public class LevenbergMarquardtOptimizer extends AbstractLeastSquaresOptimizer
This implementation should work even for over-determined systems (i.e. systems having more point than equations). Over-determined systems are solved by ignoring the point which have the smallest impact according to their jacobian column norm. Only the rank of the matrix and some loop bounds are changed to implement this.
The resolution engine is a simple translation of the MINPACK lmder routine with minor changes. The changes include the over-determined resolution, the use of inherited convergence checker and the Q.R. decomposition which has been rewritten following the algorithm described in the P. Lascaux and R. Theodor book Analyse numérique matricielle appliquée à l'art de l'ingénieur, Masson 1986.
The authors of the original fortran version are:
| Minpack Copyright Notice (1999) University of Chicago. All rights reserved |
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the
following conditions are met:
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evaluations, iterations| Constructor and Description |
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LevenbergMarquardtOptimizer()
Build an optimizer for least squares problems with default values
for all the tuning parameters (see the
other contructor. |
LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
Constructor that allows the specification of a custom convergence
checker.
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LevenbergMarquardtOptimizer(double initialStepBoundFactorIn,
ConvergenceChecker<PointVectorValuePair> checker,
double costRelativeToleranceIn,
double parRelativeToleranceIn,
double orthoToleranceIn,
double threshold)
Constructor that allows the specification of a custom convergence
checker, in addition to the standard ones.
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LevenbergMarquardtOptimizer(double costRelativeToleranceIn,
double parRelativeToleranceIn,
double orthoToleranceIn)
Build an optimizer for least squares problems with default values
for some of the tuning parameters (see the
other contructor. |
LevenbergMarquardtOptimizer(double initialStepBoundFactorIn,
double costRelativeToleranceIn,
double parRelativeToleranceIn,
double orthoToleranceIn,
double threshold)
The arguments control the behaviour of the default convergence checking
procedure.
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| Modifier and Type | Method and Description |
|---|---|
protected PointVectorValuePair |
doOptimize()
Performs the bulk of the optimization algorithm.
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computeCost, computeCovariances, computeResiduals, computeSigma, computeWeightedJacobian, getChiSquare, getRMS, getWeightSquareRoot, optimize, setCostcomputeJacobiancomputeObjectiveValue, getTarget, getTargetSize, getWeightgetLowerBound, getStartPoint, getUpperBoundgetConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCountpublic LevenbergMarquardtOptimizer()
other contructor.
The default values for the algorithm settings are:
Precision.SAFE_MINpublic LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
Precision.SAFE_MINchecker - Convergence checker.public LevenbergMarquardtOptimizer(double initialStepBoundFactorIn,
ConvergenceChecker<PointVectorValuePair> checker,
double costRelativeToleranceIn,
double parRelativeToleranceIn,
double orthoToleranceIn,
double threshold)
initialStepBoundFactorIn - Positive input variable used in
determining the initial step bound. This bound is set to the
product of initialStepBoundFactor and the euclidean norm of diag * x if non-zero, or else to
initialStepBoundFactor itself. In most cases factor should lie in the interval
(0.1, 100.0). 100 is a generally recommended value.checker - Convergence checker.costRelativeToleranceIn - Desired relative error in the sum of
squares.parRelativeToleranceIn - Desired relative error in the approximate
solution parameters.orthoToleranceIn - Desired max cosine on the orthogonality between
the function vector and the columns of the Jacobian.threshold - Desired threshold for QR ranking. If the squared norm
of a column vector is smaller or equal to this threshold during QR
decomposition, it is considered to be a zero vector and hence the rank
of the matrix is reduced.public LevenbergMarquardtOptimizer(double costRelativeToleranceIn,
double parRelativeToleranceIn,
double orthoToleranceIn)
other contructor.
The default values for the algorithm settings are:
Precision.SAFE_MINcostRelativeToleranceIn - Desired relative error in the sum of
squares.parRelativeToleranceIn - Desired relative error in the approximate
solution parameters.orthoToleranceIn - Desired max cosine on the orthogonality between
the function vector and the columns of the Jacobian.public LevenbergMarquardtOptimizer(double initialStepBoundFactorIn,
double costRelativeToleranceIn,
double parRelativeToleranceIn,
double orthoToleranceIn,
double threshold)
ConvergenceChecker.initialStepBoundFactorIn - Positive input variable used in
determining the initial step bound. This bound is set to the
product of initialStepBoundFactor and the euclidean norm of diag * x if non-zero, or else to
initialStepBoundFactor itself. In most cases factor should lie in the interval
(0.1, 100.0). 100 is a generally recommended value.costRelativeToleranceIn - Desired relative error in the sum of
squares.parRelativeToleranceIn - Desired relative error in the approximate
solution parameters.orthoToleranceIn - Desired max cosine on the orthogonality between
the function vector and the columns of the Jacobian.threshold - Desired threshold for QR ranking. If the squared norm
of a column vector is smaller or equal to this threshold during QR
decomposition, it is considered to be a zero vector and hence the rank
of the matrix is reduced.protected PointVectorValuePair doOptimize()
doOptimize in class BaseOptimizer<PointVectorValuePair>Copyright © 2018 CNES. All Rights Reserved.