gtsam::GaussianFactorGraph Class Reference

Detailed Description

A Linear Factor Graph is a factor graph where all factors are Gaussian, i.e.

Factor == GaussianFactor VectorValues = A values structure of vectors Most of the time, linear factor graphs arise by linearizing a non-linear factor graph.

Inheritance diagram for gtsam::GaussianFactorGraph:

Public Member Functions
	GaussianFactorGraph ()
	Default constructor.
template<typename ITERATOR >
	GaussianFactorGraph (ITERATOR firstFactor, ITERATOR lastFactor)
	Construct from iterator over factors.
template<class CONTAINER >
	GaussianFactorGraph (const CONTAINER &factors)
	Construct from container of factors (shared_ptr or plain objects)
template<class DERIVEDFACTOR >
	GaussianFactorGraph (const FactorGraph< DERIVEDFACTOR > &graph)
	Implicit copy/downcast constructor to override explicit template container constructor.
virtual	~GaussianFactorGraph ()
	Virtual destructor.
void	add (const GaussianFactor &factor)
	Add a factor by value - makes a copy.
void	add (const sharedFactor &factor)
	Add a factor by pointer - stores pointer without copying the factor.
void	add (const Vector &b)
	Add a null factor.
void	add (Key key1, const Matrix &A1, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Add a unary factor.
void	add (Key key1, const Matrix &A1, Key key2, const Matrix &A2, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Add a binary factor.
void	add (Key key1, const Matrix &A1, Key key2, const Matrix &A2, Key key3, const Matrix &A3, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Add a ternary factor.
template<class TERMS >
void	add (const TERMS &terms, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
	Add an n-ary factor.
Keys	keys () const
std::map< Key, size_t >	getKeyDimMap () const
double	error (const VectorValues &x) const
	unnormalized error
double	probPrime (const VectorValues &c) const
	Unnormalized probability. More...
virtual GaussianFactorGraph	clone () const
	Clone() performs a deep-copy of the graph, including all of the factors. More...
virtual GaussianFactorGraph::shared_ptr	cloneToPtr () const
	CloneToPtr() performs a simple assignment to a new graph and returns it. More...
GaussianFactorGraph	negate () const
	Returns the negation of all factors in this graph - corresponds to antifactors. More...
Testable
bool	equals (const This &fg, double tol=1e-9) const
Linear Algebra
std::vector< std::tuple< int, int, double > >	sparseJacobian (const Ordering &ordering, size_t &nrows, size_t &ncols) const
	Returns a sparse augmented Jacbian matrix as a vector of i, j, and s, where i(k) and j(k) are the base 0 row and column indices, and s(k) is the entry as a double. More...
std::vector< std::tuple< int, int, double > >	sparseJacobian () const
	Returns a sparse augmented Jacobian matrix with default ordering.
Matrix	sparseJacobian_ () const
	Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] entries such that S(i(k),j(k)) = s(k), which can be given to MATLAB's sparse. More...
Matrix	augmentedJacobian (const Ordering &ordering) const
	Return a dense \( [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \) Jacobian matrix, augmented with b with the noise models baked into A and b. More...
Matrix	augmentedJacobian () const
	Return a dense \( [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \) Jacobian matrix, augmented with b with the noise models baked into A and b. More...
std::pair< Matrix, Vector >	jacobian (const Ordering &ordering) const
	Return the dense Jacobian \( A \) and right-hand-side \( b \), with the noise models baked into A and b. More...
std::pair< Matrix, Vector >	jacobian () const
	Return the dense Jacobian \( A \) and right-hand-side \( b \), with the noise models baked into A and b. More...
Matrix	augmentedHessian (const Ordering &ordering) const
	Return a dense \( \Lambda \in \mathbb{R}^{n+1 \times n+1} \) Hessian matrix, augmented with the information vector \( \eta \). More...
Matrix	augmentedHessian () const
	Return a dense \( \Lambda \in \mathbb{R}^{n+1 \times n+1} \) Hessian matrix, augmented with the information vector \( \eta \). More...
std::pair< Matrix, Vector >	hessian (const Ordering &ordering) const
	Return the dense Hessian \( \Lambda \) and information vector \( \eta \), with the noise models baked in. More...
std::pair< Matrix, Vector >	hessian () const
	Return the dense Hessian \( \Lambda \) and information vector \( \eta \), with the noise models baked in. More...
virtual VectorValues	hessianDiagonal () const
	Return only the diagonal of the Hessian A'*A, as a VectorValues.
virtual std::map< Key, Matrix >	hessianBlockDiagonal () const
	Return the block diagonal of the Hessian for this factor.
VectorValues	optimize (const Eliminate &function=EliminationTraitsType::DefaultEliminate) const
	Solve the factor graph by performing multifrontal variable elimination in COLAMD order using the dense elimination function specified in function (default EliminatePreferCholesky), followed by back-substitution in the Bayes tree resulting from elimination. More...
VectorValues	optimize (const Ordering &, const Eliminate &function=EliminationTraitsType::DefaultEliminate) const
	Solve the factor graph by performing multifrontal variable elimination in COLAMD order using the dense elimination function specified in function (default EliminatePreferCholesky), followed by back-substitution in the Bayes tree resulting from elimination. More...
VectorValues	optimizeDensely () const
	Optimize using Eigen's dense Cholesky factorization.
VectorValues	gradient (const VectorValues &x0) const
	Compute the gradient of the energy function, \( \nabla_{x=x_0} \left\Vert \Sigma^{-1} A x - b \right\Vert^2 \), centered around \( x = x_0 \). More...
virtual VectorValues	gradientAtZero () const
	Compute the gradient of the energy function, \( \nabla_{x=0} \left\Vert \Sigma^{-1} A x - b \right\Vert^2 \), centered around zero. More...
VectorValues	optimizeGradientSearch () const
	Optimize along the gradient direction, with a closed-form computation to perform the line search. More...
VectorValues	transposeMultiply (const Errors &e) const
	x = A'*e More...
void	transposeMultiplyAdd (double alpha, const Errors &e, VectorValues &x) const
	x += alpha*A'*e
Errors	gaussianErrors (const VectorValues &x) const
	return A*x-b
Errors	operator* (const VectorValues &x) const
	‍** return A*x *‍/
void	multiplyHessianAdd (double alpha, const VectorValues &x, VectorValues &y) const
	‍** y += alpha*A'A*x *‍/
void	multiplyInPlace (const VectorValues &x, Errors &e) const
	‍** In-place version e <- A*x that overwrites e. *‍/
void	multiplyInPlace (const VectorValues &x, const Errors::iterator &e) const
	In-place version e <- A*x that takes an iterator.
void	printErrors (const VectorValues &x, const std::string &str="GaussianFactorGraph: ", const KeyFormatter &keyFormatter=DefaultKeyFormatter, const std::function< bool(const Factor *, double, size_t)> &printCondition=[](const Factor *, double, size_t) { return true;}) const
Public Member Functions inherited from gtsam::FactorGraph< GaussianFactor >
virtual	~FactorGraph ()=default
	Default destructor.
void	reserve (size_t size)
	Reserve space for the specified number of factors if you know in advance how many there will be (works like FastVector::reserve).
IsDerived< DERIVEDFACTOR >	push_back (boost::shared_ptr< DERIVEDFACTOR > factor)
	Add a factor directly using a shared_ptr.
IsDerived< DERIVEDFACTOR >	push_back (const DERIVEDFACTOR &factor)
	Add a factor by value, will be copy-constructed (use push_back with a shared_ptr to avoid the copy).
IsDerived< DERIVEDFACTOR >	emplace_shared (Args &&... args)
	Emplace a shared pointer to factor of given type.
IsDerived< DERIVEDFACTOR >	add (boost::shared_ptr< DERIVEDFACTOR > factor)
	add is a synonym for push_back.
std::enable_if< std::is_base_of< FactorType, DERIVEDFACTOR >::value, boost::assign::list_inserter< RefCallPushBack< This > > >::type	operator+= (boost::shared_ptr< DERIVEDFACTOR > factor)
	+= works well with boost::assign list inserter.
HasDerivedElementType< ITERATOR >	push_back (ITERATOR firstFactor, ITERATOR lastFactor)
	Push back many factors with an iterator over shared_ptr (factors are not copied)
HasDerivedValueType< ITERATOR >	push_back (ITERATOR firstFactor, ITERATOR lastFactor)
	Push back many factors with an iterator (factors are copied)
HasDerivedElementType< CONTAINER >	push_back (const CONTAINER &container)
	Push back many factors as shared_ptr's in a container (factors are not copied)
HasDerivedValueType< CONTAINER >	push_back (const CONTAINER &container)
	Push back non-pointer objects in a container (factors are copied).
void	add (const FACTOR_OR_CONTAINER &factorOrContainer)
	Add a factor or container of factors, including STL collections, BayesTrees, etc.
boost::assign::list_inserter< CRefCallPushBack< This > >	operator+= (const FACTOR_OR_CONTAINER &factorOrContainer)
	Add a factor or container of factors, including STL collections, BayesTrees, etc.
std::enable_if< std::is_base_of< This, typenameCLIQUE::FactorGraphType >::value >::type	push_back (const BayesTree< CLIQUE > &bayesTree)
	Push back a BayesTree as a collection of factors. More...
FactorIndices	add_factors (const CONTAINER &factors, bool useEmptySlots=false)
	Add new factors to a factor graph and returns a list of new factor indices, optionally finding and reusing empty factor slots.
virtual void	print (const std::string &s="FactorGraph", const KeyFormatter &formatter=DefaultKeyFormatter) const
	print out graph
bool	equals (const This &fg, double tol=1e-9) const
	Check equality.
size_t	size () const
	return the number of factors (including any null factors set by remove() ).
bool	empty () const
	Check if the graph is empty (null factors set by remove() will cause this to return false).
const sharedFactor	at (size_t i) const
	Get a specific factor by index (this checks array bounds and may throw an exception, as opposed to operator[] which does not).
sharedFactor &	at (size_t i)
	Get a specific factor by index (this checks array bounds and may throw an exception, as opposed to operator[] which does not).
const sharedFactor	operator[] (size_t i) const
	Get a specific factor by index (this does not check array bounds, as opposed to at() which does).
sharedFactor &	operator[] (size_t i)
	Get a specific factor by index (this does not check array bounds, as opposed to at() which does).
const_iterator	begin () const
	Iterator to beginning of factors.
const_iterator	end () const
	Iterator to end of factors.
sharedFactor	front () const
	Get the first factor.
sharedFactor	back () const
	Get the last factor.
iterator	begin ()
	non-const STL-style begin()
iterator	end ()
	non-const STL-style end()
void	resize (size_t size)
	Directly resize the number of factors in the graph. More...
void	remove (size_t i)
	delete factor without re-arranging indexes by inserting a nullptr pointer
void	replace (size_t index, sharedFactor factor)
	replace a factor by index
iterator	erase (iterator item)
	Erase factor and rearrange other factors to take up the empty space.
iterator	erase (iterator first, iterator last)
	Erase factors and rearrange other factors to take up the empty space.
size_t	nrFactors () const
	return the number of non-null factors
KeySet	keys () const
	Potentially slow function to return all keys involved, sorted, as a set.
KeyVector	keyVector () const
	Potentially slow function to return all keys involved, sorted, as a vector.
bool	exists (size_t idx) const
	MATLAB interface utility: Checks whether a factor index idx exists in the graph and is a live pointer.
Public Member Functions inherited from gtsam::EliminateableFactorGraph< GaussianFactorGraph >
boost::shared_ptr< BayesNetType >	eliminateSequential (OptionalOrderingType orderingType=boost::none, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do sequential elimination of all variables to produce a Bayes net. More...
boost::shared_ptr< BayesNetType >	eliminateSequential (const Ordering &ordering, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do sequential elimination of all variables to produce a Bayes net. More...
boost::shared_ptr< BayesTreeType >	eliminateMultifrontal (OptionalOrderingType orderingType=boost::none, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do multifrontal elimination of all variables to produce a Bayes tree. More...
boost::shared_ptr< BayesTreeType >	eliminateMultifrontal (const Ordering &ordering, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do multifrontal elimination of all variables to produce a Bayes tree. More...
std::pair< boost::shared_ptr< BayesNetType >, boost::shared_ptr< FactorGraphType > >	eliminatePartialSequential (const Ordering &ordering, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do sequential elimination of some variables, in ordering provided, to produce a Bayes net and a remaining factor graph. More...
std::pair< boost::shared_ptr< BayesNetType >, boost::shared_ptr< FactorGraphType > >	eliminatePartialSequential (const KeyVector &variables, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do sequential elimination of the given variables in an ordering computed by COLAMD to produce a Bayes net and a remaining factor graph. More...
std::pair< boost::shared_ptr< BayesTreeType >, boost::shared_ptr< FactorGraphType > >	eliminatePartialMultifrontal (const Ordering &ordering, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do multifrontal elimination of some variables, in ordering provided, to produce a Bayes tree and a remaining factor graph. More...
std::pair< boost::shared_ptr< BayesTreeType >, boost::shared_ptr< FactorGraphType > >	eliminatePartialMultifrontal (const KeyVector &variables, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Do multifrontal elimination of the given variables in an ordering computed by COLAMD to produce a Bayes net and a remaining factor graph. More...
boost::shared_ptr< BayesNetType >	marginalMultifrontalBayesNet (boost::variant< const Ordering &, const KeyVector & > variables, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Compute the marginal of the requested variables and return the result as a Bayes net. More...
boost::shared_ptr< BayesNetType >	marginalMultifrontalBayesNet (boost::variant< const Ordering &, const KeyVector & > variables, const Ordering &marginalizedVariableOrdering, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Compute the marginal of the requested variables and return the result as a Bayes net. More...
boost::shared_ptr< BayesTreeType >	marginalMultifrontalBayesTree (boost::variant< const Ordering &, const KeyVector & > variables, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Compute the marginal of the requested variables and return the result as a Bayes tree. More...
boost::shared_ptr< BayesTreeType >	marginalMultifrontalBayesTree (boost::variant< const Ordering &, const KeyVector & > variables, const Ordering &marginalizedVariableOrdering, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Compute the marginal of the requested variables and return the result as a Bayes tree. More...
boost::shared_ptr< FactorGraphType >	marginal (const KeyVector &variables, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
	Compute the marginal factor graph of the requested variables.

Public Types
typedef GaussianFactorGraph	This
	Typedef to this class.
typedef FactorGraph< GaussianFactor >	Base
	Typedef to base factor graph type.
typedef EliminateableFactorGraph< This >	BaseEliminateable
	Typedef to base elimination class.
typedef boost::shared_ptr< This >	shared_ptr
	shared_ptr to this class
typedef KeySet	Keys
	Return the set of variables involved in the factors (computes a set union).
Public Types inherited from gtsam::FactorGraph< GaussianFactor >
typedef GaussianFactor	FactorType
	factor type
typedef boost::shared_ptr< GaussianFactor >	sharedFactor
	Shared pointer to a factor.
typedef sharedFactor	value_type
typedef FastVector< sharedFactor >::iterator	iterator
typedef FastVector< sharedFactor >::const_iterator	const_iterator
Public Types inherited from gtsam::EliminateableFactorGraph< GaussianFactorGraph >
typedef EliminationTraits< FactorGraphType >	EliminationTraitsType
	Typedef to the specific EliminationTraits for this graph.
typedef EliminationTraitsType::ConditionalType	ConditionalType
	Conditional type stored in the Bayes net produced by elimination.
typedef EliminationTraitsType::BayesNetType	BayesNetType
	Bayes net type produced by sequential elimination.
typedef EliminationTraitsType::EliminationTreeType	EliminationTreeType
	Elimination tree type that can do sequential elimination of this graph.
typedef EliminationTraitsType::BayesTreeType	BayesTreeType
	Bayes tree type produced by multifrontal elimination.
typedef EliminationTraitsType::JunctionTreeType	JunctionTreeType
	Junction tree type that can do multifrontal elimination of this graph.
typedef std::pair< boost::shared_ptr< ConditionalType >, boost::shared_ptr< _FactorType > >	EliminationResult
	The pair of conditional and remaining factor produced by a single dense elimination step on a subgraph.
typedef std::function< EliminationResult(const FactorGraphType &, const Ordering &)>	Eliminate
	The function type that does a single dense elimination step on a subgraph.
typedef boost::optional< const VariableIndex & >	OptionalVariableIndex
	Typedef for an optional variable index as an argument to elimination functions.
typedef boost::optional< Ordering::OrderingType >	OptionalOrderingType
	Typedef for an optional ordering type.

Friends
class	boost::serialization::access
	Serialization function.

Additional Inherited Members
Protected Member Functions inherited from gtsam::FactorGraph< GaussianFactor >
	FactorGraph ()
	Default constructor.
	FactorGraph (ITERATOR firstFactor, ITERATOR lastFactor)
	Constructor from iterator over factors (shared_ptr or plain objects)
	FactorGraph (const CONTAINER &factors)
	Construct from container of factors (shared_ptr or plain objects)
Protected Attributes inherited from gtsam::FactorGraph< GaussianFactor >
FastVector< sharedFactor >	factors_
	concept check, makes sure FACTOR defines print and equals More...

Member Function Documentation

augmentedHessian() [1/2]

Matrix gtsam::GaussianFactorGraph::augmentedHessian

(

)

const

Return a dense \( \Lambda \in \mathbb{R}^{n+1 \times n+1} \) Hessian matrix, augmented with the information vector \( \eta \).

The augmented Hessian is

\[ \left[ \begin{array}{ccc} \Lambda & \eta \\ \eta^T & c \end{array} \right] \]

and the negative log-likelihood is \( \frac{1}{2} x^T \Lambda x + \eta^T x + c \).

augmentedHessian() [2/2]

Matrix gtsam::GaussianFactorGraph::augmentedHessian

(

const Ordering &

ordering

)

const

Return a dense \( \Lambda \in \mathbb{R}^{n+1 \times n+1} \) Hessian matrix, augmented with the information vector \( \eta \).

The augmented Hessian is

\[ \left[ \begin{array}{ccc} \Lambda & \eta \\ \eta^T & c \end{array} \right] \]

and the negative log-likelihood is \( \frac{1}{2} x^T \Lambda x + \eta^T x + c \).

augmentedJacobian() [1/2]

Matrix gtsam::GaussianFactorGraph::augmentedJacobian

(

)

const

Return a dense \( [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \) Jacobian matrix, augmented with b with the noise models baked into A and b.

The negative log-likelihood is \( \frac{1}{2} \Vert Ax-b \Vert^2 \). See also GaussianFactorGraph::jacobian and GaussianFactorGraph::sparseJacobian.

augmentedJacobian() [2/2]

Matrix gtsam::GaussianFactorGraph::augmentedJacobian

(

const Ordering &

ordering

)

const

Return a dense \( [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \) Jacobian matrix, augmented with b with the noise models baked into A and b.

The negative log-likelihood is \( \frac{1}{2} \Vert Ax-b \Vert^2 \). See also GaussianFactorGraph::jacobian and GaussianFactorGraph::sparseJacobian.

clone()

GaussianFactorGraph gtsam::GaussianFactorGraph::clone ( ) const

virtual

Clone() performs a deep-copy of the graph, including all of the factors.

Cloning preserves null factors so indices for the original graph are still valid for the cloned graph.

cloneToPtr()

GaussianFactorGraph::shared_ptr gtsam::GaussianFactorGraph::cloneToPtr ( ) const

virtual

CloneToPtr() performs a simple assignment to a new graph and returns it.

There is no preservation of null factors!

gradient()

VectorValues gtsam::GaussianFactorGraph::gradient

(

const VectorValues &

x0

)

const

Compute the gradient of the energy function, \( \nabla_{x=x_0} \left\Vert \Sigma^{-1} A x - b \right\Vert^2 \), centered around \( x = x_0 \).

The gradient is \( A^T(Ax-b) \).

Parameters

fg	The Jacobian factor graph $(A,b)$
x0	The center about which to compute the gradient

Returns

The gradient as a VectorValues

gradientAtZero()

VectorValues gtsam::GaussianFactorGraph::gradientAtZero ( ) const

virtual

Compute the gradient of the energy function, \( \nabla_{x=0} \left\Vert \Sigma^{-1} A x - b \right\Vert^2 \), centered around zero.

The gradient is \( A^T(Ax-b) \).

Parameters

fg	The Jacobian factor graph $(A,b)$
[output]	g A VectorValues to store the gradient, which must be preallocated, see allocateVectorValues

Returns

The gradient as a VectorValues

hessian() [1/2]

pair< Matrix, Vector > gtsam::GaussianFactorGraph::hessian

(

)

const

Return the dense Hessian \( \Lambda \) and information vector \( \eta \), with the noise models baked in.

The negative log-likelihood is \frac{1}{2} x^T \Lambda x + \eta^T x + c. See also GaussianFactorGraph::augmentedHessian.

hessian() [2/2]

pair< Matrix, Vector > gtsam::GaussianFactorGraph::hessian

(

const Ordering &

ordering

)

const

Return the dense Hessian \( \Lambda \) and information vector \( \eta \), with the noise models baked in.

The negative log-likelihood is \frac{1}{2} x^T \Lambda x + \eta^T x + c. See also GaussianFactorGraph::augmentedHessian.

jacobian() [1/2]

pair< Matrix, Vector > gtsam::GaussianFactorGraph::jacobian

(

)

const

Return the dense Jacobian \( A \) and right-hand-side \( b \), with the noise models baked into A and b.

The negative log-likelihood is \( \frac{1}{2} \Vert Ax-b \Vert^2 \). See also GaussianFactorGraph::augmentedJacobian and GaussianFactorGraph::sparseJacobian.

jacobian() [2/2]

pair< Matrix, Vector > gtsam::GaussianFactorGraph::jacobian

(

const Ordering &

ordering

)

const

Return the dense Jacobian \( A \) and right-hand-side \( b \), with the noise models baked into A and b.

The negative log-likelihood is \( \frac{1}{2} \Vert Ax-b \Vert^2 \). See also GaussianFactorGraph::augmentedJacobian and GaussianFactorGraph::sparseJacobian.

negate()

GaussianFactorGraph gtsam::GaussianFactorGraph::negate

(

)

const

Returns the negation of all factors in this graph - corresponds to antifactors.

Will convert all factors to HessianFactors due to negation of information. Cloning preserves null factors so indices for the original graph are still valid for the cloned graph.

optimize() [1/2]

VectorValues gtsam::GaussianFactorGraph::optimize

(

const Eliminate &

function = EliminationTraitsType::DefaultEliminate

)

const

Solve the factor graph by performing multifrontal variable elimination in COLAMD order using the dense elimination function specified in function (default EliminatePreferCholesky), followed by back-substitution in the Bayes tree resulting from elimination.

Is equivalent to calling graph.eliminateMultifrontal()->optimize().

optimize() [2/2]

VectorValues gtsam::GaussianFactorGraph::optimize	(	const Ordering &	ordering,
		const Eliminate &	function = EliminationTraitsType::DefaultEliminate
	)		const

Solve the factor graph by performing multifrontal variable elimination in COLAMD order using the dense elimination function specified in function (default EliminatePreferCholesky), followed by back-substitution in the Bayes tree resulting from elimination.

Is equivalent to calling graph.eliminateMultifrontal()->optimize().

optimizeGradientSearch()

VectorValues gtsam::GaussianFactorGraph::optimizeGradientSearch

(

)

const

Optimize along the gradient direction, with a closed-form computation to perform the line search.

The gradient is computed about \( \delta x=0 \).

This function returns \( \delta x \) that minimizes a reparametrized problem. The error function of a GaussianBayesNet is

\[ f(\delta x) = \frac{1}{2} |R \delta x - d|^2 = \frac{1}{2}d^T d - d^T R \delta x + \frac{1}{2} \delta x^T R^T R \delta x \]

with gradient and Hessian

\[ g(\delta x) = R^T(R\delta x - d), \qquad G(\delta x) = R^T R. \]

This function performs the line search in the direction of the gradient evaluated at \( g = g(\delta x = 0) \) with step size \( \alpha \) that minimizes \( f(\delta x = \alpha g) \):

\[ f(\alpha) = \frac{1}{2} d^T d + g^T \delta x + \frac{1}{2} \alpha^2 g^T G g \]

Optimizing by setting the derivative to zero yields \( \hat \alpha = (-g^T g) / (g^T G g) \). For efficiency, this function evaluates the denominator without computing the Hessian \( G \), returning

\[ \delta x = \hat\alpha g = \frac{-g^T g}{(R g)^T(R g)} \]

probPrime()

double gtsam::GaussianFactorGraph::probPrime ( const VectorValues &  c ) const

inline

Unnormalized probability.

O(n)

sparseJacobian()

SparseTriplets gtsam::GaussianFactorGraph::sparseJacobian	(	const Ordering &	ordering,
		size_t &	nrows,
		size_t &	ncols
	)		const

Returns a sparse augmented Jacbian matrix as a vector of i, j, and s, where i(k) and j(k) are the base 0 row and column indices, and s(k) is the entry as a double.

The standard deviations are baked into A and b

Returns

the sparse matrix as a std::vector of std::tuples

Parameters

	ordering	the column ordering
[out]	nrows	The number of rows in the augmented Jacobian
[out]	ncols	The number of columns in the augmented Jacobian

sparseJacobian_()

Matrix gtsam::GaussianFactorGraph::sparseJacobian_

(

)

const

Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] entries such that S(i(k),j(k)) = s(k), which can be given to MATLAB's sparse.

Note: i, j are 1-indexed. The standard deviations are baked into A and b

transposeMultiply()

VectorValues gtsam::GaussianFactorGraph::transposeMultiply

(

const Errors &

e

)

const

x = A'*e

• ************************************************************************* *‍/* ************************************************************************* *‍/

---

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

• /Users/dellaert/git/github/gtsam/linear/GaussianFactorGraph.h
• /Users/dellaert/git/github/gtsam/linear/GaussianFactorGraph.cpp