Detailed Description

A Gaussian factor in the squared-error form.

JacobianFactor implements a Gaussian, which has quadratic negative log-likelihood

\[ E(x) = \frac{1}{2} (Ax-b)^T \Sigma^{-1} (Ax-b) \]

where \( \Sigma \) is a diagonal covariance matrix. The matrix \( A \), r.h.s. vector \( b \), and diagonal noise model \( \Sigma \) are stored in this class.

This factor represents the sum-of-squares error of a linear measurement function, and is created upon linearization of a NoiseModelFactor, which in turn is a sum-of-squares factor with a nonlinear measurement function.

Here is an example of how this factor represents a sum-of-squares error:

Letting \( h(x) \) be a linear measurement prediction function, \( z \) be the actual observed measurement, the residual is

\[ f(x) = h(x) - z . \]

If we expect noise with diagonal covariance matrix \( \Sigma \) on this measurement, then the negative log-likelihood of the Gaussian induced by this measurement model is

\[ E(x) = \frac{1}{2} (h(x) - z)^T \Sigma^{-1} (h(x) - z) . \]

Because \( h(x) \) is linear, we can write it as

\[ h(x) = Ax + e \]

and thus we have

\[ E(x) = \frac{1}{2} (Ax-b)^T \Sigma^{-1} (Ax-b) \]

where \( b = z - e \).

This factor can involve an arbitrary number of variables, and in the above example \( x \) would almost always be only be a subset of the variables in the entire factor graph. There are special constructors for 1-, 2-, and 3- way JacobianFactors, and additional constructors for creating n-way JacobianFactors. The Jacobian matrix \( A \) is passed to these constructors in blocks, for example, for a 2-way factor, the constructor would accept \( A1 \) and \( A2 \), as well as the variable indices \( j1 \) and \( j2 \) and the negative log-likelihood represented by this factor would be

\[ E(x) = \frac{1}{2} (A_1 x_{j1} + A_2 x_{j2} - b)^T \Sigma^{-1} (A_1 x_{j1} + A_2 x_{j2} - b) . \]

Inheritance diagram for gtsam::JacobianFactor:

Public Member Functions
	JacobianFactor (const GaussianFactor &gf)
	Convert from other GaussianFactor.

	JacobianFactor (const JacobianFactor &jf)
	Copy constructor.

	JacobianFactor (const HessianFactor &hf)
	Conversion from HessianFactor (does Cholesky to obtain Jacobian matrix)

	JacobianFactor ()
	default constructor for I/O

	JacobianFactor (const Vector &b_in)
	Construct Null factor.

	JacobianFactor (Key i1, const Matrix &A1, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Construct unary factor.

	JacobianFactor (Key i1, const Matrix &A1, Key i2, const Matrix &A2, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Construct binary factor.

	JacobianFactor (Key i1, const Matrix &A1, Key i2, const Matrix &A2, Key i3, const Matrix &A3, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Construct ternary factor.

template<typename TERMS >
	JacobianFactor (const TERMS &terms, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Construct an n-ary factor. More...

template<typename KEYS >
	JacobianFactor (const KEYS &keys, const VerticalBlockMatrix &augmentedMatrix, const SharedDiagonal &sigmas=SharedDiagonal())
	Constructor with arbitrary number keys, and where the augmented matrix is given all together instead of in block terms. More...

	JacobianFactor (const GaussianFactorGraph &graph, boost::optional< const Ordering & > ordering=boost::none, boost::optional< const VariableSlots & > p_variableSlots=boost::none)
	Build a dense joint factor from all the factors in a factor graph. More...

virtual	~JacobianFactor ()
	Virtual destructor.

virtual GaussianFactor::shared_ptr	clone () const
	Clone this JacobianFactor.

virtual void	print (const std::string &s="", const KeyFormatter &formatter=DefaultKeyFormatter) const

virtual bool	equals (const GaussianFactor &lf, double tol=1e-9) const
	Equals for testable.

Vector	unweighted_error (const VectorValues &c) const

Vector	error_vector (const VectorValues &c) const
	(A*x-b)

virtual double	error (const VectorValues &c) const
	(A*x-b)/sigma

virtual Matrix	augmentedInformation () const
	0.5(Ax-b)'D(A*x-b) More...

virtual Matrix	information () const
	Return the non-augmented information matrix represented by this GaussianFactor.

virtual VectorValues	hessianDiagonal () const
	Return the diagonal of the Hessian for this factor.

virtual void	hessianDiagonal (double *d) const
	Raw memory access version of hessianDiagonal.

virtual std::map< Key, Matrix >	hessianBlockDiagonal () const
	Return the block diagonal of the Hessian for this factor.

virtual std::pair< Matrix, Vector >	jacobian () const
	Returns (dense) A,b pair associated with factor, bakes in the weights.

std::pair< Matrix, Vector >	jacobianUnweighted () const
	Returns (dense) A,b pair associated with factor, does not bake in weights.

virtual Matrix	augmentedJacobian () const
	Return (dense) matrix associated with factor. More...

Matrix	augmentedJacobianUnweighted () const
	Return (dense) matrix associated with factor. More...

const VerticalBlockMatrix &	matrixObject () const
	Return the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object. More...

VerticalBlockMatrix &	matrixObject ()
	Mutable access to the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object. More...

virtual GaussianFactor::shared_ptr	negate () const
	Construct the corresponding anti-factor to negate information stored stored in this factor. More...

virtual bool	empty () const
	Check if the factor is empty. More...

bool	isConstrained () const
	is noise model constrained ?

virtual DenseIndex	getDim (const_iterator variable) const
	Return the dimension of the variable pointed to by the given key iterator todo: Remove this in favor of keeping track of dimensions with variables?

size_t	rows () const
	return the number of rows in the corresponding linear system

size_t	cols () const
	return the number of columns in the corresponding linear system

const SharedDiagonal &	get_model () const
	get a copy of model

SharedDiagonal &	get_model ()
	get a copy of model (non-const version)

const constBVector	getb () const
	Get a view of the r.h.s. More...

constABlock	getA (const_iterator variable) const
	Get a view of the A matrix for the variable pointed to by the given key iterator.

constABlock	getA () const
	Get a view of the A matrix, not weighted by noise.

BVector	getb ()
	Get a view of the r.h.s. More...

ABlock	getA (iterator variable)
	Get a view of the A matrix for the variable pointed to by the given key iterator (non-const version)

ABlock	getA ()
	Get a view of the A matrix.

void	updateHessian (const KeyVector &keys, SymmetricBlockMatrix *info) const
	Update an information matrix by adding the information corresponding to this factor (used internally during elimination). More...

Vector	operator * (const VectorValues &x) const
	Return A*x.

void	transposeMultiplyAdd (double alpha, const Vector &e, VectorValues &x) const
	x += A'*e. More...

void	multiplyHessianAdd (double alpha, const VectorValues &x, VectorValues &y) const
	y += alpha * A'Ax

void	multiplyHessianAdd (double alpha, const double x, double y, const std::vector< size_t > &accumulatedDims) const
	Raw memory access version of multiplyHessianAdd y += alpha * A'Ax Requires the vector accumulatedDims to tell the dimension of each variable: e.g. More...

VectorValues	gradientAtZero () const
	A'*b for Jacobian.

virtual void	gradientAtZero (double *d) const
	A'*b for Jacobian (raw memory version)

Vector	gradient (Key key, const VectorValues &x) const
	Compute the gradient wrt a key at any values.

JacobianFactor	whiten () const
	Return a whitened version of the factor, i.e. More...

std::pair< boost::shared_ptr< GaussianConditional >, shared_ptr >	eliminate (const Ordering &keys)
	Eliminate the requested variables. More...

void	setModel (bool anyConstrained, const Vector &sigmas)
	set noiseModel correctly

boost::shared_ptr< GaussianConditional >	splitConditional (size_t nrFrontals)
	splits a pre-factorized factor into a conditional, and changes the current factor to be the remaining component. More...

Public Member Functions inherited from gtsam::GaussianFactor
	GaussianFactor ()
	Default constructor creates empty factor.

template<typename CONTAINER >
	GaussianFactor (const CONTAINER &keys)
	Construct from container of keys. More...

virtual	~GaussianFactor ()
	Destructor.

Public Member Functions inherited from gtsam::Factor
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

void	print (const std::string &s="Factor", const KeyFormatter &formatter=DefaultKeyFormatter) const
	print

void	printKeys (const std::string &s="Factor", const KeyFormatter &formatter=DefaultKeyFormatter) const
	print only keys

KeyVector &	keys ()

iterator	begin ()
	Iterator at beginning of involved variable keys.

iterator	end ()
	Iterator at end of involved variable keys.

Public Types
typedef JacobianFactor	This
	Typedef to this class.

typedef GaussianFactor	Base
	Typedef to base class.

typedef boost::shared_ptr< This >	shared_ptr
	shared_ptr to this class

typedef VerticalBlockMatrix::Block	ABlock

typedef VerticalBlockMatrix::constBlock	constABlock

typedef ABlock::ColXpr	BVector

typedef constABlock::ConstColXpr	constBVector

Public Types inherited from gtsam::GaussianFactor
typedef GaussianFactor	This
	This class.

typedef boost::shared_ptr< This >	shared_ptr
	shared_ptr to this class

typedef Factor	Base
	Our base class.

Public Types inherited from gtsam::Factor
typedef KeyVector::iterator	iterator
	Iterator over keys.

typedef KeyVector::const_iterator	const_iterator
	Const iterator over keys.

Protected Member Functions
template<typename TERMS >
void	fillTerms (const TERMS &terms, const Vector &b, const SharedDiagonal &noiseModel)
	Internal function to fill blocks and set dimensions.

Protected Member Functions inherited from gtsam::Factor
	Factor ()
	Default constructor for I/O.

template<typename CONTAINER >
	Factor (const CONTAINER &keys)
	Construct factor from container of keys. More...

template<typename ITERATOR >
	Factor (ITERATOR first, ITERATOR last)
	Construct factor from iterator keys. More...

bool	equals (const This &other, double tol=1e-9) const
	check equality

Protected Attributes
VerticalBlockMatrix	Ab_

noiseModel::Diagonal::shared_ptr	model_

Protected Attributes inherited from gtsam::Factor
KeyVector	keys_
	The keys involved in this factor.

Friends
template<typename T >
class	ExpressionFactor

class	boost::serialization::access
	Serialization function.

GTSAM_EXPORT std::pair< boost::shared_ptr< GaussianConditional >, shared_ptr >	EliminateQR (const GaussianFactorGraph &factors, const Ordering &keys)
	Multiply all factors and eliminate the given keys from the resulting factor using a QR variant that handles constraints (zero sigmas). More...

Additional Inherited Members
Static Public Member Functions inherited from gtsam::GaussianFactor
template<typename CONTAINER >
static DenseIndex	Slot (const CONTAINER &keys, Key key)

Static Protected Member Functions inherited from gtsam::Factor
template<typename CONTAINER >
static Factor	FromKeys (const CONTAINER &keys)
	Construct factor from container of keys. More...

template<typename ITERATOR >
static Factor	FromIterators (ITERATOR first, ITERATOR last)
	Construct factor from iterator keys. More...

Constructor & Destructor Documentation

◆ JacobianFactor() [1/3]

template<typename TERMS >

gtsam::JacobianFactor::JacobianFactor	(	const TERMS &	terms,
		const Vector &	b,
		const SharedDiagonal &	model = `SharedDiagonal()`
	)

Construct an n-ary factor.

Template Parameters

TERMS A container whose value type is std::pair<Key, Matrix>, specifying the collection of keys and matrices making up the factor.

◆ JacobianFactor() [2/3]

template<typename KEYS >

gtsam::JacobianFactor::JacobianFactor	(	const KEYS &	keys,
		const VerticalBlockMatrix &	augmentedMatrix,
		const SharedDiagonal &	sigmas = `SharedDiagonal()`
	)

Constructor with arbitrary number keys, and where the augmented matrix is given all together instead of in block terms.

Note that only the active view of the provided augmented matrix is used, and that the matrix data is copied into a newly-allocated matrix in the constructed factor.

◆ JacobianFactor() [3/3]

gtsam::JacobianFactor::JacobianFactor	(	const GaussianFactorGraph &	graph,
		boost::optional< const Ordering & >	ordering = `boost::none`,
		boost::optional< const VariableSlots & >	p_variableSlots = `boost::none`
	)

explicit

Build a dense joint factor from all the factors in a factor graph.

If a VariableSlots structure computed for graph is already available, providing it will reduce the amount of computation performed.

Member Function Documentation

◆ augmentedInformation()

Matrix gtsam::JacobianFactor::augmentedInformation ( ) const

virtual

0.5*(A*x-b)'D(A*x-b)

Return the augmented information matrix represented by this GaussianFactor. The augmented information matrix contains the information matrix with an additional column holding the information vector, and an additional row holding the transpose of the information vector. The lower-right entry contains the constant error term (when \( \delta x = 0 \)). The augmented information matrix is described in more detail in HessianFactor, which in fact stores an augmented information matrix.

Implements gtsam::GaussianFactor.

◆ augmentedJacobian()

Matrix gtsam::JacobianFactor::augmentedJacobian ( ) const

virtual

Return (dense) matrix associated with factor.

The returned system is an augmented matrix: [A b] weights are baked in

Implements gtsam::GaussianFactor.

◆ augmentedJacobianUnweighted()

Matrix gtsam::JacobianFactor::augmentedJacobianUnweighted ( ) const

Return (dense) matrix associated with factor.

The returned system is an augmented matrix: [A b] weights are not baked in

◆ eliminate()

std::pair< GaussianConditional::shared_ptr, JacobianFactor::shared_ptr > gtsam::JacobianFactor::eliminate ( const Ordering & keys )

Eliminate the requested variables.

◆ empty()

virtual bool gtsam::JacobianFactor::empty ( ) const

inlinevirtual

Check if the factor is empty.

TODO: How should this be defined?

Implements gtsam::GaussianFactor.

◆ getb() [1/2]

const constBVector gtsam::JacobianFactor::getb ( ) const

inline

Get a view of the r.h.s.

vector b, not weighted by noise

◆ getb() [2/2]

BVector gtsam::JacobianFactor::getb ( )

inline

Get a view of the r.h.s.

vector b (non-const version)

◆ matrixObject() [1/2]

const VerticalBlockMatrix& gtsam::JacobianFactor::matrixObject ( ) const

inline

Return the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object.

◆ matrixObject() [2/2]

VerticalBlockMatrix& gtsam::JacobianFactor::matrixObject ( )

inline

Mutable access to the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object.

◆ multiplyHessianAdd()

void gtsam::JacobianFactor::multiplyHessianAdd	(	double	alpha,
		const double *	x,
		double *	y,
		const std::vector< size_t > &	accumulatedDims
	)		const

Raw memory access version of multiplyHessianAdd y += alpha * A'*A*x Requires the vector accumulatedDims to tell the dimension of each variable: e.g.

Raw memory access version of multiplyHessianAdd y += alpha * A'*A*x Note: this is not assuming a fixed dimension for the variables, but requires the vector accumulatedDims to tell the dimension of each variable: e.g.

: x0 has dim 3, x2 has dim 6, x3 has dim 2, then accumulatedDims is [0 3 9 11 13] NOTE: size of accumulatedDims is size of keys + 1!! TODO(frank): we should probably kill this if no longer needed

: x0 has dim 3, x2 has dim 6, x3 has dim 2, then accumulatedDims is [0 3 9 11 13] NOTE: size of accumulatedDims is size of keys + 1!! TODO Frank asks: why is this here if not regular ????

Use Eigen magic to access raw memory

Just iterate over all A matrices and multiply in correct config part (looping over keys) E.g.: Jacobian A = [A0 A1 A2] multiplies x = [x0 x1 x2]' Hence: Ax = A0 x0 + A1 x1 + A2 x2 (hence we loop over the keys and accumulate)

Deal with noise properly, need to Double* whiten as we are dividing by variance

multiply with alpha

Again iterate over all A matrices and insert Ai^T into y

◆ negate()

GaussianFactor::shared_ptr gtsam::JacobianFactor::negate ( ) const

virtual

Construct the corresponding anti-factor to negate information stored stored in this factor.

Returns: a HessianFactor with negated Hessian matrices

Implements gtsam::GaussianFactor.

◆ splitConditional()

GaussianConditional::shared_ptr gtsam::JacobianFactor::splitConditional ( size_t nrFrontals )

splits a pre-factorized factor into a conditional, and changes the current factor to be the remaining component.

Performs same operation as eliminate(), but without running QR. NOTE: looks at dimension of noise model to determine how many rows to keep.

Parameters

nrFrontals number of keys to eliminate

◆ transposeMultiplyAdd()

void gtsam::JacobianFactor::transposeMultiplyAdd	(	double	alpha,
		const Vector &	e,
		VectorValues &	x
	)		const

x += A'*e.

If x is initially missing any values, they are created and assumed to start as zero vectors.

◆ updateHessian()

void gtsam::JacobianFactor::updateHessian	(	const KeyVector &	keys,
		SymmetricBlockMatrix *	info
	)		const

virtual

Update an information matrix by adding the information corresponding to this factor (used internally during elimination).

Parameters

scatter	A mapping from variable index to slot index in this HessianFactor
info	The information matrix to be updated

Implements gtsam::GaussianFactor.

◆ whiten()

JacobianFactor gtsam::JacobianFactor::whiten ( ) const

Return a whitened version of the factor, i.e.

with unit diagonal noise model.

Friends And Related Function Documentation

◆ EliminateQR

GTSAM_EXPORT std::pair<boost::shared_ptr<GaussianConditional>, shared_ptr> EliminateQR	(	const GaussianFactorGraph &	factors,
		const Ordering &	keys
	)

friend

Multiply all factors and eliminate the given keys from the resulting factor using a QR variant that handles constraints (zero sigmas).

Computation happens in noiseModel::Gaussian::QR Returns a conditional on those keys, and a new factor on the separator.

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

/Users/dellaert/git/gtsam/gtsam/linear/JacobianFactor.h
/Users/dellaert/git/gtsam/gtsam/linear/JacobianFactor-inl.h
/Users/dellaert/git/gtsam/gtsam/linear/JacobianFactor.cpp

Detailed Description

Public Member Functions

Public Types

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Constructor & Destructor Documentation

◆ JacobianFactor() [1/3]

◆ JacobianFactor() [2/3]

◆ JacobianFactor() [3/3]

Member Function Documentation

◆ augmentedInformation()

◆ augmentedJacobian()

◆ augmentedJacobianUnweighted()

◆ eliminate()

◆ empty()

◆ getb() [1/2]

◆ getb() [2/2]

◆ matrixObject() [1/2]

◆ matrixObject() [2/2]

◆ multiplyHessianAdd()

◆ negate()

◆ splitConditional()

◆ transposeMultiplyAdd()

◆ updateHessian()

◆ whiten()

Friends And Related Function Documentation

◆ EliminateQR