenedError (const Values &x, OptionalMatrixVecType H=nullptr) const override
	This implements the unwhitenedError virtual function by calling the n-key specific version of evaluateError, which is pure virtual so must be implemented in the derived class.
Public Member Functions inherited from gtsam::NoiseModelFactor
	NoiseModelFactor ()
	Default constructor for I/O only.
	~NoiseModelFactor () override
	Destructor.
template<typename CONTAINER>
	NoiseModelFactor (const SharedNoiseModel &noiseModel, const CONTAINER &keys)
	Constructor.
void	print (const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter) const override
	Print.
size_t	dim () const override
	get the dimension of the factor (number of rows on linearization)
const SharedNoiseModel &	noiseModel () const
	access to the noise model
Vector	unwhitenedError (const Values &x, std::vector< Matrix > &H) const
	support taking in the actual vector instead of the pointer as well to get access to this version of the function from derived classes one will need to use the "using" keyword and specify that like this: public: using NoiseModelFactor::unwhitenedError;
Vector	whitenedError (const Values &c) const
	Vector of errors, whitened This is the raw error, i.e., i.e.
Vector	unweightedWhitenedError (const Values &c) const
	Vector of errors, whitened, but unweighted by any loss function.
double	weight (const Values &c) const
	Compute the effective weight of the factor from the noise model.
double	error (const Values &c) const override
	Calculate the error of the factor.
shared_ptr	cloneWithNewNoiseModel (const SharedNoiseModel newNoise) const
	Creates a shared_ptr clone of the factor with a new noise model.
double	error (const HybridValues &c) const override
	All factor types need to implement an error function.
	NonlinearFactor ()
	Default constructor for I/O only.
template<typename CONTAINER>
	NonlinearFactor (const CONTAINER &keys)
	Constructor from a collection of the keys involved in this factor.
void	print (const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter) const override
	print
double	error (const HybridValues &c) const override
	All factor types need to implement an error function.
virtual bool	active (const Values &c) const
	Checks whether a factor should be used based on a set of values.
virtual shared_ptr	rekey (const std::map< Key, Key > &rekey_mapping) const
	Creates a shared_ptr clone of the factor with different keys using a map from old->new keys.
virtual shared_ptr	rekey (const KeyVector &new_keys) const
	Clones a factor and fully replaces its keys.
virtual bool	sendable () const
	Should the factor be evaluated in the same thread as the caller This is to enable factors that has shared states (like the Python GIL lock).
Public Member Functions inherited from gtsam::Factor
virtual	~Factor ()=default
	Default destructor.
bool	empty () const
	Whether the factor is empty (involves zero variables).
Key	front () const
	First key.
Key	back () const
	Last key.
const_iterator	find (Key key) const
	find
const KeyVector &	keys () const
	Access the factor's involved variable keys.
const_iterator	begin () const
	Iterator at beginning of involved variable keys.
const_iterator	end () const
	Iterator at end of involved variable keys.
size_t	size () const
virtual void	printKeys (const std::string &s="Factor", const KeyFormatter &formatter=DefaultKeyFormatter) const
	print only keys
bool	equals (const This &other, double tol=1e-9) const
	check equality
KeyVector &	keys ()
iterator	begin ()
	Iterator at beginning of involved variable keys.
iterator	end ()
	Iterator at end of involved variable keys.

Public Types
using	Base = NoiseModelFactorN<Rot3>
using	This = WahbaFactor
Public Types inherited from gtsam::NoiseModelFactorT< Vector, ValueTypes... >
using	ValueType
	The type of the I'th template param can be obtained as ValueType.
Public Types inherited from gtsam::NoiseModelFactor
typedef std::shared_ptr< This >	shared_ptr
	Noise model.
Public Types inherited from gtsam::NonlinearFactor
typedef std::shared_ptr< This >	shared_ptr
Public Types inherited from gtsam::Factor
typedef KeyVector::iterator	iterator
	Iterator over keys.
typedef KeyVector::const_iterator	const_iterator
	Const iterator over keys.

Additional Inherited Members
Static Public Attributes inherited from gtsam::NoiseModelFactorT< Vector, ValueTypes... >
static constexpr auto	N
	N is the number of variables (N-way factor).
Protected Types inherited from gtsam::NoiseModelFactorT< Vector, ValueTypes... >
using	Base
using	This
using	OptionalMatrixTypeT
using	KeyType
using	MatrixTypeT
using	IsConvertible
using	IndexIsValid
using	ContainerElementType
using	IsContainerOfKeys
using	AreAllMatrixRefs
	A helper alias to check if a list of args are all references to a matrix or not.
using	IsMatrixPointer
using	IsNullpointer
using	AreAllMatrixPtrs
	A helper alias to check if a list of args are all pointers to a matrix or not.
Protected Types inherited from gtsam::NoiseModelFactor
typedef NonlinearFactor	Base
typedef NoiseModelFactor	This
Protected Types inherited from gtsam::NonlinearFactor
typedef Factor	Base
typedef NonlinearFactor	This
Protected Member Functions inherited from gtsam::NoiseModelFactor
	NoiseModelFactor (const SharedNoiseModel &noiseModel)
	Constructor - only for subclasses, as this does not set keys.
	Factor ()
	Default constructor for I/O.
template<typename CONTAINER>
	Factor (const CONTAINER &keys)
	Construct factor from container of keys.
template<typename ITERATOR>
	Factor (ITERATOR first, ITERATOR last)
	Construct factor from iterator keys.
template<typename CONTAINER>
static Factor	FromKeys (const CONTAINER &keys)
	Construct factor from container of keys.
template<typename ITERATOR>
static Factor	FromIterators (ITERATOR first, ITERATOR last)
	Construct factor from iterator keys.
Protected Attributes inherited from gtsam::NoiseModelFactor
SharedNoiseModel	noiseModel_
Protected Attributes inherited from gtsam::Factor
KeyVector	keys_
	The keys involved in this factor.

Member Function Documentation

◆ clone()

NonlinearFactor::shared_ptr gtsam::WahbaFactor::clone ( ) const

inlineoverridevirtual

Creates a shared_ptr clone of the factor - needs to be specialized to allow for subclasses.

By default, throws exception if subclass does not implement the function.

Reimplemented from gtsam::NonlinearFactor.

◆ equals()

bool gtsam::WahbaFactor::equals	(	const NonlinearFactor &	f,
		double	tol = 1e-9 ) const

inlineoverridevirtual

Check if two factors are equal.

Reimplemented from gtsam::NoiseModelFactor.

◆ evaluateError() [1/4]

Vector gtsam::NoiseModelFactorT< Vector, ValueTypes >::evaluateError ( const ValueTypes &... x ) const

inline

No-Jacobians requested function overload.

This specializes the version below to avoid recursive calls since this is commonly used.

e.g. const Vector error = factor.evaluateError(pose, point);

◆ evaluateError() [2/4]

Vector gtsam::NoiseModelFactorT< Vector, ValueTypes >::evaluateError	(	const ValueTypes &...	x,
		MatrixTypeT< ValueTypes > &...	H ) const

inline

If all the optional arguments are matrices then redirect the call to the one which takes pointers.

To get access to this version of the function from derived classes one will need to use the "using" keyword and specify that like this: public: using NoiseModelFactorT<list the value types here>::evaluateError;

◆ evaluateError() [3/4]

AreAllMatrixRefs< Vector, OptionalJacArgs... > gtsam::NoiseModelFactorT< Vector, ValueTypes >::evaluateError	(	const ValueTypes &...	x,
		OptionalJacArgs &&...	H ) const

inline

Some (but not all) optional Jacobians are omitted (function overload) and the jacobians are l-value references to matrices.

e.g. const Vector error = factor.evaluateError(pose, point, Hpose);

◆ evaluateError() [4/4]

virtual Vector gtsam::NoiseModelFactorT< Vector, ValueTypes >::evaluateError	(	const ValueTypes &...	x,
		OptionalMatrixTypeT< ValueTypes >...	H ) const

Override evaluateError to finish implementing an n-way factor.

Both the x and H arguments are written here as parameter packs, but when overriding this method, you probably want to explicitly write them out. For example, for a 2-way factor with variable types Pose3 and Point3, you should implement:

Vector evaluateError(
    const Pose3& x1, const Point3& x2,
    OptionalMatrixType H1 = OptionalNone,
    OptionalMatrixType H2 = OptionalNone) const override { ... }

If any of the optional Matrix reference arguments are specified, it should compute both the function evaluation and its derivative(s) in the requested variables.

Parameters

	x	The values of the variables to evaluate the error for. Passed in as separate arguments.
[out]	H	The Jacobian with respect to each variable (optional).

◆ qcqpFactors()

void gtsam::WahbaFactor::qcqpFactors	(	NonlinearFactorGraph *	costs,
		NonlinearEqualityConstraints *	constraints,
		size_t	columnDimension = 1 ) const

inlineoverridevirtual

Add the exact D=1 chordal Wahba cost to a QCQP.

Reimplemented from gtsam::NonlinearFactor.

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

/tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/slam/WahbaFactor.h

Detailed Description

Public Member Functions

Public Types

Additional Inherited Members

Member Function Documentation

◆ clone()

◆ equals()

◆ evaluateError() [1/4]

◆ evaluateError() [2/4]

◆ evaluateError() [3/4]

◆ evaluateError() [4/4]

◆ qcqpFactors()