LevenbergMarquardtOptimizer (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.fitting.leastsquares.LevenbergMarquardtOptimizer

All Implemented Interfaces:: LeastSquaresOptimizer

public class LevenbergMarquardtOptimizer
extends Object
implements LeastSquaresOptimizer

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

The redistribution policy for MINPACK is available here, for convenience, it is reproduced below.

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.
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Since:: 3.3

Nested Class Summary
- Nested classes/interfaces inherited from interface org.apache.commons.math3.fitting.leastsquares.LeastSquaresOptimizer
  LeastSquaresOptimizer.Optimum

Constructor Summary

Constructors
Constructor and Description
`LevenbergMarquardtOptimizer()` Default constructor.
`LevenbergMarquardtOptimizer(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double qrRankingThreshold)` Construct an instance with all parameters specified.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`getCostRelativeTolerance()` Gets the value of a tuning parameter.
`double`	`getInitialStepBoundFactor()` Gets the value of a tuning parameter.
`double`	`getOrthoTolerance()` Gets the value of a tuning parameter.
`double`	`getParameterRelativeTolerance()` Gets the value of a tuning parameter.
`double`	`getRankingThreshold()` Gets the value of a tuning parameter.
`LeastSquaresOptimizer.Optimum`	`optimize(LeastSquaresProblem problem)` Solve the non-linear least squares problem.
`LevenbergMarquardtOptimizer`	`withCostRelativeTolerance(double newCostRelativeTolerance)`
`LevenbergMarquardtOptimizer`	`withInitialStepBoundFactor(double newInitialStepBoundFactor)`
`LevenbergMarquardtOptimizer`	`withOrthoTolerance(double newOrthoTolerance)` Modifies the given parameter.
`LevenbergMarquardtOptimizer`	`withParameterRelativeTolerance(double newParRelativeTolerance)`
`LevenbergMarquardtOptimizer`	`withRankingThreshold(double newQRRankingThreshold)`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - 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
  - 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 factor
    costRelativeTolerance - cost relative tolerance
    parRelativeTolerance - parameters relative tolerance
    orthoTolerance - orthogonality tolerance
    qrRankingThreshold - threshold in the QR decomposition. Columns with a 2 norm less than this threshold are considered to be all 0s.
- Method Detail
  - withInitialStepBoundFactor
```
public LevenbergMarquardtOptimizer withInitialStepBoundFactor(double newInitialStepBoundFactor)
```
    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 of diag * x if non-zero, or else to newInitialStepBoundFactor 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.
  - withCostRelativeTolerance
```
public LevenbergMarquardtOptimizer withCostRelativeTolerance(double newCostRelativeTolerance)
```
    Parameters:
    newCostRelativeTolerance - Desired relative error in the sum of squares.
    
    Returns:
    a new instance.
  - withParameterRelativeTolerance
```
public LevenbergMarquardtOptimizer withParameterRelativeTolerance(double newParRelativeTolerance)
```
    Parameters:
    newParRelativeTolerance - Desired relative error in the approximate solution parameters.
    
    Returns:
    a new instance.
  - withOrthoTolerance
```
public LevenbergMarquardtOptimizer withOrthoTolerance(double newOrthoTolerance)
```
    Modifies the given parameter.
    
    Parameters:
    newOrthoTolerance - Desired max cosine on the orthogonality between the function vector and the columns of the Jacobian.
    
    Returns:
    a new instance.
  - withRankingThreshold
```
public LevenbergMarquardtOptimizer withRankingThreshold(double newQRRankingThreshold)
```
    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.
  - getInitialStepBoundFactor
```
public double getInitialStepBoundFactor()
```
    Gets the value of a tuning parameter.
    
    Returns:
    the parameter's value.
    See Also:
    withInitialStepBoundFactor(double)
  - getCostRelativeTolerance
```
public double getCostRelativeTolerance()
```
    Gets the value of a tuning parameter.
    
    Returns:
    the parameter's value.
    See Also:
    withCostRelativeTolerance(double)
  - getParameterRelativeTolerance
```
public double getParameterRelativeTolerance()
```
    Gets the value of a tuning parameter.
    
    Returns:
    the parameter's value.
    See Also:
    withParameterRelativeTolerance(double)
  - getOrthoTolerance
```
public double getOrthoTolerance()
```
    Gets the value of a tuning parameter.
    
    Returns:
    the parameter's value.
    See Also:
    withOrthoTolerance(double)
  - getRankingThreshold
```
public double getRankingThreshold()
```
    Gets the value of a tuning parameter.
    
    Returns:
    the parameter's value.
    See Also:
    withRankingThreshold(double)
  - optimize
```
public LeastSquaresOptimizer.Optimum optimize(LeastSquaresProblem problem)
```
    Solve the non-linear least squares problem.
    
    Specified by:
    
    optimize in interface LeastSquaresOptimizer
    
    Parameters:
    problem - the problem definition, including model function and convergence criteria.
    
    Returns:
    The optimum.

Class LevenbergMarquardtOptimizer

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.math3.fitting.leastsquares.LeastSquaresOptimizer

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LevenbergMarquardtOptimizer

LevenbergMarquardtOptimizer

Method Detail

withInitialStepBoundFactor

withCostRelativeTolerance

withParameterRelativeTolerance

withOrthoTolerance

withRankingThreshold

getInitialStepBoundFactor

getCostRelativeTolerance

getParameterRelativeTolerance

getOrthoTolerance

getRankingThreshold

optimize