Class FiniteDifference
- java.lang.Object
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- dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction
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- dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction
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- dev.nm.analysis.differentiation.univariate.FiniteDifference
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- 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.
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
FiniteDifference.Type
the available types of finite difference-
Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function
Function.EvaluationException
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Constructor Summary
Constructors Constructor Description FiniteDifference(UnivariateRealFunction f, int order, FiniteDifference.Type type)
Construct an approximate derivative function for f using finite difference.
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Method Summary
All Methods Instance Methods Concrete Methods 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
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Methods inherited from class dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction
dimensionOfDomain, dimensionOfRange
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface dev.nm.analysis.function.Function
dimensionOfDomain, dimensionOfRange
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Constructor Detail
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FiniteDifference
public FiniteDifference(UnivariateRealFunction f, int order, FiniteDifference.Type type)
Construct an approximate derivative function for f using finite difference.- Parameters:
f
- a univariate functionorder
- the order of the derivativetype
- the type of finite difference to use, c.f.,FiniteDifference.Type
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Method Detail
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evaluate
public double evaluate(double x)
Description copied from interface:UnivariateRealFunction
Evaluate y = f(x).- Parameters:
x
- x- Returns:
- f(x)
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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 ath
- step size- Returns:
- f'(x), the numerical derivative of f at point x with step size h
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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 ath
- the increment- Returns:
- \(\Delta^n_hf(x)\)
- See Also:
- Wikipedia: Higher-order differences
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