Package org.apache.commons.math3.fitting.leastsquares

Class LevenbergMarquardtOptimizer

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.

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    Since:
    3.3

    • Constructor Details

      • 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 Details

      • 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:

      • getCostRelativeTolerance

        public double getCostRelativeTolerance()
        Gets the value of a tuning parameter.
        Returns:
        the parameter's value.
        See Also:

      • getParameterRelativeTolerance

        public double getParameterRelativeTolerance()
        Gets the value of a tuning parameter.
        Returns:
        the parameter's value.
        See Also:

      • getOrthoTolerance

        public double getOrthoTolerance()
        Gets the value of a tuning parameter.
        Returns:
        the parameter's value.
        See Also:

      • getRankingThreshold

        public double getRankingThreshold()
        Gets the value of a tuning parameter.
        Returns:
        the parameter's value.
        See Also:

      • 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.