gtsam 4.1.1 gtsam
gtsam::noiseModel::Gaussian Class Reference

## Detailed Description

Gaussian implements the mathematical model |R*x|^2 = |y|^2 with R'*R=inv(Sigma) where y = whiten(x) = R*x x = unwhiten(x) = inv(R)*y as indeed |y|^2 = y'*y = x'*R'*R*x Various derived classes are available that are more efficient.

The named constructors return a shared_ptr because, when the smart flag is true, the underlying object might be a derived class such as Diagonal.

Inheritance diagram for gtsam::noiseModel::Gaussian:

## Public Member Functions

Gaussian (size_t dim=1, const boost::optional< Matrix > &sqrt_information=boost::none)
constructor takes square root information matrix

void print (const std::string &name) const override

bool equals (const Base &expected, double tol=1e-9) const override

Vector sigmas () const override
Calculate standard deviations. More...

Vector whiten (const Vector &v) const override
Whiten an error vector. More...

Vector unwhiten (const Vector &v) const override
Unwhiten an error vector. More...

Matrix Whiten (const Matrix &H) const override
Multiply a derivative with R (derivative of whiten) Equivalent to whitening each column of the input matrix. More...

virtual void WhitenInPlace (Matrix &H) const
In-place version. More...

virtual void WhitenInPlace (Eigen::Block< Matrix > H) const
In-place version. More...

void WhitenSystem (std::vector< Matrix > &A, Vector &b) const override
Whiten a system, in place as well. More...

void WhitenSystem (Matrix &A, Vector &b) const override

void WhitenSystem (Matrix &A1, Matrix &A2, Vector &b) const override

void WhitenSystem (Matrix &A1, Matrix &A2, Matrix &A3, Vector &b) const override

virtual boost::shared_ptr< DiagonalQR (Matrix &Ab) const
Apply appropriately weighted QR factorization to the system [A b] Q' * [A b] = [R d] Dimensions: (r*m) * m*(n+1) = r*(n+1), where r = min(m,n). More...

virtual Matrix R () const
Return R itself, but note that Whiten(H) is cheaper than R*H. More...

virtual Matrix information () const
Compute information matrix.

virtual Matrix covariance () const
Compute covariance matrix.

Public Member Functions inherited from gtsam::noiseModel::Base
Base (size_t dim=1)
primary constructor More...

virtual bool isConstrained () const
true if a constrained noise model, saves slow/clumsy dynamic casting More...

virtual bool isUnit () const
true if a unit noise model, saves slow/clumsy dynamic casting More...

size_t dim () const
Dimensionality.

virtual void print (const std::string &name="") const =0

virtual bool equals (const Base &expected, double tol=1e-9) const =0

virtual Vector sigmas () const
Calculate standard deviations. More...

virtual Vector whiten (const Vector &v) const =0
Whiten an error vector. More...

virtual Matrix Whiten (const Matrix &H) const =0
Whiten a matrix. More...

virtual Vector unwhiten (const Vector &v) const =0
Unwhiten an error vector. More...

virtual double squaredMahalanobisDistance (const Vector &v) const
Squared Mahalanobis distance v'*R'*R*v = <R*v,R*v> More...

virtual double mahalanobisDistance (const Vector &v) const
Mahalanobis distance.

virtual double loss (const double squared_distance) const
loss function, input is Mahalanobis distance More...

virtual void WhitenSystem (std::vector< Matrix > &A, Vector &b) const =0

virtual void WhitenSystem (Matrix &A, Vector &b) const =0

virtual void WhitenSystem (Matrix &A1, Matrix &A2, Vector &b) const =0

virtual void WhitenSystem (Matrix &A1, Matrix &A2, Matrix &A3, Vector &b) const =0

virtual void whitenInPlace (Vector &v) const
in-place whiten, override if can be done more efficiently More...

virtual void unwhitenInPlace (Vector &v) const
in-place unwhiten, override if can be done more efficiently More...

virtual void whitenInPlace (Eigen::Block< Vector > &v) const
in-place whiten, override if can be done more efficiently More...

virtual void unwhitenInPlace (Eigen::Block< Vector > &v) const
in-place unwhiten, override if can be done more efficiently More...

virtual Vector unweightedWhiten (const Vector &v) const
Useful function for robust noise models to get the unweighted but whitened error. More...

virtual double weight (const Vector &v) const
get the weight from the effective loss function on residual vector v More...

## Static Public Member Functions

static shared_ptr SqrtInformation (const Matrix &R, bool smart=true)
A Gaussian noise model created by specifying a square root information matrix. More...

static shared_ptr Information (const Matrix &M, bool smart=true)
A Gaussian noise model created by specifying an information matrix. More...

static shared_ptr Covariance (const Matrix &covariance, bool smart=true)
A Gaussian noise model created by specifying a covariance matrix. More...

## Public Types

typedef boost::shared_ptr< Gaussianshared_ptr

Public Types inherited from gtsam::noiseModel::Base
typedef boost::shared_ptr< Baseshared_ptr

## Protected Attributes

boost::optional< Matrix > sqrt_information_
Matrix square root of information matrix (R)

Protected Attributes inherited from gtsam::noiseModel::Base
size_t dim_

## Friends

class boost::serialization::access
Serialization function.

## ◆ Covariance()

 Gaussian::shared_ptr gtsam::noiseModel::Gaussian::Covariance ( const Matrix & covariance, bool smart = true )
static

A Gaussian noise model created by specifying a covariance matrix.

Parameters
 covariance The square covariance Matrix smart check if can be simplified to derived class

## ◆ equals()

 bool gtsam::noiseModel::Gaussian::equals ( const Base & expected, double tol = 1e-9 ) const
overridevirtual

## ◆ Information()

 Gaussian::shared_ptr gtsam::noiseModel::Gaussian::Information ( const Matrix & M, bool smart = true )
static

A Gaussian noise model created by specifying an information matrix.

Parameters
 M The information matrix smart check if can be simplified to derived class

## ◆ print()

 void gtsam::noiseModel::Gaussian::print ( const std::string & name ) const
overridevirtual

## ◆ QR()

 SharedDiagonal gtsam::noiseModel::Gaussian::QR ( Matrix & Ab ) const
virtual

Apply appropriately weighted QR factorization to the system [A b] Q' * [A b] = [R d] Dimensions: (r*m) * m*(n+1) = r*(n+1), where r = min(m,n).

This routine performs an in-place factorization on Ab. Below-diagonal elements are set to zero by this routine.

Parameters
 Ab is the m*(n+1) augmented system matrix [A b]
Returns
Empty SharedDiagonal() noise model: R,d are whitened

Reimplemented in gtsam::noiseModel::Constrained.

## ◆ R()

 virtual Matrix gtsam::noiseModel::Gaussian::R ( ) const
inlinevirtual

Return R itself, but note that Whiten(H) is cheaper than R*H.

Reimplemented in gtsam::noiseModel::Diagonal.

## ◆ sigmas()

 Vector gtsam::noiseModel::Gaussian::sigmas ( ) const
overridevirtual

Calculate standard deviations.

Reimplemented from gtsam::noiseModel::Base.

Reimplemented in gtsam::noiseModel::Diagonal.

## ◆ SqrtInformation()

 Gaussian::shared_ptr gtsam::noiseModel::Gaussian::SqrtInformation ( const Matrix & R, bool smart = true )
static

A Gaussian noise model created by specifying a square root information matrix.

Parameters
 R The (upper-triangular) square root information matrix smart check if can be simplified to derived class

## ◆ unwhiten()

 Vector gtsam::noiseModel::Gaussian::unwhiten ( const Vector & v ) const
overridevirtual

## ◆ Whiten()

 Matrix gtsam::noiseModel::Gaussian::Whiten ( const Matrix & H ) const
overridevirtual

Multiply a derivative with R (derivative of whiten) Equivalent to whitening each column of the input matrix.

Implements gtsam::noiseModel::Base.

## ◆ whiten()

 Vector gtsam::noiseModel::Gaussian::whiten ( const Vector & v ) const
overridevirtual

Whiten an error vector.

Implements gtsam::noiseModel::Base.

## ◆ WhitenInPlace() [1/2]

 void gtsam::noiseModel::Gaussian::WhitenInPlace ( Eigen::Block< Matrix > H ) const
virtual

In-place version.

## ◆ WhitenInPlace() [2/2]

 void gtsam::noiseModel::Gaussian::WhitenInPlace ( Matrix & H ) const
virtual

In-place version.

## ◆ WhitenSystem() [1/4]

 void gtsam::noiseModel::Gaussian::WhitenSystem ( Matrix & A, Vector & b ) const
overridevirtual

## ◆ WhitenSystem() [2/4]

 void gtsam::noiseModel::Gaussian::WhitenSystem ( Matrix & A1, Matrix & A2, Matrix & A3, Vector & b ) const
overridevirtual

## ◆ WhitenSystem() [3/4]

 void gtsam::noiseModel::Gaussian::WhitenSystem ( Matrix & A1, Matrix & A2, Vector & b ) const
overridevirtual

## ◆ WhitenSystem() [4/4]

 void gtsam::noiseModel::Gaussian::WhitenSystem ( std::vector< Matrix > & A, Vector & b ) const
overridevirtual

Whiten a system, in place as well.

Implements gtsam::noiseModel::Base.

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