Namespaces
	imuBias
	All bias models live in the imuBias namespace.

	noiseModel
	All noise models live in the noiseModel namespace.

	treeTraversal

Classes
struct	_ValuesConstKeyValuePair

struct	_ValuesKeyValuePair

class	AcceleratedPowerMethod
	Compute maximum Eigenpair with accelerated power method. More...

class	AcceleratingScenario
	Accelerating from an arbitrary initial state, with optional rotation. More...

class	ActiveSetSolver

class	AdaptAutoDiff

struct	additive_group_tag

class	AHRS

class	AHRSFactor

class	AlgebraicDecisionTree

class	AllDiff

class	AntiFactor

class	Assignment

class	AttitudeFactor

class	BarometricFactor

class	Basis

class	BatchFixedLagSmoother

class	BayesNet

class	BayesTree

class	BayesTreeCliqueBase

struct	BayesTreeCliqueData

struct	BayesTreeCliqueStats

class	BayesTreeOrphanWrapper

class	BayesTreeOrphanWrapper< HybridBayesTreeClique >
	Class for Hybrid Bayes tree orphan subtrees. More...

struct	Bearing

struct	Bearing< Pose2, T >

struct	Bearing< Pose3, Point3 >

struct	Bearing< Pose3, Pose3 >

struct	BearingFactor

struct	BearingRange

class	BearingRangeFactor

class	BearingS2

class	BetweenConstraint

class	BetweenFactor

class	BetweenFactorEM

class	BiasedGPSFactor

class	BinaryAllDiff

struct	BinaryJacobianFactor

class	BinaryMeasurement

class	BinarySumExpression

class	BlockJacobiPreconditioner

struct	BlockJacobiPreconditionerParameters

struct	BoundingConstraint1

struct	BoundingConstraint2

class	BTree
	Binary tree. More...

class	Cal3
	Common base class for all calibration models. More...

class	Cal3_S2
	The most common 5DOF 3D->2D calibration. More...

class	Cal3_S2Stereo
	The most common 5DOF 3D->2D calibration, stereo version. More...

class	Cal3Bundler
	Calibration used by Bundler. More...

class	Cal3DS2
	Calibration of a camera with radial distortion that also supports Lie-group behaviors for optimization. More...

class	Cal3DS2_Base
	Calibration of a camera with radial distortion. More...

class	Cal3Fisheye
	Calibration of a fisheye camera. More...

class	Cal3Unified
	Calibration of a omni-directional camera with mirror + lens radial distortion. More...

class	CalibratedCamera

class	CameraSet
	A set of cameras, all with their own calibration. More...

struct	CGState

struct	Chebyshev1Basis

class	Chebyshev2

struct	Chebyshev2Basis

class	CheiralityException

class	CholeskyFailed
	Indicate Cholesky factorization failure. More...

class	ClusterTree

class	CombinedImuFactor

class	CombinedScenarioRunner

class	ComponentDerivativeFactor

class	compose_key_visitor

class	ConcurrentBatchFilter

class	ConcurrentBatchSmoother

class	ConcurrentFilter

class	ConcurrentIncrementalFilter

class	ConcurrentIncrementalSmoother

class	ConcurrentMap

class	ConcurrentSmoother

class	Conditional

class	ConjugateGradientParameters

struct	const_selector

struct	const_selector< BASIC_TYPE, BASIC_TYPE, AS_NON_CONST, AS_CONST >

struct	const_selector< const BASIC_TYPE, BASIC_TYPE, AS_NON_CONST, AS_CONST >

class	ConstantTwistScenario

class	ConstantVelocityFactor

class	Constraint

struct	ConstructorTraversalData

class	CRefCallAddCopy

class	CRefCallPushBack

class	CSP

class	CustomFactor

class	Cyclic
	Cyclic group of order N. More...

class	DecisionTree

class	DecisionTreeFactor

class	DeltaFactor

class	DeltaFactorBase

struct	DeltaImpl

class	DerivativeFactor

struct	DGroundConstraint

struct	DHeightPrior

class	DirectProduct

class	DirectSum

class	DiscreteBayesNet

class	DiscreteBayesTree
	A Bayes tree representing a Discrete distribution. More...

class	DiscreteBayesTreeClique

class	DiscreteConditional

class	DiscreteDistribution

class	DiscreteEliminationTree
	Elimination tree for discrete factors. More...

class	DiscreteEulerPoincareHelicopter

class	DiscreteFactor

class	DiscreteFactorGraph

class	DiscreteJunctionTree

struct	DiscreteKeys
	DiscreteKeys is a set of keys that can be assembled using the & operator. More...

class	DiscreteLookupDAG

class	DiscreteLookupTable
	DiscreteLookupTable table for max-productInherits from discrete conditional for convenience, but is not normalized. Is used in the max-product algorithm. More...

class	DiscreteMarginals

class	DiscreteValues

class	DoglegOptimizer

struct	DoglegOptimizerImpl

class	DoglegParams

class	Domain

struct	DotWriter
	DotWriter is a helper class for writing graphviz .dot files. More...

struct	DRollPrior

class	DSF

class	DSFBase

class	DSFMap

class	DSFVector

struct	Dummy

class	DummyFactor

class	DummyPreconditioner

struct	DummyPreconditionerParameters

class	DynamicValuesMismatched

class	EliminatableClusterTree

class	EliminateableFactorGraph

struct	EliminationData

struct	EliminationTraits

struct	EliminationTraits< DiscreteFactorGraph >

struct	EliminationTraits< GaussianFactorGraph >

struct	EliminationTraits< HybridGaussianFactorGraph >

struct	EliminationTraits< SymbolicFactorGraph >

class	EliminationTree

class	EmptyCal

class	EqualityFactorGraph

struct	equals

struct	equals_star

class	EquivInertialNavFactor_GlobalVel

class	EquivInertialNavFactor_GlobalVel_NoBias

class	EssentialMatrix

class	EssentialMatrixConstraint

class	EssentialMatrixFactor

class	EssentialMatrixFactor2

class	EssentialMatrixFactor3

class	EssentialMatrixFactor4

class	EvaluationFactor
	Factor for enforcing the scalar value of the polynomial BASIS representation at `x` is the same as the measurement `z` when using a pseudo-spectral parameterization. More...

class	Event

class	Expression

class	ExpressionFactor

class	ExpressionFactorGraph

class	ExpressionFactorN

class	ExtendedKalmanFilter

class	Factor

class	FactorGraph

class	FastList

class	FastMap

class	FastSet

class	FitBasis

struct	FixedDimension
	Give fixed size dimension of a type, fails at compile time if dynamic. More...

class	FixedLagSmoother

class	FixedVector

class	FourierBasis
	Fourier basis. More...

class	FrobeniusBetweenFactor

class	FrobeniusFactor

class	FrobeniusPrior

class	FullIMUFactor

class	FunctorizedFactor

class	FunctorizedFactor2

class	G_x1

class	GaussianBayesNet

class	GaussianBayesTree

class	GaussianBayesTreeClique

class	GaussianConditional

class	GaussianDensity

class	GaussianEliminationTree

class	GaussianFactor

class	GaussianFactorGraph

class	GaussianFactorGraphSystem

class	GaussianISAM

class	GaussianJunctionTree

class	GaussianMixture
	A conditional of gaussian mixtures indexed by discrete variables, as part of a Bayes Network. This is the result of the elimination of a continuous variable in a hybrid scheme, such that the remaining variables are discrete+continuous. More...

class	GaussianMixtureFactor
	Implementation of a discrete conditional mixture factor. Implements a joint discrete-continuous factor where the discrete variable serves to "select" a mixture component corresponding to a GaussianFactor type of measurement. More...

class	GaussMarkov1stOrderFactor

class	GaussNewtonOptimizer

class	GaussNewtonParams

class	GeneralSFMFactor

class	GeneralSFMFactor2

class	GenericProjectionFactor

class	GenericStereoFactor

class	GenericValue

class	GncOptimizer

class	GncParams

class	GPSFactor

class	GPSFactor2

struct	GraphvizFormatting

struct	group_tag
	tag to assert a type is a group More...

struct	HasBearing

struct	HasRange

struct	HasTestablePrereqs
	Requirements on type to pass it to Testable template below. More...

class	HessianFactor
	A Gaussian factor using the canonical parameters (information form) More...

class	HybridBayesNet

class	HybridBayesTree

class	HybridBayesTreeClique
	A clique in a HybridBayesTree which is a HybridConditional internally. More...

class	HybridConditional

class	HybridEliminationTree

class	HybridFactor

class	HybridFactorGraph

class	HybridGaussianFactorGraph

class	HybridGaussianISAM

class	HybridJunctionTree

class	HybridNonlinearFactorGraph

class	HybridNonlinearISAM

class	HybridSmoother

class	HybridValues

class	IMUFactor

class	ImuFactor

class	ImuFactor2

class	InconsistentEliminationRequested

class	IncrementalFixedLagSmoother

class	IndeterminantLinearSystemException

struct	index_sequence

class	IndexPair
	Small utility class for representing a wrappable pairs of ints. More...

class	InequalityFactorGraph

class	InertialNavFactor_GlobalVelocity

class	InfeasibleInitialValues

class	InfeasibleOrUnboundedProblem

struct	InitializePose3

class	InvalidArgumentThreadsafe
	Thread-safe invalid argument exception. More...

class	InvalidDenseElimination

class	InvalidMatrixBlock

class	InvalidNoiseModel

class	InvDepthCamera3

class	InvDepthFactor3

class	InvDepthFactorVariant1

class	InvDepthFactorVariant2

class	InvDepthFactorVariant3a

class	InvDepthFactorVariant3b

class	ISAM

class	ISAM2

class	ISAM2BayesTree

class	ISAM2Clique

struct	ISAM2DoglegParams

struct	ISAM2GaussNewtonParams

class	ISAM2JunctionTree

struct	ISAM2Params

struct	ISAM2Result

struct	ISAM2UpdateParams

class	IsGroup

class	IsLieGroup

class	IsTestable

class	IsVectorSpace
	Vector Space concept. More...

class	IterativeOptimizationParameters

class	IterativeSolver

class	JacobianFactor

class	JacobianFactorQ

class	JacobianFactorQR

class	JacobianFactorSVD

class	JointMarginal

class	JunctionTree

class	KalmanFilter

class	KarcherMeanFactor

class	key_formatter

class	KeyInfo

struct	KeyInfoEntry

class	LabeledSymbol

class	LevenbergMarquardtOptimizer

class	LevenbergMarquardtParams

struct	lie_group_tag
	tag to assert a type is a Lie group More...

struct	LieGroup

class	Line3

class	LinearContainerFactor

class	LinearCost

class	LinearEquality

class	LinearInequality

class	LinearizedGaussianFactor

class	LinearizedHessianFactor

class	LinearizedJacobianFactor

class	LocalOrientedPlane3Factor

struct	LP

class	LPInitSolver

struct	LPPolicy
	Policy for ActivetSetSolver to solve Linear Programming. More...

class	MagFactor

class	MagFactor1

class	MagFactor2

class	MagFactor3

class	MagPoseFactor

struct	make_index_sequence

struct	make_index_sequence< 0 >

struct	make_index_sequence< 1 >

struct	MakeJacobian
	: meta-function to generate Jacobian More...

struct	MakeOptionalJacobian
	: meta-function to generate JacobianTA optional reference Used mainly by Expressions More...

struct	manifold_tag
	tag to assert a type is a manifold More...

class	ManifoldEvaluationFactor

class	ManifoldPreintegration

class	MarginalizeNonleafException

class	Marginals

class	Mechanization_bRn2

class	MetisIndex

class	MFAS

class	MixtureFactor
	Implementation of a discrete conditional mixture factor. More...

struct	multiplicative_group_tag
	Group operator syntax flavors. More...

struct	MultiplyWithInverse

struct	MultiplyWithInverseFunction

class	MultiProjectionFactor

class	NavState

struct	needs_eigen_aligned_allocator

struct	needs_eigen_aligned_allocator< T, void_t< typename T::_eigen_aligned_allocator_trait > >

class	NoiseModelFactor

class	NoiseModelFactorN

class	NoMatchFoundForFixed

class	NonlinearClusterTree

class	NonlinearConjugateGradientOptimizer

class	NonlinearEquality

class	NonlinearEquality1

class	NonlinearEquality2

class	NonlinearFactor

class	NonlinearFactorGraph

class	NonlinearISAM

class	NonlinearOptimizer

class	NonlinearOptimizerParams

class	OdometryFactorBase

class	OptionalJacobian

class	OptionalJacobian< Eigen::Dynamic, Eigen::Dynamic >

class	Ordering

class	ordering_key_visitor

class	OrientedPlane3
	Represents an infinite plane in 3D, which is composed of a planar normal and its perpendicular distance to the origin. Currently it provides a transform of the plane, and a norm 1 differencing of two planes. Refer to Trevor12iros for more math details. More...

class	OrientedPlane3DirectionPrior

class	OrientedPlane3Factor

class	OutOfRangeThreadsafe
	Thread-safe out of range exception. More...

class	ParameterMatrix

class	PartialPriorFactor

class	PCGSolver

struct	PCGSolverParameters

class	PendulumFactor1

class	PendulumFactor2

class	PendulumFactorPk

class	PendulumFactorPk1

class	PinholeBase

class	PinholeBaseK

class	PinholeCamera

class	PinholeFactor

class	PinholePose

class	PinholeSet

class	Pose2

class	Pose3

class	Pose3AttitudeFactor

class	Pose3Upright

class	PoseBetweenFactor

class	PoseConcept

class	PosePriorFactor

class	PoseRotationPrior

class	PoseRTV

class	PoseToPointFactor

class	PoseTranslationPrior

class	PowerMethod
	Compute maximum Eigenpair with power method. More...

class	Preconditioner

struct	PreconditionerParameters

class	PredecessorMap

class	PreintegratedAhrsMeasurements

class	PreintegratedCombinedMeasurements

class	PreintegratedImuMeasurements

class	PreintegratedRotation

struct	PreintegratedRotationParams

class	PreintegrationBase

struct	PreintegrationCombinedParams

struct	PreintegrationParams

class	PriorFactor

class	ProductLieGroup

class	ProjectionFactorPPP

class	ProjectionFactorPPPC

class	ProjectionFactorRollingShutter

struct	QP

class	QPInitSolver

struct	QPPolicy
	Policy for ActivetSetSolver to solve Linear Programming. More...

class	QPSParser

class	QPSParserException

struct	Range

struct	Range< CalibratedCamera, T >

struct	Range< PinholeCamera< Calibration >, T >

struct	Range< Point2, Point2 >

struct	Range< Point3, Point3 >

struct	Range< Pose2, T >

struct	Range< Pose3, T >

struct	Range< PoseRTV, PoseRTV >

class	RangeFactor

class	RangeFactorWithTransform

class	Reconstruction

struct	RedirectCout

class	RefCallPushBack

class	ReferenceFrameFactor

class	RegularHessianFactor

class	RegularImplicitSchurFactor

class	RegularJacobianFactor

class	RelativeElevationFactor

struct	Reshape
	Reshape functor. More...

struct	Reshape< M, M, InOptions, M, M, InOptions >
	Reshape specialization that does nothing as shape stays the same (needed to not be ambiguous for square input equals square output) More...

struct	Reshape< M, N, InOptions, M, N, InOptions >
	Reshape specialization that does nothing as shape stays the same. More...

struct	Reshape< N, M, InOptions, M, N, InOptions >
	Reshape specialization that does transpose. More...

class	Rot2

class	Rot3
	Rot3 is a 3D rotation represented as a rotation matrix if the preprocessor symbol GTSAM_USE_QUATERNIONS is not defined, or as a quaternion if it is defined. More...

class	Rot3AttitudeFactor

class	RotateDirectionsFactor

class	RotateFactor

class	RuntimeErrorThreadsafe
	Thread-safe runtime error exception. More...

class	Sampler

class	ScalarMultiplyExpression

class	Scatter

class	Scenario
	Simple trajectory simulator. More...

class	ScenarioRunner

class	Scheduler

class	SDGraph

struct	SfmData
	SfmData stores a bunch of SfmTracks. More...

struct	SfmTrack

struct	SfmTrack2d
	Track containing 2D measurements associated with a single 3D point. Note: Equivalent to gtsam.SfmTrack, but without the 3d measurement. This class holds data temporarily before 3D point is initialized. More...

class	SGraph

class	ShonanAveraging

class	ShonanAveraging2

class	ShonanAveraging3

struct	ShonanAveragingParameters
	Parameters governing optimization etc. More...

class	ShonanFactor

class	ShonanGaugeFactor

class	Signature

struct	SignatureParser
	A simple parser that replaces the boost spirit parser. More...

class	Similarity2

class	Similarity3

class	SimPolygon2D

class	SimWall2D

class	SingleValue

struct	SlotEntry
	One SlotEntry stores the slot index for a variable, as well its dim. More...

class	SmartFactorBase
	Base class for smart factors. This base class has no internal point, but it has a measurement, noise model and an optional sensor pose. This class mainly computes the derivatives and returns them as a variety of factors. The methods take a CameraSet<CAMERA> argument and the value of a point, which is kept in the derived class. More...

class	SmartProjectionFactor

struct	SmartProjectionParams

class	SmartProjectionPoseFactor

class	SmartProjectionPoseFactorRollingShutter

class	SmartProjectionRigFactor

class	SmartRangeFactor

class	SmartStereoProjectionFactor

class	SmartStereoProjectionFactorPP

class	SmartStereoProjectionPoseFactor

class	SO

class	SphericalCamera

class	StereoCamera

class	StereoCheiralityException

class	StereoPoint2

struct	StreamedKey
	To use the key_formatter on Keys, they must be wrapped in a StreamedKey. More...

class	Subgraph

class	SubgraphBuilder

struct	SubgraphBuilderParameters

class	SubgraphPreconditioner

struct	SubgraphPreconditionerParameters

class	SubgraphSolver

struct	SubgraphSolverParameters

struct	Switching

class	Symbol

class	SymbolGenerator

class	SymbolicBayesNet

class	SymbolicBayesTree

class	SymbolicBayesTreeClique
	A clique in a SymbolicBayesTree. More...

class	SymbolicConditional

class	SymbolicEliminationTree

class	SymbolicFactor

class	SymbolicFactorGraph

class	SymbolicISAM

class	SymbolicJunctionTree

class	SymmetricBlockMatrix

class	System

class	TangentPreintegration

class	TbbOpenMPMixedScope

struct	Testable

class	ThreadsafeException
	Base exception type that uses tbb_allocator if GTSAM is compiled with TBB. More...

class	TimeOfArrival
	Time of arrival to given sensor. More...

class	TOAFactor
	A "Time of Arrival" factor - so little code seems hardly worth it :-) More...

struct	traits

struct	traits< AlgebraicDecisionTree< T > >

struct	traits< BearingFactor< A1, A2, T > >
	traits More...

struct	traits< BearingRange< A1, A2 > >

struct	traits< BearingRangeFactor< A1, A2, B, R > >
	traits More...

struct	traits< BearingS2 >
	traits More...

struct	traits< BetweenConstraint< VALUE > >
	traits More...

struct	traits< BetweenFactor< VALUE > >
	traits More...

struct	traits< BetweenFactorEM< VALUE > >
	traits More...

struct	traits< BinaryJacobianFactor< M, N1, N2 > >

struct	traits< Cal3_S2 >

struct	traits< Cal3_S2Stereo >

struct	traits< Cal3Bundler >

struct	traits< Cal3DS2 >

struct	traits< Cal3Fisheye >

struct	traits< Cal3Unified >

struct	traits< CalibratedCamera >

struct	traits< CameraSet< CAMERA > >

struct	traits< CombinedImuFactor >

struct	traits< ConcurrentBatchFilter >
	traits More...

struct	traits< ConcurrentBatchSmoother >
	traits More...

struct	traits< ConcurrentIncrementalFilter >
	traits More...

struct	traits< ConcurrentIncrementalSmoother >
	traits More...

struct	traits< const Cal3_S2 >

struct	traits< const Cal3_S2Stereo >

struct	traits< const Cal3Bundler >

struct	traits< const Cal3DS2 >

struct	traits< const Cal3Fisheye >

struct	traits< const Cal3Unified >

struct	traits< const CalibratedCamera >

struct	traits< const CameraSet< CAMERA > >

struct	traits< const EssentialMatrix >

struct	traits< const Line3 >

struct	traits< const OrientedPlane3 >

struct	traits< const PinholeCamera< Calibration > >

struct	traits< const PinholePose< CALIBRATION > >

struct	traits< const PinholeSet< CAMERA > >

struct	traits< const Pose2 >

struct	traits< const Pose3 >

struct	traits< const Rot2 >

struct	traits< const Rot3 >

struct	traits< const Similarity2 >

struct	traits< const Similarity3 >

struct	traits< const SO3 >

struct	traits< const SO4 >

struct	traits< const SO< N > >

struct	traits< const SphericalCamera >

struct	traits< const StereoCamera >

struct	traits< const StereoPoint2 >

struct	traits< const Unit3 >

struct	traits< Cyclic< N > >
	Define cyclic group to be a model of the Additive Group concept. More...

struct	traits< DecisionTree< L, Y > >

struct	traits< DecisionTreeFactor >

struct	traits< DirectProduct< G, H > >

struct	traits< DirectSum< G, H > >

struct	traits< DiscreteBayesNet >

struct	traits< DiscreteConditional >

struct	traits< DiscreteDistribution >

struct	traits< DiscreteFactor >

struct	traits< DiscreteFactorGraph >
	traits More...

struct	traits< DiscreteKeys >

struct	traits< DiscreteLookupDAG >

struct	traits< DiscreteValues >

struct	traits< double >
	double More...

struct	traits< Eigen::Matrix< double, -1, -1, Options, MaxRows, MaxCols > >

struct	traits< Eigen::Matrix< double, -1, 1, Options, MaxRows, MaxCols > >

struct	traits< Eigen::Matrix< double, 1, -1, Options, MaxRows, MaxCols > >

struct	traits< Eigen::Matrix< double, M, N, Options, MaxRows, MaxCols > >

struct	traits< EqualityFactorGraph >
	traits More...

struct	traits< Errors >
	traits More...

struct	traits< EssentialMatrix >

struct	traits< Event >

struct	traits< ExpressionFactor< T > >
	traits More...

struct	traits< ExpressionFactorN< T, Args... > >
	traits More...

struct	traits< float >
	float More...

struct	traits< FunctorizedFactor2< R, T1, T2 > >
	traits More...

struct	traits< FunctorizedFactor< R, T > >
	traits More...

struct	traits< GaussianBayesNet >
	traits More...

struct	traits< GaussianBayesTree >
	traits More...

struct	traits< GaussianConditional >
	traits More...

struct	traits< GaussianFactor >
	traits More...

struct	traits< GaussianFactorGraph >
	traits More...

struct	traits< GaussianISAM >
	traits More...

struct	traits< GaussianMixture >

struct	traits< GaussianMixtureFactor >

struct	traits< GaussMarkov1stOrderFactor< VALUE > >
	traits More...

struct	traits< GeneralSFMFactor2< CALIBRATION > >

struct	traits< GeneralSFMFactor< CAMERA, LANDMARK > >

struct	traits< GenericProjectionFactor< POSE, LANDMARK, CALIBRATION > >
	traits More...

struct	traits< GenericStereoFactor< T1, T2 > >
	traits More...

struct	traits< GenericValue< ValueType > >

struct	traits< HessianFactor >
	traits More...

struct	traits< HybridBayesNet >
	traits More...

struct	traits< HybridBayesTree >
	traits More...

struct	traits< HybridConditional >

struct	traits< HybridFactor >

struct	traits< HybridGaussianISAM >
	traits More...

struct	traits< HybridNonlinearFactorGraph >

struct	traits< HybridValues >

struct	traits< imuBias::ConstantBias >

struct	traits< ImuFactor >

struct	traits< ImuFactor2 >

struct	traits< InequalityFactorGraph >
	traits More...

struct	traits< InertialNavFactor_GlobalVelocity< POSE, VELOCITY, IMUBIAS > >
	traits More...

struct	traits< ISAM2 >
	traits More...

struct	traits< JacobianFactor >
	traits More...

struct	traits< JacobianFactorQ< D, ZDim > >

struct	traits< Key >

struct	traits< LabeledSymbol >
	traits More...

struct	traits< Line3 >

struct	traits< LinearContainerFactor >

struct	traits< LinearCost >
	traits More...

struct	traits< LinearEquality >
	traits More...

struct	traits< LinearInequality >
	traits More...

struct	traits< LinearizedHessianFactor >
	traits More...

struct	traits< LinearizedJacobianFactor >
	traits More...

struct	traits< LP >
	traits More...

struct	traits< NavState >

struct	traits< noiseModel::Constrained >

struct	traits< noiseModel::Diagonal >

struct	traits< noiseModel::Gaussian >
	traits More...

struct	traits< noiseModel::Isotropic >

struct	traits< noiseModel::Unit >

struct	traits< NonlinearEquality1< VALUE > >

struct	traits< NonlinearEquality2< VALUE > >

struct	traits< NonlinearEquality< VALUE > >

struct	traits< NonlinearFactor >
	traits More...

struct	traits< NonlinearFactorGraph >
	traits More...

struct	traits< Ordering >
	traits More...

struct	traits< OrientedPlane3 >

struct	traits< ParameterMatrix< M > >

struct	traits< PinholeCamera< Calibration > >

struct	traits< PinholeFactor >
	traits More...

struct	traits< PinholePose< CALIBRATION > >

struct	traits< PinholeSet< CAMERA > >

struct	traits< Pose2 >

struct	traits< Pose3 >

struct	traits< Pose3AttitudeFactor >
	traits More...

struct	traits< Pose3Upright >

struct	traits< PoseRTV >

struct	traits< PreintegratedCombinedMeasurements >

struct	traits< PreintegratedImuMeasurements >

struct	traits< PreintegratedRotation >

struct	traits< PreintegrationCombinedParams >

struct	traits< PriorFactor< VALUE > >
	traits More...

struct	traits< ProductLieGroup< G, H > >

struct	traits< ProjectionFactorPPP< POSE, LANDMARK, CALIBRATION > >
	traits More...

struct	traits< ProjectionFactorPPPC< POSE, LANDMARK, CALIBRATION > >
	traits More...

struct	traits< ProjectionFactorRollingShutter >
	traits More...

struct	traits< QUATERNION_TYPE >

struct	traits< RangeFactor< A1, A2, T > >
	traits More...

struct	traits< RangeFactorWithTransform< A1, A2, T > >
	traits More...

struct	traits< ReferenceFrameFactor< T1, T2 > >
	traits More...

struct	traits< RegularHessianFactor< D > >

struct	traits< RegularImplicitSchurFactor< CAMERA > >

struct	traits< Rot2 >

struct	traits< Rot3 >

struct	traits< Rot3AttitudeFactor >
	traits More...

struct	traits< SfmData >
	traits More...

struct	traits< SfmTrack >

struct	traits< Similarity2 >

struct	traits< Similarity3 >

struct	traits< SimWall2D >
	traits More...

struct	traits< SmartProjectionFactor< CAMERA > >
	traits More...

struct	traits< SmartProjectionPoseFactor< CALIBRATION > >
	traits More...

struct	traits< SmartProjectionPoseFactorRollingShutter< CAMERA > >
	traits More...

struct	traits< SmartProjectionRigFactor< CAMERA > >
	traits More...

struct	traits< SmartStereoProjectionFactor >
	traits More...

struct	traits< SmartStereoProjectionFactorPP >
	traits More...

struct	traits< SmartStereoProjectionPoseFactor >
	traits More...

struct	traits< SO3 >

struct	traits< SO4 >

struct	traits< SO< N > >

struct	traits< SphericalCamera >

struct	traits< StereoCamera >

struct	traits< StereoPoint2 >

struct	traits< Symbol >
	traits More...

struct	traits< SymbolicBayesNet >
	traits More...

struct	traits< SymbolicBayesTree >

struct	traits< SymbolicBayesTreeClique >
	traits More...

struct	traits< SymbolicConditional >
	traits More...

struct	traits< SymbolicEliminationTree >
	traits More...

struct	traits< SymbolicFactor >
	traits More...

struct	traits< SymbolicFactorGraph >
	traits More...

struct	traits< TransformBtwRobotsUnaryFactor< VALUE > >
	traits More...

struct	traits< TransformBtwRobotsUnaryFactorEM< VALUE > >
	traits More...

struct	traits< Unit3 >

struct	traits< Values >
	traits More...

struct	traits< VariableIndex >
	traits More...

struct	traits< VariableSlots >
	traits More...

struct	traits< VectorValues >
	traits More...

class	TransformBtwRobotsUnaryFactor

class	TransformBtwRobotsUnaryFactorEM

class	TransformCovariance

class	TranslationFactor

class	TranslationRecovery

class	TriangulationCheiralityException
	Exception thrown by triangulateDLT when landmark is behind one or more of the cameras. More...

class	TriangulationFactor

struct	TriangulationParameters

class	TriangulationResult

class	TriangulationUnderconstrainedException
	Exception thrown by triangulateDLT when SVD returns rank < 3. More...

class	Unit3
	Represents a 3D point on a unit sphere. More...

struct	UpdateImpl

class	Value

class	ValueCloneAllocator

class	Values

struct	ValuesCastHelper

struct	ValuesCastHelper< const Value, CastedKeyValuePairType, KeyValuePairType >

struct	ValuesCastHelper< Value, CastedKeyValuePairType, KeyValuePairType >

class	ValuesIncorrectType

class	ValuesKeyAlreadyExists

class	ValuesKeyDoesNotExist

struct	ValueWithDefault

class	VariableIndex

class	VariableSlots

struct	vector_space_tag
	tag to assert a type is a vector space More...

class	VectorComponentFactor

class	VectorDerivativeFactor

class	VectorEvaluationFactor

class	VectorValues

class	VelocityConstraint

class	VelocityConstraint3

struct	VelocityPrior

class	VerticalBlockMatrix

struct	Visit

struct	VisitLeaf

struct	VisitWith

class	WeightedSampler

class	WhiteNoiseFactor
	Binary factor to estimate parameters of zero-mean Gaussian white noise. More...

Typedefs
typedef std::vector< IndexPair >	IndexPairVector

typedef std::set< IndexPair >	IndexPairSet

typedef std::map< IndexPair, IndexPairSet >	IndexPairSetMap

typedef DSFMap< IndexPair >	DSFMapIndexPair

template<typename T >
using	FastVector = std::vector< T, typename internal::FastDefaultVectorAllocator< T >::type >

template<bool B, class T = void>
using	enable_if_t = typename std::enable_if< B, T >::type
	An shorthand alias for accessing the ::type inside std::enable_if that can be used in a template directly.

typedef Eigen::MatrixXd	Matrix

typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor >	MatrixRowMajor

typedef Eigen::Block< Matrix >	SubMatrix

typedef Eigen::Block< const Matrix >	ConstSubMatrix

typedef std::uint64_t	Key
	Integer nonlinear key type.

typedef std::uint64_t	FactorIndex
	Integer nonlinear factor index type.

typedef ptrdiff_t	DenseIndex
	The index type for Eigen objects.

template<typename ... >
using	void_t = void
	Convenience void_t as we assume C++11, it will not conflict the std one in C++17 as this is in `gtsam::`

template<class... T>
using	index_sequence_for = make_index_sequence< sizeof...(T)>

typedef Eigen::VectorXd	Vector

typedef Eigen::Matrix< double, 1, 1 >	Vector1

typedef Eigen::Vector2d	Vector2

typedef Eigen::Vector3d	Vector3

typedef Eigen::VectorBlock< Vector >	SubVector

typedef Eigen::VectorBlock< const Vector >	ConstSubVector

using	Weights = Eigen::Matrix< double, 1, -1 >

using	Sequence = std::map< double, double >
	Our sequence representation is a map of {x: y} values where y = f(x)

using	Sample = std::pair< double, double >
	A sample is a key-value pair from a sequence.

using	DiscreteKey = std::pair< Key, size_t >

typedef Vector2	Point2

using	Point2Pair = std::pair< Point2, Point2 >

using	Point2Pairs = std::vector< Point2Pair >

typedef std::vector< Point2, Eigen::aligned_allocator< Point2 > >	Point2Vector

typedef Vector3	Point3

typedef std::vector< Point3, Eigen::aligned_allocator< Point3 > >	Point3Vector

using	Point3Pair = std::pair< Point3, Point3 >

using	Point3Pairs = std::vector< Point3Pair >

using	Pose2Pair = std::pair< Pose2, Pose2 >

using	Pose2Pairs = std::vector< Pose2Pair >

using	Pose3Pair = std::pair< Pose3, Pose3 >

using	Pose3Pairs = std::vector< std::pair< Pose3, Pose3 > >

typedef std::vector< Pose3 >	Pose3Vector

typedef Eigen::Quaternion< double, Eigen::DontAlign >	Quaternion

using	Rot3Vector = std::vector< Rot3, Eigen::aligned_allocator< Rot3 > >
	std::vector of Rot3s, mainly for wrapper

using	PinholeCameraCal3_S2 = gtsam::PinholeCamera< gtsam::Cal3_S2 >

using	PinholeCameraCal3Bundler = gtsam::PinholeCamera< gtsam::Cal3Bundler >

using	PinholeCameraCal3DS2 = gtsam::PinholeCamera< gtsam::Cal3DS2 >

using	PinholeCameraCal3Unified = gtsam::PinholeCamera< gtsam::Cal3Unified >

using	PinholeCameraCal3Fisheye = gtsam::PinholeCamera< gtsam::Cal3Fisheye >

using	SO3 = SO< 3 >

using	SO4 = SO< 4 >

using	SOn = SO< Eigen::Dynamic >

using	DynamicJacobian = OptionalJacobian< Eigen::Dynamic, Eigen::Dynamic >

typedef std::vector< StereoPoint2 >	StereoPoint2Vector

using	CameraSetCal3Bundler = CameraSet< PinholeCamera< Cal3Bundler > >

using	CameraSetCal3_S2 = CameraSet< PinholeCamera< Cal3_S2 > >

using	CameraSetCal3DS2 = CameraSet< PinholeCamera< Cal3DS2 > >

using	CameraSetCal3Fisheye = CameraSet< PinholeCamera< Cal3Fisheye > >

using	CameraSetCal3Unified = CameraSet< PinholeCamera< Cal3Unified > >

using	CameraSetSpherical = CameraSet< SphericalCamera >

using	GaussianFactorGraphTree = DecisionTree< Key, GaussianFactorGraph >
	Alias for DecisionTree of GaussianFactorGraphs.

using	SharedFactor = std::shared_ptr< Factor >

using	MotionModel = BetweenFactor< double >

typedef FastVector< FactorIndex >	FactorIndices
	Define collection types: More...

typedef FastSet< FactorIndex >	FactorIndexSet

using	KeyFormatter = std::function< std::string(Key)>
	Typedef for a function to format a key, i.e. to convert it to a string.

using	KeyVector = FastVector< Key >
	Define collection type once and for all - also used in wrappers.

using	KeyList = FastList< Key >

using	KeySet = FastSet< Key >

using	KeyGroupMap = FastMap< Key, int >

using	Sparse = Eigen::SparseMatrix< double >

using	Errors = FastList< Vector >
	Errors is a vector of errors.

typedef noiseModel::Base::shared_ptr	SharedNoiseModel

typedef noiseModel::Gaussian::shared_ptr	SharedGaussian

typedef noiseModel::Diagonal::shared_ptr	SharedDiagonal

typedef noiseModel::Constrained::shared_ptr	SharedConstrained

typedef noiseModel::Isotropic::shared_ptr	SharedIsotropic

typedef Eigen::SparseMatrix< double, Eigen::ColMajor, int >	SparseEigen

typedef ManifoldPreintegration	PreintegrationType

typedef Expression< NavState >	NavState_

typedef Expression< Velocity3 >	Velocity3_

typedef Vector3	Velocity3
	Velocity is currently typedef'd to Vector3. More...

using	JacobianVector = std::vector< Matrix >

using	CustomErrorFunction = std::function< Vector(const CustomFactor &, const Values &, const JacobianVector *)>

typedef Expression< double >	Double_

typedef Expression< Vector1 >	Vector1_

typedef Expression< Vector2 >	Vector2_

typedef Expression< Vector3 >	Vector3_

typedef Expression< Vector4 >	Vector4_

typedef Expression< Vector5 >	Vector5_

typedef Expression< Vector6 >	Vector6_

typedef Expression< Vector7 >	Vector7_

typedef Expression< Vector8 >	Vector8_

typedef Expression< Vector9 >	Vector9_

typedef FastMap< char, Vector >	ISAM2ThresholdMap

typedef ISAM2ThresholdMap::value_type	ISAM2ThresholdMapValue

using	OptionalMatrixType = Matrix *

using	OptionalMatrixVecType = std::vector< Matrix > *

typedef NonlinearOptimizerParams	SuccessiveLinearizationParams

typedef std::map< std::pair< Key, Key >, double >	KeyPairDoubleMap

typedef PinholeCamera< Cal3Bundler >	SfmCamera
	Define the structure for the camera poses.

typedef std::pair< size_t, Point2 >	SfmMeasurement
	A measurement with its camera index.

typedef std::pair< size_t, size_t >	SiftIndex
	Sift index for SfmTrack.

using	SfmTrack2dVector = std::vector< SfmTrack2d >

using	ShonanAveragingParameters2 = ShonanAveragingParameters< 2 >

using	ShonanAveragingParameters3 = ShonanAveragingParameters< 3 >

using	ShonanFactor2 = ShonanFactor< 2 >

using	ShonanFactor3 = ShonanFactor< 3 >

typedef std::pair< size_t, Pose2 >	IndexedPose
	Return type for auxiliary functions.

typedef std::pair< size_t, Point2 >	IndexedLandmark

typedef std::pair< std::pair< size_t, size_t >, Pose2 >	IndexedEdge

using	GraphAndValues = std::pair< NonlinearFactorGraph::shared_ptr, Values::shared_ptr >

using	BetweenFactorPose2s = std::vector< BetweenFactor< Pose2 >::shared_ptr >

using	BetweenFactorPose3s = std::vector< BetweenFactor< Pose3 >::shared_ptr >

using	BinaryMeasurementsUnit3 = std::vector< BinaryMeasurement< Unit3 > >

using	BinaryMeasurementsPoint3 = std::vector< BinaryMeasurement< Point3 > >

using	BinaryMeasurementsRot3 = std::vector< BinaryMeasurement< Rot3 > >

typedef Expression< Point2 >	Point2_

typedef Expression< Rot2 >	Rot2_

typedef Expression< Pose2 >	Pose2_

typedef Expression< Point3 >	Point3_

typedef Expression< Unit3 >	Unit3_

typedef Expression< Rot3 >	Rot3_

typedef Expression< Pose3 >	Pose3_

typedef Expression< Line3 >	Line3_

typedef Expression< OrientedPlane3 >	OrientedPlane3_

typedef Expression< Cal3_S2 >	Cal3_S2_

typedef Expression< Cal3Bundler >	Cal3Bundler_

typedef std::map< Key, std::vector< size_t > >	KeyVectorMap

typedef std::map< Key, Rot3 >	KeyRotMap

typedef DSF< int >	DSFInt

using	Domains = std::map< Key, Domain >

typedef std::vector< SimPolygon2D >	SimPolygon2DVector

typedef std::vector< SimWall2D >	SimWall2DVector

typedef Eigen::RowVectorXd	RowVector

using	KeyDimMap = std::map< Key, size_t >
	Mapping between variable's key and its corresponding dimensionality.

using	LPSolver = ActiveSetSolver< LP, LPPolicy, LPInitSolver >

using	QPSolver = ActiveSetSolver< QP, QPPolicy, QPInitSolver >

typedef ConcurrentBatchFilter::Result	ConcurrentBatchFilterResult
	Typedef for Matlab wrapping.

typedef ConcurrentBatchSmoother::Result	ConcurrentBatchSmootherResult
	Typedef for Matlab wrapping.

typedef ConcurrentIncrementalFilter::Result	ConcurrentIncrementalFilterResult
	Typedef for Matlab wrapping.

typedef ConcurrentIncrementalSmoother::Result	ConcurrentIncrementalSmootherResult
	Typedef for Matlab wrapping.

typedef FixedLagSmoother::KeyTimestampMap	FixedLagSmootherKeyTimestampMap
	Typedef for matlab wrapping.

typedef FixedLagSmootherKeyTimestampMap::value_type	FixedLagSmootherKeyTimestampMapValue

typedef FixedLagSmoother::Result	FixedLagSmootherResult

typedef SmartProjectionParams	SmartStereoProjectionParams

Enumerations
enum	GncLossType { GM, TLS }
	Choice of robust loss function for GNC.

enum	NoiseFormat { NoiseFormatG2O, NoiseFormatTORO, NoiseFormatGRAPH, NoiseFormatCOV, NoiseFormatAUTO }
	Indicates how noise parameters are stored in file. More...

enum	KernelFunctionType { KernelFunctionTypeNONE, KernelFunctionTypeHUBER, KernelFunctionTypeTUKEY }
	Robust kernel type to wrap around quadratic noise model.

enum	LinearizationMode { HESSIAN, IMPLICIT_SCHUR, JACOBIAN_Q, JACOBIAN_SVD }
	Linearization mode: what factor to linearize to. More...

enum	DegeneracyMode { IGNORE_DEGENERACY, ZERO_ON_DEGENERACY, HANDLE_INFINITY }
	How to manage degeneracy.

Functions
template<typename T >
void	testDefaultChart (TestResult &result_, const std::string &name_, const T &value)

GTSAM_EXPORT std::pair< size_t, bool >	choleskyCareful (Matrix &ATA, int order=-1)

GTSAM_EXPORT bool	choleskyPartial (Matrix &ABC, size_t nFrontal, size_t topleft=0)

bool GTSAM_EXPORT	guardedIsDebug (const std::string &s)

void GTSAM_EXPORT	guardedSetDebug (const std::string &s, const bool v)

bool GTSAM_EXPORT	isDebugVersion ()

IndexPairVector	IndexPairSetAsArray (IndexPairSet &set)

template<class T >
GenericValue< T >	genericValue (const T &v)

template<typename G >
	GTSAM_CONCEPT_REQUIRES (IsGroup< G >, bool) check_group_invariants(const G &a
	Check invariants.

template<class Class >
Class	between_default (const Class &l1, const Class &l2)

template<class Class >
Vector	logmap_default (const Class &l0, const Class &lp)

template<class Class >
Class	expmap_default (const Class &t, const Vector &d)

template<class T >
T	BCH (const T &X, const T &Y)
	AGC: bracket() only appears in Rot3 tests, should this be used elsewhere? More...

template<class T >
Matrix	wedge (const Vector &x)

template<class T >
T	expm (const Vector &x, int K=7)

template<typename T >
T	interpolate (const T &X, const T &Y, double t, typename MakeOptionalJacobian< T, T >::type Hx={}, typename MakeOptionalJacobian< T, T >::type Hy={})

template<typename T , typename ... Args>
gtsam::enable_if_t< needs_eigen_aligned_allocator< T >::value, std::shared_ptr< T > >	make_shared (Args &&... args)

template<typename T , typename ... Args>
gtsam::enable_if_t<!needs_eigen_aligned_allocator< T >::value, std::shared_ptr< T > >	make_shared (Args &&... args)
	Fall back to the boost version if no need for alignment.

template<typename T >
	GTSAM_CONCEPT_REQUIRES (IsTestable< T >, bool) check_manifold_invariants(const T &a
	Check invariants for Manifold type.

const Eigen::IOFormat &	matlabFormat ()

template<class MATRIX >
bool	equal_with_abs_tol (const Eigen::DenseBase< MATRIX > &A, const Eigen::DenseBase< MATRIX > &B, double tol=1e-9)

bool	operator== (const Matrix &A, const Matrix &B)

bool	operator!= (const Matrix &A, const Matrix &B)

GTSAM_EXPORT bool	assert_equal (const Matrix &A, const Matrix &B, double tol=1e-9)

GTSAM_EXPORT bool	assert_inequal (const Matrix &A, const Matrix &B, double tol=1e-9)

GTSAM_EXPORT bool	assert_equal (const std::list< Matrix > &As, const std::list< Matrix > &Bs, double tol=1e-9)

GTSAM_EXPORT bool	linear_independent (const Matrix &A, const Matrix &B, double tol=1e-9)

GTSAM_EXPORT bool	linear_dependent (const Matrix &A, const Matrix &B, double tol=1e-9)

GTSAM_EXPORT Vector	operator^ (const Matrix &A, const Vector &v)

template<class MATRIX >
MATRIX	prod (const MATRIX &A, const MATRIX &B)

GTSAM_EXPORT void	print (const Matrix &A, const std::string &s, std::ostream &stream)

GTSAM_EXPORT void	print (const Matrix &A, const std::string &s="")

GTSAM_EXPORT void	save (const Matrix &A, const std::string &s, const std::string &filename)

GTSAM_EXPORT std::istream &	operator>> (std::istream &inputStream, Matrix &destinationMatrix)

template<class MATRIX >
Eigen::Block< const MATRIX >	sub (const MATRIX &A, size_t i1, size_t i2, size_t j1, size_t j2)

template<typename Derived1 , typename Derived2 >
void	insertSub (Eigen::MatrixBase< Derived1 > &fullMatrix, const Eigen::MatrixBase< Derived2 > &subMatrix, size_t i, size_t j)

GTSAM_EXPORT Matrix	diag (const std::vector< Matrix > &Hs)

template<class MATRIX >
const MATRIX::ConstColXpr	column (const MATRIX &A, size_t j)

template<class MATRIX >
const MATRIX::ConstRowXpr	row (const MATRIX &A, size_t j)

template<class MATRIX >
void	zeroBelowDiagonal (MATRIX &A, size_t cols=0)

Matrix	trans (const Matrix &A)

template<int OutM, int OutN, int OutOptions, int InM, int InN, int InOptions>
Reshape< OutM, OutN, OutOptions, InM, InN, InOptions >::ReshapedType	reshape (const Eigen::Matrix< double, InM, InN, InOptions > &m)

GTSAM_EXPORT std::pair< Matrix, Matrix >	qr (const Matrix &A)

GTSAM_EXPORT void	inplace_QR (Matrix &A)

GTSAM_EXPORT std::list< std::tuple< Vector, double, double > >	weighted_eliminate (Matrix &A, Vector &b, const Vector &sigmas)

GTSAM_EXPORT void	householder_ (Matrix &A, size_t k, bool copy_vectors=true)

GTSAM_EXPORT void	householder (Matrix &A, size_t k)

GTSAM_EXPORT Vector	backSubstituteUpper (const Matrix &U, const Vector &b, bool unit=false)

GTSAM_EXPORT Vector	backSubstituteUpper (const Vector &b, const Matrix &U, bool unit=false)

GTSAM_EXPORT Vector	backSubstituteLower (const Matrix &L, const Vector &b, bool unit=false)

GTSAM_EXPORT Matrix	stack (size_t nrMatrices,...)

GTSAM_EXPORT Matrix	stack (const std::vector< Matrix > &blocks)

GTSAM_EXPORT Matrix	collect (const std::vector< const Matrix *> &matrices, size_t m=0, size_t n=0)

GTSAM_EXPORT Matrix	collect (size_t nrMatrices,...)

GTSAM_EXPORT void	vector_scale_inplace (const Vector &v, Matrix &A, bool inf_mask=false)

GTSAM_EXPORT Matrix	vector_scale (const Vector &v, const Matrix &A, bool inf_mask=false)

GTSAM_EXPORT Matrix	vector_scale (const Matrix &A, const Vector &v, bool inf_mask=false)

Matrix3	skewSymmetric (double wx, double wy, double wz)

template<class Derived >
Matrix3	skewSymmetric (const Eigen::MatrixBase< Derived > &w)

GTSAM_EXPORT Matrix	inverse_square_root (const Matrix &A)

GTSAM_EXPORT Matrix	cholesky_inverse (const Matrix &A)

GTSAM_EXPORT void	svd (const Matrix &A, Matrix &U, Vector &S, Matrix &V)

GTSAM_EXPORT std::tuple< int, double, Vector >	DLT (const Matrix &A, double rank_tol=1e-9)

GTSAM_EXPORT Matrix	expm (const Matrix &A, size_t K=7)

std::string	formatMatrixIndented (const std::string &label, const Matrix &matrix, bool makeVectorHorizontal=false)

GTSAM_EXPORT Matrix	LLt (const Matrix &A)

GTSAM_EXPORT Matrix	RtR (const Matrix &A)

GTSAM_EXPORT Vector	columnNormSquare (const Matrix &A)

template<class X , int N = traits<X>::dimension>
Eigen::Matrix< double, N, 1 >	numericalGradient (std::function< double(const X &)> h, const X &x, double delta=1e-5)
	Numerically compute gradient of scalar function. More...

template<class Y , class X , int N = traits<X>::dimension>
internal::FixedSizeMatrix< Y, X >::type	numericalDerivative11 (std::function< Y(const X &)> h, const X &x, double delta=1e-5)
	New-style numerical derivatives using manifold_traits. More...

template<class Y , class X >
internal::FixedSizeMatrix< Y, X >::type	numericalDerivative11 (Y(*h)(const X &), const X &x, double delta=1e-5)

template<class Y , class X1 , class X2 , int N = traits<X1>::dimension>
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative21 (const std::function< Y(const X1 &, const X2 &)> &h, const X1 &x1, const X2 &x2, double delta=1e-5)

template<class Y , class X1 , class X2 >
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative21 (Y(*h)(const X1 &, const X2 &), const X1 &x1, const X2 &x2, double delta=1e-5)

template<class Y , class X1 , class X2 , int N = traits<X2>::dimension>
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative22 (std::function< Y(const X1 &, const X2 &)> h, const X1 &x1, const X2 &x2, double delta=1e-5)

template<class Y , class X1 , class X2 >
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative22 (Y(*h)(const X1 &, const X2 &), const X1 &x1, const X2 &x2, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , int N = traits<X1>::dimension>
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative31 (std::function< Y(const X1 &, const X2 &, const X3 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative31 (Y(*h)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , int N = traits<X2>::dimension>
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative32 (std::function< Y(const X1 &, const X2 &, const X3 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative32 (Y(*h)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , int N = traits<X3>::dimension>
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative33 (std::function< Y(const X1 &, const X2 &, const X3 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative33 (Y(*h)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X1>::dimension>
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative41 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 >
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative41 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X2>::dimension>
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative42 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 >
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative42 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X3>::dimension>
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative43 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 >
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative43 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X4>::dimension>
internal::FixedSizeMatrix< Y, X4 >::type	numericalDerivative44 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 >
internal::FixedSizeMatrix< Y, X4 >::type	numericalDerivative44 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X1>::dimension>
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative51 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 >
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative51 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X2>::dimension>
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative52 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 >
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative52 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X3>::dimension>
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative53 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 >
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative53 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X4>::dimension>
internal::FixedSizeMatrix< Y, X4 >::type	numericalDerivative54 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 >
internal::FixedSizeMatrix< Y, X4 >::type	numericalDerivative54 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X5>::dimension>
internal::FixedSizeMatrix< Y, X5 >::type	numericalDerivative55 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 >
internal::FixedSizeMatrix< Y, X5 >::type	numericalDerivative55 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X1>::dimension>
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative61 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 >
internal::FixedSizeMatrix< Y, X1 >::type	numericalDerivative61 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X2>::dimension>
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative62 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 >
internal::FixedSizeMatrix< Y, X2 >::type	numericalDerivative62 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X3>::dimension>
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative63 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 >
internal::FixedSizeMatrix< Y, X3 >::type	numericalDerivative63 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X4>::dimension>
internal::FixedSizeMatrix< Y, X4 >::type	numericalDerivative64 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 >
internal::FixedSizeMatrix< Y, X4 >::type	numericalDerivative64 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X5>::dimension>
internal::FixedSizeMatrix< Y, X5 >::type	numericalDerivative65 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 >
internal::FixedSizeMatrix< Y, X5 >::type	numericalDerivative65 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X6>::dimension>
internal::FixedSizeMatrix< Y, X6 >::type	numericalDerivative66 (std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)> h, const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 >
internal::FixedSizeMatrix< Y, X6 >::type	numericalDerivative66 (Y(*h)(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &), const X1 &x1, const X2 &x2, const X3 &x3, const X4 &x4, const X5 &x5, const X6 &x6, double delta=1e-5)

template<class X >
internal::FixedSizeMatrix< X, X >::type	numericalHessian (std::function< double(const X &)> f, const X &x, double delta=1e-5)

template<class X >
internal::FixedSizeMatrix< X, X >::type	numericalHessian (double(*f)(const X &), const X &x, double delta=1e-5)

template<class X1 , class X2 >
internal::FixedSizeMatrix< X1, X2 >::type	numericalHessian212 (std::function< double(const X1 &, const X2 &)> f, const X1 &x1, const X2 &x2, double delta=1e-5)

template<class X1 , class X2 >
internal::FixedSizeMatrix< X1, X2 >::type	numericalHessian212 (double(*f)(const X1 &, const X2 &), const X1 &x1, const X2 &x2, double delta=1e-5)

template<class X1 , class X2 >
internal::FixedSizeMatrix< X1, X1 >::type	numericalHessian211 (std::function< double(const X1 &, const X2 &)> f, const X1 &x1, const X2 &x2, double delta=1e-5)

template<class X1 , class X2 >
internal::FixedSizeMatrix< X1, X1 >::type	numericalHessian211 (double(*f)(const X1 &, const X2 &), const X1 &x1, const X2 &x2, double delta=1e-5)

template<class X1 , class X2 >
internal::FixedSizeMatrix< X2, X2 >::type	numericalHessian222 (std::function< double(const X1 &, const X2 &)> f, const X1 &x1, const X2 &x2, double delta=1e-5)

template<class X1 , class X2 >
internal::FixedSizeMatrix< X2, X2 >::type	numericalHessian222 (double(*f)(const X1 &, const X2 &), const X1 &x1, const X2 &x2, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X1, X1 >::type	numericalHessian311 (std::function< double(const X1 &, const X2 &, const X3 &)> f, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X1, X1 >::type	numericalHessian311 (double(*f)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X2, X2 >::type	numericalHessian322 (std::function< double(const X1 &, const X2 &, const X3 &)> f, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X2, X2 >::type	numericalHessian322 (double(*f)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X3, X3 >::type	numericalHessian333 (std::function< double(const X1 &, const X2 &, const X3 &)> f, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X3, X3 >::type	numericalHessian333 (double(*f)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X1, X2 >::type	numericalHessian312 (std::function< double(const X1 &, const X2 &, const X3 &)> f, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X1, X3 >::type	numericalHessian313 (std::function< double(const X1 &, const X2 &, const X3 &)> f, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X2, X3 >::type	numericalHessian323 (std::function< double(const X1 &, const X2 &, const X3 &)> f, const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X1, X2 >::type	numericalHessian312 (double(*f)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X1, X3 >::type	numericalHessian313 (double(*f)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

template<class X1 , class X2 , class X3 >
internal::FixedSizeMatrix< X2, X3 >::type	numericalHessian323 (double(*f)(const X1 &, const X2 &, const X3 &), const X1 &x1, const X2 &x2, const X3 &x3, double delta=1e-5)

void	print (float v, const std::string &s="")

void	print (double v, const std::string &s="")

template<class T >
bool	equal (const T &obj1, const T &obj2, double tol)

template<class T >
bool	equal (const T &obj1, const T &obj2)

template<class V >
bool	assert_equal (const V &expected, const V &actual, double tol=1e-9)

bool	assert_equal (const Key &expected, const Key &actual, double tol=0.0)

template<class V >
bool	assert_equal (const std::optional< V > &expected, const std::optional< V > &actual, double tol=1e-9)

template<class V >
bool	assert_equal (const V &expected, const std::optional< V > &actual, double tol=1e-9)

template<class V >
bool	assert_equal (const V &expected, const std::optional< std::reference_wrapper< const V >> &actual, double tol=1e-9)

template<class V1 , class V2 >
bool	assert_container_equal (const std::map< V1, V2 > &expected, const std::map< V1, V2 > &actual, double tol=1e-9)

template<class V2 >
bool	assert_container_equal (const std::map< size_t, V2 > &expected, const std::map< size_t, V2 > &actual, double tol=1e-9)

template<class V1 , class V2 >
bool	assert_container_equal (const std::vector< std::pair< V1, V2 > > &expected, const std::vector< std::pair< V1, V2 > > &actual, double tol=1e-9)

template<class V >
bool	assert_container_equal (const V &expected, const V &actual, double tol=1e-9)

template<class V2 >
bool	assert_container_equality (const std::map< size_t, V2 > &expected, const std::map< size_t, V2 > &actual)

template<class V >
bool	assert_container_equality (const V &expected, const V &actual)

bool	assert_equal (const std::string &expected, const std::string &actual)

template<class V >
bool	assert_inequal (const V &expected, const V &actual, double tol=1e-9)

template<class V >
bool	assert_stdout_equal (const std::string &expected, const V &actual)

template<class V >
bool	assert_print_equal (const std::string &expected, const V &actual, const std::string &s="")

template<typename G >
void	testLieGroupDerivatives (TestResult &result_, const std::string &name_, const G &t1, const G &t2)

template<typename G >
void	testChartDerivatives (TestResult &result_, const std::string &name_, const G &t1, const G &t2)

void	tictoc_finishedIteration_ ()

void	tictoc_print_ ()

void	tictoc_print2_ ()

void	tictoc_reset_ ()

std::string GTSAM_EXPORT	demangle (const char *name)
	Function to demangle type name of variable, e.g. demangle(typeid(x).name())

GTSAM_EXPORT bool	fpEqual (double a, double b, double tol, bool check_relative_also=true)

GTSAM_EXPORT void	print (const Vector &v, const std::string &s, std::ostream &stream)

GTSAM_EXPORT void	print (const Vector &v, const std::string &s="")

GTSAM_EXPORT void	save (const Vector &A, const std::string &s, const std::string &filename)

GTSAM_EXPORT bool	operator== (const Vector &vec1, const Vector &vec2)

GTSAM_EXPORT bool	greaterThanOrEqual (const Vector &v1, const Vector &v2)

GTSAM_EXPORT bool	equal_with_abs_tol (const Vector &vec1, const Vector &vec2, double tol=1e-9)

GTSAM_EXPORT bool	equal_with_abs_tol (const SubVector &vec1, const SubVector &vec2, double tol=1e-9)

bool	equal (const Vector &vec1, const Vector &vec2, double tol)

bool	equal (const Vector &vec1, const Vector &vec2)

GTSAM_EXPORT bool	assert_equal (const Vector &vec1, const Vector &vec2, double tol=1e-9)

GTSAM_EXPORT bool	assert_inequal (const Vector &vec1, const Vector &vec2, double tol=1e-9)

GTSAM_EXPORT bool	assert_equal (const SubVector &vec1, const SubVector &vec2, double tol=1e-9)

GTSAM_EXPORT bool	assert_equal (const ConstSubVector &vec1, const ConstSubVector &vec2, double tol=1e-9)

GTSAM_EXPORT bool	linear_dependent (const Vector &vec1, const Vector &vec2, double tol=1e-9)

GTSAM_EXPORT Vector	ediv_ (const Vector &a, const Vector &b)

template<class V1 , class V2 >
double	dot (const V1 &a, const V2 &b)

template<class V1 , class V2 >
double	inner_prod (const V1 &a, const V2 &b)

GTSAM_EXPORT std::pair< double, Vector >	house (const Vector &x)

GTSAM_EXPORT double	houseInPlace (Vector &x)

GTSAM_EXPORT std::pair< Vector, double >	weightedPseudoinverse (const Vector &v, const Vector &weights)

GTSAM_EXPORT double	weightedPseudoinverse (const Vector &a, const Vector &weights, Vector &pseudo)

GTSAM_EXPORT Vector	concatVectors (const std::list< Vector > &vs)

GTSAM_EXPORT Vector	concatVectors (size_t nrVectors,...)

template<size_t M>
Matrix	kroneckerProductIdentity (const Weights &w)
	Function for computing the kronecker product of the 1*N Weight vector `w` with the MxM identity matrix `I` efficiently. The main reason for this is so we don't need to use Eigen's Unsupported library. More...

template<int M>
std::ostream &	operator<< (std::ostream &os, const ParameterMatrix< M > &parameterMatrix)

template<typename L , typename Y >
DecisionTree< L, Y >	apply (const DecisionTree< L, Y > &f, const typename DecisionTree< L, Y >::Unary &op)
	Apply unary operator `op` to DecisionTree `f`. More...

template<typename L , typename Y >
DecisionTree< L, Y >	apply (const DecisionTree< L, Y > &f, const typename DecisionTree< L, Y >::UnaryAssignment &op)
	Apply unary operator `op` with Assignment to DecisionTree `f`.

template<typename L , typename Y >
DecisionTree< L, Y >	apply (const DecisionTree< L, Y > &f, const DecisionTree< L, Y > &g, const typename DecisionTree< L, Y >::Binary &op)
	Apply binary operator `op` to DecisionTree `f`.

template<typename L , typename T1 , typename T2 >
std::pair< DecisionTree< L, T1 >, DecisionTree< L, T2 > >	unzip (const DecisionTree< L, std::pair< T1, T2 > > &input)
	unzip a DecisionTree with `std::pair` values. More...

std::vector< double >	expNormalize (const std::vector< double > &logProbs)
	Normalize a set of log probabilities. More...

GTSAM_EXPORT std::pair< std::shared_ptr< DiscreteConditional >, DecisionTreeFactor::shared_ptr >	EliminateDiscrete (const DiscreteFactorGraph &factors, const Ordering &keys)
	Main elimination function for DiscreteFactorGraph. More...

std::pair< DiscreteConditional::shared_ptr, DecisionTreeFactor::shared_ptr >	EliminateForMPE (const DiscreteFactorGraph &factors, const Ordering &frontalKeys)

GTSAM_EXPORT DiscreteKeys	operator & (const DiscreteKey &key1, const DiscreteKey &key2)
	Create a list from two keys.

std::string	markdown (const DiscreteValues &values, const KeyFormatter &keyFormatter=DefaultKeyFormatter, const DiscreteValues::Names &names={})
	Free version of markdown.

std::string	html (const DiscreteValues &values, const KeyFormatter &keyFormatter=DefaultKeyFormatter, const DiscreteValues::Names &names={})
	Free version of html.

GTSAM_EXPORT Signature	operator\| (const DiscreteKey &key, const DiscreteKey &parent)

GTSAM_EXPORT Signature	operator% (const DiscreteKey &key, const std::string &parent)

GTSAM_EXPORT Signature	operator% (const DiscreteKey &key, const Signature::Table &parent)

template<typename Cal , size_t Dim>
void	calibrateJacobians (const Cal &calibration, const Point2 &pn, OptionalJacobian< 2, Dim > Dcal={}, OptionalJacobian< 2, 2 > Dp={})

GTSAM_EXPORT Line3	transformTo (const Pose3 &wTc, const Line3 &wL, OptionalJacobian< 4, 6 > Dpose={}, OptionalJacobian< 4, 4 > Dline={})

GTSAM_EXPORT std::ostream &	operator<< (std::ostream &os, const gtsam::Point2Pair &p)

GTSAM_EXPORT double	norm2 (const Point2 &p, OptionalJacobian< 1, 2 > H={})
	Distance of the point from the origin, with Jacobian.

GTSAM_EXPORT double	distance2 (const Point2 &p1, const Point2 &q, OptionalJacobian< 1, 2 > H1={}, OptionalJacobian< 1, 2 > H2={})
	distance between two points

Point2	operator* (double s, const Point2 &p)
	multiply with scalar

GTSAM_EXPORT std::optional< Point2 >	circleCircleIntersection (double R_d, double r_d, double tol=1e-9)

GTSAM_EXPORT std::list< Point2 >	circleCircleIntersection (Point2 c1, Point2 c2, std::optional< Point2 > fh)

GTSAM_EXPORT Point2Pair	means (const std::vector< Point2Pair > &abPointPairs)
	Calculate the two means of a set of Point2 pairs.

GTSAM_EXPORT std::list< Point2 >	circleCircleIntersection (Point2 c1, double r1, Point2 c2, double r2, double tol=1e-9)
	Intersect 2 circles. More...

GTSAM_EXPORT std::ostream &	operator<< (std::ostream &os, const gtsam::Point3Pair &p)

GTSAM_EXPORT double	distance3 (const Point3 &p1, const Point3 &q, OptionalJacobian< 1, 3 > H1={}, OptionalJacobian< 1, 3 > H2={})
	distance between two points

GTSAM_EXPORT double	norm3 (const Point3 &p, OptionalJacobian< 1, 3 > H={})
	Distance of the point from the origin, with Jacobian.

GTSAM_EXPORT Point3	normalize (const Point3 &p, OptionalJacobian< 3, 3 > H={})
	normalize, with optional Jacobian

GTSAM_EXPORT Point3	cross (const Point3 &p, const Point3 &q, OptionalJacobian< 3, 3 > H_p={}, OptionalJacobian< 3, 3 > H_q={})
	cross product More...

GTSAM_EXPORT double	dot (const Point3 &p, const Point3 &q, OptionalJacobian< 1, 3 > H_p={}, OptionalJacobian< 1, 3 > H_q={})
	dot product

template<class CONTAINER >
Point3	mean (const CONTAINER &points)
	mean

GTSAM_EXPORT Point3Pair	means (const std::vector< Point3Pair > &abPointPairs)
	Calculate the two means of a set of Point3 pairs.

template<>
Matrix	wedge< Pose2 > (const Vector &xi)

template<>
Matrix	wedge< Pose3 > (const Vector &xi)

GTSAM_EXPORT std::pair< Matrix3, Vector3 >	RQ (const Matrix3 &A, OptionalJacobian< 3, 9 > H={})

template<>
Matrix	wedge< Similarity3 > (const Vector &xi)

GTSAM_EXPORT Matrix3	topLeft (const SO4 &Q, OptionalJacobian< 9, 6 > H={})

GTSAM_EXPORT Matrix43	stiefel (const SO4 &Q, OptionalJacobian< 12, 6 > H={})

GTSAM_EXPORT Vector4	triangulateHomogeneousDLT (const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &projection_matrices, const Point2Vector &measurements, double rank_tol=1e-9)

GTSAM_EXPORT Vector4	triangulateHomogeneousDLT (const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &projection_matrices, const std::vector< Unit3 > &measurements, double rank_tol=1e-9)

GTSAM_EXPORT Point3	triangulateDLT (const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &projection_matrices, const Point2Vector &measurements, double rank_tol=1e-9)

GTSAM_EXPORT Point3	triangulateDLT (const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &projection_matrices, const std::vector< Unit3 > &measurements, double rank_tol=1e-9)

GTSAM_EXPORT Point3	triangulateLOST (const std::vector< Pose3 > &poses, const Point3Vector &calibratedMeasurements, const SharedIsotropic &measurementNoise)
	Triangulation using the LOST (Linear Optimal Sine Triangulation) algorithm proposed in https://arxiv.org/pdf/2205.12197.pdf by Sebastien Henry and John Christian. More...

template<class CALIBRATION >
std::pair< NonlinearFactorGraph, Values >	triangulationGraph (const std::vector< Pose3 > &poses, std::shared_ptr< CALIBRATION > sharedCal, const Point2Vector &measurements, Key landmarkKey, const Point3 &initialEstimate, const SharedNoiseModel &model=noiseModel::Unit::Create(2))

template<class CAMERA >
std::pair< NonlinearFactorGraph, Values >	triangulationGraph (const CameraSet< CAMERA > &cameras, const typename CAMERA::MeasurementVector &measurements, Key landmarkKey, const Point3 &initialEstimate, const SharedNoiseModel &model=nullptr)

GTSAM_EXPORT Point3	optimize (const NonlinearFactorGraph &graph, const Values &values, Key landmarkKey)

template<class CALIBRATION >
Point3	triangulateNonlinear (const std::vector< Pose3 > &poses, std::shared_ptr< CALIBRATION > sharedCal, const Point2Vector &measurements, const Point3 &initialEstimate, const SharedNoiseModel &model=nullptr)

template<class CAMERA >
Point3	triangulateNonlinear (const CameraSet< CAMERA > &cameras, const typename CAMERA::MeasurementVector &measurements, const Point3 &initialEstimate, const SharedNoiseModel &model=nullptr)

template<class CAMERA >
std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 > >	projectionMatricesFromCameras (const CameraSet< CAMERA > &cameras)

template<class CALIBRATION >
std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 > >	projectionMatricesFromPoses (const std::vector< Pose3 > &poses, std::shared_ptr< CALIBRATION > sharedCal)

template<class CALIBRATION >
Cal3_S2	createPinholeCalibration (const CALIBRATION &cal)

template<class CALIBRATION , class MEASUREMENT >
MEASUREMENT	undistortMeasurementInternal (const CALIBRATION &cal, const MEASUREMENT &measurement, std::optional< Cal3_S2 > pinholeCal={})

template<class CALIBRATION >
Point2Vector	undistortMeasurements (const CALIBRATION &cal, const Point2Vector &measurements)

template<>
Point2Vector	undistortMeasurements (const Cal3_S2 &cal, const Point2Vector &measurements)

template<class CAMERA >
CAMERA::MeasurementVector	undistortMeasurements (const CameraSet< CAMERA > &cameras, const typename CAMERA::MeasurementVector &measurements)

template<class CAMERA = PinholeCamera<Cal3_S2>>
PinholeCamera< Cal3_S2 >::MeasurementVector	undistortMeasurements (const CameraSet< PinholeCamera< Cal3_S2 >> &cameras, const PinholeCamera< Cal3_S2 >::MeasurementVector &measurements)

template<class CAMERA = SphericalCamera>
SphericalCamera::MeasurementVector	undistortMeasurements (const CameraSet< SphericalCamera > &cameras, const SphericalCamera::MeasurementVector &measurements)

template<class CALIBRATION >
Point3Vector	calibrateMeasurementsShared (const CALIBRATION &cal, const Point2Vector &measurements)

template<class CAMERA >
Point3Vector	calibrateMeasurements (const CameraSet< CAMERA > &cameras, const typename CAMERA::MeasurementVector &measurements)

template<class CAMERA = SphericalCamera>
Point3Vector	calibrateMeasurements (const CameraSet< SphericalCamera > &cameras, const SphericalCamera::MeasurementVector &measurements)

template<class CALIBRATION >
Point3	triangulatePoint3 (const std::vector< Pose3 > &poses, std::shared_ptr< CALIBRATION > sharedCal, const Point2Vector &measurements, double rank_tol=1e-9, bool optimize=false, const SharedNoiseModel &model=nullptr, const bool useLOST=false)

template<class CAMERA >
Point3	triangulatePoint3 (const CameraSet< CAMERA > &cameras, const typename CAMERA::MeasurementVector &measurements, double rank_tol=1e-9, bool optimize=false, const SharedNoiseModel &model=nullptr, const bool useLOST=false)

template<class CALIBRATION >
Point3	triangulatePoint3 (const CameraSet< PinholeCamera< CALIBRATION >> &cameras, const Point2Vector &measurements, double rank_tol=1e-9, bool optimize=false, const SharedNoiseModel &model=nullptr, const bool useLOST=false)
	Pinhole-specific version.

template<class CAMERA >
TriangulationResult	triangulateSafe (const CameraSet< CAMERA > &cameras, const typename CAMERA::MeasurementVector &measured, const TriangulationParameters &params)
	triangulateSafe: extensive checking of the outcome

std::set< DiscreteKey >	DiscreteKeysAsSet (const DiscreteKeys &discreteKeys)
	Return the DiscreteKey vector as a set.

KeyVector	CollectKeys (const KeyVector &continuousKeys, const DiscreteKeys &discreteKeys)

KeyVector	CollectKeys (const KeyVector &keys1, const KeyVector &keys2)

DiscreteKeys	CollectDiscreteKeys (const DiscreteKeys &key1, const DiscreteKeys &key2)

GTSAM_EXPORT std::pair< std::shared_ptr< HybridConditional >, std::shared_ptr< Factor > >	EliminateHybrid (const HybridGaussianFactorGraph &factors, const Ordering &keys)
	Main elimination function for HybridGaussianFactorGraph. More...

GTSAM_EXPORT const Ordering	HybridOrdering (const HybridGaussianFactorGraph &graph)
	Return a Colamd constrained ordering where the discrete keys are eliminated after the continuous keys. More...

HybridGaussianFactorGraph::shared_ptr	makeSwitchingChain (size_t n, std::function< Key(int)> keyFunc=X, std::function< Key(int)> dKeyFunc=M)
	Create a switching system chain. A switching system is a continuous system which depends on a discrete mode at each time step of the chain. More...

std::pair< KeyVector, std::vector< int > >	makeBinaryOrdering (std::vector< Key > &input)
	Return the ordering as a binary tree such that all parent nodes are above their children. More...

template<class CLIQUE >
bool	check_sharedCliques (const std::pair< Key, typename BayesTree< CLIQUE >::sharedClique > &v1, const std::pair< Key, typename BayesTree< CLIQUE >::sharedClique > &v2)

template<class KEY >
std::list< KEY >	predecessorMap2Keys (const PredecessorMap< KEY > &p_map)

template<class G , class F , class KEY >
SDGraph< KEY >	toBoostGraph (const G &graph)

template<class G , class V , class KEY >
std::tuple< G, V, std::map< KEY, V > >	predecessorMap2Graph (const PredecessorMap< KEY > &p_map)

template<class G , class Factor , class POSE , class KEY >
std::shared_ptr< Values >	composePoses (const G &graph, const PredecessorMap< KEY > &tree, const POSE &rootPose)

template<class G , class KEY , class FACTOR2 >
PredecessorMap< KEY >	findMinimumSpanningTree (const G &fg)

template<class G , class KEY , class FACTOR2 >
void	split (const G &g, const PredecessorMap< KEY > &tree, G &Ab1, G &Ab2)

GTSAM_EXPORT std::string	_defaultKeyFormatter (Key key)

GTSAM_EXPORT std::string	_multirobotKeyFormatter (gtsam::Key key)

GTSAM_EXPORT void	PrintKey (Key key, const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter)
	Utility function to print one key with optional prefix.

GTSAM_EXPORT void	PrintKeyList (const KeyList &keys, const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter)
	Utility function to print sets of keys with optional prefix.

GTSAM_EXPORT void	PrintKeyVector (const KeyVector &keys, const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter)
	Utility function to print sets of keys with optional prefix.

GTSAM_EXPORT void	PrintKeySet (const KeySet &keys, const std::string &s="", const KeyFormatter &keyFormatter=DefaultKeyFormatter)
	Utility function to print sets of keys with optional prefix.

Key	mrsymbol (unsigned char c, unsigned char label, size_t j)

unsigned char	mrsymbolChr (Key key)

unsigned char	mrsymbolLabel (Key key)

size_t	mrsymbolIndex (Key key)

Key	symbol (unsigned char c, std::uint64_t j)

unsigned char	symbolChr (Key key)

std::uint64_t	symbolIndex (Key key)

template<class S , class V >
V	preconditionedConjugateGradient (const S &system, const V &initial, const ConjugateGradientParameters &parameters)

GTSAM_EXPORT Errors	createErrors (const VectorValues &V)
	Break V into pieces according to its start indices.

GTSAM_EXPORT void	print (const Errors &e, const std::string &s="Errors")
	Print an Errors instance.

GTSAM_EXPORT bool	equality (const Errors &actual, const Errors &expected, double tol=1e-9)

GTSAM_EXPORT Errors	operator+ (const Errors &a, const Errors &b)
	Addition.

GTSAM_EXPORT Errors	operator- (const Errors &a, const Errors &b)
	Subtraction.

GTSAM_EXPORT Errors	operator- (const Errors &a)
	Negation.

GTSAM_EXPORT double	dot (const Errors &a, const Errors &b)
	Dot product.

GTSAM_EXPORT void	axpy (double alpha, const Errors &x, Errors &y)
	BLAS level 2 style AXPY, `y := alpha*x + y`

GTSAM_EXPORT bool	hasConstraints (const GaussianFactorGraph &factors)

GTSAM_EXPORT std::pair< std::shared_ptr< GaussianConditional >, std::shared_ptr< HessianFactor > >	EliminateCholesky (const GaussianFactorGraph &factors, const Ordering &keys)

GTSAM_EXPORT std::pair< std::shared_ptr< GaussianConditional >, std::shared_ptr< GaussianFactor > >	EliminatePreferCholesky (const GaussianFactorGraph &factors, const Ordering &keys)

template<class S , class V , class E >
V	conjugateGradients (const S &Ab, V x, const ConjugateGradientParameters &parameters, bool steepest)

GTSAM_EXPORT Vector	steepestDescent (const System &Ab, const Vector &x, const IterativeOptimizationParameters &parameters)

GTSAM_EXPORT Vector	conjugateGradientDescent (const System &Ab, const Vector &x, const ConjugateGradientParameters &parameters)

GTSAM_EXPORT Vector	steepestDescent (const Matrix &A, const Vector &b, const Vector &x, const ConjugateGradientParameters &parameters)

GTSAM_EXPORT Vector	conjugateGradientDescent (const Matrix &A, const Vector &b, const Vector &x, const ConjugateGradientParameters &parameters)

GTSAM_EXPORT VectorValues	steepestDescent (const GaussianFactorGraph &fg, const VectorValues &x, const ConjugateGradientParameters &parameters)

GTSAM_EXPORT VectorValues	conjugateGradientDescent (const GaussianFactorGraph &fg, const VectorValues &x, const ConjugateGradientParameters &parameters)

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

std::shared_ptr< Preconditioner >	createPreconditioner (const std::shared_ptr< PreconditionerParameters > parameters)

SparseEigen	sparseJacobianEigen (const GaussianFactorGraph &gfg, const Ordering &ordering)
	Constructs an Eigen-format SparseMatrix of a GaussianFactorGraph.

SparseEigen	sparseJacobianEigen (const GaussianFactorGraph &gfg)

GaussianFactorGraph	buildFactorSubgraph (const GaussianFactorGraph &gfg, const Subgraph &subgraph, const bool clone)

std::pair< GaussianFactorGraph, GaussianFactorGraph >	splitFactorGraph (const GaussianFactorGraph &factorGraph, const Subgraph &subgraph)

Rot3_	attitude (const NavState_ &X)

Point3_	position (const NavState_ &X)

Velocity3_	velocity (const NavState_ &X)

std::unique_ptr< internal::ExecutionTraceStorage[]>	allocAligned (size_t size)

template<typename T >
Expression< T >	operator* (const Expression< T > &expression1, const Expression< T > &expression2)
	Construct a product expression, assumes T::compose(T) -> T. More...

template<typename T >
std::vector< Expression< T > >	createUnknowns (size_t n, char c, size_t start)
	Construct an array of leaves. More...

template<typename T , typename A >
Expression< T >	linearExpression (const std::function< T(A)> &f, const Expression< A > &expression, const Eigen::Matrix< double, traits< T >::dimension, traits< A >::dimension > &dTdA)

template<typename T >
ScalarMultiplyExpression< T >	operator* (double s, const Expression< T > &e)

template<typename T >
BinarySumExpression< T >	operator+ (const Expression< T > &e1, const Expression< T > &e2)

template<typename T >
BinarySumExpression< T >	operator- (const Expression< T > &e1, const Expression< T > &e2)
	Construct an expression that subtracts one expression from another.

template<typename T >
Expression< T >	between (const Expression< T > &t1, const Expression< T > &t2)

template<typename T >
Expression< T >	compose (const Expression< T > &t1, const Expression< T > &t2)

JacobianFactor	linearizeNumerically (const NoiseModelFactor &factor, const Values &values, double delta=1e-5)

template<typename T , typename R , typename FUNC >
FunctorizedFactor< R, T >	MakeFunctorizedFactor (Key key, const R &z, const SharedNoiseModel &model, const FUNC func)

template<typename T1 , typename T2 , typename R , typename FUNC >
FunctorizedFactor2< R, T1, T2 >	MakeFunctorizedFactor2 (Key key1, Key key2, const R &z, const SharedNoiseModel &model, const FUNC func)

size_t	optimizeWildfire (const ISAM2Clique::shared_ptr &root, double threshold, const KeySet &replaced, VectorValues *delta)

size_t	optimizeWildfireNonRecursive (const ISAM2Clique::shared_ptr &root, double threshold, const KeySet &replaced, VectorValues *delta)

template<class S , class V , class W >
double	lineSearch (const S &system, const V currentValues, const W &gradient)

template<class S , class V >
std::tuple< V, int >	nonlinearConjugateGradient (const S &system, const V &initial, const NonlinearOptimizerParams &params, const bool singleIteration, const bool gradientDescent=false)

GTSAM_EXPORT bool	checkConvergence (double relativeErrorTreshold, double absoluteErrorTreshold, double errorThreshold, double currentError, double newError, NonlinearOptimizerParams::Verbosity verbosity=NonlinearOptimizerParams::SILENT)

GTSAM_EXPORT bool	checkConvergence (const NonlinearOptimizerParams &params, double currentError, double newError)

GTSAM_EXPORT SfmData	readBal (const std::string &filename)
	This function parses a "Bundle Adjustment in the Large" (BAL) file and returns the data as a SfmData structure. Mainly used by wrapped code. More...

GTSAM_EXPORT bool	writeBAL (const std::string &filename, const SfmData &data)
	This function writes a "Bundle Adjustment in the Large" (BAL) file from a SfmData structure. More...

GTSAM_EXPORT bool	writeBALfromValues (const std::string &filename, const SfmData &data, const Values &values)
	This function writes a "Bundle Adjustment in the Large" (BAL) file from a SfmData structure and a value structure (measurements are the same as the SfM input data, while camera poses and values are read from Values) More...

GTSAM_EXPORT Pose3	openGL2gtsam (const Rot3 &R, double tx, double ty, double tz)
	This function converts an openGL camera pose to an GTSAM camera pose. More...

GTSAM_EXPORT Pose3	gtsam2openGL (const Rot3 &R, double tx, double ty, double tz)
	This function converts a GTSAM camera pose to an openGL camera pose. More...

GTSAM_EXPORT Pose3	gtsam2openGL (const Pose3 &PoseGTSAM)
	This function converts a GTSAM camera pose to an openGL camera pose. More...

GTSAM_EXPORT Values	initialCamerasEstimate (const SfmData &db)
	This function creates initial values for cameras from db. More...

GTSAM_EXPORT Values	initialCamerasAndPointsEstimate (const SfmData &db)
	This function creates initial values for cameras and points from db. More...

GTSAM_EXPORT std::string	findExampleDataFile (const std::string &name)

GTSAM_EXPORT std::string	createRewrittenFileName (const std::string &name)

template<typename T >
GTSAM_EXPORT std::map< size_t, T >	parseVariables (const std::string &filename, size_t maxIndex=0)

template<typename T >
GTSAM_EXPORT std::vector< BinaryMeasurement< T > >	parseMeasurements (const std::string &filename, const noiseModel::Diagonal::shared_ptr &model=nullptr, size_t maxIndex=0)

template<typename T >
GTSAM_EXPORT std::vector< typename BetweenFactor< T >::shared_ptr >	parseFactors (const std::string &filename, const noiseModel::Diagonal::shared_ptr &model=nullptr, size_t maxIndex=0)

GTSAM_EXPORT std::optional< IndexedPose >	parseVertexPose (std::istream &is, const std::string &tag)

GTSAM_EXPORT std::optional< IndexedLandmark >	parseVertexLandmark (std::istream &is, const std::string &tag)

GTSAM_EXPORT std::optional< IndexedEdge >	parseEdge (std::istream &is, const std::string &tag)

GTSAM_EXPORT GraphAndValues	load2D (std::pair< std::string, SharedNoiseModel > dataset, size_t maxIndex=0, bool addNoise=false, bool smart=true, NoiseFormat noiseFormat=NoiseFormatAUTO, KernelFunctionType kernelFunctionType=KernelFunctionTypeNONE)

GTSAM_EXPORT GraphAndValues	load2D (const std::string &filename, SharedNoiseModel model=SharedNoiseModel(), size_t maxIndex=0, bool addNoise=false, bool smart=true, NoiseFormat noiseFormat=NoiseFormatAUTO, KernelFunctionType kernelFunctionType=KernelFunctionTypeNONE)

GTSAM_EXPORT void	save2D (const NonlinearFactorGraph &graph, const Values &config, const noiseModel::Diagonal::shared_ptr model, const std::string &filename)

GTSAM_EXPORT GraphAndValues	readG2o (const std::string &g2oFile, const bool is3D=false, KernelFunctionType kernelFunctionType=KernelFunctionTypeNONE)
	This function parses a g2o file and stores the measurements into a NonlinearFactorGraph and the initial guess in a Values structure. More...

GTSAM_EXPORT void	writeG2o (const NonlinearFactorGraph &graph, const Values &estimate, const std::string &filename)
	This function writes a g2o file from NonlinearFactorGraph and a Values structure. More...

GTSAM_EXPORT GraphAndValues	load3D (const std::string &filename)
	Load TORO 3D Graph.

GTSAM_EXPORT BetweenFactorPose2s	parse2DFactors (const std::string &filename, const noiseModel::Diagonal::shared_ptr &model=nullptr, size_t maxIndex=0)

GTSAM_EXPORT BetweenFactorPose3s	parse3DFactors (const std::string &filename, const noiseModel::Diagonal::shared_ptr &model=nullptr, size_t maxIndex=0)

Point2_	transformTo (const Pose2_ &x, const Point2_ &p)

Double_	range (const Point2_ &p, const Point2_ &q)

Point3_	transformTo (const Pose3_ &x, const Point3_ &p)

Point3_	transformFrom (const Pose3_ &x, const Point3_ &p)

Line3_	transformTo (const Pose3_ &wTc, const Line3_ &wL)

Pose3_	transformPoseTo (const Pose3_ &p, const Pose3_ &q)

Point3_	normalize (const Point3_ &a)

Point3_	cross (const Point3_ &a, const Point3_ &b)

Double_	dot (const Point3_ &a, const Point3_ &b)

Rot3_	rotation (const Pose3_ &pose)

Point3_	translation (const Pose3_ &pose)

Point3_	rotate (const Rot3_ &x, const Point3_ &p)

Point3_	point3 (const Unit3_ &v)

Unit3_	rotate (const Rot3_ &x, const Unit3_ &p)

Point3_	unrotate (const Rot3_ &x, const Point3_ &p)

Unit3_	unrotate (const Rot3_ &x, const Unit3_ &p)

Double_	distance (const OrientedPlane3_ &p)

Unit3_	normal (const OrientedPlane3_ &p)

Point2_	project (const Point3_ &p_cam)
	Expression version of PinholeBase::Project.

Point2_	project (const Unit3_ &p_cam)

template<class CAMERA , class POINT >
Point2_	project2 (const Expression< CAMERA > &camera_, const Expression< POINT > &p_)

template<class CALIBRATION , class POINT >
Point2_	project3 (const Pose3_ &x, const Expression< POINT > &p, const Expression< CALIBRATION > &K)

template<class CALIBRATION >
Point2_	uncalibrate (const Expression< CALIBRATION > &K, const Point2_ &xy_hat)

template<class CALIBRATION >
Pose3_	getPose (const Expression< PinholeCamera< CALIBRATION > > &cam)

template<typename T >
gtsam::Expression< typename gtsam::traits< T >::TangentVector >	logmap (const gtsam::Expression< T > &x1, const gtsam::Expression< T > &x2)
	logmap

GTSAM_EXPORT SharedNoiseModel	ConvertNoiseModel (const SharedNoiseModel &model, size_t n, bool defaultToUnit=true)

template<class T , class ALLOC >
T	FindKarcherMeanImpl (const vector< T, ALLOC > &rotations)

template<class T >
T	FindKarcherMean (const std::vector< T > &rotations)

template<class T >
T	FindKarcherMean (const std::vector< T, Eigen::aligned_allocator< T >> &rotations)

template<class T >
T	FindKarcherMean (std::initializer_list< T > &&rotations)

template<class T , class P >
P	transform_point (const T &trans, const P &global, OptionalMatrixType Dtrans, OptionalMatrixType Dglobal)

GTSAM_EXPORT std::pair< std::shared_ptr< SymbolicConditional >, std::shared_ptr< SymbolicFactor > >	EliminateSymbolic (const SymbolicFactorGraph &factors, const Ordering &keys)

std::pair< Pose2, bool >	moveWithBounce (const Pose2 &cur_pose, double step_size, const std::vector< SimWall2D > walls, Sampler &angle_drift, Sampler &reflect_noise, const Rot2 &bias=Rot2())

template<class PROBLEM >
Key	maxKey (const PROBLEM &problem)

template<class LinearGraph >
KeyDimMap	collectKeyDim (const LinearGraph &linearGraph)

void GTSAM_UNSTABLE_EXPORT	synchronize (ConcurrentFilter &filter, ConcurrentSmoother &smoother)

std::string	serializeGraph (const NonlinearFactorGraph &graph)

NonlinearFactorGraph::shared_ptr	deserializeGraph (const std::string &serialized_graph)

std::string	serializeGraphXML (const NonlinearFactorGraph &graph, const std::string &name="graph")

NonlinearFactorGraph::shared_ptr	deserializeGraphXML (const std::string &serialized_graph, const std::string &name="graph")

std::string	serializeValues (const Values &values)

Values::shared_ptr	deserializeValues (const std::string &serialized_values)

std::string	serializeValuesXML (const Values &values, const std::string &name="values")

Values::shared_ptr	deserializeValuesXML (const std::string &serialized_values, const std::string &name="values")

bool	serializeGraphToFile (const NonlinearFactorGraph &graph, const std::string &fname)

bool	serializeGraphToXMLFile (const NonlinearFactorGraph &graph, const std::string &fname, const std::string &name="graph")

bool	serializeValuesToFile (const Values &values, const std::string &fname)

bool	serializeValuesToXMLFile (const Values &values, const std::string &fname, const std::string &name="values")

NonlinearFactorGraph::shared_ptr	deserializeGraphFromFile (const std::string &fname)

NonlinearFactorGraph::shared_ptr	deserializeGraphFromXMLFile (const std::string &fname, const std::string &name="graph")

Values::shared_ptr	deserializeValuesFromFile (const std::string &fname)

Values::shared_ptr	deserializeValuesFromXMLFile (const std::string &fname, const std::string &name="values")

Standard serialization
Serialization in default compressed format
template<class T >
void	serializeToStream (const T &input, std::ostream &out_archive_stream)

template<class T >
void	deserializeFromStream (std::istream &in_archive_stream, T &output)
	deserializes from a stream

template<class T >
std::string	serializeToString (const T &input)
	serializes to a string

template<class T >
void	deserializeFromString (const std::string &serialized, T &output)
	deserializes from a string

template<class T >
bool	serializeToFile (const T &input, const std::string &filename)
	serializes to a file

template<class T >
bool	deserializeFromFile (const std::string &filename, T &output)
	deserializes from a file

template<class T >
std::string	serialize (const T &input)
	serializes to a string

template<class T >
void	deserialize (const std::string &serialized, T &output)
	deserializes from a string

XML Serialization
Serialization to XML format with named structures
template<class T >
void	serializeToXMLStream (const T &input, std::ostream &out_archive_stream, const std::string &name="data")

template<class T >
void	deserializeFromXMLStream (std::istream &in_archive_stream, T &output, const std::string &name="data")
	deserializes from a stream in XML

template<class T >
std::string	serializeToXMLString (const T &input, const std::string &name="data")
	serializes to a string in XML

template<class T >
void	deserializeFromXMLString (const std::string &serialized, T &output, const std::string &name="data")
	deserializes from a string in XML

template<class T >
bool	serializeToXMLFile (const T &input, const std::string &filename, const std::string &name="data")
	serializes to an XML file

template<class T >
bool	deserializeFromXMLFile (const std::string &filename, T &output, const std::string &name="data")
	deserializes from an XML file

template<class T >
std::string	serializeXML (const T &input, const std::string &name="data")
	serializes to a string in XML

template<class T >
void	deserializeXML (const std::string &serialized, T &output, const std::string &name="data")
	deserializes from a string in XML

Binary Serialization
Serialization to binary format with named structures
template<class T >
void	serializeToBinaryStream (const T &input, std::ostream &out_archive_stream, const std::string &name="data")

template<class T >
void	deserializeFromBinaryStream (std::istream &in_archive_stream, T &output, const std::string &name="data")
	deserializes from a stream in binary

template<class T >
std::string	serializeToBinaryString (const T &input, const std::string &name="data")
	serializes to a string in binary

template<class T >
void	deserializeFromBinaryString (const std::string &serialized, T &output, const std::string &name="data")
	deserializes from a string in binary

template<class T >
bool	serializeToBinaryFile (const T &input, const std::string &filename, const std::string &name="data")
	serializes to a binary file

template<class T >
bool	deserializeFromBinaryFile (const std::string &filename, T &output, const std::string &name="data")
	deserializes from a binary file

template<class T >
std::string	serializeBinary (const T &input, const std::string &name="data")
	serializes to a string in binary

template<class T >
void	deserializeBinary (const std::string &serialized, T &output, const std::string &name="data")
	deserializes from a string in binary

utility functions
VectorValues	buildVectorValues (const Vector &v, const Ordering &ordering, const std::map< Key, size_t > &dimensions)
	Create VectorValues from a Vector.

VectorValues	buildVectorValues (const Vector &v, const KeyInfo &keyInfo)
	Create VectorValues from a Vector and a KeyInfo class.

Variables
GTSAM_EXTERN_EXPORT FastMap< std::string, ValueWithDefault< bool, false > >	debugFlags

const G &	b

const G double	tol

const double	logSqrt2PI = log(std::sqrt(2.0 * M_PI))
	constant needed below

Detailed Description

Global functions in a separate testing namespace

These should not be used outside of tests, as they are just remappings of the original functions. We use these to avoid needing to do too much std::bind magic or writing a bunch of separate proxy functions.

Don't expect all classes to work for all of these functions.

Matrix is a typedef in the gtsam namespace TODO: make a version to work with matlab wrapping we use the default < double,col_major,unbounded_array<double> >

This file supports creating continuous functions f(x;p) as a linear combination of basis functions such as the Fourier basis on SO(2) or a set of Chebyshev polynomials on [-1,1].

In the expression f(x;p) the variable x is the continuous argument at which the function is evaluated, and p are the parameters which are coefficients of the different basis functions, e.g. p = [4; 3; 2] => 4 + 3x + 2x^2 for a polynomial. However, different parameterizations are also possible.

The Basis class below defines a number of functors that can be used to evaluate f(x;p) at a given x, and these functors also calculate the Jacobian of f(x;p) with respect to the parameters p. This is actually the most important calculation, as it will allow GTSAM to optimize over the parameters p.

This functionality is implemented using the CRTP or "Curiously recurring template pattern" C++ idiom, which is a meta-programming technique in which the derived class is passed as a template argument to Basis<DERIVED>. The DERIVED class is assumed to satisfy a C++ concept, i.e., we expect it to define the following types and methods:

type Parameters: the parameters p in f(x;p)
CalculateWeights(size_t N, double x, double a=default, double b=default)
DerivativeWeights(size_t N, double x, double a=default, double b=default)

where Weights is an N*1 row vector which defines the basis values for the polynomial at the specified point x.

E.g. A Fourier series would give the following:

CalculateWeights -> For N=5, the values for the bases: [1, cos(x), sin(x), cos(2x), sin(2x)]
DerivativeWeights -> For N=5, these are: [0, -sin(x), cos(x), -2sin(2x), 2cos(x)]

Note that for a pseudo-spectral basis (as in Chebyshev2), the weights are instead the values for the Barycentric interpolation formula, since the values at the polynomial points (e.g. Chebyshev points) define the bases.

triangulationFactor.h

Date: March 2, 2014

Author: Frank Dellaert

Typedef Documentation

◆ FactorIndices

typedef FastVector< FactorIndex > gtsam::FactorIndices

Define collection types:

Define collection type:

◆ GraphAndValues

using gtsam::GraphAndValues = typedef std::pair<NonlinearFactorGraph::shared_ptr, Values::shared_ptr>

Return type for load functions, which return a graph and initial values. For landmarks, the gtsam::Symbol L(index) is used to insert into the Values. Bearing-range measurements also refer to landmarks with L(index).

◆ OptionalMatrixType

using gtsam::OptionalMatrixType = typedef Matrix*

This typedef will be used everywhere boost::optional<Matrix&> reference was used previously. This is used to indicate that the Jacobian is optional. In the future we will change this to OptionalJacobian

◆ OptionalMatrixVecType

using gtsam::OptionalMatrixVecType = typedef std::vector<Matrix>*

The OptionalMatrixVecType is a pointer to a vector of matrices. It will be used in situations where a vector of matrices is optional, like in unwhitenedError.

◆ PinholeCameraCal3_S2

using gtsam::PinholeCameraCal3_S2 = typedef gtsam::PinholeCamera<gtsam::Cal3_S2>

Convenient aliases for Pinhole camera classes with different calibrations. Also needed as forward declarations in the wrapper.

◆ Point2

typedef Vector2 gtsam::Point2

As of GTSAM 4, in order to make GTSAM more lean, it is now possible to just typedef Point2 to Vector2

◆ Point3

typedef Vector3 gtsam::Point3

As of GTSAM 4, in order to make GTSAM more lean, it is now possible to just typedef Point3 to Vector3

◆ SharedNoiseModel

typedef noiseModel::Base::shared_ptr gtsam::SharedNoiseModel

Aliases. Deliberately not in noiseModel namespace.

◆ SparseEigen

typedef Eigen::SparseMatrix<double, Eigen::ColMajor, int> gtsam::SparseEigen

Eigen-format sparse matrix. Note: ColMajor is ~20% faster since InnerIndices must be sorted

◆ Velocity3

typedef Vector3 gtsam::Velocity3

Velocity is currently typedef'd to Vector3.

Syntactic sugar to clarify components.

Enumeration Type Documentation

◆ LinearizationMode

enum gtsam::LinearizationMode

Linearization mode: what factor to linearize to.

SmartFactorParams: parameters and (linearization/degeneracy) modes for SmartProjection and SmartStereoProjection factors

◆ NoiseFormat

enum gtsam::NoiseFormat

Indicates how noise parameters are stored in file.

Enumerator
NoiseFormatG2O	Information matrix I11, I12, I13, I22, I23, I33.
NoiseFormatTORO	Information matrix, but inf_ff inf_fs inf_ss inf_rr inf_fr inf_sr.
NoiseFormatGRAPH	default: toro-style order, but covariance matrix !
NoiseFormatCOV	Covariance matrix C11, C12, C13, C22, C23, C33.
NoiseFormatAUTO	Try to guess covariance matrix layout.

Function Documentation

◆ apply()

template<typename L , typename Y >

DecisionTree<L, Y> gtsam::apply	(	const DecisionTree< L, Y > &	f,
		const typename DecisionTree< L, Y >::Unary &	op
	)

Apply unary operator op to DecisionTree f.

free versions of apply

◆ assert_container_equal() [1/4]

template<class V1 , class V2 >

bool gtsam::assert_container_equal	(	const std::map< V1, V2 > &	expected,
		const std::map< V1, V2 > &	actual,
		double	tol = `1e-9`
	)

Function for comparing maps of testable->testable TODO: replace with more generalized version

◆ assert_container_equal() [2/4]

template<class V2 >

bool gtsam::assert_container_equal	(	const std::map< size_t, V2 > &	expected,
		const std::map< size_t, V2 > &	actual,
		double	tol = `1e-9`
	)

Function for comparing maps of size_t->testable

◆ assert_container_equal() [3/4]

template<class V1 , class V2 >

bool gtsam::assert_container_equal	(	const std::vector< std::pair< V1, V2 > > &	expected,
		const std::vector< std::pair< V1, V2 > > &	actual,
		double	tol = `1e-9`
	)

Function for comparing vector of pairs (testable, testable)

◆ assert_container_equal() [4/4]

template<class V >

bool gtsam::assert_container_equal	(	const V &	expected,
		const V &	actual,
		double	tol = `1e-9`
	)

General function for comparing containers of testable objects

◆ assert_container_equality() [1/2]

template<class V2 >

bool gtsam::assert_container_equality	(	const std::map< size_t, V2 > &	expected,
		const std::map< size_t, V2 > &	actual
	)

Function for comparing maps of size_t->testable Types are assumed to have operator ==

◆ assert_container_equality() [2/2]

template<class V >

bool gtsam::assert_container_equality	(	const V &	expected,
		const V &	actual
	)

General function for comparing containers of objects with operator==

◆ assert_equal() [1/8]

bool gtsam::assert_equal	(	const Key &	expected,
		const Key &	actual,
		double	tol = `0.0`
	)

inline

Equals testing for basic types

◆ assert_equal() [2/8]

template<class V >

bool gtsam::assert_equal	(	const std::optional< V > &	expected,
		const std::optional< V > &	actual,
		double	tol = `1e-9`
	)

Comparisons for std.optional objects that checks whether objects exist before comparing their values. First version allows for both to be std::nullopt, but the second, with expected given rather than optional

Concept requirement: V is testable

◆ assert_equal() [3/8]

template<class V >

bool gtsam::assert_equal	(	const V &	expected,
		const V &	actual,
		double	tol = `1e-9`
	)

This template works for any type with equals

◆ assert_equal() [4/8]

GTSAM_EXPORT bool gtsam::assert_equal	(	const Matrix &	A,
		const Matrix &	B,
		double	tol = `1e-9`
	)

equals with an tolerance, prints out message if unequal

◆ assert_equal() [5/8]

GTSAM_EXPORT bool gtsam::assert_equal	(	const std::list< Matrix > &	As,
		const std::list< Matrix > &	Bs,
		double	tol = `1e-9`
	)

equals with an tolerance, prints out message if unequal

◆ assert_equal() [6/8]

GTSAM_EXPORT bool gtsam::assert_equal	(	const Vector &	vec1,
		const Vector &	vec2,
		double	tol = `1e-9`
	)

Same, prints if error

Parameters

vec1	Vector
vec2	Vector
tol	1e-9

Returns: bool

◆ assert_equal() [7/8]

GTSAM_EXPORT bool gtsam::assert_equal	(	const SubVector &	vec1,
		const SubVector &	vec2,
		double	tol = `1e-9`
	)

Same, prints if error

Parameters

vec1	Vector
vec2	Vector
tol	1e-9

Returns: bool

◆ assert_equal() [8/8]

bool gtsam::assert_equal	(	const std::string &	expected,
		const std::string &	actual
	)

inline

Compare strings for unit tests

◆ assert_inequal() [1/3]

GTSAM_EXPORT bool gtsam::assert_inequal	(	const Matrix &	A,
		const Matrix &	B,
		double	tol = `1e-9`
	)

inequals with an tolerance, prints out message if within tolerance

◆ assert_inequal() [2/3]

GTSAM_EXPORT bool gtsam::assert_inequal	(	const Vector &	vec1,
		const Vector &	vec2,
		double	tol = `1e-9`
	)

Not the same, prints if error

Parameters

vec1	Vector
vec2	Vector
tol	1e-9

Returns: bool

◆ assert_inequal() [3/3]

template<class V >

bool gtsam::assert_inequal	(	const V &	expected,
		const V &	actual,
		double	tol = `1e-9`
	)

Allow for testing inequality

◆ assert_print_equal()

template<class V >

bool gtsam::assert_print_equal	(	const std::string &	expected,
		const V &	actual,
		const std::string &	s = `""`
	)

Capture print function output and compare against string.

Parameters

s	Optional string to pass to the print() method.

◆ assert_stdout_equal()

template<class V >

bool gtsam::assert_stdout_equal	(	const std::string &	expected,
		const V &	actual
	)

Capture std out via cout stream and compare against string.

◆ backSubstituteLower()

GTSAM_EXPORT Vector gtsam::backSubstituteLower	(	const Matrix &	L,
		const Vector &	b,
		bool	unit = `false`
	)

backSubstitute L*x=b

Parameters

L	an lower triangular matrix
b	an RHS vector
unit,set	true if unit triangular

Returns: the solution x of L*x=b

◆ backSubstituteUpper() [1/2]

GTSAM_EXPORT Vector gtsam::backSubstituteUpper	(	const Matrix &	U,
		const Vector &	b,
		bool	unit = `false`
	)

backSubstitute U*x=b

Parameters

U	an upper triangular matrix
b	an RHS vector
unit,set	true if unit triangular

Returns: the solution x of U*x=b

◆ backSubstituteUpper() [2/2]

GTSAM_EXPORT Vector gtsam::backSubstituteUpper	(	const Vector &	b,
		const Matrix &	U,
		bool	unit = `false`
	)

backSubstitute x'*U=b'

Parameters

U	an upper triangular matrix
b	an RHS vector
unit,set	true if unit triangular

Returns: the solution x of x'*U=b'

◆ BCH()

template<class T >

T gtsam::BCH	(	const T &	X,
		const T &	Y
	)

AGC: bracket() only appears in Rot3 tests, should this be used elsewhere?

Three term approximation of the Baker-Campbell-Hausdorff formula In non-commutative Lie groups, when composing exp(Z) = exp(X)exp(Y) it is not true that Z = X+Y. Instead, Z can be calculated using the BCH formula: Z = X + Y + [X,Y]/2 + [X-Y,[X,Y]]/12 - [Y,[X,[X,Y]]]/24 http://en.wikipedia.org/wiki/Baker-Campbell-Hausdorff_formula

◆ between_default()

template<class Class >

Class gtsam::between_default	(	const Class &	l1,
		const Class &	l2
	)

inline

These core global functions can be specialized by new Lie types for better performance.Compute l0 s.t. l2=l1*l0

◆ buildFactorSubgraph()

GaussianFactorGraph gtsam::buildFactorSubgraph	(	const GaussianFactorGraph &	gfg,
		const Subgraph &	subgraph,
		const bool	clone
	)

Select the factors in a factor graph according to the subgraph.

◆ calibrateJacobians()

template<typename Cal , size_t Dim>

void gtsam::calibrateJacobians	(	const Cal &	calibration,
		const Point2 &	pn,
		OptionalJacobian< 2, Dim >	Dcal = `{}`,
		OptionalJacobian< 2, 2 >	Dp = `{}`
	)

Function which makes use of the Implicit Function Theorem to compute the Jacobians of calibrate using uncalibrate. This is useful when there are iterative operations in the calibrate function which make computing jacobians difficult.

Given f(pi, pn) = uncalibrate(pn) - pi, and g(pi) = calibrate, we can easily compute the Jacobians: df/pi = -I (pn and pi are independent args) Dp = -inv(H_uncal_pn) * df/pi = -inv(H_uncal_pn) * (-I) = inv(H_uncal_pn) Dcal = -inv(H_uncal_pn) * df/K = -inv(H_uncal_pn) * H_uncal_K

Template Parameters

Cal	Calibration model.
Dim	The number of parameters in the calibration model.

Parameters

p	Calibrated point.
Dcal	optional 2*p Jacobian wrpt `p` Cal3DS2 parameters.
Dp	optional 2*2 Jacobian wrpt intrinsic coordinates.

◆ calibrateMeasurements() [1/2]

template<class CAMERA >

Point3Vector gtsam::calibrateMeasurements	(	const CameraSet< CAMERA > &	cameras,
		const typename CAMERA::MeasurementVector &	measurements
	)

inline

Convert pixel measurements in image to homogeneous measurements in the image plane using camera intrinsics of each measurement.

Template Parameters

CAMERA Camera type to use.

Parameters

cameras	Cameras corresponding to each measurement.
measurements	Vector of measurements to undistort.

Returns: homogeneous measurements in image plane

◆ calibrateMeasurements() [2/2]

template<class CAMERA = SphericalCamera>

Point3Vector gtsam::calibrateMeasurements	(	const CameraSet< SphericalCamera > &	cameras,
		const SphericalCamera::MeasurementVector &	measurements
	)

inline

Specialize for SphericalCamera to do nothing.

◆ calibrateMeasurementsShared()

template<class CALIBRATION >

Point3Vector gtsam::calibrateMeasurementsShared	(	const CALIBRATION &	cal,
		const Point2Vector &	measurements
	)

inline

Convert pixel measurements in image to homogeneous measurements in the image plane using shared camera intrinsics.

Template Parameters

CALIBRATION Calibration type to use.

Parameters

cal	Calibration with which measurements were taken.
measurements	Vector of measurements to undistort.

Returns: homogeneous measurements in image plane

◆ checkConvergence()

GTSAM_EXPORT bool gtsam::checkConvergence	(	double	relativeErrorTreshold,
		double	absoluteErrorTreshold,
		double	errorThreshold,
		double	currentError,
		double	newError,
		NonlinearOptimizerParams::Verbosity	verbosity = `NonlinearOptimizerParams::SILENT`
	)

Check whether the relative error decrease is less than relativeErrorTreshold, the absolute error decrease is less than absoluteErrorTreshold, or the error itself is less than errorThreshold.

◆ cholesky_inverse()

GTSAM_EXPORT Matrix gtsam::cholesky_inverse ( const Matrix & A )

Return the inverse of a S.P.D. matrix. Inversion is done via Cholesky decomposition.

◆ choleskyCareful()

GTSAM_EXPORT std::pair<size_t,bool> gtsam::choleskyCareful	(	Matrix &	ATA,
		int	order = `-1`
	)

"Careful" Cholesky computes the positive square-root of a positive symmetric semi-definite matrix (i.e. that may be rank-deficient). Unlike standard Cholesky, the square-root factor may have all-zero rows for free variables.

Additionally, this function returns the index of the row after the last non-zero row in the computed factor, so that it may be truncated to an upper-trapazoidal matrix.

The second element of the return value is true if the matrix was factored successfully, or false if it was non-positive-semidefinite (i.e. indefinite or negative-(semi-)definite.

Note that this returned index is the rank of the matrix if and only if all of the zero-rows of the factor occur after any non-zero rows. This is (always?) the case during elimination of a fully-constrained least-squares problem.

The optional order argument specifies the size of the square upper-left submatrix to operate on, ignoring the rest of the matrix.

◆ choleskyPartial()

GTSAM_EXPORT bool gtsam::choleskyPartial	(	Matrix &	ABC,
		size_t	nFrontal,
		size_t	topleft = `0`
	)

Partial Cholesky computes a factor [R S such that [R' 0 [R S = [A B 0 L] S' I] 0 L] B' C]. The input to this function is the matrix ABC = [A B], and the parameter [B' C] nFrontal determines the split between A, B, and C, with A being of size nFrontal x nFrontal.

if non-zero, factorization proceeds in bottom-right corner starting at topleft

Returns: true if the decomposition is successful, false if A was not positive-definite.

◆ circleCircleIntersection()

GTSAM_EXPORT std::list<Point2> gtsam::circleCircleIntersection	(	Point2	c1,
		double	r1,
		Point2	c2,
		double	r2,
		double	tol = `1e-9`
	)

Intersect 2 circles.

Parameters

c1	center of first circle
r1	radius of first circle
c2	center of second circle
r2	radius of second circle
tol	absolute tolerance below which we consider touching circles

Returns: list of solutions (0,1, or 2). Identical circles will return empty list, as well.

◆ collect()

GTSAM_EXPORT Matrix gtsam::collect	(	const std::vector< const Matrix *> &	matrices,
		size_t	m = `0`,
		size_t	n = `0`
	)

create a matrix by concatenating Given a set of matrices: A1, A2, A3... If all matrices have the same size, specifying single matrix dimensions will avoid the lookup of dimensions

Parameters

matrices	is a vector of matrices in the order to be collected
m	is the number of rows of a single matrix
n	is the number of columns of a single matrix

Returns: combined matrix [A1 A2 A3]

◆ column()

template<class MATRIX >

const MATRIX::ConstColXpr gtsam::column	(	const MATRIX &	A,
		size_t	j
	)

Extracts a column view from a matrix that avoids a copy

Parameters

A	matrix to extract column from
j	index of the column

Returns: a const view of the matrix

◆ composePoses()

template<class G , class Factor , class POSE , class KEY >

std::shared_ptr< Values > gtsam::composePoses	(	const G &	graph,
		const PredecessorMap< KEY > &	tree,
		const POSE &	rootPose
	)

Compose the poses by following the chain specified by the spanning tree

◆ concatVectors() [1/2]

GTSAM_EXPORT Vector gtsam::concatVectors ( const std::list< Vector > & vs )

concatenate Vectors

◆ concatVectors() [2/2]

GTSAM_EXPORT Vector gtsam::concatVectors	(	size_t	nrVectors,
			...
	)

concatenate Vectors

◆ conjugateGradientDescent() [1/3]

GTSAM_EXPORT Vector gtsam::conjugateGradientDescent	(	const System &	Ab,
		const Vector &	x,
		const ConjugateGradientParameters &	parameters
	)

Method of conjugate gradients (CG), System version

◆ conjugateGradientDescent() [2/3]

GTSAM_EXPORT Vector gtsam::conjugateGradientDescent	(	const Matrix &	A,
		const Vector &	b,
		const Vector &	x,
		const ConjugateGradientParameters &	parameters
	)

Method of conjugate gradients (CG), Matrix version

◆ conjugateGradientDescent() [3/3]

GTSAM_EXPORT VectorValues gtsam::conjugateGradientDescent	(	const GaussianFactorGraph &	fg,
		const VectorValues &	x,
		const ConjugateGradientParameters &	parameters
	)

Method of conjugate gradients (CG), Gaussian Factor Graph version

◆ conjugateGradients()

template<class S , class V , class E >

V gtsam::conjugateGradients	(	const S &	Ab,
		V	x,
		const ConjugateGradientParameters &	parameters,
		bool	steepest = `false`
	)

Method of conjugate gradients (CG) template "System" class S needs gradient(S,v), e=S*v, v=S^e "Vector" class V needs dot(v,v), -v, v+v, s*v "Vector" class E needs dot(v,v)

Parameters

Ab,the	"system" that needs to be solved, examples below
x	is the initial estimate
steepest	flag, if true does steepest descent, not CG

◆ ConvertNoiseModel()

GTSAM_EXPORT SharedNoiseModel gtsam::ConvertNoiseModel	(	const SharedNoiseModel &	model,
		size_t	n,
		bool	defaultToUnit = `true`
	)

When creating (any) FrobeniusFactor we can convert a Rot/Pose BetweenFactor noise model into a n-dimensional isotropic noise model used to weight the Frobenius norm. If the noise model passed is null we return a n-dimensional isotropic noise model with sigma=1.0. If not, we we check if the d-dimensional noise model on rotations is isotropic. If it is, we extend to 'n' dimensions, otherwise we throw an error. If the noise model is a robust error model, we use the sigmas of the underlying noise model.

If defaultToUnit == false throws an exception on unexepcted input.

◆ createPinholeCalibration()

template<class CALIBRATION >

Cal3_S2 gtsam::createPinholeCalibration ( const CALIBRATION & cal )

Create a pinhole calibration from a different Cal3 object, removing distortion.

Template Parameters

CALIBRATION Original calibration object.

Parameters

cal	Input calibration object.

Returns: Cal3_S2 with only the pinhole elements of cal.

◆ createRewrittenFileName()

GTSAM_EXPORT std::string gtsam::createRewrittenFileName ( const std::string & name )

Creates a temporary file name that needs to be ignored in .gitingnore for checking read-write oprations

◆ createUnknowns()

template<typename T >

std::vector< Expression< T > > gtsam::createUnknowns	(	size_t	n,
		char	c,
		size_t	start = `0`
	)

Construct an array of leaves.

Construct an array of unknown expressions with successive symbol keys Example: createUnknowns<Pose2>(3,'x') creates unknown expressions for x0,x1,x2

◆ cross()

GTSAM_EXPORT Point3 gtsam::cross	(	const Point3 &	p,
		const Point3 &	q,
		OptionalJacobian< 3, 3 >	H_p = `{}`,
		OptionalJacobian< 3, 3 >	H_q = `{}`
	)

cross product

Returns: this x q

◆ diag()

GTSAM_EXPORT Matrix gtsam::diag ( const std::vector< Matrix > & Hs )

Create a matrix with submatrices along its diagonal

◆ DLT()

GTSAM_EXPORT std::tuple<int, double, Vector> gtsam::DLT	(	const Matrix &	A,
		double	rank_tol = `1e-9`
	)

Direct linear transform algorithm that calls svd to find a vector v that minimizes the algebraic error A*v

Parameters

A	of size mn, where m>=n (pad with zero rows if not!) Returns rank of A, minimum error (singular value), and corresponding eigenvector (column of V, with A=US*V')

◆ dot()

template<class V1 , class V2 >

double gtsam::dot	(	const V1 &	a,
		const V2 &	b
	)

inline

Dot product

◆ ediv_()

GTSAM_EXPORT Vector gtsam::ediv_	(	const Vector &	a,
		const Vector &	b
	)

elementwise division, but 0/0 = 0, not inf

Parameters

a	first vector
b	second vector

Returns: vector [a(i)/b(i)]

◆ EliminateQR()

GTSAM_EXPORT std::pair<std::shared_ptr<GaussianConditional>, std::shared_ptr<JacobianFactor> > gtsam::EliminateQR	(	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). Computation happens in noiseModel::Gaussian::QR Returns a conditional on those keys, and a new factor on the separator.

◆ EliminateSymbolic()

GTSAM_EXPORT std::pair<std::shared_ptr<SymbolicConditional>, std::shared_ptr<SymbolicFactor> > gtsam::EliminateSymbolic	(	const SymbolicFactorGraph &	factors,
		const Ordering &	keys
	)

Dense elimination function for symbolic factors. This is usually provided as an argument to one of the factor graph elimination functions (see EliminateableFactorGraph). The factor graph elimination functions do sparse variable elimination, and use this function to eliminate single variables or variable cliques.

◆ equal() [1/4]

template<class T >

bool gtsam::equal	(	const T &	obj1,
		const T &	obj2,
		double	tol
	)

inline

Call equal on the object

◆ equal() [2/4]

template<class T >

bool gtsam::equal	(	const T &	obj1,
		const T &	obj2
	)

inline

Call equal without tolerance (use default tolerance)

◆ equal() [3/4]

bool gtsam::equal	(	const Vector &	vec1,
		const Vector &	vec2,
		double	tol
	)

inline

Override of equal in Lie.h

◆ equal() [4/4]

bool gtsam::equal	(	const Vector &	vec1,
		const Vector &	vec2
	)

inline

Override of equal in Lie.h

◆ equal_with_abs_tol() [1/2]

template<class MATRIX >

bool gtsam::equal_with_abs_tol	(	const Eigen::DenseBase< MATRIX > &	A,
		const Eigen::DenseBase< MATRIX > &	B,
		double	tol = `1e-9`
	)

equals with a tolerance

◆ equal_with_abs_tol() [2/2]

GTSAM_EXPORT bool gtsam::equal_with_abs_tol	(	const Vector &	vec1,
		const Vector &	vec2,
		double	tol = `1e-9`
	)

VecA == VecB up to tolerance

◆ expm() [1/2]

template<class T >

T gtsam::expm	(	const Vector &	x,
		int	K = `7`
	)

Exponential map given exponential coordinates class T needs a wedge<> function and a constructor from Matrix

Parameters

x	exponential coordinates, vector of size n @ return a T

◆ expm() [2/2]

GTSAM_EXPORT Matrix gtsam::expm	(	const Matrix &	A,
		size_t	K = `7`
	)

Numerical exponential map, naive approach, not industrial strength !!!

Parameters

A	matrix to exponentiate
K	number of iterations

◆ expmap_default()

template<class Class >

Class gtsam::expmap_default	(	const Class &	t,
		const Vector &	d
	)

inline

Exponential map centered at l0, s.t. exp(t,d) = t*exp(d)

◆ expNormalize()

std::vector<double> gtsam::expNormalize ( const std::vector< double > & logProbs )

Normalize a set of log probabilities.

Normalizing a set of log probabilities in a numerically stable way is tricky. To avoid overflow/underflow issues, we compute the largest (finite) log probability and subtract it from each log probability before normalizing. This comes from the observation that if: p_i = exp(L_i) / ( sum_j exp(L_j) ), Then, p_i = exp(Z) exp(L_i - Z) / (exp(Z) sum_j exp(L_j - Z)), = exp(L_i - Z) / ( sum_j exp(L_j - Z) )

Setting Z = max_j L_j, we can avoid numerical issues that arise when all of the (unnormalized) log probabilities are either very large or very small.

◆ findExampleDataFile()

GTSAM_EXPORT std::string gtsam::findExampleDataFile ( const std::string & name )

Find the full path to an example dataset distributed with gtsam. The name may be specified with or without a file extension - if no extension is given, this function first looks for the .graph extension, then .txt. We first check the gtsam source tree for the file, followed by the installed example dataset location. Both the source tree and installed locations are obtained from CMake during compilation.

Returns: The full path and filename to the requested dataset.

Exceptions

std::invalid_argument if no matching file could be found using the search process described above.

◆ FindKarcherMean()

template<class T >

T gtsam::FindKarcherMean ( const std::vector< T, Eigen::aligned_allocator< T >> & rotations )

Optimize for the Karcher mean, minimizing the geodesic distance to each of the given rotations, by constructing a factor graph out of simple PriorFactors.

◆ findMinimumSpanningTree()

template<class G , class KEY , class FACTOR2 >

PredecessorMap< KEY > gtsam::findMinimumSpanningTree ( const G & g )

find the minimum spanning tree using boost graph library

◆ fpEqual()

GTSAM_EXPORT bool gtsam::fpEqual	(	double	a,
		double	b,
		double	tol,
		bool	check_relative_also = `true`
	)

Ensure we are not including a different version of Eigen in user code than while compiling gtsam, since it can lead to hard-to-understand runtime crashes. Numerically stable function for comparing if floating point values are equal within epsilon tolerance. Used for vector and matrix comparison with C++11 compatible functions.

If either value is NaN or Inf, we check for both values to be NaN or Inf respectively for the comparison to be true. If one is NaN/Inf and the other is not, returns false.

Parameters

check_relative_also is a flag which toggles additional checking for relative error. This means that if either the absolute error or the relative error is within the tolerance, the result will be true. By default, the flag is true.

Return true if two numbers are close wrt tol.

◆ genericValue()

template<class T >

GenericValue<T> gtsam::genericValue ( const T & v )

Functional constructor of GenericValue<T> so T can be automatically deduced

◆ greaterThanOrEqual()

GTSAM_EXPORT bool gtsam::greaterThanOrEqual	(	const Vector &	v1,
		const Vector &	v2
	)

Greater than or equal to operation returns true if all elements in v1 are greater than corresponding elements in v2

◆ gtsam2openGL() [1/2]

GTSAM_EXPORT Pose3 gtsam::gtsam2openGL	(	const Rot3 &	R,
		double	tx,
		double	ty,
		double	tz
	)

This function converts a GTSAM camera pose to an openGL camera pose.

Parameters

R	rotation in GTSAM
tx	x component of the translation in GTSAM
ty	y component of the translation in GTSAM
tz	z component of the translation in GTSAM

Returns: Pose3 in openGL format

◆ gtsam2openGL() [2/2]

GTSAM_EXPORT Pose3 gtsam::gtsam2openGL ( const Pose3 & PoseGTSAM )

This function converts a GTSAM camera pose to an openGL camera pose.

Parameters

PoseGTSAM pose in GTSAM format

Returns: Pose3 in openGL format

◆ hasConstraints()

GTSAM_EXPORT bool gtsam::hasConstraints ( const GaussianFactorGraph & factors )

Evaluates whether linear factors have any constrained noise models

Returns: true if any factor is constrained.

◆ house()

GTSAM_EXPORT std::pair<double,Vector> gtsam::house ( const Vector & x )

house(x,j) computes HouseHolder vector v and scaling factor beta from x, such that the corresponding Householder reflection zeroes out all but x.(j), j is base 0. Golub & Van Loan p 210.

◆ householder()

GTSAM_EXPORT void gtsam::householder	(	Matrix &	A,
		size_t	k
	)

Householder tranformation, zeros below diagonal

Parameters

k	number of columns to zero out below diagonal
A	matrix

Returns: nothing: in place !!!

◆ householder_()

GTSAM_EXPORT void gtsam::householder_	(	Matrix &	A,
		size_t	k,
		bool	copy_vectors = `true`
	)

Householder transformation, Householder vectors below diagonal

Parameters

k	number of columns to zero out below diagonal
A	matrix
copy_vectors	- true to copy Householder vectors below diagonal

Returns: nothing: in place !!!

◆ houseInPlace()

GTSAM_EXPORT double gtsam::houseInPlace ( Vector & x )

beta = house(x) computes the HouseHolder vector in place

◆ HybridOrdering()

GTSAM_EXPORT const Ordering gtsam::HybridOrdering ( const HybridGaussianFactorGraph & graph )

Return a Colamd constrained ordering where the discrete keys are eliminated after the continuous keys.

Returns: const Ordering

◆ initialCamerasAndPointsEstimate()

GTSAM_EXPORT Values gtsam::initialCamerasAndPointsEstimate ( const SfmData & db )

This function creates initial values for cameras and points from db.

Note: Pose keys are simply integer indices, points use Symbol('p', j).

Parameters

SfmData

Returns: Values

◆ initialCamerasEstimate()

GTSAM_EXPORT Values gtsam::initialCamerasEstimate ( const SfmData & db )

This function creates initial values for cameras from db.

No symbol is used, so camera keys are simply integer indices.

Parameters

SfmData

Returns: Values

◆ inner_prod()

template<class V1 , class V2 >

double gtsam::inner_prod	(	const V1 &	a,
		const V2 &	b
	)

inline

compatibility version for ublas' inner_prod()

◆ inplace_QR()

GTSAM_EXPORT void gtsam::inplace_QR ( Matrix & A )

QR factorization using Eigen's internal block QR algorithm

Parameters

A	is the input matrix, and is the output
clear_below_diagonal	enables zeroing out below diagonal

◆ insertSub()

template<typename Derived1 , typename Derived2 >

void gtsam::insertSub	(	Eigen::MatrixBase< Derived1 > &	fullMatrix,
		const Eigen::MatrixBase< Derived2 > &	subMatrix,
		size_t	i,
		size_t	j
	)

insert a submatrix IN PLACE at a specified location in a larger matrix NOTE: there is no size checking

Parameters

fullMatrix	matrix to be updated
subMatrix	matrix to be inserted
i	is the row of the upper left corner insert location
j	is the column of the upper left corner insert location

◆ interpolate()

template<typename T >

T gtsam::interpolate	(	const T &	X,
		const T &	Y,
		double	t,
		typename MakeOptionalJacobian< T, T >::type	Hx = `{}`,
		typename MakeOptionalJacobian< T, T >::type	Hy = `{}`
	)

Linear interpolation between X and Y by coefficient t. Typically t [0,1], but can also be used to extrapolate before pose X or after pose Y.

◆ inverse_square_root()

GTSAM_EXPORT Matrix gtsam::inverse_square_root ( const Matrix & A )

Use Cholesky to calculate inverse square root of a matrix

◆ linear_dependent() [1/2]

GTSAM_EXPORT bool gtsam::linear_dependent	(	const Matrix &	A,
		const Matrix &	B,
		double	tol = `1e-9`
	)

check whether the rows of two matrices are linear dependent

◆ linear_dependent() [2/2]

GTSAM_EXPORT bool gtsam::linear_dependent	(	const Vector &	vec1,
		const Vector &	vec2,
		double	tol = `1e-9`
	)

check whether two vectors are linearly dependent

Parameters

vec1	Vector
vec2	Vector
tol	1e-9

Returns: bool

◆ linear_independent()

GTSAM_EXPORT bool gtsam::linear_independent	(	const Matrix &	A,
		const Matrix &	B,
		double	tol = `1e-9`
	)

check whether the rows of two matrices are linear independent

◆ linearExpression()

template<typename T , typename A >

Expression<T> gtsam::linearExpression	(	const std::function< T(A)> &	f,
		const Expression< A > &	expression,
		const Eigen::Matrix< double, traits< T >::dimension, traits< A >::dimension > &	dTdA
	)

Create an expression out of a linear function f:T->A with (constant) Jacobian dTdA TODO(frank): create a more efficient version like ScalarMultiplyExpression. This version still does a malloc every linearize.

◆ linearizeNumerically()

JacobianFactor gtsam::linearizeNumerically	(	const NoiseModelFactor &	factor,
		const Values &	values,
		double	delta = `1e-5`
	)

inline

Linearize a nonlinear factor using numerical differentiation The benefit of this method is that it does not need to know what types are involved to evaluate the factor. If all the machinery of gtsam is working correctly, we should get the correct numerical derivatives out the other side. NOTE(frank): factors that have non vector-space measurements use between or LocalCoordinates to evaluate the error, and their derivatives will only be correct for near-zero errors. This is fixable but expensive, and does not matter in practice as most factors will sit near zero errors anyway. However, it means that below will only be exact for the correct measurement.

◆ lineSearch()

template<class S , class V , class W >

double gtsam::lineSearch	(	const S &	system,
		const V	currentValues,
		const W &	gradient
	)

Implement the golden-section line search algorithm

◆ load2D() [1/2]

GTSAM_EXPORT GraphAndValues gtsam::load2D	(	std::pair< std::string, SharedNoiseModel >	dataset,
		size_t	maxIndex = `0`,
		bool	addNoise = `false`,
		bool	smart = `true`,
		NoiseFormat	noiseFormat = `NoiseFormatAUTO`,
		KernelFunctionType	kernelFunctionType = `KernelFunctionTypeNONE`
	)

Load TORO 2D Graph

Parameters

dataset/model	pair as constructed by [dataset]
maxIndex	if non-zero cut out vertices >= maxIndex
addNoise	add noise to the edges
smart	try to reduce complexity of covariance to cheapest model

◆ load2D() [2/2]

GTSAM_EXPORT GraphAndValues gtsam::load2D	(	const std::string &	filename,
		SharedNoiseModel	model = `SharedNoiseModel()`,
		size_t	maxIndex = `0`,
		bool	addNoise = `false`,
		bool	smart = `true`,
		NoiseFormat	noiseFormat = `NoiseFormatAUTO`,
		KernelFunctionType	kernelFunctionType = `KernelFunctionTypeNONE`
	)

Load TORO/G2O style graph files

Parameters

filename
model	optional noise model to use instead of one specified by file
maxIndex	if non-zero cut out vertices >= maxIndex
addNoise	add noise to the edges
smart	try to reduce complexity of covariance to cheapest model
noiseFormat	how noise parameters are stored
kernelFunctionType	whether to wrap the noise model in a robust kernel

Returns: graph and initial values

◆ logmap_default()

template<class Class >

Vector gtsam::logmap_default	(	const Class &	l0,
		const Class &	lp
	)

inline

Log map centered at l0, s.t. exp(l0,log(l0,lp)) = lp

◆ make_shared()

template<typename T , typename ... Args>

gtsam::enable_if_t<needs_eigen_aligned_allocator<T>::value, std::shared_ptr<T> > gtsam::make_shared ( Args &&... args )

Add our own make_shared as a layer of wrapping on std::make_shared This solves the problem with the stock make_shared that custom alignment is not respected, causing SEGFAULTs at runtime, which is notoriously hard to debug.

Explanation

The template needs_eigen_aligned_allocator<T>::value will evaluate to std::true_type if the type alias _eigen_aligned_allocator_trait = void is present in a class, which is automatically added by the GTSAM_MAKE_ALIGNED_OPERATOR_NEW macro.

This function declaration will only be taken when the above condition is true, so if some object does not need to be aligned, gtsam::make_shared will fall back to the next definition, which is a simple wrapper for std::make_shared.

Template Parameters

T	The type of object being constructed
Args	Type of the arguments of the constructor

Parameters

args	Arguments of the constructor

Returns: The object created as a std::shared_ptr<T>

◆ makeBinaryOrdering()

std::pair<KeyVector, std::vector<int> > gtsam::makeBinaryOrdering ( std::vector< Key > & input )

inline

Return the ordering as a binary tree such that all parent nodes are above their children.

This will result in a nested dissection Bayes tree after elimination.

Parameters

input The original ordering.

Returns: std::pair<KeyVector, std::vector<int>>

◆ MakeFunctorizedFactor()

template<typename T , typename R , typename FUNC >

FunctorizedFactor<R, T> gtsam::MakeFunctorizedFactor	(	Key	key,
		const R &	z,
		const SharedNoiseModel &	model,
		const FUNC	func
	)

Helper function to create a functorized factor.

Uses function template deduction to identify return type and functor type, so template list only needs the functor argument type.

◆ MakeFunctorizedFactor2()

template<typename T1 , typename T2 , typename R , typename FUNC >

FunctorizedFactor2<R, T1, T2> gtsam::MakeFunctorizedFactor2	(	Key	key1,
		Key	key2,
		const R &	z,
		const SharedNoiseModel &	model,
		const FUNC	func
	)

Helper function to create a functorized factor.

Uses function template deduction to identify return type and functor type, so template list only needs the functor argument type.

◆ makeSwitchingChain()

HybridGaussianFactorGraph::shared_ptr gtsam::makeSwitchingChain	(	size_t	n,
		std::function< Key(int)>	keyFunc = `X`,
		std::function< Key(int)>	dKeyFunc = `M`
	)

inline

Create a switching system chain. A switching system is a continuous system which depends on a discrete mode at each time step of the chain.

Parameters

n	The number of chain elements.
keyFunc	The functional to help specify the continuous key.
dKeyFunc	The functional to help specify the discrete key.

Returns: HybridGaussianFactorGraph::shared_ptr

◆ maxKey()

template<class PROBLEM >

Key gtsam::maxKey ( const PROBLEM & problem )

Find the max key in a problem. Useful to determine unique keys for additional slack variables

◆ moveWithBounce()

std::pair<Pose2, bool> gtsam::moveWithBounce	(	const Pose2 &	cur_pose,
		double	step_size,
		const std::vector< SimWall2D >	walls,
		Sampler &	angle_drift,
		Sampler &	reflect_noise,
		const Rot2 &	bias = `Rot2()`
	)

Calculates the next pose in a trajectory constrained by walls, with noise on angular drift and reflection noise

Parameters

cur_pose	is the pose of the robot
step_size	is the size of the forward step the robot tries to take
walls	is a set of walls to use for bouncing
angle_drift	is a sampler for angle drift (dim=1)
reflect_noise	is a sampler for scatter after hitting a wall (dim=3)

Returns: the next pose for the robot NOTE: samplers cannot be const

◆ mrsymbol()

Key gtsam::mrsymbol	(	unsigned char	c,
		unsigned char	label,
		size_t	j
	)

inline

Create a symbol key from a character, label and index, i.e. xA5.

◆ mrsymbolChr()

unsigned char gtsam::mrsymbolChr ( Key key )

inline

Return the character portion of a symbol key.

◆ mrsymbolIndex()

size_t gtsam::mrsymbolIndex ( Key key )

inline

Return the index portion of a symbol key.

◆ mrsymbolLabel()

unsigned char gtsam::mrsymbolLabel ( Key key )

inline

Return the label portion of a symbol key.

◆ nonlinearConjugateGradient()

template<class S , class V >

std::tuple<V, int> gtsam::nonlinearConjugateGradient	(	const S &	system,
		const V &	initial,
		const NonlinearOptimizerParams &	params,
		const bool	singleIteration,
		const bool	gradientDescent = `false`
	)

Implement the nonlinear conjugate gradient method using the Polak-Ribiere formula suggested in http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method.

The S (system) class requires three member functions: error(state), gradient(state) and advance(state, step-size, direction). The V class denotes the state or the solution.

The last parameter is a switch between gradient-descent and conjugate gradient

◆ numericalDerivative11() [1/2]

template<class Y , class X , int N = traits<X>::dimension>

internal::FixedSizeMatrix<Y, X>::type gtsam::numericalDerivative11	(	std::function< Y(const X &)>	h,
		const X &	x,
		double	delta = `1e-5`
	)

New-style numerical derivatives using manifold_traits.

Computes numerical derivative in argument 1 of unary function

Parameters

h	unary function yielding m-vector
x	n-dimensional value at which to evaluate h
delta	increment for numerical derivative Class Y is the output argument Class X is the input argument

Template Parameters

int	N is the dimension of the X input value if variable dimension type but known at test time

Returns: m*n Jacobian computed via central differencing

◆ numericalDerivative11() [2/2]

template<class Y , class X >

internal::FixedSizeMatrix<Y,X>::type gtsam::numericalDerivative11	(	Y(*)(const X &)	h,
		const X &	x,
		double	delta = `1e-5`
	)

use a raw C++ function pointer

◆ numericalDerivative21() [1/2]

template<class Y , class X1 , class X2 , int N = traits<X1>::dimension>

internal::FixedSizeMatrix<Y,X1>::type gtsam::numericalDerivative21	(	const std::function< Y(const X1 &, const X2 &)> &	h,
		const X1 &	x1,
		const X2 &	x2,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 1 of binary function

Parameters

h	binary function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X1 input value if variable dimension type but known at test time

◆ numericalDerivative21() [2/2]

template<class Y , class X1 , class X2 >

internal::FixedSizeMatrix<Y,X1>::type gtsam::numericalDerivative21	(	Y(*)(const X1 &, const X2 &)	h,
		const X1 &	x1,
		const X2 &	x2,
		double	delta = `1e-5`
	)

use a raw C++ function pointer

◆ numericalDerivative22() [1/2]

template<class Y , class X1 , class X2 , int N = traits<X2>::dimension>

internal::FixedSizeMatrix<Y,X2>::type gtsam::numericalDerivative22	(	std::function< Y(const X1 &, const X2 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 2 of binary function

Parameters

h	binary function yielding m-vector
x1	first argument value
x2	n-dimensional second argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X2 input value if variable dimension type but known at test time

◆ numericalDerivative22() [2/2]

template<class Y , class X1 , class X2 >

internal::FixedSizeMatrix<Y,X2>::type gtsam::numericalDerivative22	(	Y(*)(const X1 &, const X2 &)	h,
		const X1 &	x1,
		const X2 &	x2,
		double	delta = `1e-5`
	)

use a raw C++ function pointer

◆ numericalDerivative31()

template<class Y , class X1 , class X2 , class X3 , int N = traits<X1>::dimension>

internal::FixedSizeMatrix<Y,X1>::type gtsam::numericalDerivative31	(	std::function< Y(const X1 &, const X2 &, const X3 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 1 of ternary function

Parameters

h	ternary function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing All classes Y,X1,X2,X3 need dim, expmap, logmap

Template Parameters

int	N is the dimension of the X1 input value if variable dimension type but known at test time

◆ numericalDerivative32()

template<class Y , class X1 , class X2 , class X3 , int N = traits<X2>::dimension>

internal::FixedSizeMatrix<Y,X2>::type gtsam::numericalDerivative32	(	std::function< Y(const X1 &, const X2 &, const X3 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 2 of ternary function

Parameters

h	ternary function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing All classes Y,X1,X2,X3 need dim, expmap, logmap

Template Parameters

int	N is the dimension of the X2 input value if variable dimension type but known at test time

◆ numericalDerivative33()

template<class Y , class X1 , class X2 , class X3 , int N = traits<X3>::dimension>

internal::FixedSizeMatrix<Y,X3>::type gtsam::numericalDerivative33	(	std::function< Y(const X1 &, const X2 &, const X3 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 3 of ternary function

Parameters

h	ternary function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing All classes Y,X1,X2,X3 need dim, expmap, logmap

Template Parameters

int	N is the dimension of the X3 input value if variable dimension type but known at test time

◆ numericalDerivative41()

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X1>::dimension>

internal::FixedSizeMatrix<Y,X1>::type gtsam::numericalDerivative41	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 1 of 4-argument function

Parameters

h	quartic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X1 input value if variable dimension type but known at test time

◆ numericalDerivative42()

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X2>::dimension>

internal::FixedSizeMatrix<Y,X2>::type gtsam::numericalDerivative42	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 2 of 4-argument function

Parameters

h	quartic function yielding m-vector
x1	first argument value
x2	n-dimensional second argument value
x3	third argument value
x4	fourth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X2 input value if variable dimension type but known at test time

◆ numericalDerivative43()

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X3>::dimension>

internal::FixedSizeMatrix<Y,X3>::type gtsam::numericalDerivative43	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 3 of 4-argument function

Parameters

h	quartic function yielding m-vector
x1	first argument value
x2	second argument value
x3	n-dimensional third argument value
x4	fourth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X3 input value if variable dimension type but known at test time

◆ numericalDerivative44()

template<class Y , class X1 , class X2 , class X3 , class X4 , int N = traits<X4>::dimension>

internal::FixedSizeMatrix<Y,X4>::type gtsam::numericalDerivative44	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 4 of 4-argument function

Parameters

h	quartic function yielding m-vector
x1	first argument value
x2	second argument value
x3	third argument value
x4	n-dimensional fourth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X4 input value if variable dimension type but known at test time

◆ numericalDerivative51()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X1>::dimension>

internal::FixedSizeMatrix<Y,X1>::type gtsam::numericalDerivative51	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 1 of 5-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X1 input value if variable dimension type but known at test time

◆ numericalDerivative52()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X2>::dimension>

internal::FixedSizeMatrix<Y,X2>::type gtsam::numericalDerivative52	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 2 of 5-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X2 input value if variable dimension type but known at test time

◆ numericalDerivative53()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X3>::dimension>

internal::FixedSizeMatrix<Y,X3>::type gtsam::numericalDerivative53	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 3 of 5-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X3 input value if variable dimension type but known at test time

◆ numericalDerivative54()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X4>::dimension>

internal::FixedSizeMatrix<Y,X4>::type gtsam::numericalDerivative54	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 4 of 5-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X4 input value if variable dimension type but known at test time

◆ numericalDerivative55()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , int N = traits<X5>::dimension>

internal::FixedSizeMatrix<Y,X5>::type gtsam::numericalDerivative55	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 5 of 5-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X5 input value if variable dimension type but known at test time

◆ numericalDerivative61()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X1>::dimension>

internal::FixedSizeMatrix<Y,X1>::type gtsam::numericalDerivative61	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		const X6 &	x6,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 1 of 6-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
x6	sixth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X1 input value if variable dimension type but known at test time

◆ numericalDerivative62()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X2>::dimension>

internal::FixedSizeMatrix<Y,X2>::type gtsam::numericalDerivative62	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		const X6 &	x6,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 2 of 6-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
x6	sixth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X2 input value if variable dimension type but known at test time

◆ numericalDerivative63()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X3>::dimension>

internal::FixedSizeMatrix<Y,X3>::type gtsam::numericalDerivative63	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		const X6 &	x6,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 3 of 6-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
x6	sixth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X3 input value if variable dimension type but known at test time

◆ numericalDerivative64()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X4>::dimension>

internal::FixedSizeMatrix<Y,X4>::type gtsam::numericalDerivative64	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		const X6 &	x6,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 4 of 6-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
x6	sixth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X4 input value if variable dimension type but known at test time

◆ numericalDerivative65()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X5>::dimension>

internal::FixedSizeMatrix<Y,X5>::type gtsam::numericalDerivative65	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		const X6 &	x6,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 5 of 6-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
x6	sixth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X5 input value if variable dimension type but known at test time

◆ numericalDerivative66()

template<class Y , class X1 , class X2 , class X3 , class X4 , class X5 , class X6 , int N = traits<X6>::dimension>

internal::FixedSizeMatrix<Y, X6>::type gtsam::numericalDerivative66	(	std::function< Y(const X1 &, const X2 &, const X3 &, const X4 &, const X5 &, const X6 &)>	h,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		const X4 &	x4,
		const X5 &	x5,
		const X6 &	x6,
		double	delta = `1e-5`
	)

Compute numerical derivative in argument 6 of 6-argument function

Parameters

h	quintic function yielding m-vector
x1	n-dimensional first argument value
x2	second argument value
x3	third argument value
x4	fourth argument value
x5	fifth argument value
x6	sixth argument value
delta	increment for numerical derivative

Returns: m*n Jacobian computed via central differencing

Template Parameters

int	N is the dimension of the X6 input value if variable dimension type but known at test time

◆ numericalGradient()

template<class X , int N = traits<X>::dimension>

Eigen::Matrix<double, N, 1> gtsam::numericalGradient	(	std::function< double(const X &)>	h,
		const X &	x,
		double	delta = `1e-5`
	)

Numerically compute gradient of scalar function.

Returns: n-dimensional gradient computed via central differencing Class X is the input argument The class X needs to have dim, expmap, logmap int N is the dimension of the X input value if variable dimension type but known at test time

◆ numericalHessian()

template<class X >

internal::FixedSizeMatrix<X,X>::type gtsam::numericalHessian	(	std::function< double(const X &)>	f,
		const X &	x,
		double	delta = `1e-5`
	)

inline

Compute numerical Hessian matrix. Requires a single-argument Lie->scalar function. This is implemented simply as the derivative of the gradient.

Parameters

f	A function taking a Lie object as input and returning a scalar
x	The center point for computing the Hessian
delta	The numerical derivative step size

Returns: n*n Hessian matrix computed via central differencing

◆ numericalHessian311()

template<class X1 , class X2 , class X3 >

internal::FixedSizeMatrix<X1,X1>::type gtsam::numericalHessian311	(	std::function< double(const X1 &, const X2 &, const X3 &)>	f,
		const X1 &	x1,
		const X2 &	x2,
		const X3 &	x3,
		double	delta = `1e-5`
	)

inline

Numerical Hessian for tenary functions

◆ openGL2gtsam()

GTSAM_EXPORT Pose3 gtsam::openGL2gtsam	(	const Rot3 &	R,
		double	tx,
		double	ty,
		double	tz
	)

This function converts an openGL camera pose to an GTSAM camera pose.

Parameters

R	rotation in openGL
tx	x component of the translation in openGL
ty	y component of the translation in openGL
tz	z component of the translation in openGL

Returns: Pose3 in GTSAM format

◆ operator!=()

bool gtsam::operator!=	(	const Matrix &	A,
		const Matrix &	B
	)

inline

inequality

◆ operator%() [1/2]

GTSAM_EXPORT Signature gtsam::operator%	(	const DiscreteKey &	key,
		const std::string &	parent
	)

Helper function to create Signature objects example: Signature s(D % "99/1");

◆ operator%() [2/2]

GTSAM_EXPORT Signature gtsam::operator%	(	const DiscreteKey &	key,
		const Signature::Table &	parent
	)

Helper function to create Signature objects, using table construction directly example: Signature s(D % table);

◆ operator*() [1/2]

template<typename T >

ScalarMultiplyExpression<T> gtsam::operator*	(	double	s,
		const Expression< T > &	e
	)

Construct an expression that executes the scalar multiplication with an input expression The type T must be a vector space Example: Expression<Point2> a(0), b = 12 * a;

◆ operator*() [2/2]

template<typename T >

Expression< T > gtsam::operator*	(	const Expression< T > &	e1,
		const Expression< T > &	e2
	)

Construct a product expression, assumes T::compose(T) -> T.

Construct a product expression, assumes T::compose(T) -> T Example: Expression<Point2> a(0), b(1), c = a*b;

◆ operator+()

template<typename T >

BinarySumExpression<T> gtsam::operator+	(	const Expression< T > &	e1,
		const Expression< T > &	e2
	)

Construct an expression that sums two input expressions of the same type T The type T must be a vector space Example: Expression<Point2> a(0), b(1), c = a + b;

◆ operator==() [1/2]

bool gtsam::operator==	(	const Matrix &	A,
		const Matrix &	B
	)

inline

equality is just equal_with_abs_tol 1e-9

◆ operator==() [2/2]

GTSAM_EXPORT bool gtsam::operator==	(	const Vector &	vec1,
		const Vector &	vec2
	)

operator==()

◆ operator>>()

GTSAM_EXPORT std::istream& gtsam::operator>>	(	std::istream &	inputStream,
		Matrix &	destinationMatrix
	)

Read a matrix from an input stream, such as a file. Entries can be either tab-, space-, or comma-separated, similar to the format read by the MATLAB dlmread command.

◆ operator^()

GTSAM_EXPORT Vector gtsam::operator^	(	const Matrix &	A,
		const Vector &	v
	)

overload ^ for trans(A)*v We transpose the vectors for speed.

◆ operator|()

GTSAM_EXPORT Signature gtsam::operator\|	(	const DiscreteKey &	key,
		const DiscreteKey &	parent
	)

Helper function to create Signature objects example: Signature s = D | E;

◆ optimize()

GTSAM_EXPORT Point3 gtsam::optimize	(	const NonlinearFactorGraph &	graph,
		const Values &	values,
		Key	landmarkKey
	)

Optimize for triangulation

Parameters

graph	nonlinear factors for projection
values	initial values
landmarkKey	to refer to landmark

Returns: refined Point3

◆ optimizeWildfire()

size_t gtsam::optimizeWildfire	(	const ISAM2Clique::shared_ptr &	root,
		double	threshold,
		const KeySet &	replaced,
		VectorValues *	delta
	)

Optimize the BayesTree, starting from the root.

Parameters

threshold	The maximum change against the PREVIOUS delta for non-replaced variables that can be ignored, ie. the old delta entry is kept and recursive backsubstitution might eventually stop if none of the changed variables are contained in the subtree.
replaced	Needs to contain all variables that are contained in the top of the Bayes tree that has been redone.

Returns: The number of variables that were solved for.

Parameters

delta The current solution, an offset from the linearization point.

◆ parseEdge()

GTSAM_EXPORT std::optional<IndexedEdge> gtsam::parseEdge	(	std::istream &	is,
		const std::string &	tag
	)

Parse TORO/G2O edge "id1 id2 x y yaw"

Parameters

is	input stream
tag	string parsed from input stream, will only parse if edge type

◆ parseFactors()

template<typename T >

GTSAM_EXPORT std::vector<typename BetweenFactor<T>::shared_ptr> gtsam::parseFactors	(	const std::string &	filename,
		const noiseModel::Diagonal::shared_ptr &	model = `nullptr`,
		size_t	maxIndex = `0`
	)

Parse BetweenFactors in a line-based text format (like g2o) into a vector of shared pointers. Instantiated in .cpp T equal to Pose2 and Pose3.

◆ parseMeasurements()

template<typename T >

GTSAM_EXPORT std::vector<BinaryMeasurement<T> > gtsam::parseMeasurements	(	const std::string &	filename,
		const noiseModel::Diagonal::shared_ptr &	model = `nullptr`,
		size_t	maxIndex = `0`
	)

Parse binary measurements in a line-based text format (like g2o) into a vector. Instantiated in .cpp for Pose2, Rot2, Pose3, and Rot3. The rotation versions parse poses and extract only the rotation part, using the marginal covariance as noise model.

◆ parseVariables()

template<typename T >

GTSAM_EXPORT std::map<size_t, T> gtsam::parseVariables	(	const std::string &	filename,
		size_t	maxIndex = `0`
	)

Parse variables in a line-based text format (like g2o) into a map. Instantiated in .cpp Pose2, Point2, Pose3, and Point3. Note the map keys are integer indices, not gtsam::Keys. This is is different below where landmarks will use L(index) symbols.

◆ parseVertexLandmark()

GTSAM_EXPORT std::optional<IndexedLandmark> gtsam::parseVertexLandmark	(	std::istream &	is,
		const std::string &	tag
	)

Parse G2O landmark vertex "id x y"

Parameters

is	input stream
tag	string parsed from input stream, will only parse if vertex type

◆ parseVertexPose()

GTSAM_EXPORT std::optional<IndexedPose> gtsam::parseVertexPose	(	std::istream &	is,
		const std::string &	tag
	)

Parse TORO/G2O vertex "id x y yaw"

Parameters

is	input stream
tag	string parsed from input stream, will only parse if vertex type

◆ predecessorMap2Graph()

template<class G , class V , class KEY >

std::tuple< G, V, std::map< KEY, V > > gtsam::predecessorMap2Graph ( const PredecessorMap< KEY > & p_map )

Build takes a predecessor map, and builds a directed graph corresponding to the tree. G = Graph type V = Vertex type

◆ predecessorMap2Keys()

template<class KEY >

std::list< KEY > gtsam::predecessorMap2Keys ( const PredecessorMap< KEY > & p_map )

Generate a list of keys from a spanning tree represented by its predecessor map

◆ print() [1/4]

GTSAM_EXPORT void gtsam::print	(	const Vector &	v,
		const std::string &	s,
		std::ostream &	stream
	)

print without optional string, must specify cout yourself

◆ print() [2/4]

GTSAM_EXPORT void gtsam::print	(	const Vector &	v,
		const std::string &	s = `""`
	)

print with optional string to cout

◆ print() [3/4]

GTSAM_EXPORT void gtsam::print	(	const Matrix &	A,
		const std::string &	s,
		std::ostream &	stream
	)

print without optional string, must specify cout yourself

◆ print() [4/4]

GTSAM_EXPORT void gtsam::print	(	const Matrix &	A,
		const std::string &	s = `""`
	)

print with optional string to cout

◆ prod()

template<class MATRIX >

MATRIX gtsam::prod	(	const MATRIX &	A,
		const MATRIX &	B
	)

inline

products using old-style format to improve compatibility

◆ qr()

GTSAM_EXPORT std::pair<Matrix,Matrix> gtsam::qr ( const Matrix & A )

QR factorization, inefficient, best use imperative householder below m*n matrix -> m*m Q, m*n R

Parameters

A a matrix

Returns: <Q,R> rotation matrix Q, upper triangular R

◆ readBal()

GTSAM_EXPORT SfmData gtsam::readBal ( const std::string & filename )

This function parses a "Bundle Adjustment in the Large" (BAL) file and returns the data as a SfmData structure. Mainly used by wrapped code.

Parameters

filename The name of the BAL file.

Returns: SfM structure where the data is stored.

◆ readG2o()

GTSAM_EXPORT GraphAndValues gtsam::readG2o	(	const std::string &	g2oFile,
		const bool	is3D = `false`,
		KernelFunctionType	kernelFunctionType = `KernelFunctionTypeNONE`
	)

This function parses a g2o file and stores the measurements into a NonlinearFactorGraph and the initial guess in a Values structure.

Parameters

filename	The name of the g2o file\
is3D	indicates if the file describes a 2D or 3D problem
kernelFunctionType	whether to wrap the noise model in a robust kernel

Returns: graph and initial values

◆ row()

template<class MATRIX >

const MATRIX::ConstRowXpr gtsam::row	(	const MATRIX &	A,
		size_t	j
	)

Extracts a row view from a matrix that avoids a copy

Parameters

A	matrix to extract row from
j	index of the row

Returns: a const view of the matrix

◆ RQ()

GTSAM_EXPORT std::pair<Matrix3, Vector3> gtsam::RQ	(	const Matrix3 &	A,
		OptionalJacobian< 3, 9 >	H = `{}`
	)

[RQ] receives a 3 by 3 matrix and returns an upper triangular matrix R and 3 rotation angles corresponding to the rotation matrix Q=Qz'*Qy'*Qx' such that A = R*Q = R*Qz'*Qy'*Qx'. When A is a rotation matrix, R will be the identity and Q is a yaw-pitch-roll decomposition of A. The implementation uses Givens rotations and is based on Hartley-Zisserman.

Parameters

A	3 by 3 matrix A=RQ

Returns: an upper triangular matrix R; a vector [thetax, thetay, thetaz] in radians.

◆ save() [1/2]

GTSAM_EXPORT void gtsam::save	(	const Vector &	A,
		const std::string &	s,
		const std::string &	filename
	)

save a vector to file, which can be loaded by matlab

◆ save() [2/2]

GTSAM_EXPORT void gtsam::save	(	const Matrix &	A,
		const std::string &	s,
		const std::string &	filename
	)

save a matrix to file, which can be loaded by matlab

◆ save2D()

GTSAM_EXPORT void gtsam::save2D	(	const NonlinearFactorGraph &	graph,
		const Values &	config,
		const noiseModel::Diagonal::shared_ptr	model,
		const std::string &	filename
	)

save 2d graph

◆ serializeToBinaryStream()

template<class T >

void gtsam::serializeToBinaryStream	(	const T &	input,
		std::ostream &	out_archive_stream,
		const std::string &	name = `"data"`
	)

serializes to a stream in binary

◆ serializeToStream()

template<class T >

void gtsam::serializeToStream	(	const T &	input,
		std::ostream &	out_archive_stream
	)

serializes to a stream

◆ serializeToXMLStream()

template<class T >

void gtsam::serializeToXMLStream	(	const T &	input,
		std::ostream &	out_archive_stream,
		const std::string &	name = `"data"`
	)

serializes to a stream in XML

◆ skewSymmetric()

Matrix3 gtsam::skewSymmetric	(	double	wx,
		double	wy,
		double	wz
	)

inline

skew symmetric matrix returns this: 0 -wz wy wz 0 -wx -wy wx 0

Parameters

wx	3 dimensional vector
wy
wz

Returns: a 3*3 skew symmetric matrix

◆ split()

template<class G , class KEY , class FACTOR2 >

void gtsam::split	(	const G &	g,
		const PredecessorMap< KEY > &	tree,
		G &	Ab1,
		G &	Ab2
	)

Split the graph into two parts: one corresponds to the given spanning tree, and the other corresponds to the rest of the factors

◆ splitFactorGraph()

std::pair<GaussianFactorGraph, GaussianFactorGraph> gtsam::splitFactorGraph	(	const GaussianFactorGraph &	factorGraph,
		const Subgraph &	subgraph
	)

Split the graph into a subgraph and the remaining edges. Note that the remaining factorgraph has null factors.

◆ stack()

GTSAM_EXPORT Matrix gtsam::stack	(	size_t	nrMatrices,
			...
	)

create a matrix by stacking other matrices Given a set of matrices: A1, A2, A3...

Parameters

...	pointers to matrices to be stacked

Returns: combined matrix [A1; A2; A3]

◆ steepestDescent() [1/3]

GTSAM_EXPORT Vector gtsam::steepestDescent	(	const System &	Ab,
		const Vector &	x,
		const IterativeOptimizationParameters &	parameters
	)

Method of steepest gradients, System version

◆ steepestDescent() [2/3]

GTSAM_EXPORT Vector gtsam::steepestDescent	(	const Matrix &	A,
		const Vector &	b,
		const Vector &	x,
		const ConjugateGradientParameters &	parameters
	)

convenience calls using matrices, will create System class internally: Method of steepest gradients, Matrix version

◆ steepestDescent() [3/3]

GTSAM_EXPORT VectorValues gtsam::steepestDescent	(	const GaussianFactorGraph &	fg,
		const VectorValues &	x,
		const ConjugateGradientParameters &	parameters
	)

Method of steepest gradients, Gaussian Factor Graph version

◆ stiefel()

GTSAM_EXPORT Matrix43 gtsam::stiefel	(	const SO4 &	Q,
		OptionalJacobian< 12, 6 >	H = `{}`
	)

Project to Stiefel manifold of 4*3 orthonormal 3-frames in R^4, i.e., pi(Q) -> \( S \in St(3,4) \).

◆ sub()

template<class MATRIX >

Eigen::Block<const MATRIX> gtsam::sub	(	const MATRIX &	A,
		size_t	i1,
		size_t	i2,
		size_t	j1,
		size_t	j2
	)

extract submatrix, slice semantics, i.e. range = [i1,i2[ excluding i2

Parameters

A	matrix
i1	first row index
i2	last row index + 1
j1	first col index
j2	last col index + 1

Returns: submatrix A(i1:i2-1,j1:j2-1)

◆ svd()

GTSAM_EXPORT void gtsam::svd	(	const Matrix &	A,
		Matrix &	U,
		Vector &	S,
		Matrix &	V
	)

SVD computes economy SVD A=U*S*V'

Parameters

A	an m*n matrix
U	output argument: rotation matrix
S	output argument: sorted vector of singular values
V	output argument: rotation matrix if m > n then USV' = (mn)(nn)(nn) if m < n then USV' = (mm)(mm)(mn) Careful! The dimensions above reflect V', not V, which is n*m if m<n. U is a basis in R^m, V is a basis in R^n You can just pass empty matrices U,V, and vector S, they will be re-allocated.

◆ symbol()

Key gtsam::symbol	(	unsigned char	c,
		std::uint64_t	j
	)

inline

Create a symbol key from a character and index, i.e. x5.

◆ symbolChr()

unsigned char gtsam::symbolChr ( Key key )

inline

Return the character portion of a symbol key.

◆ symbolIndex()

std::uint64_t gtsam::symbolIndex ( Key key )

inline

Return the index portion of a symbol key.

◆ toBoostGraph()

template<class G , class F , class KEY >

SDGraph< KEY > gtsam::toBoostGraph ( const G & graph )

Convert the factor graph to an SDGraph G = Graph type F = Factor type Key = Key type

◆ topLeft()

GTSAM_EXPORT Matrix3 gtsam::topLeft	(	const SO4 &	Q,
		OptionalJacobian< 9, 6 >	H = `{}`
	)

Project to top-left 3*3 matrix. Note this is not in general SO(3).

◆ trans()

Matrix gtsam::trans ( const Matrix & A )

inline

static transpose function, just calls Eigen transpose member function

◆ transform_point()

template<class T , class P >

P gtsam::transform_point	(	const T &	trans,
		const P &	global,
		OptionalMatrixType	Dtrans,
		OptionalMatrixType	Dglobal
	)

Transform function that must be specialized specific domains

Template Parameters

T	is a Transform type
P	is a point type

◆ transformTo()

GTSAM_EXPORT Line3 gtsam::transformTo	(	const Pose3 &	wTc,
		const Line3 &	wL,
		OptionalJacobian< 4, 6 >	Dpose = `{}`,
		OptionalJacobian< 4, 4 >	Dline = `{}`
	)

Transform a line from world to camera frame

Parameters

wTc	- Pose3 of camera in world frame
wL	- Line3 in world frame
Dpose	- OptionalJacobian of transformed line with respect to p
Dline	- OptionalJacobian of transformed line with respect to l

Returns: Transformed line in camera frame

◆ triangulateDLT() [1/2]

GTSAM_EXPORT Point3 gtsam::triangulateDLT	(	const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &	projection_matrices,
		const Point2Vector &	measurements,
		double	rank_tol = `1e-9`
	)

DLT triangulation: See Hartley and Zisserman, 2nd Ed., page 312

Parameters

projection_matrices	Projection matrices (K*P^-1)
measurements	2D measurements
rank_tol	SVD rank tolerance

Returns: Triangulated Point3

◆ triangulateDLT() [2/2]

GTSAM_EXPORT Point3 gtsam::triangulateDLT	(	const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &	projection_matrices,
		const std::vector< Unit3 > &	measurements,
		double	rank_tol = `1e-9`
	)

overload of previous function to work with Unit3 (projected to canonical camera)

◆ triangulateHomogeneousDLT() [1/2]

GTSAM_EXPORT Vector4 gtsam::triangulateHomogeneousDLT	(	const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &	projection_matrices,
		const Point2Vector &	measurements,
		double	rank_tol = `1e-9`
	)

DLT triangulation: See Hartley and Zisserman, 2nd Ed., page 312

Parameters

projection_matrices	Projection matrices (K*P^-1)
measurements	2D measurements
rank_tol	SVD rank tolerance

Returns: Triangulated point, in homogeneous coordinates

◆ triangulateHomogeneousDLT() [2/2]

GTSAM_EXPORT Vector4 gtsam::triangulateHomogeneousDLT	(	const std::vector< Matrix34, Eigen::aligned_allocator< Matrix34 >> &	projection_matrices,
		const std::vector< Unit3 > &	measurements,
		double	rank_tol = `1e-9`
	)

Same math as Hartley and Zisserman, 2nd Ed., page 312, but with unit-norm bearing vectors (contrarily to pinhole projection, the z entry is not assumed to be 1 as in Hartley and Zisserman)

Parameters

projection_matrices	Projection matrices (K*P^-1)
measurements	Unit3 bearing measurements
rank_tol	SVD rank tolerance

Returns: Triangulated point, in homogeneous coordinates

◆ triangulateLOST()

GTSAM_EXPORT Point3 gtsam::triangulateLOST	(	const std::vector< Pose3 > &	poses,
		const Point3Vector &	calibratedMeasurements,
		const SharedIsotropic &	measurementNoise
	)

Triangulation using the LOST (Linear Optimal Sine Triangulation) algorithm proposed in https://arxiv.org/pdf/2205.12197.pdf by Sebastien Henry and John Christian.

Parameters

poses	camera poses in world frame
calibratedMeasurements	measurements in homogeneous coordinates in each camera pose
measurementNoise	isotropic noise model for the measurements

Returns: triangulated point in world coordinates

◆ triangulateNonlinear() [1/2]

template<class CALIBRATION >

Point3 gtsam::triangulateNonlinear	(	const std::vector< Pose3 > &	poses,
		std::shared_ptr< CALIBRATION >	sharedCal,
		const Point2Vector &	measurements,
		const Point3 &	initialEstimate,
		const SharedNoiseModel &	model = `nullptr`
	)

Given an initial estimate , refine a point using measurements in several cameras

Parameters

poses	Camera poses
sharedCal	shared pointer to single calibration object
measurements	2D measurements
initialEstimate

Returns: refined Point3

◆ triangulateNonlinear() [2/2]

template<class CAMERA >

Point3 gtsam::triangulateNonlinear	(	const CameraSet< CAMERA > &	cameras,
		const typename CAMERA::MeasurementVector &	measurements,
		const Point3 &	initialEstimate,
		const SharedNoiseModel &	model = `nullptr`
	)

Given an initial estimate , refine a point using measurements in several cameras

Parameters

cameras	pinhole cameras (monocular or stereo)
measurements	2D measurements
initialEstimate

Returns: refined Point3

◆ triangulatePoint3() [1/2]

template<class CALIBRATION >

Point3 gtsam::triangulatePoint3	(	const std::vector< Pose3 > &	poses,
		std::shared_ptr< CALIBRATION >	sharedCal,
		const Point2Vector &	measurements,
		double	rank_tol = `1e-9`,
		bool	optimize = `false`,
		const SharedNoiseModel &	model = `nullptr`,
		const bool	useLOST = `false`
	)

Function to triangulate 3D landmark point from an arbitrary number of poses (at least 2) using the DLT. The function checks that the resulting point lies in front of all cameras, but has no other checks to verify the quality of the triangulation.

Parameters

poses	A vector of camera poses
sharedCal	shared pointer to single calibration object
measurements	A vector of camera measurements
rank_tol	rank tolerance, default 1e-9
optimize	Flag to turn on nonlinear refinement of triangulation
useLOST	whether to use the LOST algorithm instead of DLT

Returns: Returns a Point3

◆ triangulatePoint3() [2/2]

template<class CAMERA >

Point3 gtsam::triangulatePoint3	(	const CameraSet< CAMERA > &	cameras,
		const typename CAMERA::MeasurementVector &	measurements,
		double	rank_tol = `1e-9`,
		bool	optimize = `false`,
		const SharedNoiseModel &	model = `nullptr`,
		const bool	useLOST = `false`
	)

Function to triangulate 3D landmark point from an arbitrary number of poses (at least 2) using the DLT. This function is similar to the one above, except that each camera has its own calibration. The function checks that the resulting point lies in front of all cameras, but has no other checks to verify the quality of the triangulation.

Parameters

cameras	pinhole cameras
measurements	A vector of camera measurements
rank_tol	rank tolerance, default 1e-9
optimize	Flag to turn on nonlinear refinement of triangulation
useLOST	whether to use the LOST algorithm instead of DLT

Returns: Returns a Point3

◆ triangulationGraph() [1/2]

template<class CALIBRATION >

std::pair<NonlinearFactorGraph, Values> gtsam::triangulationGraph	(	const std::vector< Pose3 > &	poses,
		std::shared_ptr< CALIBRATION >	sharedCal,
		const Point2Vector &	measurements,
		Key	landmarkKey,
		const Point3 &	initialEstimate,
		const SharedNoiseModel &	model = `noiseModel::Unit::Create(2)`
	)

Create a factor graph with projection factors from poses and one calibration

Parameters

poses	Camera poses
sharedCal	shared pointer to single calibration object (monocular only!)
measurements	2D measurements
landmarkKey	to refer to landmark
initialEstimate

Returns: graph and initial values

◆ triangulationGraph() [2/2]

template<class CAMERA >

std::pair<NonlinearFactorGraph, Values> gtsam::triangulationGraph	(	const CameraSet< CAMERA > &	cameras,
		const typename CAMERA::MeasurementVector &	measurements,
		Key	landmarkKey,
		const Point3 &	initialEstimate,
		const SharedNoiseModel &	model = `nullptr`
	)

Create a factor graph with projection factors from pinhole cameras (each camera has a pose and calibration)

Parameters

cameras	pinhole cameras (monocular or stereo)
measurements	2D measurements
landmarkKey	to refer to landmark
initialEstimate

Returns: graph and initial values

◆ undistortMeasurementInternal()

template<class CALIBRATION , class MEASUREMENT >

MEASUREMENT gtsam::undistortMeasurementInternal	(	const CALIBRATION &	cal,
		const MEASUREMENT &	measurement,
		std::optional< Cal3_S2 >	pinholeCal = `{}`
	)

Internal undistortMeasurement to be used by undistortMeasurement and undistortMeasurements

◆ undistortMeasurements() [1/5]

template<class CALIBRATION >

Point2Vector gtsam::undistortMeasurements	(	const CALIBRATION &	cal,
		const Point2Vector &	measurements
	)

Remove distortion for measurements so as if the measurements came from a pinhole camera.

Removes distortion but maintains the K matrix of the initial cal. Operates by calibrating using full calibration and uncalibrating with only the pinhole component of the calibration.

Template Parameters

CALIBRATION Calibration type to use.

Parameters

cal	Calibration with which measurements were taken.
measurements	Vector of measurements to undistort.

Returns: measurements with the effect of the distortion of sharedCal removed.

◆ undistortMeasurements() [2/5]

template<>

Point2Vector gtsam::undistortMeasurements	(	const Cal3_S2 &	cal,
		const Point2Vector &	measurements
	)

inline

Specialization for Cal3_S2 as it doesn't need to be undistorted.

◆ undistortMeasurements() [3/5]

template<class CAMERA >

CAMERA::MeasurementVector gtsam::undistortMeasurements	(	const CameraSet< CAMERA > &	cameras,
		const typename CAMERA::MeasurementVector &	measurements
	)

Remove distortion for measurements so as if the measurements came from a pinhole camera.

Removes distortion but maintains the K matrix of the initial calibrations. Operates by calibrating using full calibration and uncalibrating with only the pinhole component of the calibration.

Template Parameters

CAMERA Camera type to use.

Parameters

cameras	Cameras corresponding to each measurement.
measurements	Vector of measurements to undistort.

Returns: measurements with the effect of the distortion of the camera removed.

◆ undistortMeasurements() [4/5]

template<class CAMERA = PinholeCamera<Cal3_S2>>

PinholeCamera<Cal3_S2>::MeasurementVector gtsam::undistortMeasurements	(	const CameraSet< PinholeCamera< Cal3_S2 >> &	cameras,
		const PinholeCamera< Cal3_S2 >::MeasurementVector &	measurements
	)

inline

Specialize for Cal3_S2 to do nothing.

◆ undistortMeasurements() [5/5]

template<class CAMERA = SphericalCamera>

SphericalCamera::MeasurementVector gtsam::undistortMeasurements	(	const CameraSet< SphericalCamera > &	cameras,
		const SphericalCamera::MeasurementVector &	measurements
	)

inline

Specialize for SphericalCamera to do nothing.

◆ unzip()

template<typename L , typename T1 , typename T2 >

std::pair<DecisionTree<L, T1>, DecisionTree<L, T2> > gtsam::unzip ( const DecisionTree< L, std::pair< T1, T2 > > & input )

unzip a DecisionTree with std::pair values.

Parameters

input the DecisionTree with (T1,T2) values.

Returns: a pair of DecisionTree on T1 and T2, respectively.

◆ vector_scale_inplace()

GTSAM_EXPORT void gtsam::vector_scale_inplace	(	const Vector &	v,
		Matrix &	A,
		bool	inf_mask = `false`
	)

scales a matrix row or column by the values in a vector Arguments (Matrix, Vector) scales the columns, (Vector, Matrix) scales the rows

Parameters

inf_mask when true, will not scale with a NaN or inf value.

◆ wedge()

template<class T >

Matrix gtsam::wedge ( const Vector & x )

Declaration of wedge (see Murray94book) used to convert from n exponential coordinates to n*n element of the Lie algebra

◆ wedge< Pose2 >()

template<>

Matrix gtsam::wedge< Pose2 > ( const Vector & xi )

inline

specialization for pose2 wedge function (generic template in Lie.h)

◆ wedge< Pose3 >()

template<>

Matrix gtsam::wedge< Pose3 > ( const Vector & xi )

inline

wedge for Pose3:

Parameters

xi	6-dim twist (omega,v) where omega = 3D angular velocity v = 3D velocity

Returns: xihat, 4*4 element of Lie algebra that can be exponentiated

◆ weighted_eliminate()

GTSAM_EXPORT std::list<std::tuple<Vector, double, double> > gtsam::weighted_eliminate	(	Matrix &	A,
		Vector &	b,
		const Vector &	sigmas
	)

Imperative algorithm for in-place full elimination with weights and constraint handling

Parameters

A	is a matrix to eliminate
b	is the rhs
sigmas	is a vector of the measurement standard deviation

Returns: list of r vectors, d and sigma

◆ weightedPseudoinverse()

GTSAM_EXPORT std::pair<Vector, double> gtsam::weightedPseudoinverse	(	const Vector &	v,
		const Vector &	weights
	)

Weighted Householder solution vector, a.k.a., the pseudoinverse of the column NOTE: if any sigmas are zero (indicating a constraint) the pseudoinverse will be a selection vector, and the variance will be zero

Parameters

v	is the first column of the matrix to solve
weights	is a vector of weights/precisions where w=1/(s*s)

Returns: a pair of the pseudoinverse of v and the associated precision/weight

◆ writeBAL()

GTSAM_EXPORT bool gtsam::writeBAL	(	const std::string &	filename,
		const SfmData &	data
	)

This function writes a "Bundle Adjustment in the Large" (BAL) file from a SfmData structure.

Parameters

filename	The name of the BAL file to write
data	SfM structure where the data is stored

Returns: true if the parsing was successful, false otherwise

◆ writeBALfromValues()

GTSAM_EXPORT bool gtsam::writeBALfromValues	(	const std::string &	filename,
		const SfmData &	data,
		const Values &	values
	)

This function writes a "Bundle Adjustment in the Large" (BAL) file from a SfmData structure and a value structure (measurements are the same as the SfM input data, while camera poses and values are read from Values)

Parameters

filename	The name of the BAL file to write
data	SfM structure where the data is stored
values	structure where the graph values are stored (values can be either Pose3 or PinholeCamera<Cal3Bundler> for the cameras, and should be Point3 for the 3D points). Note: assumes that the keys are "i" for pose i and "Symbol::('p',j)" for landmark j.

Returns: true if the parsing was successful, false otherwise

◆ writeG2o()

GTSAM_EXPORT void gtsam::writeG2o	(	const NonlinearFactorGraph &	graph,
		const Values &	estimate,
		const std::string &	filename
	)

This function writes a g2o file from NonlinearFactorGraph and a Values structure.

Parameters

filename	The name of the g2o file to write
graph	NonlinearFactor graph storing the measurements
estimate	Values

Note:behavior change in PR #471: to be consistent with load2D and load3D, we write the indices to file and not the full Keys. This change really only affects landmarks, which get read as indices but stored in values with the symbol L(index).

◆ zeroBelowDiagonal()

template<class MATRIX >

void gtsam::zeroBelowDiagonal	(	MATRIX &	A,
		size_t	cols = `0`
	)

Zeros all of the elements below the diagonal of a matrix, in place

Parameters

A	is a matrix, to be modified in place
cols	is the number of columns to zero, use zero for all columns

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ FactorIndices

◆ GraphAndValues

◆ OptionalMatrixType

◆ OptionalMatrixVecType

◆ PinholeCameraCal3_S2

◆ Point2

◆ Point3

◆ SharedNoiseModel

◆ SparseEigen

◆ Velocity3

Enumeration Type Documentation

◆ LinearizationMode

◆ NoiseFormat

Function Documentation

◆ apply()

◆ assert_container_equal() [1/4]

◆ assert_container_equal() [2/4]

◆ assert_container_equal() [3/4]

◆ assert_container_equal() [4/4]

◆ assert_container_equality() [1/2]

◆ assert_container_equality() [2/2]

◆ assert_equal() [1/8]

◆ assert_equal() [2/8]

◆ assert_equal() [3/8]

◆ assert_equal() [4/8]

◆ assert_equal() [5/8]

◆ assert_equal() [6/8]

◆ assert_equal() [7/8]

◆ assert_equal() [8/8]

◆ assert_inequal() [1/3]

◆ assert_inequal() [2/3]

◆ assert_inequal() [3/3]

◆ assert_print_equal()

◆ assert_stdout_equal()

◆ backSubstituteLower()

◆ backSubstituteUpper() [1/2]

◆ backSubstituteUpper() [2/2]

◆ BCH()

◆ between_default()

◆ buildFactorSubgraph()

◆ calibrateJacobians()

◆ calibrateMeasurements() [1/2]

◆ calibrateMeasurements() [2/2]

◆ calibrateMeasurementsShared()

◆ checkConvergence()

◆ cholesky_inverse()

◆ choleskyCareful()

◆ choleskyPartial()

◆ circleCircleIntersection()

◆ collect()

◆ column()

◆ composePoses()

◆ concatVectors() [1/2]

◆ concatVectors() [2/2]

◆ conjugateGradientDescent() [1/3]

◆ conjugateGradientDescent() [2/3]

◆ conjugateGradientDescent() [3/3]

◆ conjugateGradients()

◆ ConvertNoiseModel()

◆ createPinholeCalibration()

◆ createRewrittenFileName()

◆ createUnknowns()

◆ cross()

◆ diag()

◆ DLT()

◆ dot()

◆ ediv_()

◆ EliminateQR()

◆ EliminateSymbolic()

◆ equal() [1/4]

◆ equal() [2/4]

◆ equal() [3/4]