NumericalDerivative (Fiji Javadocs 0-SNAPSHOT API)

java.lang.Object
- pal.math.NumericalDerivative

```
public class NumericalDerivative
extends Object
```
approximates numerically the first and second derivatives of a function of a single variable and approximates gradient and diagonal of Hessian for multivariate functions

Author:

Korbinian Strimmer

Constructor Summary

Constructors
Constructor and Description

NumericalDerivative()

Constructors
Constructor and Description
`NumericalDerivative()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double[]`	`diagonalHessian(MultivariateFunction f, double[] x)` determine diagonal of Hessian
`static double`	`firstDerivative(UnivariateFunction f, double x)` determine first derivative
`static double[]`	`gradient(MultivariateFunction f, double[] x)` determine gradient
`static void`	`gradient(MultivariateFunction f, double[] x, double[] grad)` determine gradient
`static double`	`secondDerivative(UnivariateFunction f, double x)` determine second derivative

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

- Constructor Detail
  - NumericalDerivative
```
public NumericalDerivative()
```
- Method Detail
  - firstDerivative
```
public static double firstDerivative(UnivariateFunction f,
                                     double x)
```
    determine first derivative
    
    Parameters:
    
    f - univariate function
    
    x - argument
    
    Returns:
    
    first derivate at x
  - secondDerivative
```
public static double secondDerivative(UnivariateFunction f,
                                      double x)
```
    determine second derivative
    
    Parameters:
    
    f - univariate function
    
    x - argument
    
    Returns:
    
    second derivate at x
  - gradient
```
public static double[] gradient(MultivariateFunction f,
                                double[] x)
```
    determine gradient
    
    Parameters:
    
    f - multivariate function
    
    x - argument vector
    
    Returns:
    
    gradient at x
  - gradient
```
public static void gradient(MultivariateFunction f,
                            double[] x,
                            double[] grad)
```
    determine gradient
    
    Parameters:
    
    f - multivariate function
    
    x - argument vector
    
    grad - vector for gradient
  - diagonalHessian
```
public static double[] diagonalHessian(MultivariateFunction f,
                                       double[] x)
```
    determine diagonal of Hessian
    
    Parameters:
    
    f - multivariate function
    
    x - argument vector
    
    Returns:
    
    vector with diagonal entries of Hessian

Class NumericalDerivative

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

NumericalDerivative

Method Detail

firstDerivative

secondDerivative

gradient

gradient

diagonalHessian