Gaussian (ImgLib2 Javadocs 0-SNAPSHOT API)

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

All Implemented Interfaces:

FitFunction
```
public class Gaussian
extends Object
implements FitFunction
```
A n-dimensional, symmetric Gaussian peak function.
This fitting target function is defined over dimension n, by the following n+2 parameters:
```
 k = 0..n-1  - x₀ᵢ (with i = k)
 k = n       - A
 k = n+1           - b
 
```
with
```
 f(x) = A × exp( - S )
 
```
and
```
 S = b × ∑ (xᵢ - x₀ᵢ)²
 
```
Author:

Jean-Yves Tinevez - 2013

Constructor Summary

Constructors
Constructor and Description

Gaussian()

Constructors
Constructor and Description
`Gaussian()`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`grad(double[] x, double[] a, int k)` Partial derivatives indices are ordered as follow:
`double`	`hessian(double[] x, double[] a, int rIn, int cIn)` Evaluates the hessian value of the function, taken with respect to the `r`^th and `c`^th parameters, evaluated at point `x`.
`String`	`toString()`
`double`	`val(double[] x, double[] a)` Evaluates this function at point `x`.

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

- Constructor Detail
  - Gaussian
```
public Gaussian()
```
- Method Detail
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - val
```
public final double val(double[] x,
                        double[] a)
```
    Description copied from interface: FitFunction
    
    Evaluates this function at point x. The function is otherwise defined over an array of parameters a, that is the target of the fitting procedure.
    
    Specified by:
    
    val in interface FitFunction
    
    Parameters:
    
    x - the multidimensional to evaluate the function at
    
    a - the set of parameters that defines the function
    
    Returns:
    
    a double value, the function evaluated at x
  - grad
```
public final double grad(double[] x,
                         double[] a,
                         int k)
```
    Partial derivatives indices are ordered as follow:
```
k = 0..n-1  - x_i (with i = k)
k = n       - A
k = n+1     - b
```
    Specified by:
    
    grad in interface FitFunction
    
    Parameters:
    
    x - the point to evaluate the gradient at
    
    a - the set of parameters that defines the function
    
    k - the index of the parameter to compute the gradient
    
    Returns:
    
    the kth component of the gradient df(x,a)/da_k
    
    See Also:
    
    FitFunction.val(double[], double[])
  - hessian
```
public final double hessian(double[] x,
                            double[] a,
                            int rIn,
                            int cIn)
```
    Description copied from interface: FitFunction
    
    Evaluates the hessian value of the function, taken with respect to the r^th and c^th parameters, evaluated at point x.
    
    Specified by:
    
    hessian in interface FitFunction
    
    Parameters:
    
    x - the point to evaluate the gradient at
    
    a - the set of parameters that defines the function
    
    rIn - the index of the first parameter to compute the gradient
    
    cIn - the index of the second parameter to compute the gradient
    
    Returns:
    
    the (r, c) element of the hessian matrix d²f(x,a)/(da_r da_c)
    
    See Also:
    
    FitFunction.val(double[], double[])

Class Gaussian

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Gaussian

Method Detail

toString

val

grad

hessian