Package elki.math.linearalgebra.fitting

Class LevenbergMarquardtMethod

  • public class LevenbergMarquardtMethod
extends java.lang.Object
    Function parameter fitting using Levenberg-Marquardt method.

    The Levenberg-Marquardt Algorithm (LMA) is a combination of the Gauss-Newton Algorithm (GNA) and the method of steepest descent. As such it usually gives more stable results and better convergence.

    Implemented loosely based on the book:
    Numerical Recipes In C: The Art Of Scientific Computing
    Press, W.H. and Teukolsky, S.A. and Vetterling, W.T. and Flannery, B.P.
    Cambridge University Press, Cambridge, Mass, 1992

    Due to their license, we cannot use their code, but we have to implement the mathematics ourselves. We hope the loss in precision isn't too big.

    TODO: Replace implementation by one based on
    M.I.A. Lourakis levmar
    Levenberg-Marquardt nonlinear least squares algorithms in C/C++

    Which supposedly offers increased robustness.

    Since:
    0.2
    Author:
    Erich Schubert

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double[][] alpha
      Working space for alphas
      private double[] beta  
      private double chisq
      Chi-Squared information for parameters
      private double[][] covmat
      Working space for covariance matrix
      private double[] deltaparams  
      private boolean[] dofit
      Which parameters to fit
      FittingFunction func
      Function to fit to
      private double lambda
      Lambda (refinement step size)
      int maxruns
      Maximum number of iterations in run()
      int maxsmall
      Maximum number of small improvements (stopping condition)
      private int numfit
      Number of parameters to fit
      private int numparams
      Number of parameters
      private double[] params
      Parameters to use in fitting
      private double[] paramstry
      More working buffers
      private double[] s  
      double small
      "Small value" condition for stopping
      private double[] x
      Data to fit the function to
      private double[] y  

    • Constructor Summary

      Constructors 
      Constructor Description
      LevenbergMarquardtMethod​(FittingFunction func, double[] params, boolean[] dofit, double[] x, double[] y, double[] s)
      Function fitting using Levenberg-Marquardt Method.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double getChiSq()
      Get current ChiSquared (squared error sum)
      double[][] getCovmat()
      Get the final covariance matrix.
      double[] getParams()
      Get current parameters.
      void iterate()
      Perform an iteration of the approximation loop.
      void run()
      Iterate until convergence, at most 100 times.
      private double simulateParameters​(double[] curparams)
      Compute new chisquared error

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Field Detail

      • x

        private double[] x
        Data to fit the function to

      • y

        private double[] y

      • s

        private double[] s

      • numparams

        private int numparams
        Number of parameters

      • params

        private double[] params
        Parameters to use in fitting

      • chisq

        private double chisq
        Chi-Squared information for parameters

      • numfit

        private int numfit
        Number of parameters to fit

      • dofit

        private boolean[] dofit
        Which parameters to fit

      • covmat

        private double[][] covmat
        Working space for covariance matrix

      • alpha

        private double[][] alpha
        Working space for alphas

      • lambda

        private double lambda
        Lambda (refinement step size)

      • paramstry

        private double[] paramstry
        More working buffers

      • beta

        private double[] beta

      • deltaparams

        private double[] deltaparams

      • maxruns

        public int maxruns
        Maximum number of iterations in run()

      • maxsmall

        public int maxsmall
        Maximum number of small improvements (stopping condition)

      • small

        public double small
        "Small value" condition for stopping

    • Constructor Detail

      • LevenbergMarquardtMethod

        public LevenbergMarquardtMethod​(FittingFunction func,
                                double[] params,
                                boolean[] dofit,
                                double[] x,
                                double[] y,
                                double[] s)
        Function fitting using Levenberg-Marquardt Method.
        Parameters:
        func - Function to fit to
        x - Measurement points
        y - Actual function values
        s - Confidence / Variance in measurement data
        params - Initial parameters
        dofit - Flags on which parameters to optimize

    • Method Detail

      • simulateParameters

        private double simulateParameters​(double[] curparams)
        Compute new chisquared error

        This function also modifies the alpha and beta matrixes!

        Parameters:
        curparams - Parameters to use in computation.
        Returns:
        new chi squared

      • iterate

        public void iterate()
        Perform an iteration of the approximation loop.

      • getCovmat

        public double[][] getCovmat()
        Get the final covariance matrix.

        Parameters that were not to be optimized are filled with zeros.

        Returns:
        covariance matrix for all parameters

      • getParams

        public double[] getParams()
        Get current parameters.
        Returns:
        parameters

      • getChiSq

        public double getChiSq()
        Get current ChiSquared (squared error sum)
        Returns:
        error measure

      • run

        public void run()
        Iterate until convergence, at most 100 times.