Class 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.

    Minpack Copyright Notice (1999) University of Chicago. All rights reserved
    Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
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      Since:
      2.0
      • Field Detail

        • TWO_EPS

          private static final double TWO_EPS
          Deprecated.
          Twice the "epsilon machine".
        • solvedCols

          private int solvedCols
          Deprecated.
          Number of solved point.
        • diagR

          private double[] diagR
          Deprecated.
          Diagonal elements of the R matrix in the Q.R. decomposition.
        • jacNorm

          private double[] jacNorm
          Deprecated.
          Norms of the columns of the jacobian matrix.
        • beta

          private double[] beta
          Deprecated.
          Coefficients of the Householder transforms vectors.
        • permutation

          private int[] permutation
          Deprecated.
          Columns permutation array.
        • rank

          private int rank
          Deprecated.
          Rank of the jacobian matrix.
        • lmPar

          private double lmPar
          Deprecated.
          Levenberg-Marquardt parameter.
        • lmDir

          private double[] lmDir
          Deprecated.
          Parameters evolution direction associated with lmPar.
        • initialStepBoundFactor

          private final double initialStepBoundFactor
          Deprecated.
          Positive input variable used in determining the initial step bound.
        • costRelativeTolerance

          private final double costRelativeTolerance
          Deprecated.
          Desired relative error in the sum of squares.
        • parRelativeTolerance

          private final double parRelativeTolerance
          Deprecated.
          Desired relative error in the approximate solution parameters.
        • orthoTolerance

          private final double orthoTolerance
          Deprecated.
          Desired max cosine on the orthogonality between the function vector and the columns of the jacobian.
        • qrRankingThreshold

          private final double qrRankingThreshold
          Deprecated.
          Threshold for QR ranking.
        • weightedResidual

          private double[] weightedResidual
          Deprecated.
          Weighted residuals.
        • weightedJacobian

          private double[][] weightedJacobian
          Deprecated.
          Weighted Jacobian.
      • Constructor Detail

        • 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 Detail

        • determineLMParameter

          private void determineLMParameter​(double[] qy,
                                            double delta,
                                            double[] diag,
                                            double[] work1,
                                            double[] work2,
                                            double[] work3)
          Deprecated.
          Determine the Levenberg-Marquardt parameter.

          This implementation is a translation in Java of the MINPACK lmpar routine.

          This method sets the lmPar and lmDir attributes.

          The authors of the original fortran function are:

          • Argonne National Laboratory. MINPACK project. March 1980
          • Burton S. Garbow
          • Kenneth E. Hillstrom
          • Jorge J. More

          Luc Maisonobe did the Java translation.

          Parameters:
          qy - array containing qTy
          delta - upper bound on the euclidean norm of diagR * lmDir
          diag - diagonal matrix
          work1 - work array
          work2 - work array
          work3 - work array
        • determineLMDirection

          private void determineLMDirection​(double[] qy,
                                            double[] diag,
                                            double[] lmDiag,
                                            double[] work)
          Deprecated.
          Solve a*x = b and d*x = 0 in the least squares sense.

          This implementation is a translation in Java of the MINPACK qrsolv routine.

          This method sets the lmDir and lmDiag attributes.

          The authors of the original fortran function are:

          • Argonne National Laboratory. MINPACK project. March 1980
          • Burton S. Garbow
          • Kenneth E. Hillstrom
          • Jorge J. More

          Luc Maisonobe did the Java translation.

          Parameters:
          qy - array containing qTy
          diag - diagonal matrix
          lmDiag - diagonal elements associated with lmDir
          work - work array
        • qrDecomposition

          private void qrDecomposition​(RealMatrix jacobian)
                                throws ConvergenceException
          Deprecated.
          Decompose a matrix A as A.P = Q.R using Householder transforms.

          As suggested in the P. Lascaux and R. Theodor book Analyse numérique matricielle appliquée à l'art de l'ingénieur (Masson, 1986), instead of representing the Householder transforms with uk unit vectors such that:

           Hk = I - 2uk.ukt
           
          we use k non-unit vectors such that:
           Hk = I - betakvk.vkt
           
          where vk = ak - alphak ek. The betak coefficients are provided upon exit as recomputing them from the vk vectors would be costly.

          This decomposition handles rank deficient cases since the tranformations are performed in non-increasing columns norms order thanks to columns pivoting. The diagonal elements of the R matrix are therefore also in non-increasing absolute values order.

          Parameters:
          jacobian - Weighted Jacobian matrix at the current point.
          Throws:
          ConvergenceException - if the decomposition cannot be performed
        • qTy

          private void qTy​(double[] y)
          Deprecated.
          Compute the product Qt.y for some Q.R. decomposition.
          Parameters:
          y - vector to multiply (will be overwritten with the result)