gtsam  4.1.0
gtsam
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...
 
VectorValues optimize (boost::none_t, const Eliminate &function=EliminationTraitsType::DefaultEliminate) const
 
Testable
bool equals (const This &fg, double tol=1e-9) const
 
Linear Algebra
std::vector< boost::tuple< size_t, size_t, double > > sparseJacobian () const
 Return vector of i, j, and s to generate an m-by-n sparse Jacobian matrix, where i(k) and j(k) are the base 0 row and column indices, s(k) a double. More...
 
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.
 
- Public Member Functions inherited from gtsam::FactorGraph< GaussianFactor >
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, typename CLIQUE::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.
 
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).
 
sharedFactorat (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).
 
sharedFactoroperator[] (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< BayesNetTypeeliminateSequential (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< BayesNetTypeeliminateSequential (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< BayesNetTypeeliminateSequential (const Ordering &ordering, const Eliminate &function, OptionalVariableIndex variableIndex, OptionalOrderingType orderingType) const
 
boost::shared_ptr< BayesNetTypeeliminateSequential (const Eliminate &function, OptionalVariableIndex variableIndex=boost::none, OptionalOrderingType orderingType=boost::none) const
 
boost::shared_ptr< BayesTreeTypeeliminateMultifrontal (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< BayesTreeTypeeliminateMultifrontal (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...
 
boost::shared_ptr< BayesTreeTypeeliminateMultifrontal (const Ordering &ordering, const Eliminate &function, OptionalVariableIndex variableIndex, OptionalOrderingType orderingType) const
 
boost::shared_ptr< BayesTreeTypeeliminateMultifrontal (const Eliminate &function, OptionalVariableIndex variableIndex=boost::none, OptionalOrderingType orderingType=boost::none) const
 
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< BayesNetTypemarginalMultifrontalBayesNet (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< BayesNetTypemarginalMultifrontalBayesNet (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< BayesNetTypemarginalMultifrontalBayesNet (boost::variant< const Ordering &, const KeyVector & > variables, boost::none_t, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
 
boost::shared_ptr< BayesTreeTypemarginalMultifrontalBayesTree (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< BayesTreeTypemarginalMultifrontalBayesTree (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< BayesTreeTypemarginalMultifrontalBayesTree (boost::variant< const Ordering &, const KeyVector & > variables, boost::none_t, const Eliminate &function=EliminationTraitsType::DefaultEliminate, OptionalVariableIndex variableIndex=boost::none) const
 
boost::shared_ptr< FactorGraphTypemarginal (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< GaussianFactorBase
 Typedef to base factor graph type.
 
typedef EliminateableFactorGraph< ThisBaseEliminateable
 Typedef to base elimination class.
 
typedef boost::shared_ptr< Thisshared_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< GaussianFactorsharedFactor
 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< FactorGraphTypeEliminationTraitsType
 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 boost::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::OrderingTypeOptionalOrderingType
 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< sharedFactorfactors_
 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
fgThe Jacobian factor graph $(A,b)$
x0The 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
fgThe 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() [1/3]

VectorValues gtsam::GaussianFactorGraph::optimize ( boost::none_t  ,
const Eliminate function = EliminationTraitsType::DefaultEliminate 
) const

◆ optimize() [2/3]

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() [3/3]

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()

vector< boost::tuple< size_t, size_t, double > > gtsam::GaussianFactorGraph::sparseJacobian ( ) const

Return vector of i, j, and s to generate an m-by-n sparse Jacobian matrix, where i(k) and j(k) are the base 0 row and column indices, s(k) a double.

The standard deviations are baked into A and b

◆ 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.

The standard deviations are baked into A and b

◆ transposeMultiply()

VectorValues gtsam::GaussianFactorGraph::transposeMultiply ( const Errors e) const

x = A'*e

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