#include <GaussianBayesNet.h>

Inheritance diagram for gtsam::GaussianBayesNet:

Collaboration diagram for gtsam::GaussianBayesNet:

Public Types
typedef BayesNet< GaussianConditional >	Base

typedef GaussianBayesNet	This

typedef GaussianConditional	ConditionalType

typedef std::shared_ptr< This >	shared_ptr

typedef std::shared_ptr< ConditionalType >	sharedConditional

typedef GaussianConditional	FactorType
	factor type

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

typedef sharedFactor	value_type

typedef FastVector< sharedFactor >::iterator	iterator

typedef FastVector< sharedFactor >::const_iterator	const_iterator

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)

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

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

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

double	evaluate (const VectorValues &x) const

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

VectorValues	optimize () const

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

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.

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

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

VectorValues	backSubstitute (const VectorValues &gx) const

VectorValues	backSubstituteTranspose (const VectorValues &gx) const

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

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

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

HybridValues methods
double	logProbability (const HybridValues &x) const

double	evaluate (const HybridValues &c) const

Adding Single Factors
void	reserve (size_t size)

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

IsDerived< DERIVEDFACTOR >	push_back (const DERIVEDFACTOR &factor)

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

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

Adding via iterators
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)

Adding via container
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).

void	add (const FACTOR_OR_CONTAINER &factorOrContainer)

Specialized versions
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)

Testable
bool	equals (const This &fg, double tol=1e-9) const
	Check equality up to tolerance.

Standard Interface
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

double	error (const HybridValues &values) const

Modifying Factor Graphs (imperative, discouraged)
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)

Advanced Interface
size_t	nrFactors () const

KeySet	keys () const

KeyVector	keyVector () const

bool	exists (size_t idx) const

Protected Member Functions
bool	isEqual (const FactorGraph &other) const
	Check exact equality of the factor pointers. Useful for derived ==.

Protected Attributes
FastVector< sharedFactor >	factors_

Detailed Description

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

Constructor & Destructor Documentation

◆ GaussianBayesNet() [1/5]

gtsam::GaussianBayesNet::GaussianBayesNet ( )

inline

Construct empty bayes net

◆ GaussianBayesNet() [2/5]

template<typename ITERATOR >

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

inline

Construct from iterator over conditionals

◆ GaussianBayesNet() [3/5]

template<class CONTAINER >

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

inlineexplicit

Construct from container of factors (shared_ptr or plain objects)

◆ GaussianBayesNet() [4/5]

template<class DERIVEDCONDITIONAL >

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

inlineexplicit

Implicit copy/downcast constructor to override explicit template container constructor

◆ 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>(), ...};

Member Function Documentation

◆ add()

void gtsam::FactorGraph< GaussianConditional >::add ( const FACTOR_OR_CONTAINER & factorOrContainer )

inlineinherited

Add a factor or container of factors, including STL collections, BayesTrees, etc.

◆ add_factors()

FactorIndices gtsam::FactorGraph< GaussianConditional >::add_factors	(	const CONTAINER &	factors,
		bool	useEmptySlots = `false`
	)

inherited

Add new factors to a factor graph and returns a list of new factor indices, optionally finding and reusing empty factor slots.

◆ at() [1/2]

const sharedFactor gtsam::FactorGraph< GaussianConditional >::at ( size_t i ) const

inlineinherited

Get a specific factor by index (this checks array bounds and may throw an exception, as opposed to operator[] which does not).

◆ at() [2/2]

sharedFactor& gtsam::FactorGraph< GaussianConditional >::at ( size_t i )

inlineinherited

Get a specific factor by index (this checks array bounds and may throw an exception, as opposed to operator[] which does not).

◆ back()

sharedFactor gtsam::FactorGraph< GaussianConditional >::back ( ) const

inlineinherited

Get the last factor

◆ 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

◆ 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

◆ begin() [1/2]

const_iterator gtsam::FactorGraph< GaussianConditional >::begin ( ) const

inlineinherited

Iterator to beginning of factors.

◆ begin() [2/2]

iterator gtsam::FactorGraph< GaussianConditional >::begin ( )

inlineinherited

non-const STL-style begin()

◆ 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

◆ empty()

bool gtsam::FactorGraph< GaussianConditional >::empty ( ) const

inlineinherited

Check if the graph is empty (null factors set by remove() will cause this to return false).

◆ end() [1/2]

const_iterator gtsam::FactorGraph< GaussianConditional >::end ( ) const

inlineinherited

Iterator to end of factors.

◆ end() [2/2]

iterator gtsam::FactorGraph< GaussianConditional >::end ( )

inlineinherited

non-const STL-style end()

◆ equals()

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

Check equality

◆ erase() [1/2]

iterator gtsam::FactorGraph< GaussianConditional >::erase ( iterator item )

inlineinherited

Erase factor and rearrange other factors to take up the empty space

◆ erase() [2/2]

iterator gtsam::FactorGraph< GaussianConditional >::erase	(	iterator	first,
		iterator	last
	)

inlineinherited

Erase factors and rearrange other factors to take up the empty space

◆ error()

double gtsam::FactorGraph< GaussianConditional >::error ( const HybridValues & values ) const

inherited

Add error for all factors.

◆ 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.

◆ exists()

bool gtsam::FactorGraph< GaussianConditional >::exists ( size_t idx ) const

inlineinherited

MATLAB interface utility: Checks whether a factor index idx exists in the graph and is a live pointer

◆ front()

sharedFactor gtsam::FactorGraph< GaussianConditional >::front ( ) const

inlineinherited

Get the first factor

◆ 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

◆ 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

◆ keys()

KeySet gtsam::FactorGraph< GaussianConditional >::keys ( ) const

inherited

Potentially slow function to return all keys involved, sorted, as a set

◆ keyVector()

KeyVector gtsam::FactorGraph< GaussianConditional >::keyVector ( ) const

inherited

Potentially slow function to return all keys involved, sorted, as a vector

◆ 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

◆ matrix() [1/2]

std::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.

◆ matrix() [2/2]

std::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.

◆ nrFactors()

size_t gtsam::FactorGraph< GaussianConditional >::nrFactors ( ) const

inherited

return the number of non-null factors

◆ operator[]() [1/2]

const sharedFactor gtsam::FactorGraph< GaussianConditional >::operator[] ( size_t i ) const

inlineinherited

Get a specific factor by index (this does not check array bounds, as opposed to at() which does).

◆ operator[]() [2/2]

sharedFactor& gtsam::FactorGraph< GaussianConditional >::operator[] ( size_t i )

inlineinherited

Get a specific factor by index (this does not check array bounds, as opposed to at() which does).

◆ optimize()

VectorValues gtsam::GaussianBayesNet::optimize ( ) const

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

◆ 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

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

◆ 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.

◆ push_back() [1/4]

IsDerived<DERIVEDFACTOR> gtsam::FactorGraph< GaussianConditional >::push_back ( const DERIVEDFACTOR & factor )

inlineinherited

Add a factor by value, will be copy-constructed (use push_back with a shared_ptr to avoid the copy).

◆ push_back() [2/4]

HasDerivedElementType<ITERATOR> gtsam::FactorGraph< GaussianConditional >::push_back	(	ITERATOR	firstFactor,
		ITERATOR	lastFactor
	)

inlineinherited

Push back many factors with an iterator over shared_ptr (factors are not copied)

◆ push_back() [3/4]

HasDerivedElementType<CONTAINER> gtsam::FactorGraph< GaussianConditional >::push_back ( const CONTAINER & container )

inlineinherited

Push back many factors as shared_ptr's in a container (factors are not copied)

◆ push_back() [4/4]

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

inlineinherited

Push back a BayesTree as a collection of factors. NOTE: This should be hidden in derived classes in favor of a type-specialized version that calls this templated function.

◆ remove()

void gtsam::FactorGraph< GaussianConditional >::remove ( size_t i )

inlineinherited

delete factor without re-arranging indexes by inserting a nullptr pointer

◆ replace()

void gtsam::FactorGraph< GaussianConditional >::replace	(	size_t	index,
		sharedFactor	factor
	)

inlineinherited

replace a factor by index

◆ reserve()

void gtsam::FactorGraph< GaussianConditional >::reserve ( size_t size )

inlineinherited

Reserve space for the specified number of factors if you know in advance how many there will be (works like FastVector::reserve).

◆ resize()

virtual void gtsam::FactorGraph< GaussianConditional >::resize ( size_t size )

inlinevirtualinherited

Directly resize the number of factors in the graph. If the new size is less than the original, factors at the end will be removed. If the new size is larger than the original, null factors will be appended.

◆ sample() [1/2]

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

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

◆ sample() [2/2]

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);

◆ size()

size_t gtsam::FactorGraph< GaussianConditional >::size ( ) const

inlineinherited

return the number of factors (including any null factors set by remove() ).

Member Data Documentation

◆ factors_

FastVector<sharedFactor> gtsam::FactorGraph< GaussianConditional >::factors_

protectedinherited

concept check, makes sure FACTOR defines print and equals Collection of factors

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/GaussianBayesNet.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ GaussianBayesNet() [1/5]

◆ GaussianBayesNet() [2/5]

◆ GaussianBayesNet() [3/5]

◆ GaussianBayesNet() [4/5]

◆ GaussianBayesNet() [5/5]

Member Function Documentation

◆ add()

◆ add_factors()

◆ at() [1/2]

◆ at() [2/2]

◆ back()

◆ backSubstitute()

◆ backSubstituteTranspose()

◆ begin() [1/2]

◆ begin() [2/2]

◆ determinant()

◆ empty()

◆ end() [1/2]

◆ end() [2/2]

◆ equals()

◆ erase() [1/2]

◆ erase() [2/2]

◆ error()

◆ evaluate()

◆ exists()

◆ front()

◆ gradient()

◆ gradientAtZero()

◆ keys()

◆ keyVector()

◆ logDeterminant()

◆ matrix() [1/2]

◆ matrix() [2/2]

◆ nrFactors()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ optimize()

◆ optimizeGradientSearch()

◆ ordering()

◆ push_back() [1/4]

◆ push_back() [2/4]

◆ push_back() [3/4]

◆ push_back() [4/4]

◆ remove()

◆ replace()

◆ reserve()

◆ resize()

◆ sample() [1/2]

◆ sample() [2/2]

◆ size()

Member Data Documentation

◆ factors_