math.numerics
Class Derivative

java.lang.Object
  math.numerics.Derivative

public class Derivative
extends java.lang.Object

Class Integral defines various derivative algorithms. This class cannot be subclassed or instantiated because all methods are static.

Author:

Wolfgang Christian

Method Summary

static double	centered(Function f, double x, double h) Calculates the derivative of a function using the centered difference approximation.
static double	centeredPartial(MultiVarFunction f, double[] x, int n, double tol)
static double[][]	fillArray(Function f, double start, double stop, double tol, double[][] data) Fills an array with the derivatives of a function.
static double[][]	fillArray(Function f, double start, double stop, double tol, int n)
static double	romberg(Function f, double x0, double h, double tol) Calculates the derivative using the Romberg scheme for Richardson extrapolation.
static double	second(Function f, double x, double tol)
static double[][]	secondFillArray(Function f, double start, double stop, double tol, double[][] data) Fills an array with the second derivative of a function.
static double[][]	secondFillArray(Function f, double start, double stop, double tol, int n) Fills an array with the second derivative of a function.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

romberg

public static double romberg(Function f,
                             double x0,
                             double h,
                             double tol)

Calculates the derivative using the Romberg scheme for Richardson extrapolation. This method runs until all Romberg rows are filled or until the step size drops below defaultNumericalPrecision or if the desired tolerance is reached.

Parameters:

f - the function

x0 - where derivative is to be calculated

h - initial step size

tol - desired accuracy

Returns:

centered

public static double centered(Function f,
                              double x,
                              double h)

Calculates the derivative of a function using the centered difference approximation.

Parameters:

f - the function

x - the x value

h -

Returns:

centeredPartial

public static double centeredPartial(MultiVarFunction f,
                                     double[] x,
                                     int n,
                                     double tol)

second

public static double second(Function f,
                            double x,
                            double tol)

secondFillArray

public static double[][] secondFillArray(Function f,
                                         double start,
                                         double stop,
                                         double tol,
                                         int n)

Fills an array with the second derivative of a function.

Parameters:

f -

start -

stop -

tol -

n -

Returns:

secondFillArray

public static double[][] secondFillArray(Function f,
                                         double start,
                                         double stop,
                                         double tol,
                                         double[][] data)

Fills an array with the second derivative of a function.

Parameters:

f - Function

start - double

stop - double

tol - double

data - double[][]

Returns:

double[][]

fillArray

public static double[][] fillArray(Function f,
                                   double start,
                                   double stop,
                                   double tol,
                                   double[][] data)

Fills an array with the derivatives of a function.

Parameters:

f -

start -

stop -

tol -

data -

Returns:

fillArray

public static double[][] fillArray(Function f,
                                   double start,
                                   double stop,
                                   double tol,
                                   int n)