gtsam::PowerMethod< Operator > Class Template Reference

Detailed Description

template<class Operator>
class gtsam::PowerMethod< Operator >

Compute maximum Eigenpair with power method.

References : 1) G. Golub and C. V. Loan, Matrix Computations, 3rd ed. Baltimore, Johns Hopkins University Press, 1996, pp.405-411 2) Rosen, D. and Carlone, L., 2017, September. Computational enhancements for certifiably correct SLAM. In Proceedings of the International Conference on Intelligent Robots and Systems. 3) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv 4) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. 58–67

It performs the following iteration: \( x_{k+1} = A * x_k \) where A is the aim matrix we want to get eigenpair of, x is the Ritz vector

Template argument Operator just needs multiplication operator

Inheritance diagram for gtsam::PowerMethod< Operator >:

Public Member Functions
Standard Constructors
	PowerMethod (const Operator &A, const boost::optional< Vector > initial=boost::none)
	Construct from the aim matrix and intial ritz vector.
Vector	powerIteration (const Vector &x) const
	Run power iteration to get ritzVector with previous ritzVector x, and return A * x / || A * x ||.
Vector	powerIteration () const
	Run power iteration to get ritzVector with previous ritzVector x, and return A * x / || A * x ||.
bool	converged (double tol) const
	After Perform power iteration on a single Ritz value, check if the Ritz residual for the current Ritz pair is less than the required convergence tol, return true if yes, else false.
size_t	nrIterations () const
	Return the number of iterations.
bool	compute (size_t maxIterations, double tol)
	Start the power/accelerated iteration, after performing the power/accelerated iteration, calculate the ritz error, repeat this operation until the ritz error converge. More...
double	eigenvalue () const
	Return the eigenvalue.
Vector	eigenvector () const
	Return the eigenvector.

Protected Attributes
const Operator &	A_
	Const reference to an externally-held matrix whose minimum-eigenvalue we want to compute.
const int	dim_
size_t	nrIterations_
double	ritzValue_
Vector	ritzVector_

Member Function Documentation

compute()

template<class Operator >

bool gtsam::PowerMethod< Operator >::compute ( size_t  maxIterations, double  tol  )

inline

Start the power/accelerated iteration, after performing the power/accelerated iteration, calculate the ritz error, repeat this operation until the ritz error converge.

If converged return true, else false.

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

• /Users/dellaert/git/github/gtsam/linear/PowerMethod.h