#include <GaussianBayesNet.h>

Inheritance diagram for gtsam::GaussianBayesNet:

Public Types
typedef FactorGraph< GaussianConditional >	Base

typedef GaussianConditional	ConditionalType

typedef boost::shared_ptr< This >	shared_ptr

typedef boost::shared_ptr< ConditionalType >	sharedConditional

typedef GaussianBayesNet	This

Public Types inherited from gtsam::FactorGraph< GaussianConditional >
typedef FastVector< sharedFactor >::const_iterator	const_iterator

typedef GaussianConditional	FactorType
	factor type More...

typedef FastVector< sharedFactor >::iterator	iterator

typedef boost::shared_ptr< GaussianConditional >	sharedFactor
	Shared pointer to a factor. More...

typedef sharedFactor	value_type

Public Member Functions
Standard Constructors
	GaussianBayesNet ()

template<typename ITERATOR >
	GaussianBayesNet (ITERATOR firstConditional, ITERATOR lastConditional)

template<class CONTAINER >
	GaussianBayesNet (const CONTAINER &conditionals)

template<class DERIVEDCONDITIONAL >
	GaussianBayesNet (const FactorGraph< DERIVEDCONDITIONAL > &graph)

virtual	~GaussianBayesNet ()
	Destructor. More...

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

Standard Interface
VectorValues	optimize () const
	Solve the GaussianBayesNet, i.e. return $x = R^{-1}*d$ , by back-substitution. More...

VectorValues	optimize (const VectorValues &solutionForMissing) const
	Version of optimize for incomplete BayesNet, needs solution for missing variables. More...

Ordering	ordering () const

Linear Algebra
std::pair< Matrix, Vector >	matrix (const Ordering &ordering) const

std::pair< Matrix, Vector >	matrix () 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

VectorValues	backSubstitute (const VectorValues &gx) const

VectorValues	backSubstituteTranspose (const VectorValues &gx) const

void	print (const std::string &s="", const KeyFormatter &formatter=DefaultKeyFormatter) const override
	print graph More...

void	saveGraph (const std::string &s, const KeyFormatter &keyFormatter=DefaultKeyFormatter) const
	Save the GaussianBayesNet as an image. Requires `dot` to be installed. More...

Public Member Functions inherited from gtsam::FactorGraph< GaussianConditional >
virtual	~FactorGraph ()=default
	Default destructor. More...

void	reserve (size_t size)

IsDerived< DERIVEDFACTOR >	push_back (boost::shared_ptr< DERIVEDFACTOR > factor)
	Add a factor directly using a shared_ptr. More...

IsDerived< DERIVEDFACTOR >	push_back (const DERIVEDFACTOR &factor)

IsDerived< DERIVEDFACTOR >	emplace_shared (Args &&...args)
	Emplace a shared pointer to factor of given type. More...

IsDerived< DERIVEDFACTOR >	add (boost::shared_ptr< DERIVEDFACTOR > factor)
	`add` is a synonym for push_back. More...

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. More...

HasDerivedElementType< ITERATOR >	push_back (ITERATOR firstFactor, ITERATOR lastFactor)

HasDerivedValueType< ITERATOR >	push_back (ITERATOR firstFactor, ITERATOR lastFactor)
	Push back many factors with an iterator (factors are copied) More...

HasDerivedElementType< CONTAINER >	push_back (const CONTAINER &container)

HasDerivedValueType< CONTAINER >	push_back (const CONTAINER &container)
	Push back non-pointer objects in a container (factors are copied). More...

void	add (const FACTOR_OR_CONTAINER &factorOrContainer)

boost::assign::list_inserter< CRefCallPushBack< This > >	operator+= (const FACTOR_OR_CONTAINER &factorOrContainer)

std::enable_if< std::is_base_of< This, typename CLIQUE::FactorGraphType >::value >::type	push_back (const BayesTree< CLIQUE > &bayesTree)

FactorIndices	add_factors (const CONTAINER &factors, bool useEmptySlots=false)

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

size_t	size () const

bool	empty () const

const sharedFactor	at (size_t i) const

sharedFactor &	at (size_t i)

const sharedFactor	operator[] (size_t i) const

sharedFactor &	operator[] (size_t i)

const_iterator	begin () const

const_iterator	end () const

sharedFactor	front () const

sharedFactor	back () const

iterator	begin ()

iterator	end ()

void	resize (size_t size)

void	remove (size_t i)

void	replace (size_t index, sharedFactor factor)

iterator	erase (iterator item)

iterator	erase (iterator first, iterator last)

size_t	nrFactors () const

KeySet	keys () const

KeyVector	keyVector () const

bool	exists (size_t idx) const

Private Member Functions
template<class ARCHIVE >
void	serialize (ARCHIVE &ar, const unsigned int)

Friends
class	boost::serialization::access

Additional Inherited Members
Protected Member Functions inherited from gtsam::FactorGraph< GaussianConditional >
	FactorGraph ()

	FactorGraph (ITERATOR firstFactor, ITERATOR lastFactor)

	FactorGraph (const CONTAINER &factors)

Protected Attributes inherited from gtsam::FactorGraph< GaussianConditional >
FastVector< sharedFactor >	factors_

Detailed Description

A Bayes net made from linear-Gaussian densities

Definition at line 30 of file GaussianBayesNet.h.

Member Typedef Documentation

typedef FactorGraph<GaussianConditional> gtsam::GaussianBayesNet::Base

Definition at line 34 of file GaussianBayesNet.h.

typedef GaussianConditional gtsam::GaussianBayesNet::ConditionalType

Definition at line 36 of file GaussianBayesNet.h.

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

Definition at line 37 of file GaussianBayesNet.h.

typedef boost::shared_ptr<ConditionalType> gtsam::GaussianBayesNet::sharedConditional

Definition at line 38 of file GaussianBayesNet.h.

typedef GaussianBayesNet gtsam::GaussianBayesNet::This

Definition at line 35 of file GaussianBayesNet.h.

Constructor & Destructor Documentation

gtsam::GaussianBayesNet::GaussianBayesNet ( )

inline

Construct empty factor graph

Definition at line 44 of file GaussianBayesNet.h.

template<typename ITERATOR >

gtsam::GaussianBayesNet::GaussianBayesNet	(	ITERATOR	firstConditional,
		ITERATOR	lastConditional
	)

inline

Construct from iterator over conditionals

Definition at line 48 of file GaussianBayesNet.h.

template<class CONTAINER >

gtsam::GaussianBayesNet::GaussianBayesNet ( const CONTAINER & conditionals )

inlineexplicit

Construct from container of factors (shared_ptr or plain objects)

Definition at line 52 of file GaussianBayesNet.h.

template<class DERIVEDCONDITIONAL >

gtsam::GaussianBayesNet::GaussianBayesNet ( const FactorGraph< DERIVEDCONDITIONAL > & graph )

inline

Implicit copy/downcast constructor to override explicit template container constructor

Definition at line 56 of file GaussianBayesNet.h.

virtual gtsam::GaussianBayesNet::~GaussianBayesNet ( )

inlinevirtual

Destructor.

Definition at line 59 of file GaussianBayesNet.h.

Member Function Documentation

VectorValues gtsam::GaussianBayesNet::backSubstitute ( const VectorValues & gx ) const

Backsubstitute with a different RHS vector than the one stored in this BayesNet. gy=inv(R*inv(Sigma))*gx

Definition at line 84 of file GaussianBayesNet.cpp.

VectorValues gtsam::GaussianBayesNet::backSubstituteTranspose ( const VectorValues & gx ) const

Transpose backsubstitute with a different RHS vector than the one stored in this BayesNet. gy=inv(L)*gx by solving L*gy=gx. gy=inv(R'*inv(Sigma))*gx gz'*R'=gx', gy = gz.*sigmas

Definition at line 100 of file GaussianBayesNet.cpp.

double gtsam::GaussianBayesNet::determinant ( ) const

Computes the determinant of a GassianBayesNet. A GaussianBayesNet is 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.

Parameters

bayesNet The input GaussianBayesNet

Returns: The determinant

************************************************************************* */* ************************************************************************* */

Definition at line 186 of file GaussianBayesNet.cpp.

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

Check equality

Definition at line 35 of file GaussianBayesNet.cpp.

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

0.5 * sum of squared Mahalanobis distances.

Definition at line 79 of file GaussianBayesNet.cpp.

VectorValues gtsam::GaussianBayesNet::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 GaussianBayesNet.cpp.

VectorValues gtsam::GaussianBayesNet::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&).

Parameters

[output] g A VectorValues to store the gradient, which must be preallocated, see allocateVectorValues

Definition at line 74 of file GaussianBayesNet.cpp.

double gtsam::GaussianBayesNet::logDeterminant ( ) const

Computes the log of the determinant of a GassianBayesNet. A GaussianBayesNet is an upper triangular matrix and for an upper triangular matrix determinant is the product of the diagonal elements.

Parameters

bayesNet The input GaussianBayesNet

Returns: The determinant

Definition at line 192 of file GaussianBayesNet.cpp.

pair< Matrix, Vector > gtsam::GaussianBayesNet::matrix ( const Ordering & ordering ) const

Return (dense) upper-triangular matrix representation Will return upper-triangular matrix only when using 'ordering' above. In case Bayes net is incomplete zero columns are added to the end.

Definition at line 160 of file GaussianBayesNet.cpp.

pair< Matrix, Vector > gtsam::GaussianBayesNet::matrix ( ) const

Return (dense) upper-triangular matrix representation Will return upper-triangular matrix only when using 'ordering' above. In case Bayes net is incomplete zero columns are added to the end.

Definition at line 167 of file GaussianBayesNet.cpp.

VectorValues gtsam::GaussianBayesNet::optimize ( ) const

Solve the GaussianBayesNet, i.e. return $x = R^{-1}*d$ , by back-substitution.

Definition at line 41 of file GaussianBayesNet.cpp.

VectorValues gtsam::GaussianBayesNet::optimize ( const VectorValues & solutionForMissing ) const

Version of optimize for incomplete BayesNet, needs solution for missing variables.

solve each node in turn in topological sort order (parents first)

Definition at line 48 of file GaussianBayesNet.cpp.

VectorValues gtsam::GaussianBayesNet::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 GaussianBayesNet.cpp.

Ordering gtsam::GaussianBayesNet::ordering ( ) const

Return ordering corresponding to a topological sort. There are many topological sorts of a Bayes net. This one corresponds to the one that makes 'matrix' below upper-triangular. In case Bayes net is incomplete any non-frontal are added to the end.

************************************************************************* */

Definition at line 142 of file GaussianBayesNet.cpp.

void gtsam::GaussianBayesNet::print	(	const std::string &	s = `""`,
		const KeyFormatter &	formatter = `DefaultKeyFormatter`
	)		const

inlineoverridevirtual

print graph

Reimplemented from gtsam::FactorGraph< GaussianConditional >.

Definition at line 184 of file GaussianBayesNet.h.

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

Save the GaussianBayesNet as an image. Requires dot to be installed.

Parameters

s	The name of the figure.
keyFormatter	Formatter to use for styling keys in the graph.

Definition at line 208 of file GaussianBayesNet.cpp.

template<class ARCHIVE >

void gtsam::GaussianBayesNet::serialize	(	ARCHIVE &	ar,
		const unsigned	int
	)

inlineprivate

Definition at line 206 of file GaussianBayesNet.h.

Friends And Related Function Documentation

friend class boost::serialization::access

friend

Serialization function

Definition at line 204 of file GaussianBayesNet.h.

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

Public Types

Public Member Functions

Private Member Functions

Friends

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation