Package org.apache.commons.math.optimization.general

Class LevenbergMarquardtOptimizer

  • All Implemented Interfaces:
    DifferentiableMultivariateVectorialOptimizer
    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:
      $Revision: 1073272 $ $Date: 2011-02-22 10:22:25 +0100 (mar. 22 févr. 2011) $

      • Method Detail

        • setInitialStepBoundFactor

          public void setInitialStepBoundFactor​(double initialStepBoundFactor)
          Set the 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 nonzero, or else to initialStepBoundFactor itself. In most cases factor should lie in the interval (0.1, 100.0). 100.0 is a generally recommended value.
          Parameters:
          initialStepBoundFactor - initial step bound factor

        • setCostRelativeTolerance

          public void setCostRelativeTolerance​(double costRelativeTolerance)
          Set the desired relative error in the sum of squares.

          This setting is used only if the vectorial convergence checker is set to null.

          Parameters:
          costRelativeTolerance - desired relative error in the sum of squares

        • setParRelativeTolerance

          public void setParRelativeTolerance​(double parRelativeTolerance)
          Set the desired relative error in the approximate solution parameters.

          This setting is used only if the vectorial convergence checker is set to null.

          Parameters:
          parRelativeTolerance - desired relative error in the approximate solution parameters

        • setOrthoTolerance

          public void setOrthoTolerance​(double orthoTolerance)
          Set the desired max cosine on the orthogonality.

          This setting is always used, regardless of the vectorial convergence checker being null or non-null.

          Parameters:
          orthoTolerance - desired max cosine on the orthogonality between the function vector and the columns of the jacobian

        • setQRRankingThreshold

          public void setQRRankingThreshold​(double threshold)
          Set the 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.

          Parameters:
          threshold - threshold for QR ranking
          Since:
          2.2