org.apache.commons.math3.optim.nonlinear.vector.jacobian
Class LevenbergMarquardtOptimizer
java.lang.Object
org.apache.commons.math3.optim.BaseOptimizer<PAIR>
org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointVectorValuePair>
org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer
org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer
org.apache.commons.math3.optim.nonlinear.vector.jacobian.AbstractLeastSquaresOptimizer
org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer
public class LevenbergMarquardtOptimizer
- extends AbstractLeastSquaresOptimizer
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.
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- Since:
- 2.0
- Version:
- $Id: LevenbergMarquardtOptimizer.java 7721 2013-02-14 14:07:13Z CardosoP $
|
Constructor Summary |
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. |
LevenbergMarquardtOptimizer(double initialStepBoundFactor,
ConvergenceChecker<PointVectorValuePair> checker,
double costRelativeTolerance,
double parRelativeTolerance,
double orthoTolerance,
double threshold)
Constructor that allows the specification of a custom convergence
checker, in addition to the standard ones. |
LevenbergMarquardtOptimizer(double costRelativeTolerance,
double parRelativeTolerance,
double orthoTolerance)
Build an optimizer for least squares problems with default values
for some of the tuning parameters (see the other contructor. |
LevenbergMarquardtOptimizer(double initialStepBoundFactor,
double costRelativeTolerance,
double parRelativeTolerance,
double orthoTolerance,
double threshold)
The arguments control the behaviour of the default convergence checking
procedure. |
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer()
- Build an optimizer for least squares problems with default values
for all the tuning parameters (see the
other 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
LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
- 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.
LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(double initialStepBoundFactor,
ConvergenceChecker<PointVectorValuePair> checker,
double costRelativeTolerance,
double parRelativeTolerance,
double orthoTolerance,
double threshold)
- 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 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.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.
LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(double costRelativeTolerance,
double parRelativeTolerance,
double orthoTolerance)
- Build an optimizer for least squares problems with default values
for some of the tuning parameters (see the
other contructor.
The default values for the algorithm settings are:
- 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.
LevenbergMarquardtOptimizer
public LevenbergMarquardtOptimizer(double initialStepBoundFactor,
double costRelativeTolerance,
double parRelativeTolerance,
double orthoTolerance,
double threshold)
- The arguments control the behaviour of the default convergence checking
procedure.
Additional criteria can defined through the setting of a
ConvergenceChecker.
- 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 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.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.
doOptimize
protected PointVectorValuePair doOptimize()
- Performs the bulk of the optimization algorithm.
- Specified by:
doOptimize in class BaseOptimizer<PointVectorValuePair>
- Returns:
- the point/value pair giving the optimal value of the
objective function.
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