gtsam  4.0.0 gtsam
gtsam::JacobianFactor Class Reference

## Detailed Description

A Gaussian factor in the squared-error form.

JacobianFactor implements a Gaussian, which has quadratic negative log-likelihood

$E(x) = \frac{1}{2} (Ax-b)^T \Sigma^{-1} (Ax-b)$

where $$\Sigma$$ is a diagonal covariance matrix. The matrix $$A$$, r.h.s. vector $$b$$, and diagonal noise model $$\Sigma$$ are stored in this class.

This factor represents the sum-of-squares error of a linear measurement function, and is created upon linearization of a NoiseModelFactor, which in turn is a sum-of-squares factor with a nonlinear measurement function.

Here is an example of how this factor represents a sum-of-squares error:

Letting $$h(x)$$ be a linear measurement prediction function, $$z$$ be the actual observed measurement, the residual is

$f(x) = h(x) - z .$

If we expect noise with diagonal covariance matrix $$\Sigma$$ on this measurement, then the negative log-likelihood of the Gaussian induced by this measurement model is

$E(x) = \frac{1}{2} (h(x) - z)^T \Sigma^{-1} (h(x) - z) .$

Because $$h(x)$$ is linear, we can write it as

$h(x) = Ax + e$

and thus we have

$E(x) = \frac{1}{2} (Ax-b)^T \Sigma^{-1} (Ax-b)$

where $$b = z - e$$.

This factor can involve an arbitrary number of variables, and in the above example $$x$$ would almost always be only be a subset of the variables in the entire factor graph. There are special constructors for 1-, 2-, and 3- way JacobianFactors, and additional constructors for creating n-way JacobianFactors. The Jacobian matrix $$A$$ is passed to these constructors in blocks, for example, for a 2-way factor, the constructor would accept $$A1$$ and $$A2$$, as well as the variable indices $$j1$$ and $$j2$$ and the negative log-likelihood represented by this factor would be

$E(x) = \frac{1}{2} (A_1 x_{j1} + A_2 x_{j2} - b)^T \Sigma^{-1} (A_1 x_{j1} + A_2 x_{j2} - b) .$ Inheritance diagram for gtsam::JacobianFactor:

## Public Member Functions

JacobianFactor (const GaussianFactor &gf)
Convert from other GaussianFactor.

JacobianFactor (const JacobianFactor &jf)
Copy constructor.

JacobianFactor (const HessianFactor &hf)
Conversion from HessianFactor (does Cholesky to obtain Jacobian matrix)

JacobianFactor ()
default constructor for I/O

JacobianFactor (const Vector &b_in)
Construct Null factor.

JacobianFactor (Key i1, const Matrix &A1, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
Construct unary factor.

JacobianFactor (Key i1, const Matrix &A1, Key i2, const Matrix &A2, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
Construct binary factor.

JacobianFactor (Key i1, const Matrix &A1, Key i2, const Matrix &A2, Key i3, const Matrix &A3, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
Construct ternary factor.

template<typename TERMS >
JacobianFactor (const TERMS &terms, const Vector &b, const SharedDiagonal &model=SharedDiagonal())
Construct an n-ary factor. More...

template<typename KEYS >
JacobianFactor (const KEYS &keys, const VerticalBlockMatrix &augmentedMatrix, const SharedDiagonal &sigmas=SharedDiagonal())
Constructor with arbitrary number keys, and where the augmented matrix is given all together instead of in block terms. More...

JacobianFactor (const GaussianFactorGraph &graph, boost::optional< const Ordering & > ordering=boost::none, boost::optional< const VariableSlots & > p_variableSlots=boost::none)
Build a dense joint factor from all the factors in a factor graph. More...

virtual ~JacobianFactor ()
Virtual destructor.

virtual GaussianFactor::shared_ptr clone () const
Clone this JacobianFactor.

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

virtual bool equals (const GaussianFactor &lf, double tol=1e-9) const
Equals for testable.

Vector unweighted_error (const VectorValues &c) const

Vector error_vector (const VectorValues &c) const
(A*x-b)

virtual double error (const VectorValues &c) const
(A*x-b)/sigma

virtual Matrix augmentedInformation () const
0.5*(A*x-b)'D(A*x-b) More...

virtual Matrix information () const
Return the non-augmented information matrix represented by this GaussianFactor.

virtual VectorValues hessianDiagonal () const
Return the diagonal of the Hessian for this factor.

virtual void hessianDiagonal (double *d) const
Raw memory access version of hessianDiagonal.

virtual std::map< Key, Matrix > hessianBlockDiagonal () const
Return the block diagonal of the Hessian for this factor.

virtual std::pair< Matrix, Vector > jacobian () const
Returns (dense) A,b pair associated with factor, bakes in the weights.

std::pair< Matrix, Vector > jacobianUnweighted () const
Returns (dense) A,b pair associated with factor, does not bake in weights.

virtual Matrix augmentedJacobian () const
Return (dense) matrix associated with factor. More...

Matrix augmentedJacobianUnweighted () const
Return (dense) matrix associated with factor. More...

const VerticalBlockMatrixmatrixObject () const
Return the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object. More...

VerticalBlockMatrixmatrixObject ()
Mutable access to the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object. More...

virtual GaussianFactor::shared_ptr negate () const
Construct the corresponding anti-factor to negate information stored stored in this factor. More...

virtual bool empty () const
Check if the factor is empty. More...

bool isConstrained () const
is noise model constrained ?

virtual DenseIndex getDim (const_iterator variable) const
Return the dimension of the variable pointed to by the given key iterator todo: Remove this in favor of keeping track of dimensions with variables?

size_t rows () const
return the number of rows in the corresponding linear system

size_t cols () const
return the number of columns in the corresponding linear system

const SharedDiagonal & get_model () const
get a copy of model

SharedDiagonal & get_model ()
get a copy of model (non-const version)

const constBVector getb () const
Get a view of the r.h.s. More...

constABlock getA (const_iterator variable) const
Get a view of the A matrix for the variable pointed to by the given key iterator.

constABlock getA () const
Get a view of the A matrix, not weighted by noise.

BVector getb ()
Get a view of the r.h.s. More...

ABlock getA (iterator variable)
Get a view of the A matrix for the variable pointed to by the given key iterator (non-const version)

ABlock getA ()
Get a view of the A matrix.

void updateHessian (const KeyVector &keys, SymmetricBlockMatrix *info) const
Update an information matrix by adding the information corresponding to this factor (used internally during elimination). More...

Vector operator * (const VectorValues &x) const
Return A*x.

void transposeMultiplyAdd (double alpha, const Vector &e, VectorValues &x) const
x += A'*e. More...

void multiplyHessianAdd (double alpha, const VectorValues &x, VectorValues &y) const
y += alpha * A'*A*x

void multiplyHessianAdd (double alpha, const double *x, double *y, const std::vector< size_t > &accumulatedDims) const
Raw memory access version of multiplyHessianAdd y += alpha * A'*A*x Requires the vector accumulatedDims to tell the dimension of each variable: e.g. More...

A'*b for Jacobian.

virtual void gradientAtZero (double *d) const
A'*b for Jacobian (raw memory version)

Vector gradient (Key key, const VectorValues &x) const
Compute the gradient wrt a key at any values.

JacobianFactor whiten () const
Return a whitened version of the factor, i.e. More...

std::pair< boost::shared_ptr< GaussianConditional >, shared_ptreliminate (const Ordering &keys)
Eliminate the requested variables. More...

void setModel (bool anyConstrained, const Vector &sigmas)
set noiseModel correctly

boost::shared_ptr< GaussianConditionalsplitConditional (size_t nrFrontals)
splits a pre-factorized factor into a conditional, and changes the current factor to be the remaining component. More... Public Member Functions inherited from gtsam::GaussianFactor
GaussianFactor ()
Default constructor creates empty factor.

template<typename CONTAINER >
GaussianFactor (const CONTAINER &keys)
Construct from container of keys. More...

virtual ~GaussianFactor ()
Destructor. Public Member Functions inherited from gtsam::Factor
Key front () const
First key.

Key back () const
Last key.

const_iterator find (Key key) const
find

const KeyVectorkeys () const
Access the factor's involved variable keys.

const_iterator begin () const
Iterator at beginning of involved variable keys.

const_iterator end () const
Iterator at end of involved variable keys.

size_t size () const

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

void printKeys (const std::string &s="Factor", const KeyFormatter &formatter=DefaultKeyFormatter) const
print only keys

KeyVectorkeys ()

iterator begin ()
Iterator at beginning of involved variable keys.

iterator end ()
Iterator at end of involved variable keys.

## Public Types

typedef JacobianFactor This
Typedef to this class.

typedef GaussianFactor Base
Typedef to base class.

typedef boost::shared_ptr< Thisshared_ptr
shared_ptr to this class

typedef VerticalBlockMatrix::Block ABlock

typedef VerticalBlockMatrix::constBlock constABlock

typedef ABlock::ColXpr BVector

typedef constABlock::ConstColXpr constBVector Public Types inherited from gtsam::GaussianFactor
typedef GaussianFactor This
This class.

typedef boost::shared_ptr< Thisshared_ptr
shared_ptr to this class

typedef Factor Base
Our base class. Public Types inherited from gtsam::Factor
typedef KeyVector::iterator iterator
Iterator over keys.

typedef KeyVector::const_iterator const_iterator
Const iterator over keys.

## Protected Member Functions

template<typename TERMS >
void fillTerms (const TERMS &terms, const Vector &b, const SharedDiagonal &noiseModel)
Internal function to fill blocks and set dimensions. Protected Member Functions inherited from gtsam::Factor
Factor ()
Default constructor for I/O.

template<typename CONTAINER >
Factor (const CONTAINER &keys)
Construct factor from container of keys. More...

template<typename ITERATOR >
Factor (ITERATOR first, ITERATOR last)
Construct factor from iterator keys. More...

bool equals (const This &other, double tol=1e-9) const
check equality

## Protected Attributes

VerticalBlockMatrix Ab_

noiseModel::Diagonal::shared_ptr model_ Protected Attributes inherited from gtsam::Factor
KeyVector keys_
The keys involved in this factor.

## Friends

template<typename T >
class ExpressionFactor

class boost::serialization::access
Serialization function.

GTSAM_EXPORT std::pair< boost::shared_ptr< GaussianConditional >, shared_ptrEliminateQR (const GaussianFactorGraph &factors, const Ordering &keys)
Multiply all factors and eliminate the given keys from the resulting factor using a QR variant that handles constraints (zero sigmas). More... Static Public Member Functions inherited from gtsam::GaussianFactor
template<typename CONTAINER >
static DenseIndex Slot (const CONTAINER &keys, Key key) Static Protected Member Functions inherited from gtsam::Factor
template<typename CONTAINER >
static Factor FromKeys (const CONTAINER &keys)
Construct factor from container of keys. More...

template<typename ITERATOR >
static Factor FromIterators (ITERATOR first, ITERATOR last)
Construct factor from iterator keys. More...

## ◆ JacobianFactor() [1/3]

template<typename TERMS >
 gtsam::JacobianFactor::JacobianFactor ( const TERMS & terms, const Vector & b, const SharedDiagonal & model = SharedDiagonal() )

Construct an n-ary factor.

Template Parameters
 TERMS A container whose value type is std::pair, specifying the collection of keys and matrices making up the factor.

## ◆ JacobianFactor() [2/3]

template<typename KEYS >
 gtsam::JacobianFactor::JacobianFactor ( const KEYS & keys, const VerticalBlockMatrix & augmentedMatrix, const SharedDiagonal & sigmas = SharedDiagonal() )

Constructor with arbitrary number keys, and where the augmented matrix is given all together instead of in block terms.

Note that only the active view of the provided augmented matrix is used, and that the matrix data is copied into a newly-allocated matrix in the constructed factor.

## ◆ JacobianFactor() [3/3]

 gtsam::JacobianFactor::JacobianFactor ( const GaussianFactorGraph & graph, boost::optional< const Ordering & > ordering = boost::none, boost::optional< const VariableSlots & > p_variableSlots = boost::none )
explicit

Build a dense joint factor from all the factors in a factor graph.

If a VariableSlots structure computed for graph is already available, providing it will reduce the amount of computation performed.

## ◆ augmentedInformation()

 Matrix gtsam::JacobianFactor::augmentedInformation ( ) const
virtual

0.5*(A*x-b)'D(A*x-b)

Return the augmented information matrix represented by this GaussianFactor. The augmented information matrix contains the information matrix with an additional column holding the information vector, and an additional row holding the transpose of the information vector. The lower-right entry contains the constant error term (when $$\delta x = 0$$). The augmented information matrix is described in more detail in HessianFactor, which in fact stores an augmented information matrix.

Implements gtsam::GaussianFactor.

## ◆ augmentedJacobian()

 Matrix gtsam::JacobianFactor::augmentedJacobian ( ) const
virtual

Return (dense) matrix associated with factor.

The returned system is an augmented matrix: [A b] weights are baked in

Implements gtsam::GaussianFactor.

## ◆ augmentedJacobianUnweighted()

 Matrix gtsam::JacobianFactor::augmentedJacobianUnweighted ( ) const

Return (dense) matrix associated with factor.

The returned system is an augmented matrix: [A b] weights are not baked in

## ◆ eliminate()

 std::pair< GaussianConditional::shared_ptr, JacobianFactor::shared_ptr > gtsam::JacobianFactor::eliminate ( const Ordering & keys )

Eliminate the requested variables.

## ◆ empty()

 virtual bool gtsam::JacobianFactor::empty ( ) const
inlinevirtual

Check if the factor is empty.

TODO: How should this be defined?

Implements gtsam::GaussianFactor.

## ◆ getb() [1/2]

 const constBVector gtsam::JacobianFactor::getb ( ) const
inline

Get a view of the r.h.s.

vector b, not weighted by noise

## ◆ getb() [2/2]

 BVector gtsam::JacobianFactor::getb ( )
inline

Get a view of the r.h.s.

vector b (non-const version)

## ◆ matrixObject() [1/2]

 const VerticalBlockMatrix& gtsam::JacobianFactor::matrixObject ( ) const
inline

Return the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object.

## ◆ matrixObject() [2/2]

 VerticalBlockMatrix& gtsam::JacobianFactor::matrixObject ( )
inline

Mutable access to the full augmented Jacobian matrix of this factor as a VerticalBlockMatrix object.

 void gtsam::JacobianFactor::multiplyHessianAdd ( double alpha, const double * x, double * y, const std::vector< size_t > & accumulatedDims ) const

Raw memory access version of multiplyHessianAdd y += alpha * A'*A*x Requires the vector accumulatedDims to tell the dimension of each variable: e.g.

Raw memory access version of multiplyHessianAdd y += alpha * A'*A*x Note: this is not assuming a fixed dimension for the variables, but requires the vector accumulatedDims to tell the dimension of each variable: e.g.

: x0 has dim 3, x2 has dim 6, x3 has dim 2, then accumulatedDims is [0 3 9 11 13] NOTE: size of accumulatedDims is size of keys + 1!! TODO(frank): we should probably kill this if no longer needed

: x0 has dim 3, x2 has dim 6, x3 has dim 2, then accumulatedDims is [0 3 9 11 13] NOTE: size of accumulatedDims is size of keys + 1!! TODO Frank asks: why is this here if not regular ????

Use Eigen magic to access raw memory

Just iterate over all A matrices and multiply in correct config part (looping over keys) E.g.: Jacobian A = [A0 A1 A2] multiplies x = [x0 x1 x2]' Hence: Ax = A0 x0 + A1 x1 + A2 x2 (hence we loop over the keys and accumulate)

Deal with noise properly, need to Double* whiten as we are dividing by variance

multiply with alpha

Again iterate over all A matrices and insert Ai^T into y

## ◆ negate()

 GaussianFactor::shared_ptr gtsam::JacobianFactor::negate ( ) const
virtual

Construct the corresponding anti-factor to negate information stored stored in this factor.

Returns
a HessianFactor with negated Hessian matrices

Implements gtsam::GaussianFactor.

## ◆ splitConditional()

 GaussianConditional::shared_ptr gtsam::JacobianFactor::splitConditional ( size_t nrFrontals )

splits a pre-factorized factor into a conditional, and changes the current factor to be the remaining component.

Performs same operation as eliminate(), but without running QR. NOTE: looks at dimension of noise model to determine how many rows to keep.

Parameters
 nrFrontals number of keys to eliminate

 void gtsam::JacobianFactor::transposeMultiplyAdd ( double alpha, const Vector & e, VectorValues & x ) const

x += A'*e.

If x is initially missing any values, they are created and assumed to start as zero vectors.

## ◆ updateHessian()

 void gtsam::JacobianFactor::updateHessian ( const KeyVector & keys, SymmetricBlockMatrix * info ) const
virtual

Update an information matrix by adding the information corresponding to this factor (used internally during elimination).

Parameters
 scatter A mapping from variable index to slot index in this HessianFactor info The information matrix to be updated

Implements gtsam::GaussianFactor.

## ◆ whiten()

 JacobianFactor gtsam::JacobianFactor::whiten ( ) const

Return a whitened version of the factor, i.e.

with unit diagonal noise model.

## ◆ EliminateQR

 GTSAM_EXPORT std::pair, shared_ptr> EliminateQR ( const GaussianFactorGraph & factors, const Ordering & keys )
friend

Multiply all factors and eliminate the given keys from the resulting factor using a QR variant that handles constraints (zero sigmas).

Computation happens in noiseModel::Gaussian::QR Returns a conditional on those keys, and a new factor on the separator.

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