Ocean::Geometry::NonLinearOptimization Class Reference

This class implements the basic functions for least square or robust optimization algorithms for non linear functions. More...

#include <NonLinearOptimization.h>

Inheritance diagram for Ocean::Geometry::NonLinearOptimization:

Data Structures
class	AdvancedDenseOptimizationProvider
	This class implements the base for an advanced dense optimization provider. More...
class	AdvancedSparseOptimizationProvider
	This class implements the base class for an advanced sparse optimization provider. More...
class	CorrespondenceGroupsAccessor
	This class implements the base class for an accessor of groups of pairs. More...
class	ObjectPointGroupsAccessor
	This class implements an abstract specialization of the accessor for groups of pairs for object points. More...
class	ObjectPointToPoseIndexImagePointCorrespondenceAccessor
	This class implements a group accessor providing access to pairs of poses and image points. More...
class	OptimizationProvider
	This class implements the base optimization provider. More...
class	PoseGroupsAccessor
	This class implements an abstract specialization of the accessor for groups of pairs for poses. More...

Static Public Member Functions
template<typename T >
static bool	denseOptimization (T &provider, const unsigned int iterations=5u, const Estimator::EstimatorType estimator=Estimator::ET_SQUARE, Scalar lambda=Scalar(0.001), const Scalar lambdaFactor=Scalar(5), Scalar *initialError=nullptr, Scalar *finalError=nullptr, const Matrix *invertedCovariances=nullptr, Scalars *intermediateErrors=nullptr)
	Invokes the optimization of a dense (matrix) optimization problem.
template<typename T , Estimator::EstimatorType tEstimator>
static bool	denseOptimization (T &provider, const unsigned int iterations=5u, Scalar lambda=Scalar(0.001), const Scalar lambdaFactor=Scalar(5), Scalar *initialError=nullptr, Scalar *finalError=nullptr, const Matrix *invertedCovariances=nullptr, Scalars *intermediateErrors=nullptr)
	Invokes the optimization of a dense (matrix) optimization problem.
template<typename T >
static bool	sparseOptimization (T &provider, const unsigned int iterations=5u, const Estimator::EstimatorType estimator=Estimator::ET_SQUARE, Scalar lambda=Scalar(0.001), const Scalar lambdaFactor=Scalar(5), Scalar *initialError=nullptr, Scalar *finalError=nullptr, const Matrix *invertedCovariances=nullptr, Scalars *intermediateErrors=nullptr)
	Invokes the optimization of a sparse (matrix) optimization problem.
template<typename T , Estimator::EstimatorType tEstimator>
static bool	sparseOptimization (T &provider, const unsigned int iterations=5u, Scalar lambda=Scalar(0.001), const Scalar lambdaFactor=Scalar(5), Scalar *initialError=nullptr, Scalar *finalError=nullptr, const Matrix *invertedCovariances=nullptr, Scalars *intermediateErrors=nullptr)
	Invokes the optimization of a sparse (matrix) optimization problem.
template<typename T >
static bool	advancedDenseOptimization (T &advancedDenseProvider, const unsigned int iterations, Scalar lambda, const Scalar lambdaFactor, Scalar *initialError=nullptr, Scalar *finalError=nullptr, Scalars *intermediateErrors=nullptr)
	Invokes the optimization of a dense (matrix) optimization problem using an advanced optimization provider.
template<typename T >
static bool	advancedSparseOptimization (T &advancedSparseProvider, const unsigned int iterations, Scalar lambda, const Scalar lambdaFactor, Scalar *initialError=nullptr, Scalar *finalError=nullptr, Scalars *intermediateErrors=nullptr)
	Invokes the optimization of a sparse (matrix) optimization problem using an advanced optimization provider.
template<Estimator::EstimatorType tEstimator>
static Scalar	sqrErrors2robustErrors2 (const Scalars &sqrErrors, const size_t modelParameters, Vector2 *weightedErrors, Vector2 *weightVectors, const SquareMatrix2 *transposedInvertedCovariances)
	Translates the n/2 squared errors that correspond to n elements in the error vector to robust errors.
template<Estimator::EstimatorType tEstimator, size_t tDimension>
static Scalar	sqrErrors2robustErrors (const Scalars &sqrErrors, const size_t modelParameters, StaticBuffer< Scalar, tDimension > *weightedErrors, StaticBuffer< Scalar, tDimension > *weightVectors, const Matrix *transposedInvertedCovariances)
	Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.
template<Estimator::EstimatorType tEstimator>
static Scalar	sqrErrors2robustErrors_i (const Scalars &sqrErrors, const size_t modelParameters, const size_t dimension, Scalar *weightedErrors_i, Scalar *weightVectors_i, const Matrix *transposedInvertedCovariances_i)
	Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.
static Scalar	sqrErrors2robustErrors2 (const Estimator::EstimatorType estimator, const Scalars &sqrErrors, const size_t modelParameters, Vector2 *weightedErrors, Vector2 *weightVectors, const SquareMatrix2 *transposedInvertedCovariances)
	Translates the n/2 squared errors that correspond to n elements in the error vector to robust errors.
template<size_t tDimension>
static Scalar	sqrErrors2robustErrors (const Estimator::EstimatorType estimator, const Scalars &sqrErrors, const size_t modelParameters, StaticBuffer< Scalar, tDimension > *weightedErrors, StaticBuffer< Scalar, tDimension > *weightVectors, const Matrix *transposedInvertedCovariances)
	Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.
static Scalar	sqrErrors2robustErrors_i (const Estimator::EstimatorType estimator, const Scalars &sqrErrors, const size_t modelParameters, const size_t dimension, Scalar *weightedErrors_i, Scalar *weightVectors_i, const Matrix *transposedInvertedCovariances_i)
	Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.

Friends
template<unsigned int , unsigned int , unsigned int >
class	NonLinearUniversalOptimizationDense

Detailed Description

This class implements the basic functions for least square or robust optimization algorithms for non linear functions.

The actual optimization algorithms are located in derived functions.

Member Function Documentation

advancedDenseOptimization()

template<typename T >

bool Ocean::Geometry::NonLinearOptimization::advancedDenseOptimization ( T &  advancedDenseProvider, const unsigned int  iterations, Scalar  lambda, const Scalar  lambdaFactor, Scalar *  initialError = nullptr, Scalar *  finalError = nullptr, Scalars *  intermediateErrors = nullptr  )

static

Invokes the optimization of a dense (matrix) optimization problem using an advanced optimization provider.

The optimization can use a Levenberg-Marquardt approach or a Gauss-Newton approach.

Parameters

advancedDenseProvider	The advanced dense optimization provider that is used during the optimization
iterations	Number of optimization iterations
lambda	Initial Levenberg-Marquardt damping value which may be changed after each iteration using the damping factor, with range [0, infinity), 0 to apply a Gauss-Newton optimization approach
lambdaFactor	Levenberg-Marquardt damping factor to be applied to the damping value, with range [1, infinity), 1 to apply a Gauss-Newton optimization approach
initialError	Optional resulting averaged robust (depending on estimator) pixel error for the given initial parameters
finalError	Optional resulting averaged robust (depending on estimator) pixel error for the final optimized parameters
intermediateErrors	Optional resulting intermediate (improving) errors

Returns

True, if at least one successful optimization iteration has been executed

Template Parameters

T	Data type of the advanced dense optimization provider, must be derived from AdvancedDenseOptimizationProvider

Now the provider will determine the (n x n) Hessian matrix and the (n x 1) Jacobian-Error matrix, may be the approximated Hessian. The Hessian matrix is calculated by J^T * J. The Jacobian-Error matrix is calculated by J^T * E, with E the error vector. The model has dimension n.

advancedSparseOptimization()

template<typename T >

bool Ocean::Geometry::NonLinearOptimization::advancedSparseOptimization ( T &  advancedSparseProvider, const unsigned int  iterations, Scalar  lambda, const Scalar  lambdaFactor, Scalar *  initialError = nullptr, Scalar *  finalError = nullptr, Scalars *  intermediateErrors = nullptr  )

static

Invokes the optimization of a sparse (matrix) optimization problem using an advanced optimization provider.

The optimization can use a Levenberg-Marquardt approach or a Gauss-Newton approach.

Parameters

advancedSparseProvider	The advanced sparse optimization provider that is used during the optimization
iterations	Number of optimization iterations
lambda	Initial Levenberg-Marquardt damping value which may be changed after each iteration using the damping factor, with range [0, infinity), 0 to apply a Gauss-Newton optimization approach
lambdaFactor	Levenberg-Marquardt damping factor to be applied to the damping value, with range [1, infinity), 1 to apply a Gauss-Newton optimization approach
initialError	Optional resulting averaged robust (depending on estimator) pixel error for the given initial parameters
finalError	Optional resulting averaged robust (depending on estimator) pixel error for the final optimized parameters
intermediateErrors	Optional resulting intermediate (improving) errors

Returns

True, if at least one successful optimization iteration has been executed

Template Parameters

T	Data type of the advanced sparse optimization provider, must be derived from AdvancedSparseOptimizationProvider

Now the provider will determine all parameters like the Jacobian, the transposed Jacobian, the Hessian and the Jacobian-Error matrix. However, the provider may also determine parts of the values or abstract information as long as the provider is able to solve the linear equation later.

denseOptimization() [1/2]

template<typename T >

bool Ocean::Geometry::NonLinearOptimization::denseOptimization ( T &  provider, const unsigned int  iterations = 5u, const Estimator::EstimatorType  estimator = Estimator::ET_SQUARE, Scalar  lambda = Scalar(0.001), const Scalar  lambdaFactor = Scalar(5), Scalar *  initialError = nullptr, Scalar *  finalError = nullptr, const Matrix *  invertedCovariances = nullptr, Scalars *  intermediateErrors = nullptr  )

inlinestatic

Invokes the optimization of a dense (matrix) optimization problem.

Parameters

provider	The optimization provider that is used during the optimization
iterations	Number of optimization iterations
estimator	Robust estimator to be applied
lambda	Initial Levenberg-Marquardt damping value which may be changed after each iteration using the damping factor, with range [0, infinity)
lambdaFactor	Levenberg-Marquardt damping factor to be applied to the damping value, with range [1, infinity)
initialError	Optional resulting averaged robust (depending on estimator) pixel error for the given initial parameters
finalError	Optional resulting averaged robust (depending on estimator) pixel error for the final optimized parameters
invertedCovariances	Optional set of inverted covariances that define the individual uncertainties of the measurements
intermediateErrors	Optional resulting intermediate (improving) errors in relation to the defined estimator

Returns

True, if at least one successful optimization iteration has been executed

Template Parameters

T	Data type of the optimization provider

denseOptimization() [2/2]

template<typename T , Estimator::EstimatorType tEstimator>

bool Ocean::Geometry::NonLinearOptimization::denseOptimization ( T &  provider, const unsigned int  iterations = 5u, Scalar  lambda = Scalar(0.001), const Scalar  lambdaFactor = Scalar(5), Scalar *  initialError = nullptr, Scalar *  finalError = nullptr, const Matrix *  invertedCovariances = nullptr, Scalars *  intermediateErrors = nullptr  )

static

Invokes the optimization of a dense (matrix) optimization problem.

Parameters

provider	The optimization provider that is used during the optimization
iterations	Number of optimization iterations
lambda	Initial Levenberg-Marquardt damping value which may be changed after each iteration using the damping factor, with range [0, infinity)
lambdaFactor	Levenberg-Marquardt damping factor to be applied to the damping value, with range [1, infinity)
initialError	Optional resulting averaged robust (depending on estimator) pixel error for the given initial parameters
finalError	Optional resulting averaged robust (depending on estimator) pixel error for the final optimized parameters
invertedCovariances	Optional set of inverted covariances that define the individual uncertainties of the measurements
intermediateErrors	Optional resulting intermediate (improving) errors

Returns

True, if at least one successful optimization iteration has been executed

Template Parameters

T	Data type of the optimization provider
tEstimator	Type of the robust estimator to be applied

sparseOptimization() [1/2]

template<typename T >

bool Ocean::Geometry::NonLinearOptimization::sparseOptimization ( T &  provider, const unsigned int  iterations = 5u, const Estimator::EstimatorType  estimator = Estimator::ET_SQUARE, Scalar  lambda = Scalar(0.001), const Scalar  lambdaFactor = Scalar(5), Scalar *  initialError = nullptr, Scalar *  finalError = nullptr, const Matrix *  invertedCovariances = nullptr, Scalars *  intermediateErrors = nullptr  )

static

Invokes the optimization of a sparse (matrix) optimization problem.

Parameters

provider	The optimization provider that is used during the optimization
iterations	Number of optimization iterations
estimator	Robust estimator to be applied
lambda	Initial Levenberg-Marquardt damping value which may be changed after each iteration using the damping factor, with range [0, infinity)
lambdaFactor	Levenberg-Marquardt damping factor to be applied to the damping value, with range [1, infinity)
initialError	Optional resulting averaged robust (depending on estimator) pixel error for the given initial parameters
finalError	Optional resulting averaged robust (depending on estimator) pixel error for the final optimized parameters
invertedCovariances	Optional set of inverted covariances that define the individual uncertainties of the measurements
intermediateErrors	Optional resulting intermediate (improving) errors

Returns

True, if at least one successful optimization iteration has been executed

Template Parameters

T	Data type of the optimization provider

sparseOptimization() [2/2]

template<typename T , Estimator::EstimatorType tEstimator>

bool Ocean::Geometry::NonLinearOptimization::sparseOptimization ( T &  provider, const unsigned int  iterations = 5u, Scalar  lambda = Scalar(0.001), const Scalar  lambdaFactor = Scalar(5), Scalar *  initialError = nullptr, Scalar *  finalError = nullptr, const Matrix *  invertedCovariances = nullptr, Scalars *  intermediateErrors = nullptr  )

static

Invokes the optimization of a sparse (matrix) optimization problem.

Parameters

provider	The optimization provider that is used during the optimization
iterations	Number of optimization iterations
lambda	Initial Levenberg-Marquardt damping value which may be changed after each iteration using the damping factor, with range [0, infinity)
lambdaFactor	Levenberg-Marquardt damping factor to be applied to the damping value, with range [1, infinity)
initialError	Optional resulting averaged robust (depending on estimator) pixel error for the given initial parameters
finalError	Optional resulting averaged robust (depending on estimator) pixel error for the final optimized parameters
invertedCovariances	Optional set of inverted covariances that define the individual uncertainties of the measurements
intermediateErrors	Optional resulting intermediate (improving) errors

Returns

True, if at least one successful optimization iteration has been executed

Template Parameters

T	Data type of the optimization provider
tEstimator	Type of the robust estimator to be applied

sqrErrors2robustErrors() [1/2]

template<size_t tDimension>

Scalar Ocean::Geometry::NonLinearOptimization::sqrErrors2robustErrors ( const Estimator::EstimatorType  estimator, const Scalars &  sqrErrors, const size_t  modelParameters, StaticBuffer< Scalar, tDimension > *  weightedErrors, StaticBuffer< Scalar, tDimension > *  weightVectors, const Matrix *  transposedInvertedCovariances  )

inlinestatic

Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.

Parameters

estimator	Robust error estimator to be used
sqrErrors	The n/i squared errors
modelParameters	Number of parameters that define the model that has to be optimized
weightedErrors	Initial n errors that will be translated to robust errors
weightVectors	The n individual weights that have been applied to the errors
transposedInvertedCovariances	Optional transposed ixi inverted covariance matrices, one for each pair of errors

Returns

Resulting averaged robust error of the entire data set

Template Parameters

tDimension

Dimension of one error element

sqrErrors2robustErrors() [2/2]

template<Estimator::EstimatorType tEstimator, size_t tDimension>

Scalar Ocean::Geometry::NonLinearOptimization::sqrErrors2robustErrors ( const Scalars &  sqrErrors, const size_t  modelParameters, StaticBuffer< Scalar, tDimension > *  weightedErrors, StaticBuffer< Scalar, tDimension > *  weightVectors, const Matrix *  transposedInvertedCovariances  )

static

Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.

Parameters

sqrErrors	The n/i squared errors
modelParameters	Number of parameters that define the model that has to be optimized
weightedErrors	Initial n errors that will be translated to robust errors
weightVectors	The n individual weights that have been applied to the errors
transposedInvertedCovariances	Optional transposed ixi inverted covariance matrices, one for each pair of errors

Returns

Resulting averaged robust error of the entire data set

Template Parameters

tEstimator	Robust error estimator to be used
tDimension	Dimension of one error element

sqrErrors2robustErrors2() [1/2]

Scalar Ocean::Geometry::NonLinearOptimization::sqrErrors2robustErrors2 ( const Estimator::EstimatorType  estimator, const Scalars &  sqrErrors, const size_t  modelParameters, Vector2 *  weightedErrors, Vector2 *  weightVectors, const SquareMatrix2 *  transposedInvertedCovariances  )

inlinestatic

Translates the n/2 squared errors that correspond to n elements in the error vector to robust errors.

Parameters

estimator	Robust error estimator to be used
sqrErrors	The n/2 squared errors
modelParameters	Number of parameters that define the model that has to be optimized
weightedErrors	Initial n errors that will be translated to robust errors
weightVectors	The n individual weights that have been applied to the errors
transposedInvertedCovariances	Optional transposed 2x2 inverted covariance matrices, one for each pair of errors

Returns

Resulting averaged robust error of the entire data set

sqrErrors2robustErrors2() [2/2]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::NonLinearOptimization::sqrErrors2robustErrors2 ( const Scalars &  sqrErrors, const size_t  modelParameters, Vector2 *  weightedErrors, Vector2 *  weightVectors, const SquareMatrix2 *  transposedInvertedCovariances  )

static

Translates the n/2 squared errors that correspond to n elements in the error vector to robust errors.

Parameters

sqrErrors	The n/2 squared errors
modelParameters	Number of parameters that define the model that has to be optimized
weightedErrors	Initial n errors that will be translated to robust errors
weightVectors	The n individual weights that have been applied to the errors
transposedInvertedCovariances	Optional transposed 2x2 inverted covariance matrices, one for each pair of errors

Returns

Resulting averaged robust error of the entire data set

Template Parameters

tEstimator

Robust error estimator to be used

sqrErrors2robustErrors_i() [1/2]

Scalar Ocean::Geometry::NonLinearOptimization::sqrErrors2robustErrors_i ( const Estimator::EstimatorType  estimator, const Scalars &  sqrErrors, const size_t  modelParameters, const size_t  dimension, Scalar *  weightedErrors_i, Scalar *  weightVectors_i, const Matrix *  transposedInvertedCovariances_i  )

inlinestatic

Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.

Parameters

estimator	Robust error estimator to be used
sqrErrors	The n/i squared errors
modelParameters	Number of parameters that define the model that has to be optimized
dimension	The dimension of one error element, with range [1, infinity)
weightedErrors_i	Initial n errors that will be translated to robust errors
weightVectors_i	The n individual weights that have been applied to the errors
transposedInvertedCovariances_i	Optional transposed ixi inverted covariance matrices, one for each pair of errors

Returns

Resulting averaged robust error of the entire data set

sqrErrors2robustErrors_i() [2/2]

template<Estimator::EstimatorType tEstimator>

Scalar Ocean::Geometry::NonLinearOptimization::sqrErrors2robustErrors_i ( const Scalars &  sqrErrors, const size_t  modelParameters, const size_t  dimension, Scalar *  weightedErrors_i, Scalar *  weightVectors_i, const Matrix *  transposedInvertedCovariances_i  )

static

Translates the n/i squared errors that correspond to n elements in the error vector to robust errors.

Parameters

sqrErrors	The n/i squared errors
modelParameters	Number of parameters that define the model that has to be optimized
dimension	The dimension of one error element, with range [1, infinity)
weightedErrors_i	Initial n errors that will be translated to robust errors
weightVectors_i	The n individual weights that have been applied to the errors
transposedInvertedCovariances_i	Optional transposed ixi inverted covariance matrices, one for each pair of errors

Returns

Resulting averaged robust error of the entire data set

Template Parameters

tEstimator

Robust error estimator to be used

Friends And Related Symbol Documentation

NonLinearUniversalOptimizationDense

template<unsigned int , unsigned int , unsigned int >

friend class NonLinearUniversalOptimizationDense

friend

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

• NonLinearOptimization.h