gtsam::SubgraphSolver Class Reference

#include <SubgraphSolver.h>

Inheritance diagram for gtsam::SubgraphSolver:

Collaboration diagram for gtsam::SubgraphSolver:

Public Types
typedef SubgraphSolverParameters	Parameters
typedef std::shared_ptr< IterativeSolver >	shared_ptr

Public Member Functions
GTSAM_EXPORT VectorValues	optimize (const GaussianFactorGraph &gfg, const KeyInfo *=nullptr, const std::map< Key, Vector > *lambda=nullptr)
GTSAM_EXPORT VectorValues	optimize (const GaussianFactorGraph &gfg, const KeyInfo &keyInfo, const std::map< Key, Vector > &lambda)

Protected Attributes
Parameters	parameters_
std::shared_ptr< SubgraphPreconditioner >	pc_
	preconditioner object

Constructors
	SubgraphSolver (const GaussianFactorGraph &A, const Parameters &parameters, const Ordering &ordering)
	SubgraphSolver (const GaussianFactorGraph &Ab1, const GaussianFactorGraph &Ab2, const Parameters &parameters, const Ordering &ordering)
	SubgraphSolver (const GaussianBayesNet &Rc1, const GaussianFactorGraph &Ab2, const Parameters &parameters)
	~SubgraphSolver () override
	Destructor.

Implement interface
VectorValues	optimize () const
	Optimize from zero.
VectorValues	optimize (const GaussianFactorGraph &gfg, const KeyInfo &keyInfo, const std::map< Key, Vector > &lambda, const VectorValues &initial) override
	Interface that IterativeSolver subclasses have to implement.
std::pair< GaussianFactorGraph, GaussianFactorGraph >	splitGraph (const GaussianFactorGraph &gfg)
	Split graph using Kruskal algorithm, treating binary factors as edges.

Detailed Description

This class implements the linear SPCG solver presented in Dellaert et al in IROS'10.

Given a linear least-squares problem \( f(x) = |A x - b|^2 \). We split the problem into \( f(x) = |A_t - b_t|^2 + |A_c - b_c|^2 \) where \( A_t \) denotes the "tree" part, and \( A_c \) denotes the "constraint" part.

\(A_t \) is factorized into \( Q_t R_t \), and we compute \( c_t = Q_t^{-1} b_t \), and \( x_t = R_t^{-1} c_t \) accordingly.

Then we solve a reparametrized problem \( f(y) = |y|^2 + |A_c R_t^{-1} y -\bar{b_y}|^2 \), where \( y = R_t(x - x_t) \), and \( \bar{b_y} = (b_c - A_c x_t) \)

In the matrix form, it is equivalent to solving \( [A_c R_t^{-1} ; I ] y = [\bar{b_y} ; 0] \). We can solve it with the least-squares variation of the conjugate gradient method.

To use it in nonlinear optimization, please see the following example

LevenbergMarquardtParams parameters; parameters.linearSolverType = NonlinearOptimizerParams::CONJUGATE_GRADIENT; parameters.iterativeParams = std::make_shared<SubgraphSolverParameters>(); LevenbergMarquardtOptimizer optimizer(graph, initialEstimate, parameters); Values result = optimizer.optimize();

Constructor & Destructor Documentation

SubgraphSolver() [1/3]

gtsam::SubgraphSolver::SubgraphSolver	(	const GaussianFactorGraph &	A,
		const Parameters &	parameters,
		const Ordering &	ordering
	)

Given a gaussian factor graph, split it into a spanning tree (A1) + others (A2) for SPCG Will throw exception if there are ternary factors or higher arity, as we use Kruskal's algorithm to split the graph, treating binary factors as edges.

SubgraphSolver() [2/3]

gtsam::SubgraphSolver::SubgraphSolver	(	const GaussianFactorGraph &	Ab1,
		const GaussianFactorGraph &	Ab2,
		const Parameters &	parameters,
		const Ordering &	ordering
	)

The user specifies the subgraph part and the constraints part. May throw exception if A1 is underdetermined. An ordering is required to eliminate Ab1. We take Ab1 as a const reference, as it will be transformed into Rc1, but take Ab2 as a shared pointer as we need to keep it around.

SubgraphSolver() [3/3]

gtsam::SubgraphSolver::SubgraphSolver	(	const GaussianBayesNet &	Rc1,
		const GaussianFactorGraph &	Ab2,
		const Parameters &	parameters
	)

The same as above, but we assume A1 was solved by caller. We take two shared pointers as we keep both around.

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

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