com.numericalmethod.suanshu.analysis.differentiation.univariate
Class FiniteDifference

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction
      com.numericalmethod.suanshu.analysis.differentiation.univariate.FiniteDifference

All Implemented Interfaces:

Function, RealScalarFunction

public class FiniteDifference
extends UnivariateRealFunction

A finite difference (divided by a small increment) is an approximation of the derivative of a function.

The accuracy of central difference is the best while those of forward and backward differences are more or less the same.

In general, for finite difference the higher an order of a derivative, the less accurate it gets. For example, approximating the 5-th derivative is much less accurate than approximating the 1st derivative. Also, the accuracy depends on the function to take the derivative of.

See Also:

• Wikipedia: Finite difference
• Wikipedia: Difference operator

Nested Class Summary

static class

FiniteDifference.Type the types of finite difference available

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Field Summary

UnivariateRealFunction	f the univariate function to take the derivative of
int	order the order of the derivative
FiniteDifference.Type	type the type of finite difference chosen

Constructor Summary

FiniteDifference(UnivariateRealFunction f, int order, FiniteDifference.Type type)
Construct an approximation of the derivative function for f using finite difference.

Method Summary

double	df(double x, double h) Compute the finite difference for f at x with an increment h for the n-th order using either forward, backward, or central difference.
double	evaluate(double x) Numerically evaluate the derivative of f at point x.
double	evaluate(double[] x, double h) Numerically evaluate the derivative of f at point x with step size h.

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction

dimension4Domain, dimension4Range, evaluate

Methods inherited from class java.lang.Object

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

Field Detail

f

public final UnivariateRealFunction f

the univariate function to take the derivative of

order

public final int order

the order of the derivative

type

public final FiniteDifference.Type type

the type of finite difference chosen

Constructor Detail

FiniteDifference

public FiniteDifference(UnivariateRealFunction f,
                        int order,
                        FiniteDifference.Type type)

Construct an approximation of the derivative function for f using finite difference.

Parameters:

f - a univariate function

order - the order of the derivative

type - the type of finite difference type to use, c.f., FiniteDifference.Type

Method Detail

evaluate

public double evaluate(double x)

Numerically evaluate the derivative of f at point x.

Specified by:

evaluate in class UnivariateRealFunction

Parameters:

x - the point to evaluate the derivative at

Returns:

the numerical derivative of f at point x

See Also:

Wikipedia: Practical considerations

evaluate

public double evaluate(double[] x,
                       double h)

Numerically evaluate the derivative of f at point x with step size h.

Automatically determining the step size h could be challenging, esp. when |x| is near 0. An analysis that involves f' and f'' may be needed to determine the proper step size. User may want to experiment with different h's by calling this function.

Parameters:

x - the point to evaluate the derivative of f at. Although it is a double[] array, only x[0] is used (f is univariate).

h - step size

Returns:

the numerical derivative of f at point x using step size h

df

public double df(double x,
                 double h)

Compute the finite difference for f at x with an increment h for the n-th order using either forward, backward, or central difference.

Parameters:

x - evaluate the function at x

h - the increment

Returns:

dnh[f](x)

See Also:

Wikipedia: Higher-order differences