#include <GaussianBayesTree.h>

Inheritance diagram for gtsam::GaussianBayesTree:

Public Types
typedef boost::shared_ptr< This >	shared_ptr

typedef GaussianBayesTree	This

Public Types inherited from gtsam::BayesTree< GaussianBayesTreeClique >
typedef GaussianBayesTreeClique::BayesNetType	BayesNetType

typedef GaussianBayesTreeClique	Clique
	The clique type, normally BayesTreeClique. More...

typedef FastList< sharedClique >	Cliques

typedef GaussianBayesTreeClique::ConditionalType	ConditionalType

typedef FactorGraphType::Eliminate	Eliminate

typedef GaussianBayesTreeClique::EliminationTraitsType	EliminationTraitsType

typedef GaussianBayesTreeClique::FactorGraphType	FactorGraphType

typedef GaussianBayesTreeClique::FactorType	FactorType

typedef Clique	Node
	Synonym for Clique (TODO: remove) More...

typedef ConcurrentMap< Key, sharedClique >	Nodes

typedef FastVector< sharedClique >	Roots

typedef boost::shared_ptr< BayesNetType >	sharedBayesNet

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

typedef boost::shared_ptr< ConditionalType >	sharedConditional

typedef boost::shared_ptr< FactorType >	sharedFactor

typedef boost::shared_ptr< FactorGraphType >	sharedFactorGraph

typedef sharedClique	sharedNode
	Synonym for sharedClique (TODO: remove) More...

Public Member Functions
double	determinant () const

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

double	error (const VectorValues &x) const

	GaussianBayesTree ()

VectorValues	gradient (const VectorValues &x0) const

VectorValues	gradientAtZero () const

double	logDeterminant () const

Matrix	marginalCovariance (Key key) const

VectorValues	optimize () const

VectorValues	optimizeGradientSearch () const

Public Member Functions inherited from gtsam::BayesTree< GaussianBayesTreeClique >
size_t	size () const

bool	empty () const

const Nodes &	nodes () const

const sharedNode	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

void	saveGraph (const std::string &s, const KeyFormatter &keyFormatter=DefaultKeyFormatter) const

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

Private Types
typedef BayesTree< GaussianBayesTreeClique >	Base

Additional Inherited Members
Protected Types inherited from gtsam::BayesTree< GaussianBayesTreeClique >
typedef boost::shared_ptr< This >	shared_ptr

typedef BayesTree< GaussianBayesTreeClique >	This

Protected Member Functions inherited from gtsam::BayesTree< GaussianBayesTreeClique >
This &	operator= (const This &other)

	BayesTree ()

	BayesTree (const This &other)

void	getCliqueData (sharedClique clique, BayesTreeCliqueData *stats) const

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

void	removeClique (sharedClique clique)

void	fillNodesIndex (const sharedClique &subtree)

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

Protected Attributes inherited from gtsam::BayesTree< GaussianBayesTreeClique >
Nodes	nodes_

Roots	roots_

Detailed Description

A Bayes tree representing a Gaussian density

Definition at line 50 of file GaussianBayesTree.h.

Member Typedef Documentation

typedef BayesTree<GaussianBayesTreeClique> gtsam::GaussianBayesTree::Base

private

Definition at line 54 of file GaussianBayesTree.h.

typedef boost::shared_ptr<This> gtsam::GaussianBayesTree::shared_ptr

Definition at line 58 of file GaussianBayesTree.h.

typedef GaussianBayesTree gtsam::GaussianBayesTree::This

Definition at line 57 of file GaussianBayesTree.h.

Constructor & Destructor Documentation

gtsam::GaussianBayesTree::GaussianBayesTree ( )

inline

Default constructor, creates an empty Bayes tree

Definition at line 61 of file GaussianBayesTree.h.

Member Function Documentation

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.

Definition at line 96 of file GaussianBayesTree.cpp.

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

Check equality

Definition at line 50 of file GaussianBayesTree.cpp.

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

0.5 * sum of squared Mahalanobis distances.

Definition at line 79 of file GaussianBayesTree.cpp.

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

Definition at line 69 of file GaussianBayesTree.cpp.

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.

Definition at line 74 of file GaussianBayesTree.cpp.

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.

Definition at line 84 of file GaussianBayesTree.cpp.

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

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

Definition at line 102 of file GaussianBayesTree.cpp.

VectorValues gtsam::GaussianBayesTree::optimize ( ) const

Recursively optimize the BayesTree to produce a vector solution.

Definition at line 56 of file GaussianBayesTree.cpp.

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

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

Definition at line 62 of file GaussianBayesTree.cpp.

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

Public Types

Public Member Functions

Private Types

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation