gtsam::noiseModel::mEstimator::L2WithDeadZone Class Reference

#include <LossFunctions.h>

Inheritance diagram for gtsam::noiseModel::mEstimator::L2WithDeadZone:

Collaboration diagram for gtsam::noiseModel::mEstimator::L2WithDeadZone:

Public Types
typedef std::shared_ptr< L2WithDeadZone >	shared_ptr
enum	ReweightScheme { Scalar, Block }

Public Member Functions
	L2WithDeadZone (double k=1.0, const ReweightScheme reweight=Block)
double	weight (double distance) const override
double	loss (double distance) const override
void	print (const std::string &s) const override
bool	equals (const Base &expected, double tol=1e-8) const override
double	modelParameter () const
ReweightScheme	reweightScheme () const
	Returns the reweight scheme, as explained in ReweightScheme.
Vector	weight (const Vector &error) const
double	sqrtWeight (double distance) const
Vector	sqrtWeight (const Vector &error) const
void	reweight (Vector &error) const
void	reweight (std::vector< Matrix > &A, Vector &error) const
void	reweight (Matrix &A, Vector &error) const
void	reweight (Matrix &A1, Matrix &A2, Vector &error) const
void	reweight (Matrix &A1, Matrix &A2, Matrix &A3, Vector &error) const

Static Public Member Functions
static shared_ptr	Create (double k, const ReweightScheme reweight=Block)

Protected Attributes
double	k_
ReweightScheme	reweight_
	Strategy for reweighting. More...

Detailed Description

L2WithDeadZone implements a standard L2 penalty, but with a dead zone of width 2*k, centered at the origin. The resulting penalty within the dead zone is always zero, and grows quadratically outside the dead zone. In this sense, the L2WithDeadZone penalty is "robust to inliers", rather than being robust to outliers. This penalty can be used to create barrier functions in a general way.

This model has a scalar parameter "k".

• Loss (x) = 0 if |x|<k, 0.5(k-|x|)² otherwise
• Derivative (x) = 0 if |x|<k, (-k+x) if x>k, (k+x) if x<-k
• Weight w(x) = (x)/x = 0 if |x|<k, (-k+x)/x if x>k, (k+x)/x if x<-k

Member Enumeration Documentation

ReweightScheme

enum gtsam::noiseModel::mEstimator::Base::ReweightScheme

inherited

the rows can be weighted independently according to the error or uniformly with the norm of the right hand side

Member Function Documentation

loss()

double gtsam::noiseModel::mEstimator::L2WithDeadZone::loss ( double  distance ) const

overridevirtual

This method is responsible for returning the total penalty for a given amount of error. For example, this method is responsible for implementing the quadratic function for an L2 penalty, the absolute value function for an L1 penalty, etc.

TODO(mikebosse): When the loss function has as input the norm of the error vector, then it prevents implementations of asymmeric loss functions. It would be better for this function to accept the vector and internally call the norm if necessary.

This returns (x) in mEstimator

Reimplemented from gtsam::noiseModel::mEstimator::Base.

reweight()

void gtsam::noiseModel::mEstimator::Base::reweight ( Vector &  error ) const

inherited

reweight block matrices and a vector according to their weight implementation

sqrtWeight()

Vector gtsam::noiseModel::mEstimator::Base::sqrtWeight ( const Vector &  error ) const

inherited

square root version of the weight function

weight() [1/2]

Vector gtsam::noiseModel::mEstimator::Base::weight ( const Vector &  error ) const

inherited

produce a weight vector according to an error vector and the implemented robust function

weight() [2/2]

double gtsam::noiseModel::mEstimator::L2WithDeadZone::weight ( double  distance ) const

overridevirtual

This method is responsible for returning the weight function for a given amount of error. The weight function is related to the analytic derivative of the loss function. See https://members.loria.fr/MOBerger/Enseignement/Master2/Documents/ZhangIVC-97-01.pdf for details. This method is required when optimizing cost functions with robust penalties using iteratively re-weighted least squares.

This returns w(x) in mEstimator

Implements gtsam::noiseModel::mEstimator::Base.

Member Data Documentation

reweight_

ReweightScheme gtsam::noiseModel::mEstimator::Base::reweight_

protectedinherited

Strategy for reweighting.

See also

ReweightScheme

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

• /home/docs/checkouts/readthedocs.org/user_builds/gtsam-jlblanco-docs/checkouts/latest/gtsam/linear/LossFunctions.h