LevenbergMarquardtSolver (ImgLib2 Javadocs 0-SNAPSHOT API)

java.lang.Object
- net.imglib2.algorithm.localization.LevenbergMarquardtSolver

All Implemented Interfaces:

FunctionFitter
```
public class LevenbergMarquardtSolver
extends Object
implements FunctionFitter
```
A plain implementation of Levenberg-Marquardt least-square curve fitting algorithm. This solver makes use of only the function value and its gradient. That is: candidate functions need only to implement the FitFunction.val(double[], double[]) and FitFunction.grad(double[], double[], int) methods to operate with this solver.
It was adapted and stripped from jplewis (www.idiom.com/~zilla) and released under the GPL. There are various small tweaks for robustness and speed.

Author:

Jean-Yves Tinevez 2011 - 2013

Constructor Summary

Constructors
Constructor and Description
`LevenbergMarquardtSolver()` Creates a new Levenberg-Marquardt solver for least-square curve fitting problems, with default parameters set to: `lambda = 1e-3` `epsilon = 1e-1` `maxIter = 300`
`LevenbergMarquardtSolver(int maxIteration, double lambda, double termEpsilon)` Creates a new Levenberg-Marquardt solver for least-square curve fitting problems.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`chiSquared(double[][] x, double[] a, double[] y, FitFunction f)` Calculate the current sum-squared-error
`void`	`fit(double[][] x, double[] y, double[] a, FitFunction f)` Minimizes `E = sum {(y[k] - f(x[k],a)) }^2`.
`static int`	`solve(double[][] x, double[] a, double[] y, FitFunction f, double lambda, double termepsilon, int maxiter)` Minimize E = sum {(y[k] - f(x[k],a)) }^2 Note that function implements the value and gradient of f(x,a), NOT the value and gradient of E with respect to a!
`String`	`toString()`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - LevenbergMarquardtSolver
```
public LevenbergMarquardtSolver(int maxIteration,
                                double lambda,
                                double termEpsilon)
```
    Creates a new Levenberg-Marquardt solver for least-square curve fitting problems.
    
    Parameters:
    
    lambda - blend between steepest descent (lambda high) and jump to bottom of quadratic (lambda zero). Start with 0.001.
    
    termEpsilon - termination accuracy (0.01)
    
    maxIteration - stop and return after this many iterations if not done
  - LevenbergMarquardtSolver
```
public LevenbergMarquardtSolver()
```
    Creates a new Levenberg-Marquardt solver for least-square curve fitting problems, with default parameters set to:
    - lambda = 1e-3
    - epsilon = 1e-1
    - maxIter = 300
- Method Detail
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - fit
```
public void fit(double[][] x,
                double[] y,
                double[] a,
                FitFunction f)
         throws Exception
```
    Description copied from interface: FunctionFitter
    
    Minimizes E = sum {(y[k] - f(x[k],a)) }^2. Note that function implements the value and gradient of f(x,a), NOT the value and gradient of E with respect to a!
    
    Specified by:
    
    fit in interface FunctionFitter
    
    Parameters:
    
    x - array of domain points, each may be multidimensional. (For instance, for 2D data, provides a double array of N double arrays of 2 elements: x & y.)
    
    y - corresponding array of values.
    
    a - the parameters/state of the model. Is updated by the call.
    
    f - the function to fit on the domain points.
    
    Throws:
    
    Exception - if the fitting process meets a numerical problem.
  - chiSquared
```
public static final double chiSquared(double[][] x,
                                      double[] a,
                                      double[] y,
                                      FitFunction f)
```
    Calculate the current sum-squared-error
  - solve
```
public static final int solve(double[][] x,
                              double[] a,
                              double[] y,
                              FitFunction f,
                              double lambda,
                              double termepsilon,
                              int maxiter)
                       throws Exception
```
    Minimize E = sum {(y[k] - f(x[k],a)) }^2 Note that function implements the value and gradient of f(x,a), NOT the value and gradient of E with respect to a!
    
    Parameters:
    
    x - array of domain points, each may be multidimensional
    
    y - corresponding array of values
    
    a - the parameters/state of the model
    
    lambda - blend between steepest descent (lambda high) and jump to bottom of quadratic (lambda zero). Start with 0.001.
    
    termepsilon - termination accuracy (0.01)
    
    maxiter - stop and return after this many iterations if not done
    
    Returns:
    
    the number of iteration used by minimization
    
    Throws:
    
    Exception

Class LevenbergMarquardtSolver

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LevenbergMarquardtSolver

LevenbergMarquardtSolver

Method Detail

toString

fit

chiSquared

solve