# Class FiniteDifference

All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction

public class FiniteDifference
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.
• ## 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:
$$\Delta^n_hf(x)$$