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.

Add a factor by value - makes a copy.

Add a factor by pointer - stores pointer without copying the factor.

void add (Key key1, const Matrix &A1, const Vector &b, const SharedDiagonal &model=SharedDiagonal())

void add (Key key1, const Matrix &A1, Key key2, const Matrix &A2, const Vector &b, const SharedDiagonal &model=SharedDiagonal())

void add (Key key1, const Matrix &A1, Key key2, const Matrix &A2, Key key3, const Matrix &A3, const Vector &b, const SharedDiagonal &model=SharedDiagonal())

template<class TERMS >
void add (const TERMS &terms, const Vector &b, const SharedDiagonal &model=SharedDiagonal())

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...

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

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).

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. 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...

## ◆ 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!

 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

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

## ◆ 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().

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

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

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

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

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

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