#include <GaussianBayesTree.h>

Inheritance diagram for gtsam::GaussianBayesTree:

Collaboration diagram for gtsam::GaussianBayesTree:

Public Types
typedef GaussianBayesTree	This

typedef std::shared_ptr< This >	shared_ptr

typedef GaussianBayesTreeClique	Clique
	The clique type, normally BayesTreeClique.

typedef std::shared_ptr< Clique >	sharedClique
	Shared pointer to a clique.

typedef Clique	Node
	Synonym for Clique (TODO: remove)

typedef sharedClique	sharedNode
	Synonym for sharedClique (TODO: remove)

typedef GaussianBayesTreeClique ::ConditionalType	ConditionalType

typedef std::shared_ptr< ConditionalType >	sharedConditional

typedef GaussianBayesTreeClique ::BayesNetType	BayesNetType

typedef std::shared_ptr< BayesNetType >	sharedBayesNet

typedef GaussianBayesTreeClique ::FactorType	FactorType

typedef std::shared_ptr< FactorType >	sharedFactor

typedef GaussianBayesTreeClique ::FactorGraphType	FactorGraphType

typedef std::shared_ptr< FactorGraphType >	sharedFactorGraph

typedef FactorGraphType::Eliminate	Eliminate

typedef GaussianBayesTreeClique ::EliminationTraitsType	EliminationTraitsType

typedef FastList< sharedClique >	Cliques

typedef ConcurrentMap< Key, sharedClique >	Nodes

typedef FastVector< sharedClique >	Roots

Public Member Functions
	GaussianBayesTree ()

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

VectorValues	optimize () const

VectorValues	optimizeGradientSearch () const

VectorValues	gradient (const VectorValues &x0) const

VectorValues	gradientAtZero () const

double	error (const VectorValues &x) const

double	determinant () const

double	logDeterminant () const

Matrix	marginalCovariance (Key key) const

Standard Interface
size_t	size () const

bool	empty () const

const Nodes &	nodes () const

sharedClique	operator[] (Key j) const

const Roots &	roots () const

const sharedClique &	clique (Key j) const

BayesTreeCliqueData	getCliqueData () const

size_t	numCachedSeparatorMarginals () const

sharedConditional	marginalFactor (Key j, const Eliminate &function=EliminationTraitsType::DefaultEliminate) const

sharedFactorGraph	joint (Key j1, Key j2, const Eliminate &function=EliminationTraitsType::DefaultEliminate) const

sharedBayesNet	jointBayesNet (Key j1, Key j2, const Eliminate &function=EliminationTraitsType::DefaultEliminate) const

Graph Display
void	dot (std::ostream &os, const KeyFormatter &keyFormatter=DefaultKeyFormatter) const
	Output to graphviz format, stream version.

std::string	dot (const KeyFormatter &keyFormatter=DefaultKeyFormatter) const
	Output to graphviz format string.

void	saveGraph (const std::string &filename, const KeyFormatter &keyFormatter=DefaultKeyFormatter) const
	output to file with graphviz format.

Protected Attributes
Nodes	nodes_

Roots	roots_

Testable
void	print (const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter) const

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

Advanced Interface
Key	findParentClique (const CONTAINER &parents) const

void	clear ()

void	deleteCachedShortcuts ()

void	removePath (sharedClique clique, BayesNetType bn, Cliques orphans)

void	removeTop (const KeyVector &keys, BayesNetType bn, Cliques orphans)

Cliques	removeSubtree (const sharedClique &subtree)

void	insertRoot (const sharedClique &subtree)

void	addClique (const sharedClique &clique, const sharedClique &parent_clique=sharedClique())

void	addFactorsToGraph (FactorGraph< FactorType > *graph) const

void	getCliqueData (sharedClique clique, BayesTreeCliqueData *stats) const

void	dot (std::ostream &s, sharedClique clique, const KeyFormatter &keyFormatter, int parentnum=0) const

void	removeClique (sharedClique clique)

void	fillNodesIndex (const sharedClique &subtree)

Detailed Description

A Bayes tree representing a Gaussian density

Member Typedef Documentation

◆ Cliques

typedef FastList<sharedClique> gtsam::BayesTree< GaussianBayesTreeClique >::Cliques

inherited

A convenience class for a list of shared cliques

◆ Nodes

typedef ConcurrentMap<Key, sharedClique> gtsam::BayesTree< GaussianBayesTreeClique >::Nodes

inherited

Map from keys to Clique

◆ Roots

typedef FastVector<sharedClique> gtsam::BayesTree< GaussianBayesTreeClique >::Roots

inherited

Root cliques

Constructor & Destructor Documentation

◆ GaussianBayesTree()

gtsam::GaussianBayesTree::GaussianBayesTree ( )

inline

Default constructor, creates an empty Bayes tree

Member Function Documentation

◆ addClique()

void gtsam::BayesTree< GaussianBayesTreeClique >::addClique	(	const sharedClique &	clique,
		const sharedClique &	parent_clique = `sharedClique()`
	)

inherited

add a clique (top down)

◆ addFactorsToGraph()

void gtsam::BayesTree< GaussianBayesTreeClique >::addFactorsToGraph ( FactorGraph< FactorType > * graph ) const

inherited

Add all cliques in this BayesTree to the specified factor graph

◆ clear()

void gtsam::BayesTree< GaussianBayesTreeClique >::clear ( )

inherited

Remove all nodes

◆ clique()

const sharedClique& gtsam::BayesTree< GaussianBayesTreeClique >::clique ( Key j ) const

inlineinherited

alternate syntax for matlab: find the clique that contains the variable with Key j

◆ deleteCachedShortcuts()

void gtsam::BayesTree< GaussianBayesTreeClique >::deleteCachedShortcuts ( )

inherited

Clear all shortcut caches - use before timing on marginal calculation to avoid residual cache data

◆ determinant()

double gtsam::GaussianBayesTree::determinant ( ) const

Computes the determinant of a GassianBayesTree, as if the Bayes tree is reorganized into a matrix. A GassianBayesTree is equivalent to an upper triangular matrix, and for an upper triangular matrix determinant is the product of the diagonal elements. Instead of actually multiplying we add the logarithms of the diagonal elements and take the exponent at the end because this is more numerically stable.

◆ dot()

void gtsam::BayesTree< GaussianBayesTreeClique >::dot	(	std::ostream &	s,
		sharedClique	clique,
		const KeyFormatter &	keyFormatter,
		int	parentnum = `0`
	)		const

protectedinherited

private helper method for saving the Tree to a text file in GraphViz format

◆ empty()

bool gtsam::BayesTree< GaussianBayesTreeClique >::empty ( ) const

inlineinherited

Check if there are any cliques in the tree

◆ equals() [1/2]

bool gtsam::GaussianBayesTree::equals	(	const This &	other,
		double	tol = `1e-9`
	)		const

Check equality

◆ equals() [2/2]

bool gtsam::BayesTree< GaussianBayesTreeClique >::equals	(	const This &	other,
		double	tol = `1e-9`
	)		const

protectedinherited

check equality

◆ error()

double gtsam::GaussianBayesTree::error ( const VectorValues & x ) const

0.5 * sum of squared Mahalanobis distances.

◆ fillNodesIndex()

void gtsam::BayesTree< GaussianBayesTreeClique >::fillNodesIndex ( const sharedClique & subtree )

protectedinherited

Fill the nodes index for a subtree

◆ findParentClique()

Key gtsam::BayesTree< GaussianBayesTreeClique >::findParentClique ( const CONTAINER & parents ) const

inherited

Find parent clique of a conditional. It will look at all parents and return the one with the lowest index in the ordering.

◆ getCliqueData() [1/2]

BayesTreeCliqueData gtsam::BayesTree< GaussianBayesTreeClique >::getCliqueData ( ) const

inherited

Gather data on all cliques

◆ getCliqueData() [2/2]

void gtsam::BayesTree< GaussianBayesTreeClique >::getCliqueData	(	sharedClique	clique,
		BayesTreeCliqueData *	stats
	)		const

protectedinherited

Gather data on a single clique

◆ gradient()

VectorValues gtsam::GaussianBayesTree::gradient ( const VectorValues & x0 ) const

Compute the gradient of the energy function, \( \nabla_{x=x_0} \left\Vert \Sigma^{-1} R x - d \right\Vert^2 \), centered around \( x = x_0 \). The gradient is \( R^T(Rx-d) \).

Parameters

x0	The center about which to compute the gradient

Returns: The gradient as a VectorValues

◆ gradientAtZero()

VectorValues gtsam::GaussianBayesTree::gradientAtZero ( ) const

Compute the gradient of the energy function, \( \nabla_{x=0} \left\Vert \Sigma^{-1} R x - d \right\Vert^2 \), centered around zero. The gradient about zero is \( -R^T d \). See also gradient(const GaussianBayesNet&, const VectorValues&).

Returns: A VectorValues storing the gradient.

◆ insertRoot()

void gtsam::BayesTree< GaussianBayesTreeClique >::insertRoot ( const sharedClique & subtree )

inherited

Insert a new subtree with known parent clique. This function does not check that the specified parent is the correct parent. This function updates all of the internal data structures associated with adding a subtree, such as populating the nodes index.

◆ joint()

BayesTree< GaussianBayesTreeClique >::sharedFactorGraph gtsam::BayesTree< GaussianBayesTreeClique >::joint	(	Key	j1,
		Key	j2,
		const Eliminate &	function = `EliminationTraitsType::DefaultEliminate`
	)		const

inherited

return joint on two variables Limitation: can only calculate joint if cliques are disjoint or one of them is root

◆ jointBayesNet()

BayesTree< GaussianBayesTreeClique >::sharedBayesNet gtsam::BayesTree< GaussianBayesTreeClique >::jointBayesNet	(	Key	j1,
		Key	j2,
		const Eliminate &	function = `EliminationTraitsType::DefaultEliminate`
	)		const

inherited

return joint on two variables as a BayesNet Limitation: can only calculate joint if cliques are disjoint or one of them is root

◆ logDeterminant()

double gtsam::GaussianBayesTree::logDeterminant ( ) const

Computes the determinant of a GassianBayesTree, as if the Bayes tree is reorganized into a matrix. A GassianBayesTree is equivalent to an upper triangular matrix, and for an upper triangular matrix determinant is the product of the diagonal elements. Instead of actually multiplying we add the logarithms of the diagonal elements and take the exponent at the end because this is more numerically stable.

◆ marginalCovariance()

Matrix gtsam::GaussianBayesTree::marginalCovariance ( Key key ) const

Return the marginal on the requested variable as a covariance matrix. See also marginalFactor().

◆ marginalFactor()

BayesTree< GaussianBayesTreeClique >::sharedConditional gtsam::BayesTree< GaussianBayesTreeClique >::marginalFactor	(	Key	j,
		const Eliminate &	function = `EliminationTraitsType::DefaultEliminate`
	)		const

inherited

Return marginal on any variable. Note that this actually returns a conditional, for which a solution may be directly obtained by calling .solve() on the returned object. Alternatively, it may be directly used as its factor base class. For example, for Gaussian systems, this returns a GaussianConditional, which inherits from JacobianFactor and GaussianFactor.

◆ nodes()

const Nodes& gtsam::BayesTree< GaussianBayesTreeClique >::nodes ( ) const

inlineinherited

Return nodes. Each node is a clique of variables obtained after elimination.

◆ numCachedSeparatorMarginals()

size_t gtsam::BayesTree< GaussianBayesTreeClique >::numCachedSeparatorMarginals ( ) const

inherited

Collect number of cliques with cached separator marginals

◆ operator[]()

sharedClique gtsam::BayesTree< GaussianBayesTreeClique >::operator[] ( Key j ) const

inlineinherited

Access node by variable

◆ optimize()

VectorValues gtsam::GaussianBayesTree::optimize ( ) const

Recursively optimize the BayesTree to produce a vector solution.

◆ optimizeGradientSearch()

VectorValues gtsam::GaussianBayesTree::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

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

◆ print()

void gtsam::BayesTree< GaussianBayesTreeClique >::print	(	const std::string &	s = `""`,
		const KeyFormatter &	keyFormatter = `DefaultKeyFormatter`
	)		const

inherited

print

◆ removeClique()

void gtsam::BayesTree< GaussianBayesTreeClique >::removeClique ( sharedClique clique )

protectedinherited

remove a clique: warning, can result in a forest

◆ removePath()

void gtsam::BayesTree< GaussianBayesTreeClique >::removePath	(	sharedClique	clique,
		BayesNetType *	bn,
		Cliques *	orphans
	)

inherited

Remove path from clique to root and return that path as factors plus a list of orphaned subtree roots. Used in removeTop below.

◆ removeSubtree()

BayesTree< GaussianBayesTreeClique >::Cliques gtsam::BayesTree< GaussianBayesTreeClique >::removeSubtree ( const sharedClique & subtree )

inherited

Remove the requested subtree.

◆ removeTop()

void gtsam::BayesTree< GaussianBayesTreeClique >::removeTop	(	const KeyVector &	keys,
		BayesNetType *	bn,
		Cliques *	orphans
	)

inherited

Given a list of indices, turn "contaminated" part of the tree back into a factor graph. Factors and orphans are added to the in/out arguments.

◆ roots()

const Roots& gtsam::BayesTree< GaussianBayesTreeClique >::roots ( ) const

inlineinherited

return root cliques

◆ size()

size_t gtsam::BayesTree< GaussianBayesTreeClique >::size ( ) const

inherited

number of cliques

Member Data Documentation

◆ nodes_

Nodes gtsam::BayesTree< GaussianBayesTreeClique >::nodes_

protectedinherited

Map from indices to Clique

◆ roots_

Roots gtsam::BayesTree< GaussianBayesTreeClique >::roots_

protectedinherited

Root cliques

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

/home/docs/checkouts/readthedocs.org/user_builds/gtsam-jlblanco-docs/checkouts/latest/gtsam/linear/GaussianBayesTree.h

Public Types

Public Member Functions

Protected Attributes

Testable

Advanced Interface

Detailed Description

Member Typedef Documentation

◆ Cliques

◆ Nodes

◆ Roots

Constructor & Destructor Documentation

◆ GaussianBayesTree()

Member Function Documentation

◆ addClique()

◆ addFactorsToGraph()

◆ clear()

◆ clique()

◆ deleteCachedShortcuts()

◆ determinant()

◆ dot()

◆ empty()

◆ equals() [1/2]

◆ equals() [2/2]

◆ error()

◆ fillNodesIndex()

◆ findParentClique()

◆ getCliqueData() [1/2]

◆ getCliqueData() [2/2]

◆ gradient()

◆ gradientAtZero()

◆ insertRoot()

◆ joint()

◆ jointBayesNet()

◆ logDeterminant()

◆ marginalCovariance()

◆ marginalFactor()

◆ nodes()

◆ numCachedSeparatorMarginals()

◆ operator[]()

◆ optimize()

◆ optimizeGradientSearch()

◆ print()

◆ removeClique()

◆ removePath()

◆ removeSubtree()

◆ removeTop()

◆ roots()

◆ size()

Member Data Documentation

◆ nodes_

◆ roots_