de.lmu.ifi.dbs.elki.math.linearalgebra.fitting

Class LevenbergMarquardtMethod

java.lang.Object

de.lmu.ifi.dbs.elki.math.linearalgebra.fitting.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 and 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 and Description
LevenbergMarquardtMethod(FittingFunction func, double[] params, boolean[] dofit, double[] x, double[] y, double[] s) Function fitting using Levenberg-Marquardt Method.

Method Summary

Modifier and Type	Method and 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 This function also modifies the alpha and beta matrixes!

Methods inherited from class java.lang.Object

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

Field Detail

func

public FittingFunction func

Function to fit to

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.