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

java.lang.Object
  extended by org.apache.commons.math.optimization.general.AbstractLeastSquaresOptimizer
      extended by org.apache.commons.math.optimization.general.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 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 redistribution policy for MINPACK is available here, for convenience, it is reproduced below.

Minpack Copyright Notice (1999) University of Chicago. All rights reserved
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    Since:
    2.0
    Version:
    $Revision: 795978 $ $Date: 2009-07-20 15:57:08 -0400 (Mon, 20 Jul 2009) $
    Author:
    Argonne National Laboratory. MINPACK project. March 1980 (original fortran), Burton S. Garbow (original fortran), Kenneth E. Hillstrom (original fortran), Jorge J. More (original fortran)

    Field Summary
     
    Fields inherited from class org.apache.commons.math.optimization.general.AbstractLeastSquaresOptimizer
    checker, cols, cost, DEFAULT_MAX_ITERATIONS, jacobian, objective, point, residuals, rows, target, weights
     
    Constructor Summary
    LevenbergMarquardtOptimizer()
              Build an optimizer for least squares problems.
     
    Method Summary
    protected  VectorialPointValuePair doOptimize()
              Perform the bulk of optimization algorithm.
     void setCostRelativeTolerance(double costRelativeTolerance)
              Set the desired relative error in the sum of squares.
     void setInitialStepBoundFactor(double initialStepBoundFactor)
              Set the positive input variable used in determining the initial step bound.
     void setOrthoTolerance(double orthoTolerance)
              Set the desired max cosine on the orthogonality.
     void setParRelativeTolerance(double parRelativeTolerance)
              Set the desired relative error in the approximate solution parameters.
     
    Methods inherited from class org.apache.commons.math.optimization.general.AbstractLeastSquaresOptimizer
    getChiSquare, getConvergenceChecker, getCovariances, getEvaluations, getIterations, getJacobianEvaluations, getMaxEvaluations, getMaxIterations, getRMS, guessParametersErrors, incrementIterationsCounter, optimize, setConvergenceChecker, setMaxEvaluations, setMaxIterations, updateJacobian, updateResidualsAndCost
     
    Methods inherited from class java.lang.Object
    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
     

    Constructor Detail

    LevenbergMarquardtOptimizer

    public LevenbergMarquardtOptimizer()
    Build an optimizer for least squares problems.

    The default values for the algorithm settings are:

    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.

    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.

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

    setOrthoTolerance

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

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

    doOptimize

    protected VectorialPointValuePair doOptimize()
                                          throws FunctionEvaluationException,
                                                 OptimizationException,
                                                 java.lang.IllegalArgumentException
    Perform the bulk of optimization algorithm.

    Specified by:
    doOptimize in class AbstractLeastSquaresOptimizer
    Returns:
    the point/value pair giving the optimal value for objective function
    Throws:
    FunctionEvaluationException - if the objective function throws one during the search
    OptimizationException - if the algorithm failed to converge
    java.lang.IllegalArgumentException - if the start point dimension is wrong


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