Class LevenbergMarquardtOptimizer
- All Implemented Interfaces:
LeastSquaresOptimizer
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
The redistribution policy for MINPACK is available here, for convenience, it is reproduced below.
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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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.
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Nested Class Summary
Nested classes/interfaces inherited from interface org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresOptimizer
LeastSquaresOptimizer.Optimum
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Constructor Summary
ConstructorDescriptionDefault constructor.LevenbergMarquardtOptimizer
(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double qrRankingThreshold) Construct an instance with all parameters specified. -
Method Summary
Modifier and TypeMethodDescriptiondouble
Gets the value of a tuning parameter.double
Gets the value of a tuning parameter.double
Gets the value of a tuning parameter.double
Gets the value of a tuning parameter.double
Gets the value of a tuning parameter.optimize
(LeastSquaresProblem problem) Solve the non-linear least squares problem.withCostRelativeTolerance
(double newCostRelativeTolerance) Build new instance with cost relative tolerance.withInitialStepBoundFactor
(double newInitialStepBoundFactor) Build new instance with initial step bound factor.withOrthoTolerance
(double newOrthoTolerance) Build new instance with ortho tolerance.withParameterRelativeTolerance
(double newParRelativeTolerance) Build new instance with parameter relative tolerance.withRankingThreshold
(double newQRRankingThreshold) Build new instance with ranking threshold.
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Constructor Details
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LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer()Default constructor.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(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double qrRankingThreshold) Construct an instance with all parameters specified.- Parameters:
initialStepBoundFactor
- initial step bound factorcostRelativeTolerance
- cost relative toleranceparRelativeTolerance
- parameters relative toleranceorthoTolerance
- orthogonality toleranceqrRankingThreshold
- threshold in the QR decomposition. Columns with a 2 norm less than this threshold are considered to be all 0s.
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Method Details
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withInitialStepBoundFactor
Build new instance with initial step bound factor.- Parameters:
newInitialStepBoundFactor
- 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 tonewInitialStepBoundFactor
itself. In most cases factor should lie in the interval(0.1, 100.0)
.100
is a generally recommended value. of the matrix is reduced.- Returns:
- a new instance.
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withCostRelativeTolerance
Build new instance with cost relative tolerance.- Parameters:
newCostRelativeTolerance
- Desired relative error in the sum of squares.- Returns:
- a new instance.
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withParameterRelativeTolerance
Build new instance with parameter relative tolerance.- Parameters:
newParRelativeTolerance
- Desired relative error in the approximate solution parameters.- Returns:
- a new instance.
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withOrthoTolerance
Build new instance with ortho tolerance.- Parameters:
newOrthoTolerance
- Desired max cosine on the orthogonality between the function vector and the columns of the Jacobian.- Returns:
- a new instance.
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withRankingThreshold
Build new instance with ranking threshold.- Parameters:
newQRRankingThreshold
- 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.- Returns:
- a new instance.
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getInitialStepBoundFactor
public double getInitialStepBoundFactor()Gets the value of a tuning parameter.- Returns:
- the parameter's value.
- See Also:
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getCostRelativeTolerance
public double getCostRelativeTolerance()Gets the value of a tuning parameter.- Returns:
- the parameter's value.
- See Also:
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getParameterRelativeTolerance
public double getParameterRelativeTolerance()Gets the value of a tuning parameter.- Returns:
- the parameter's value.
- See Also:
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getOrthoTolerance
public double getOrthoTolerance()Gets the value of a tuning parameter.- Returns:
- the parameter's value.
- See Also:
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getRankingThreshold
public double getRankingThreshold()Gets the value of a tuning parameter.- Returns:
- the parameter's value.
- See Also:
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optimize
Solve the non-linear least squares problem.- Specified by:
optimize
in interfaceLeastSquaresOptimizer
- Parameters:
problem
- the problem definition, including model function and convergence criteria.- Returns:
- The optimum.
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