Package org.apache.commons.math3.optim.nonlinear.vector.jacobian

Class LevenbergMarquardtOptimizer

java.lang.Object
org.apache.commons.math3.optim.BaseOptimizer<PointVectorValuePair>
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
@Deprecated public class LevenbergMarquardtOptimizer extends AbstractLeastSquaresOptimizer
Deprecated.
All classes and interfaces in this package are deprecated. The optimizers that were provided here were moved to the org.apache.commons.math3.fitting.leastsquares package (cf. MATH-1008).
This class solves a least-squares problem using the Levenberg-Marquardt algorithm.
Constraints are not supported: the call to optimize will throw MathUnsupportedOperationException if bounds are passed to it.

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

    • Constructor Details

      • LevenbergMarquardtOptimizer

        public LevenbergMarquardtOptimizer()
        Deprecated.
        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)
        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.

      • 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 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)
        Deprecated.
        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)
        Deprecated.
        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.

    • Method Details