Public Types | List of all members
gtsam::GaussianBayesNet Class Reference

#include <GaussianBayesNet.h>

Inheritance diagram for gtsam::GaussianBayesNet:
Inheritance graph
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Public Types

typedef BayesNet< GaussianConditionalBase
 
typedef GaussianConditional ConditionalType
 
typedef std::shared_ptr< Thisshared_ptr
 
typedef std::shared_ptr< ConditionalTypesharedConditional
 
typedef GaussianBayesNet This
 
- Public Types inherited from gtsam::BayesNet< GaussianConditional >
typedef std::shared_ptr< GaussianConditionalsharedConditional
 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< GaussianConditionalsharedFactor
 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)
 
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...
 
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, Vectormatrix (const Ordering &ordering) const
 
std::pair< Matrix, Vectormatrix () 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
 
- 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...
 
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)
 
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
 
sharedFactorat (size_t i)
 
const sharedFactor operator[] (size_t i) const
 
sharedFactoroperator[] (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
 

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< sharedFactorfactors_
 

Detailed Description

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

Definition at line 35 of file GaussianBayesNet.h.

Member Typedef Documentation

◆ Base

Definition at line 39 of file GaussianBayesNet.h.

◆ 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

Definition at line 43 of file GaussianBayesNet.h.

◆ 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
bayesNetThe 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
x0The 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
bayesNetThe 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 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.

◆ matrix() [2/2]

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.

◆ operator()()

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

Evaluate probability density, sugar.

Definition at line 111 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 86 of file GaussianBayesNet.h.

◆ sample() [1/4]

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.

◆ sample() [2/4]

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() [3/4]

VectorValues gtsam::GaussianBayesNet::sample ( ) const

Sample using ancestral sampling, use default rng.

Definition at line 80 of file GaussianBayesNet.cpp.

◆ sample() [4/4]

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

Sample from an incomplete BayesNet, use default rng.

Definition at line 84 of file GaussianBayesNet.cpp.


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


gtsam
Author(s):
autogenerated on Tue Jul 4 2023 02:46:19