gtsam  4.1.0
gtsam
gtsam::GaussianBayesNet Class Reference

Detailed Description

A Bayes net made from linear-Gaussian densities.

+ Inheritance diagram for gtsam::GaussianBayesNet:

Public Member Functions

Standard Constructors
 GaussianBayesNet ()
 Construct empty factor graph.
 
template<typename ITERATOR >
 GaussianBayesNet (ITERATOR firstConditional, ITERATOR lastConditional)
 Construct from iterator over conditionals.
 
template<class CONTAINER >
 GaussianBayesNet (const CONTAINER &conditionals)
 Construct from container of factors (shared_ptr or plain objects)
 
template<class DERIVEDCONDITIONAL >
 GaussianBayesNet (const FactorGraph< DERIVEDCONDITIONAL > &graph)
 Implicit copy/downcast constructor to override explicit template container constructor.
 
Testable
bool equals (const This &bn, double tol=1e-9) const
 Check equality.
 
Standard Interface
VectorValues optimize () const
 Solve the GaussianBayesNet, i.e. return \( x = R^{-1}*d \), by back-substitution.
 
VectorValues optimize (const VectorValues &solutionForMissing) const
 Version of optimize for incomplete BayesNet, needs solution for missing variables. More...
 
Ordering ordering () const
 Return ordering corresponding to a topological sort. More...
 
Linear Algebra
std::pair< Matrix, Vector > matrix (const Ordering &ordering) const
 Return (dense) upper-triangular matrix representation Will return upper-triangular matrix only when using 'ordering' above. More...
 
std::pair< Matrix, Vector > matrix () const
 Return (dense) upper-triangular matrix representation Will return upper-triangular matrix only when using 'ordering' above. More...
 
VectorValues optimizeGradientSearch () const
 Optimize along the gradient direction, with a closed-form computation to perform the line search. More...
 
VectorValues 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 \( x = x_0 \). More...
 
VectorValues 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. More...
 
double error (const VectorValues &x) const
 0.5 * sum of squared Mahalanobis distances.
 
double determinant () const
 Computes the determinant of a GassianBayesNet. More...
 
double logDeterminant () const
 Computes the log of the determinant of a GassianBayesNet. More...
 
VectorValues backSubstitute (const VectorValues &gx) const
 Backsubstitute with a different RHS vector than the one stored in this BayesNet. More...
 
VectorValues backSubstituteTranspose (const VectorValues &gx) const
 Transpose backsubstitute with a different RHS vector than the one stored in this BayesNet. More...
 
- Public Member Functions inherited from gtsam::FactorGraph< GaussianConditional >
void reserve (size_t size)
 Reserve space for the specified number of factors if you know in advance how many there will be (works like FastVector::reserve).
 
IsDerived< DERIVEDFACTOR > push_back (boost::shared_ptr< DERIVEDFACTOR > factor)
 Add a factor directly using a shared_ptr.
 
IsDerived< DERIVEDFACTOR > push_back (const DERIVEDFACTOR &factor)
 Add a factor by value, will be copy-constructed (use push_back with a shared_ptr to avoid the copy).
 
IsDerived< DERIVEDFACTOR > emplace_shared (Args &&... args)
 Emplace a shared pointer to factor of given type.
 
IsDerived< DERIVEDFACTOR > add (boost::shared_ptr< DERIVEDFACTOR > factor)
 add is a synonym for push_back.
 
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.
 
HasDerivedElementType< ITERATOR > push_back (ITERATOR firstFactor, ITERATOR lastFactor)
 Push back many factors with an iterator over shared_ptr (factors are not copied)
 
HasDerivedValueType< ITERATOR > push_back (ITERATOR firstFactor, ITERATOR lastFactor)
 Push back many factors with an iterator (factors are copied)
 
HasDerivedElementType< CONTAINER > push_back (const CONTAINER &container)
 Push back many factors as shared_ptr's in a container (factors are not copied)
 
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)
 Add a factor or container of factors, including STL collections, BayesTrees, etc.
 
boost::assign::list_inserter< CRefCallPushBack< This > > operator+= (const FACTOR_OR_CONTAINER &factorOrContainer)
 Add a factor or container of factors, including STL collections, BayesTrees, etc.
 
std::enable_if< std::is_base_of< This, typename CLIQUE::FactorGraphType >::value >::type push_back (const BayesTree< CLIQUE > &bayesTree)
 Push back a BayesTree as a collection of factors. More...
 
FactorIndices add_factors (const CONTAINER &factors, bool useEmptySlots=false)
 Add new factors to a factor graph and returns a list of new factor indices, optionally finding and reusing empty factor slots.
 
void print (const std::string &s="FactorGraph", const KeyFormatter &formatter=DefaultKeyFormatter) const
 print out graph
 
bool equals (const This &fg, double tol=1e-9) const
 Check equality.
 
size_t size () const
 return the number of factors (including any null factors set by remove() ).
 
bool empty () const
 Check if the graph is empty (null factors set by remove() will cause this to return false).
 
const sharedFactor at (size_t i) const
 Get a specific factor by index (this checks array bounds and may throw an exception, as opposed to operator[] which does not).
 
sharedFactorat (size_t i)
 Get a specific factor by index (this checks array bounds and may throw an exception, as opposed to operator[] which does not).
 
const sharedFactor operator[] (size_t i) const
 Get a specific factor by index (this does not check array bounds, as opposed to at() which does).
 
sharedFactoroperator[] (size_t i)
 Get a specific factor by index (this does not check array bounds, as opposed to at() which does).
 
const_iterator begin () const
 Iterator to beginning of factors.
 
const_iterator end () const
 Iterator to end of factors.
 
sharedFactor front () const
 Get the first factor.
 
sharedFactor back () const
 Get the last factor.
 
iterator begin ()
 non-const STL-style begin()
 
iterator end ()
 non-const STL-style end()
 
void resize (size_t size)
 Directly resize the number of factors in the graph. More...
 
void remove (size_t i)
 delete factor without re-arranging indexes by inserting a nullptr pointer
 
void replace (size_t index, sharedFactor factor)
 replace a factor by index
 
iterator erase (iterator item)
 Erase factor and rearrange other factors to take up the empty space.
 
iterator erase (iterator first, iterator last)
 Erase factors and rearrange other factors to take up the empty space.
 
size_t nrFactors () const
 return the number of non-null factors
 
KeySet keys () const
 Potentially slow function to return all keys involved, sorted, as a set.
 
KeyVector keyVector () const
 Potentially slow function to return all keys involved, sorted, as a vector.
 
bool exists (size_t idx) const
 MATLAB interface utility: Checks whether a factor index idx exists in the graph and is a live pointer.
 

Public Types

typedef FactorGraph< GaussianConditionalBase
 
typedef GaussianBayesNet This
 
typedef GaussianConditional ConditionalType
 
typedef boost::shared_ptr< Thisshared_ptr
 
typedef boost::shared_ptr< ConditionalTypesharedConditional
 
- Public Types inherited from gtsam::FactorGraph< GaussianConditional >
typedef GaussianConditional FactorType
 factor type
 
typedef boost::shared_ptr< GaussianConditionalsharedFactor
 Shared pointer to a factor.
 
typedef sharedFactor value_type
 
typedef FastVector< sharedFactor >::iterator iterator
 
typedef FastVector< sharedFactor >::const_iterator const_iterator
 

Friends

class boost::serialization::access
 Serialization function.
 

Additional Inherited Members

- Protected Member Functions inherited from gtsam::FactorGraph< GaussianConditional >
 FactorGraph ()
 Default constructor.
 
 FactorGraph (ITERATOR firstFactor, ITERATOR lastFactor)
 Constructor from iterator over factors (shared_ptr or plain objects)
 
 FactorGraph (const CONTAINER &factors)
 Construct from container of factors (shared_ptr or plain objects)
 
- Protected Attributes inherited from gtsam::FactorGraph< GaussianConditional >
FastVector< sharedFactorfactors_
 concept check, makes sure FACTOR defines print and equals More...
 

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

◆ 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

◆ 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
  • ************************************************************************* *‍/* ************************************************************************* *‍/

◆ 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

◆ 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

◆ 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

◆ 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.

◆ 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.

◆ optimize()

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)

◆ 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.

  • ************************************************************************* *‍/

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