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

java.lang.Object
- elki.math.linearalgebra.fitting.GaussianFittingFunction

All Implemented Interfaces:

FittingFunction
```
public class GaussianFittingFunction
extends java.lang.Object
implements FittingFunction
```
Gaussian function for parameter fitting
Based loosely on fgauss in the book "Numerical Recipies".
We did not bother to implement all optimizations at the benefit of having easier to use parameters. Instead of position, amplitude and width used in the book, we use the traditional Gaussian parameters mean, standard deviation and a linear scaling factor (which is mostly useful when combining multiple distributions) The cost are some additional computations such as a square root and probably a slight loss in precision. This could of course have been handled by an appropriate wrapper instead.
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 big.
They are also arranged differently: the book uses amplitude, position, width whereas we use mean, stddev, scaling.
But we're obviously using essentially the same mathematics.
The function also can use a mixture of gaussians, just use an appropriate number of parameters (which obviously needs to be a multiple of 3)

Since:

0.2

Author:

Erich Schubert

Field Summary

Fields
Modifier and Type Field Description

static GaussianFittingFunction STATIC
Static instance

Constructor Summary

Constructors
Constructor Description

GaussianFittingFunction()

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`FittingFunctionResult`	`eval(double x, double[] params)`	Compute the mixture of Gaussians at the given position

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

- Field Detail
  - STATIC
```
public static final GaussianFittingFunction STATIC
```
    Static instance
- Constructor Detail
  - GaussianFittingFunction
```
public GaussianFittingFunction()
```
- Method Detail
  - eval
```
public FittingFunctionResult eval(double x,
                                  double[] params)
```
    Compute the mixture of Gaussians at the given position
    
    Specified by:
    
    eval in interface FittingFunction
    
    Parameters:
    
    x - Current coordinate
    
    params - Function parameters parameters
    
    Returns:
    
    Array consisting of y value and parameter gradients