Package dev.nm.analysis.differentiation.univariate

Class FiniteDifference

java.lang.Object

dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

dev.nm.analysis.differentiation.univariate.FiniteDifference

All Implemented Interfaces:

Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction

public class FiniteDifference
extends AbstractUnivariateRealFunction

A finite difference (divided by a small increment) is an approximation of the derivative of a function. The accuracy depends on the function to take the derivative of. In general, the accuracy of central difference is the best while those of forward and backward differences are more or less the same. 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.

See Also:

• • Wikipedia: Finite difference
  • Wikipedia: Difference operator
  • Wikipedia: Practical considerations

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	FiniteDifference.Type	the available types of finite difference

Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor	Description
FiniteDifference(UnivariateRealFunction f, int order, FiniteDifference.Type type)	Construct an approximate derivative function for f using finite difference.

Method Summary

Modifier and Type	Method	Description
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)	Evaluate y = f(x).
double	evaluate(double x, double h)	Evaluate numerically the derivative of f at point x, f'(x), with step size h.

Methods inherited from class dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

evaluate

Methods inherited from class dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dimensionOfDomain, dimensionOfRange

Methods inherited from class java.lang.Object

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

Methods inherited from interface dev.nm.analysis.function.Function

dimensionOfDomain, dimensionOfRange

Constructor Details

FiniteDifference

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

Construct an approximate derivative function for f using finite difference.

Parameters:

f - a univariate function

order - the order of the derivative

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

Method Details

evaluate

public double evaluate(double x)

Description copied from interface: UnivariateRealFunction

Evaluate y = f(x).

Parameters:

x - x

Returns:

f(x)

evaluate

public double evaluate(double x,
 double h)

Evaluate numerically the derivative of f at point x, f'(x), with step size h. It could be challenging to automatically determine the step size h, esp. when |x| is near 0. It may, for example, require an analysis that involves f' and f''. The user may want to experiment with different hs by calling this function.

Parameters:

x - the point to evaluate the derivative of f at

h - step size

Returns:

f'(x), the numerical derivative of f at point x with 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 - the point to evaluate the function at

h - the increment

Returns:

\(\Delta^n_hf(x)\)

See Also:

• Wikipedia: Higher-order differences