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< Diagonal >	QR (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< Gaussian >	shared_ptr
Public Types inherited from gtsam::noiseModel::Base
typedef boost::shared_ptr< Base >	shared_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.

Member Function Documentation

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

Implements gtsam::noiseModel::Base.

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

Implements gtsam::noiseModel::Base.

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

Unwhiten an error vector.

Implements gtsam::noiseModel::Base.

Reimplemented in gtsam::noiseModel::Diagonal, gtsam::noiseModel::Isotropic, and gtsam::noiseModel::Unit.

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.

Reimplemented in gtsam::noiseModel::Diagonal, gtsam::noiseModel::Constrained, gtsam::noiseModel::Isotropic, and gtsam::noiseModel::Unit.

whiten()

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

overridevirtual

Whiten an error vector.

Implements gtsam::noiseModel::Base.

Reimplemented in gtsam::noiseModel::Diagonal, gtsam::noiseModel::Constrained, gtsam::noiseModel::Isotropic, and gtsam::noiseModel::Unit.

WhitenInPlace() [1/2]

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

virtual

In-place version.

Reimplemented in gtsam::noiseModel::Diagonal, gtsam::noiseModel::Constrained, gtsam::noiseModel::Isotropic, and gtsam::noiseModel::Unit.

WhitenInPlace() [2/2]

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

virtual

In-place version.

Reimplemented in gtsam::noiseModel::Unit, gtsam::noiseModel::Diagonal, gtsam::noiseModel::Constrained, and gtsam::noiseModel::Isotropic.

WhitenSystem() [1/4]

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

overridevirtual

Implements gtsam::noiseModel::Base.

WhitenSystem() [2/4]

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

overridevirtual

Implements gtsam::noiseModel::Base.

WhitenSystem() [3/4]

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

overridevirtual

Implements gtsam::noiseModel::Base.

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.

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

• /Users/dellaert/git/github/gtsam/linear/NoiseModel.h
• /Users/dellaert/git/github/gtsam/linear/NoiseModel.cpp