org.apache.commons.math3.optimization.general
Class LevenbergMarquardtOptimizer

java.lang.Object
  extended by org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
      extended by org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
          extended by org.apache.commons.math3.optimization.general.LevenbergMarquardtOptimizer
All Implemented Interfaces:
BaseMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>, BaseOptimizer<PointVectorValuePair>, DifferentiableMultivariateVectorOptimizer

Deprecated. As of 3.1 (to be removed in 4.0).

@Deprecated
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:

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 1423555 2012-12-18 18:02:52Z erans $

    Field Summary
    private  double[] beta
              Deprecated. Coefficients of the Householder transforms vectors.
    private  double costRelativeTolerance
              Deprecated. Desired relative error in the sum of squares.
    private  double[] diagR
              Deprecated. Diagonal elements of the R matrix in the Q.R.
    private  double initialStepBoundFactor
              Deprecated. Positive input variable used in determining the initial step bound.
    private  double[] jacNorm
              Deprecated. Norms of the columns of the jacobian matrix.
    private  double[] lmDir
              Deprecated. Parameters evolution direction associated with lmPar.
    private  double lmPar
              Deprecated. Levenberg-Marquardt parameter.
    private  double orthoTolerance
              Deprecated. Desired max cosine on the orthogonality between the function vector and the columns of the jacobian.
    private  double parRelativeTolerance
              Deprecated. Desired relative error in the approximate solution parameters.
    private  int[] permutation
              Deprecated. Columns permutation array.
    private  double qrRankingThreshold
              Deprecated. Threshold for QR ranking.
    private  int rank
              Deprecated. Rank of the jacobian matrix.
    private  int solvedCols
              Deprecated. Number of solved point.
    private  double[][] weightedJacobian
              Deprecated. Weighted Jacobian.
    private  double[] weightedResidual
              Deprecated. Weighted residuals.
     
    Fields inherited from class org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
    cols, cost, objective, point, rows, weightedResidualJacobian, weightedResiduals
     
    Fields inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer
    evaluations
     
    Constructor Summary
    LevenbergMarquardtOptimizer()
              Deprecated. Build an optimizer for least squares problems with default values for all the tuning parameters (see the other contructor.
    LevenbergMarquardtOptimizer(ConvergenceChecker<PointVectorValuePair> checker)
              Deprecated. Constructor that allows the specification of a custom convergence checker.
    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.
    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.
    LevenbergMarquardtOptimizer(double initialStepBoundFactor, double costRelativeTolerance, double parRelativeTolerance, double orthoTolerance, double threshold)
              Deprecated. The arguments control the behaviour of the default convergence checking procedure.
     
    Method Summary
    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.
    private  void determineLMParameter(double[] qy, double delta, double[] diag, double[] work1, double[] work2, double[] work3)
              Deprecated. Determine the Levenberg-Marquardt parameter.
    protected  PointVectorValuePair doOptimize()
              Deprecated. Perform the bulk of the optimization algorithm.
    private  void qrDecomposition(RealMatrix jacobian)
              Deprecated. Decompose a matrix A as A.P = Q.R using Householder transforms.
    private  void qTy(double[] y)
              Deprecated. Compute the product Qt.y for some Q.R.
     
    Methods inherited from class org.apache.commons.math3.optimization.general.AbstractLeastSquaresOptimizer
    computeCost, computeCovariances, computeResiduals, computeSigma, computeWeightedJacobian, getChiSquare, getCovariances, getCovariances, getJacobianEvaluations, getRMS, getWeightSquareRoot, guessParametersErrors, optimize, optimize, optimizeInternal, setCost, setUp, updateJacobian, updateResidualsAndCost
     
    Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateVectorOptimizer
    computeObjectiveValue, getConvergenceChecker, getEvaluations, getMaxEvaluations, getObjectiveFunction, getStartPoint, getTarget, getTargetRef, getWeight, getWeightRef, optimize, optimizeInternal, optimizeInternal
     
    Methods inherited from class java.lang.Object
    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
     
    Methods inherited from interface org.apache.commons.math3.optimization.BaseOptimizer
    getConvergenceChecker, getEvaluations, getMaxEvaluations
     

    Field Detail

    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:


    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:

    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

    doOptimize

    protected PointVectorValuePair doOptimize()
    Deprecated. 
    Perform the bulk of the optimization algorithm.

    Specified by:
    doOptimize in class BaseAbstractMultivariateVectorOptimizer<DifferentiableMultivariateVectorFunction>
    Returns:
    the point/value pair giving the optimal value for the objective function.

    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:

    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:

    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)


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