#include <GaussianBayesNet.h>

Inheritance diagram for gtsam::GaussianBayesNet:

Public Types
typedef BayesNet< GaussianConditional >	Base

typedef GaussianConditional	ConditionalType

typedef std::shared_ptr< This >	shared_ptr

typedef std::shared_ptr< ConditionalType >	sharedConditional

typedef GaussianBayesNet	This

Public Types inherited from gtsam::BayesNet< GaussianConditional >
typedef std::shared_ptr< GaussianConditional >	sharedConditional
	A shared pointer to a conditional. More...

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 std::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)

template<class DERIVEDCONDITIONAL >
	GaussianBayesNet (std::initializer_list< std::shared_ptr< DERIVEDCONDITIONAL > > conditionals)

Standard Interface
double	error (const VectorValues &x) const
	Sum error over all variables. More...

double	logProbability (const VectorValues &x) const
	Sum logProbability over all variables. More...

double	evaluate (const VectorValues &x) const

double	operator() (const VectorValues &x) const
	Evaluate probability density, sugar. More...

VectorValues	optimize () const

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

VectorValues	sample (std::mt19937_64 *rng) const

VectorValues	sample (const VectorValues &given, std::mt19937_64 *rng) const

VectorValues	sample () const
	Sample using ancestral sampling, use default rng. More...

VectorValues	sample (const VectorValues &given) const
	Sample from an incomplete BayesNet, use default rng. 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	determinant () const

double	logDeterminant () const

double	negLogConstant () const
	Get the negative log of the normalization constant corresponding to the joint Gaussian density represented by this Bayes net. More...

VectorValues	backSubstitute (const VectorValues &gx) const

VectorValues	backSubstituteTranspose (const VectorValues &gx) const

Public Member Functions inherited from gtsam::BayesNet< GaussianConditional >
void	print (const std::string &s="BayesNet", const KeyFormatter &formatter=DefaultKeyFormatter) const override

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

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

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

double	logProbability (const HybridValues &x) const

double	evaluate (const HybridValues &c) const

Public Member Functions inherited from gtsam::FactorGraph< GaussianConditional >
	FactorGraph (std::initializer_list< std::shared_ptr< DERIVEDFACTOR >> sharedFactors)

virtual	~FactorGraph ()=default

void	reserve (size_t size)

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

std::enable_if< std::is_base_of< FactorType, DERIVEDFACTOR >::value, This >::type &	operator+= (std::shared_ptr< DERIVEDFACTOR > factor)
	Append factor to factor graph. More...

std::enable_if< std::is_base_of< FactorType, DERIVEDFACTOR >::value, This >::type &	operator, (std::shared_ptr< DERIVEDFACTOR > factor)
	Overload comma operator to allow for append chaining. 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)

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
	Check equality up to tolerance. More...

size_t	size () const

bool	empty () const

const sharedFactor	at (size_t i) const

sharedFactor &	at (size_t i)

std::shared_ptr< F >	at (size_t i)

const std::shared_ptr< F >	at (size_t i) const
	Const version of templated `at` method. More...

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

double	error (const HybridValues &values) const

iterator	begin ()

iterator	end ()

virtual 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)

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

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

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

size_t	nrFactors () const

KeySet	keys () const

KeyVector	keyVector () const

bool	exists (size_t idx) const

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

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

bool	operator== (const GaussianBayesNet &lhs, const GaussianBayesNet &rhs)
	Check exact equality. More...

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

	BayesNet (ITERATOR firstConditional, ITERATOR lastConditional)

	BayesNet (std::initializer_list< sharedConditional > conditionals)

Protected Member Functions inherited from gtsam::FactorGraph< GaussianConditional >
bool	isEqual (const FactorGraph &other) const
	Check exact equality of the factor pointers. Useful for derived ==. More...

	FactorGraph ()

	FactorGraph (ITERATOR firstFactor, ITERATOR lastFactor)

	FactorGraph (const CONTAINER &factors)

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

Detailed Description

GaussianBayesNet is a Bayes net made from linear-Gaussian conditionals.

Definition at line 35 of file GaussianBayesNet.h.

Member Typedef Documentation

◆ Base

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

Definition at line 39 of file GaussianBayesNet.h.

◆ ConditionalType

typedef GaussianConditional gtsam::GaussianBayesNet::ConditionalType

Definition at line 41 of file GaussianBayesNet.h.

◆ shared_ptr

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

Definition at line 42 of file GaussianBayesNet.h.

◆ sharedConditional

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

Definition at line 43 of file GaussianBayesNet.h.

◆ This

typedef GaussianBayesNet gtsam::GaussianBayesNet::This

Definition at line 40 of file GaussianBayesNet.h.

Constructor & Destructor Documentation

◆ GaussianBayesNet() [1/5]

gtsam::GaussianBayesNet::GaussianBayesNet ( )

inline

Construct empty bayes net

Definition at line 49 of file GaussianBayesNet.h.

◆ GaussianBayesNet() [2/5]

template<typename ITERATOR >

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

inline

Construct from iterator over conditionals

Definition at line 53 of file GaussianBayesNet.h.

◆ GaussianBayesNet() [3/5]

template<class CONTAINER >

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

inlineexplicit

Construct from container of factors (shared_ptr or plain objects)

Definition at line 58 of file GaussianBayesNet.h.

◆ GaussianBayesNet() [4/5]

template<class DERIVEDCONDITIONAL >

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

inlineexplicit

Implicit copy/downcast constructor to override explicit template container constructor

Definition at line 65 of file GaussianBayesNet.h.

◆ GaussianBayesNet() [5/5]

template<class DERIVEDCONDITIONAL >

gtsam::GaussianBayesNet::GaussianBayesNet ( std::initializer_list< std::shared_ptr< DERIVEDCONDITIONAL > > conditionals )

inline

Constructor that takes an initializer list of shared pointers. BayesNet bn = {make_shared<Conditional>(), ...};

Definition at line 73 of file GaussianBayesNet.h.

Member Function Documentation

◆ backSubstitute()

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 129 of file GaussianBayesNet.cpp.

◆ backSubstituteTranspose()

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 145 of file GaussianBayesNet.cpp.

◆ determinant()

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 231 of file GaussianBayesNet.cpp.

◆ equals()

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

Check equality

Definition at line 38 of file GaussianBayesNet.cpp.

◆ error()

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

Sum error over all variables.

Definition at line 106 of file GaussianBayesNet.cpp.

◆ evaluate()

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

Calculate probability density for given values x: exp(logProbability) where x is the vector of values.

Definition at line 124 of file GaussianBayesNet.cpp.

◆ gradient()

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 96 of file GaussianBayesNet.cpp.

◆ gradientAtZero()

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 101 of file GaussianBayesNet.cpp.

◆ logDeterminant()

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 237 of file GaussianBayesNet.cpp.

◆ logProbability()

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

Sum logProbability over all variables.

Definition at line 115 of file GaussianBayesNet.cpp.

◆ matrix() [1/2]

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 212 of file GaussianBayesNet.cpp.

◆ matrix() [2/2]

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 205 of file GaussianBayesNet.cpp.

◆ negLogConstant()

double gtsam::GaussianBayesNet::negLogConstant ( ) const

Get the negative log of the normalization constant corresponding to the joint Gaussian density represented by this Bayes net.

Returns: double

Definition at line 246 of file GaussianBayesNet.cpp.

◆ operator()()

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

inline

Evaluate probability density, sugar.

Definition at line 117 of file GaussianBayesNet.h.

◆ optimize() [1/2]

VectorValues gtsam::GaussianBayesNet::optimize ( ) const

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

Definition at line 44 of file GaussianBayesNet.cpp.

◆ optimize() [2/2]

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

Version of optimize for incomplete BayesNet, given missing variables.

Definition at line 49 of file GaussianBayesNet.cpp.

◆ optimizeGradientSearch()

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 89 of file GaussianBayesNet.cpp.

◆ ordering()

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 187 of file GaussianBayesNet.cpp.

◆ print()

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

inlineoverridevirtual

print graph

Reimplemented from gtsam::FactorGraph< GaussianConditional >.

Definition at line 92 of file GaussianBayesNet.h.

◆ sample() [1/4]

VectorValues gtsam::GaussianBayesNet::sample ( ) const

Sample using ancestral sampling, use default rng.

Definition at line 80 of file GaussianBayesNet.cpp.

◆ sample() [2/4]

VectorValues gtsam::GaussianBayesNet::sample ( const VectorValues & given ) const

Sample from an incomplete BayesNet, use default rng.

Definition at line 84 of file GaussianBayesNet.cpp.

◆ sample() [3/4]

VectorValues gtsam::GaussianBayesNet::sample	(	const VectorValues &	given,
		std::mt19937_64 *	rng
	)		const

Sample from an incomplete BayesNet, given missing variables Example: std::mt19937_64 rng(42); VectorValues given = ...; auto sample = gbn.sample(given, &rng);

Definition at line 68 of file GaussianBayesNet.cpp.

◆ sample() [4/4]

VectorValues gtsam::GaussianBayesNet::sample ( std::mt19937_64 * rng ) const

Sample using ancestral sampling Example: std::mt19937_64 rng(42); auto sample = gbn.sample(&rng);

Definition at line 63 of file GaussianBayesNet.cpp.

Friends And Related Function Documentation

◆ operator==

bool operator==	(	const GaussianBayesNet &	lhs,
		const GaussianBayesNet &	rhs
	)

friend

Check exact equality.

Definition at line 86 of file GaussianBayesNet.h.

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

Public Types

Public Member Functions

Testable

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

◆ ConditionalType

◆ shared_ptr

◆ sharedConditional

◆ This

Constructor & Destructor Documentation

◆ GaussianBayesNet() [1/5]

◆ GaussianBayesNet() [2/5]

◆ GaussianBayesNet() [3/5]

◆ GaussianBayesNet() [4/5]

◆ GaussianBayesNet() [5/5]

Member Function Documentation

◆ backSubstitute()

◆ backSubstituteTranspose()

◆ determinant()

◆ equals()

◆ error()

◆ evaluate()

◆ gradient()

◆ gradientAtZero()

◆ logDeterminant()

◆ logProbability()

◆ matrix() [1/2]

◆ matrix() [2/2]

◆ negLogConstant()

◆ operator()()

◆ optimize() [1/2]

◆ optimize() [2/2]

◆ optimizeGradientSearch()

◆ ordering()

◆ print()

◆ sample() [1/4]

◆ sample() [2/4]

◆ sample() [3/4]

◆ sample() [4/4]

Friends And Related Function Documentation

◆ operator==