LmSolver

Full name Microsoft.VisualBasic.Data.Bootstrapping.LevenbergMarquardt.LmSolver Assembly Microsoft.VisualBasic.Data.Bootstrapping.Fittings Members 9

levenberg-marquardt

A lightweight implementation of Levenberg-Marquardt algorithm

Augmented normal equation

 (H + uI) * h = -g

where:

H is the Hessian matrix of the chi-squared error function
g is the gradient (Jacobian) vector of the chi-squared error function
u is the damping value

Adjusting damping value

Damping value is adjusted at each iteration. The adjustment follows the algorithm presented in Methods for non-linear least squares problems by Kaj Madsen, Hans Bruun Nielsen, Ole Tingleff. The lecture note can be downloaded here.

00 Remarks

https://github.com/truongduy134/levenberg-marquardt

01 Syntax

Microsoft.VisualBasic.Data.Bootstrapping.LevenbergMarquardt.LmSolver

02 Methods

Name	Overloads	Summary
solve	4	Applies Levenberg-Marquadt algorithm on the input error function with the input initial guess of optimization parameters

03 Properties

Name	Overloads	Summary
DampingFactor	1
MaxNumIter	1
ErrorFunc	1
GradientEpsilon	1
ChangeEpsilon	1

04 Members

method solve #

solve(Double(), LmParamHandler, Boolean)

Applies Levenberg-Marquadt algorithm on the input error function with the input initial guess of optimization parameters

Parameters

Name	Type	Description
`optParams`	`Double()`	A vector of initial guess of values of parameters for optimization
`paramHandler`	LmParamHandler	A handler which is called to adjust values of the Levenberg-Marquadt parameters after they are updated at the end of each iteration in the algorithm. If {@code paramHandler} is null, no further adjustment to the updated parameters is performed. This is useful when Levenberg-Marquadt algorithm is performed on structures such as quaternions. Note that the way updated parameters are modified can affect correctness of the Levenberg-Marquadt algorithm
`approxHessianFlg`	`Boolean`	A boolean flag to indicate whether the Hessian matrix used in the Levenberg-Marquadt algorithm should be approximated or computed exactly. If {@code true}, the Hessian matrix will be approximated by the Jacobian matrix

method solve overload 4 #

solve(Double())

Applies Levenberg-Marquadt algorithm on the input error function with the input initial guess of optimization parameters. Note that the Hessian matrix used in the Levenberg-Marquadt will be computed exactly

Parameters

Name	Type	Description
`optParams`	`Double()`	A vector of initial guess of values of parameters for optimization

method solve overload 3 #

solve(Double(), Boolean)

Applies Levenberg-Marquadt algorithm on the input error function with the input initial guess of optimization parameters.

Parameters

Name	Type	Description
`optParams`	`Double()`	A vector of initial guess of values of parameters for optimization
`approxHessianFlg`	`Boolean`	A boolean flag to indicate whether the Hessian matrix used in the Levenberg-Marquadt algorithm should be approximated or computed exactly. If {@code true}, the Hessian matrix will be approximated by the Jacobian matrix

method solve overload 2 #

solve(Double(), LmParamHandler)

Parameters

Name	Type	Description
`optParams`	`Double()`	A vector of initial guess of values of parameters for optimization
`paramHandler`	LmParamHandler	A handler which is called to adjust values of the Levenberg-Marquadt parameters after they are updated at the end of each iteration in the algorithm. If {@code paramHandler} is null, no further adjustment to the updated parameters is performed. This is useful when Levenberg-Marquadt algorithm is performed on structures such as quaternions. Note that the way updated parameters are modified can affect correctness of the Levenberg-Marquadt algorithm

property DampingFactor #

DampingFactor

property MaxNumIter #

MaxNumIter

property ErrorFunc #

ErrorFunc

property GradientEpsilon #

GradientEpsilon

property ChangeEpsilon #

ChangeEpsilon