Compute maximum Eigenpair with accelerated power method. More...
#include <AcceleratedPowerMethod.h>
Public Member Functions | |
| Vector | acceleratedPowerIteration (const Vector &x1, const Vector &x0, const double beta) const |
| Vector | acceleratedPowerIteration () const |
| AcceleratedPowerMethod (const Operator &A, const boost::optional< Vector > initial=boost::none, double initialBeta=0.0) | |
| bool | compute (size_t maxIterations, double tol) |
| double | estimateBeta (const size_t T=10) const |
 Public Member Functions inherited from gtsam::PowerMethod< Operator > | |
| PowerMethod (const Operator &A, const boost::optional< Vector > initial=boost::none) | |
| Construct from the aim matrix and intial ritz vector. More... | |
| Vector | powerIteration (const Vector &x) const |
| Vector | powerIteration () const |
| bool | converged (double tol) const |
| size_t | nrIterations () const |
| Return the number of iterations. More... | |
| bool | compute (size_t maxIterations, double tol) |
| double | eigenvalue () const |
| Return the eigenvalue. More... | |
| Vector | eigenvector () const |
| Return the eigenvector. More... | |
Private Attributes | |
| double | beta_ = 0 |
| Vector | previousVector_ |
Additional Inherited Members | |
| Protected Attributes inherited from gtsam::PowerMethod< Operator > | |
| const Operator & | A_ |
| const int | dim_ |
| size_t | nrIterations_ |
| double | ritzValue_ |
| Vector | ritzVector_ |
Detailed Description
template<class Operator>
class gtsam::AcceleratedPowerMethod< Operator >
Compute maximum Eigenpair with accelerated 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: 
where A is the aim matrix we want to get eigenpair of, x is the Ritz vector
Template argument Operator just needs multiplication operator
Definition at line 51 of file AcceleratedPowerMethod.h.
Constructor & Destructor Documentation
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inlineexplicit |
Constructor from aim matrix A (given as Matrix or Sparse), optional intial vector as ritzVector
Definition at line 62 of file AcceleratedPowerMethod.h.
Member Function Documentation
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inline |
Run accelerated power iteration to get ritzVector with beta and previous two ritzVector x0 and x00, and return y = (A * x0 - * x00) / || A * x0
- * x00 ||
Definition at line 80 of file AcceleratedPowerMethod.h.
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inline |
Run accelerated power iteration to get ritzVector with beta and previous two ritzVector x0 and x00, and return y = (A * x0 - * x00) / || A * x0
- * x00 ||
Definition at line 92 of file AcceleratedPowerMethod.h.
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inline |
Start the accelerated iteration, after performing the accelerated iteration, calculate the ritz error, repeat this operation until the ritz error converge. If converged return true, else false.
Definition at line 156 of file AcceleratedPowerMethod.h.
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inline |
Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3), T is the iteration time to find beta with largest Rayleigh quotient
Definition at line 101 of file AcceleratedPowerMethod.h.
Member Data Documentation
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private |
Definition at line 53 of file AcceleratedPowerMethod.h.
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private |
Definition at line 55 of file AcceleratedPowerMethod.h.
The documentation for this class was generated from the following file: