Class LevenbergMarquardtOptimizer
- java.lang.Object
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- org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
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- org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
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- org.apache.commons.math3.optimization.general.LevenbergMarquardtOptimizer
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- All Implemented Interfaces:
BaseMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
,BaseOptimizer<PointVectorValuePair>
,DifferentiableMultivariateVectorOptimizer
@Deprecated public class LevenbergMarquardtOptimizer extends AbstractLeastSquaresOptimizer
Deprecated.As of 3.1 (to be removed in 4.0).This class solves a least squares problem using the Levenberg-Marquardt algorithm.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:
- Argonne National Laboratory. MINPACK project. March 1980
- Burton S. Garbow
- Kenneth E. Hillstrom
- Jorge J. More
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: - Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
- The end-user documentation included with the redistribution, if any,
must include the following acknowledgment:
This product includes software developed by the University of Chicago, as Operator of Argonne National Laboratory.
Alternately, this acknowledgment may appear in the software itself, if and wherever such third-party acknowledgments normally appear. - WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL BE CORRECTED.
- LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE POSSIBILITY OF SUCH LOSS OR DAMAGES.
- Since:
- 2.0
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Field Summary
Fields Modifier and Type Field Description private double[]
beta
Deprecated.Coefficients of the Householder transforms vectors.private double
costRelativeTolerance
Deprecated.Desired relative error in the sum of squares.private double[]
diagR
Deprecated.Diagonal elements of the R matrix in the Q.R.private double
initialStepBoundFactor
Deprecated.Positive input variable used in determining the initial step bound.private double[]
jacNorm
Deprecated.Norms of the columns of the jacobian matrix.private double[]
lmDir
Deprecated.Parameters evolution direction associated with lmPar.private double
lmPar
Deprecated.Levenberg-Marquardt parameter.private double
orthoTolerance
Deprecated.Desired max cosine on the orthogonality between the function vector and the columns of the jacobian.private double
parRelativeTolerance
Deprecated.Desired relative error in the approximate solution parameters.private int[]
permutation
Deprecated.Columns permutation array.private double
qrRankingThreshold
Deprecated.Threshold for QR ranking.private int
rank
Deprecated.Rank of the jacobian matrix.private int
solvedCols
Deprecated.Number of solved point.private double[][]
weightedJacobian
Deprecated.Weighted Jacobian.private double[]
weightedResidual
Deprecated.Weighted residuals.-
Fields inherited from class org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
cols, cost, objective, point, rows, weightedResidualJacobian, weightedResiduals
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Fields inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer
evaluations
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Constructor Summary
Constructors Constructor Description LevenbergMarquardtOptimizer()
Deprecated.Build an optimizer for least squares problems with default values for all the tuning parameters (see theother contructor
.LevenbergMarquardtOptimizer(double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance)
Deprecated.Build an optimizer for least squares problems with default values for some of the tuning parameters (see theother contructor
.LevenbergMarquardtOptimizer(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
Deprecated.The arguments control the behaviour of the default convergence checking procedure.LevenbergMarquardtOptimizer(double initialStepBoundFactor, ConvergenceChecker<PointVectorValuePair> checker, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
Deprecated.Constructor that allows the specification of a custom convergence checker, in addition to the standard ones.LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
Deprecated.Constructor that allows the specification of a custom convergence checker.
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Method Summary
All Methods Instance Methods Concrete Methods Deprecated Methods Modifier and Type Method Description private void
determineLMDirection(double[] qy, double[] diag, double[] lmDiag, double[] work)
Deprecated.Solve a*x = b and d*x = 0 in the least squares sense.private void
determineLMParameter(double[] qy, double delta, double[] diag, double[] work1, double[] work2, double[] work3)
Deprecated.Determine the Levenberg-Marquardt parameter.protected PointVectorValuePair
doOptimize()
Deprecated.Perform the bulk of the optimization algorithm.private void
qrDecomposition(RealMatrix jacobian)
Deprecated.Decompose a matrix A as A.P = Q.R using Householder transforms.private void
qTy(double[] y)
Deprecated.Compute the product Qt.y for some Q.R.-
Methods inherited from class org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
computeCost, computeCovariances, computeResiduals, computeSigma, computeWeightedJacobian, getChiSquare, getCovariances, getCovariances, getJacobianEvaluations, getRMS, getWeightSquareRoot, guessParametersErrors, optimize, optimize, optimizeInternal, setCost, setUp, updateJacobian, updateResidualsAndCost
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Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer
computeObjectiveValue, getConvergenceChecker, getEvaluations, getMaxEvaluations, getObjectiveFunction, getStartPoint, getTarget, getTargetRef, getWeight, getWeightRef, optimize, optimizeInternal, optimizeInternal
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.apache.commons.math3.optimization.BaseOptimizer
getConvergenceChecker, getEvaluations, getMaxEvaluations
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Field Detail
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solvedCols
private int solvedCols
Deprecated.Number of solved point.
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diagR
private double[] diagR
Deprecated.Diagonal elements of the R matrix in the Q.R. decomposition.
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jacNorm
private double[] jacNorm
Deprecated.Norms of the columns of the jacobian matrix.
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beta
private double[] beta
Deprecated.Coefficients of the Householder transforms vectors.
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permutation
private int[] permutation
Deprecated.Columns permutation array.
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rank
private int rank
Deprecated.Rank of the jacobian matrix.
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lmPar
private double lmPar
Deprecated.Levenberg-Marquardt parameter.
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lmDir
private double[] lmDir
Deprecated.Parameters evolution direction associated with lmPar.
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initialStepBoundFactor
private final double initialStepBoundFactor
Deprecated.Positive input variable used in determining the initial step bound.
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costRelativeTolerance
private final double costRelativeTolerance
Deprecated.Desired relative error in the sum of squares.
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parRelativeTolerance
private final double parRelativeTolerance
Deprecated.Desired relative error in the approximate solution parameters.
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orthoTolerance
private final double orthoTolerance
Deprecated.Desired max cosine on the orthogonality between the function vector and the columns of the jacobian.
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qrRankingThreshold
private final double qrRankingThreshold
Deprecated.Threshold for QR ranking.
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weightedResidual
private double[] weightedResidual
Deprecated.Weighted residuals.
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weightedJacobian
private double[][] weightedJacobian
Deprecated.Weighted Jacobian.
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Constructor Detail
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LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer()
Deprecated.Build an optimizer for least squares problems with default values for all the tuning parameters (see theother contructor
. The default values for the algorithm settings are:- Initial step bound factor: 100
- Cost relative tolerance: 1e-10
- Parameters relative tolerance: 1e-10
- Orthogonality tolerance: 1e-10
- QR ranking threshold:
Precision.SAFE_MIN
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LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
Deprecated.Constructor that allows the specification of a custom convergence checker. Note that all the usual convergence checks will be disabled. The default values for the algorithm settings are:- Initial step bound factor: 100
- Cost relative tolerance: 1e-10
- Parameters relative tolerance: 1e-10
- Orthogonality tolerance: 1e-10
- QR ranking threshold:
Precision.SAFE_MIN
- Parameters:
checker
- Convergence checker.
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LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(double initialStepBoundFactor, ConvergenceChecker<PointVectorValuePair> checker, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
Deprecated.Constructor that allows the specification of a custom convergence checker, in addition to the standard ones.- Parameters:
initialStepBoundFactor
- Positive input variable used in determining the initial step bound. This bound is set to the product of initialStepBoundFactor and the euclidean norm ofdiag * x
if non-zero, or else toinitialStepBoundFactor
itself. In most cases factor should lie in the interval(0.1, 100.0)
.100
is a generally recommended value.checker
- Convergence checker.costRelativeTolerance
- Desired relative error in the sum of squares.parRelativeTolerance
- Desired relative error in the approximate solution parameters.orthoTolerance
- 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.
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LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance)
Deprecated.Build an optimizer for least squares problems with default values for some of the tuning parameters (see theother contructor
. The default values for the algorithm settings are:- Initial step bound factor}: 100
- QR ranking threshold}:
Precision.SAFE_MIN
- Parameters:
costRelativeTolerance
- Desired relative error in the sum of squares.parRelativeTolerance
- Desired relative error in the approximate solution parameters.orthoTolerance
- Desired max cosine on the orthogonality between the function vector and the columns of the Jacobian.
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LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
Deprecated.The arguments control the behaviour of the default convergence checking procedure. Additional criteria can defined through the setting of aConvergenceChecker
.- Parameters:
initialStepBoundFactor
- Positive input variable used in determining the initial step bound. This bound is set to the product of initialStepBoundFactor and the euclidean norm ofdiag * x
if non-zero, or else toinitialStepBoundFactor
itself. In most cases factor should lie in the interval(0.1, 100.0)
.100
is a generally recommended value.costRelativeTolerance
- Desired relative error in the sum of squares.parRelativeTolerance
- Desired relative error in the approximate solution parameters.orthoTolerance
- 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.
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Method Detail
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doOptimize
protected PointVectorValuePair doOptimize()
Deprecated.Perform the bulk of the optimization algorithm.- Specified by:
doOptimize
in classBaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
- Returns:
- the point/value pair giving the optimal value for the objective function.
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determineLMParameter
private void determineLMParameter(double[] qy, double delta, double[] diag, double[] work1, double[] work2, double[] work3)
Deprecated.Determine the Levenberg-Marquardt parameter.This implementation is a translation in Java of the MINPACK lmpar routine.
This method sets the lmPar and lmDir attributes.
The authors of the original fortran function are:
- Argonne National Laboratory. MINPACK project. March 1980
- Burton S. Garbow
- Kenneth E. Hillstrom
- Jorge J. More
Luc Maisonobe did the Java translation.
- Parameters:
qy
- array containing qTydelta
- upper bound on the euclidean norm of diagR * lmDirdiag
- diagonal matrixwork1
- work arraywork2
- work arraywork3
- work array
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determineLMDirection
private void determineLMDirection(double[] qy, double[] diag, double[] lmDiag, double[] work)
Deprecated.Solve a*x = b and d*x = 0 in the least squares sense.This implementation is a translation in Java of the MINPACK qrsolv routine.
This method sets the lmDir and lmDiag attributes.
The authors of the original fortran function are:
- Argonne National Laboratory. MINPACK project. March 1980
- Burton S. Garbow
- Kenneth E. Hillstrom
- Jorge J. More
Luc Maisonobe did the Java translation.
- Parameters:
qy
- array containing qTydiag
- diagonal matrixlmDiag
- diagonal elements associated with lmDirwork
- work array
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qrDecomposition
private void qrDecomposition(RealMatrix jacobian) throws ConvergenceException
Deprecated.Decompose a matrix A as A.P = Q.R using Householder transforms.As suggested in the P. Lascaux and R. Theodor book Analyse numérique matricielle appliquée à l'art de l'ingénieur (Masson, 1986), instead of representing the Householder transforms with uk unit vectors such that:
Hk = I - 2uk.ukt
we use k non-unit vectors such that:Hk = I - betakvk.vkt
where vk = ak - alphak ek. The betak coefficients are provided upon exit as recomputing them from the vk vectors would be costly.This decomposition handles rank deficient cases since the tranformations are performed in non-increasing columns norms order thanks to columns pivoting. The diagonal elements of the R matrix are therefore also in non-increasing absolute values order.
- Parameters:
jacobian
- Weighted Jacobian matrix at the current point.- Throws:
ConvergenceException
- if the decomposition cannot be performed
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qTy
private void qTy(double[] y)
Deprecated.Compute the product Qt.y for some Q.R. decomposition.- Parameters:
y
- vector to multiply (will be overwritten with the result)
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