LevenbergMarquardtMethod (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

java.lang.Object
- de.lmu.ifi.dbs.elki.math.linearalgebra.fitting.LevenbergMarquardtMethod

```
public class LevenbergMarquardtMethod
extends 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
ISBN 0-521-43108-5
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.

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

Methods
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.

Class LevenbergMarquardtMethod

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

func

x

y

s

numparams

params

chisq

numfit

dofit

covmat

alpha

lambda

paramstry

beta

deltaparams

maxruns

maxsmall

small

Constructor Detail

LevenbergMarquardtMethod

Method Detail

simulateParameters

iterate

getCovmat

getParams

getChiSq

run