public class Ridders extends java.lang.Object implements RealScalarFunction
FiniteDifference.
Ridders' method tries a sequence of decreasing h's to compute the derivatives,
and then extrapolate to zero using Neville's algorithm.
The choice of the initial h is critical.
If h is too big, the value computed could be inaccurate.
If h is too small, due to rounding error, we might be computing the "same" value over and over again for different h's.Function.EvaluationException| Constructor and Description |
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Ridders(RealScalarFunction f,
int[] varidx)
Construct the derivative function of a vector-valued function using Ridder's method.
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Ridders(RealScalarFunction f,
int[] varidx,
double rate,
int discretization)
Construct the derivative function of a vector-valued function using Ridder's method.
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Ridders(UnivariateRealFunction f,
int order)
Construct the derivative function of a univariate function using Ridder's method.
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Ridders(UnivariateRealFunction f,
int order,
double rate,
int discretization)
Construct the derivative function of a univariate function using Ridder's method.
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| Modifier and Type | Method and Description |
|---|---|
int |
dimensionOfDomain()
Get the number of variables the function has.
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int |
dimensionOfRange()
Get the dimension of the range space of the function.
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double |
evaluate(double x)
Evaluate f'(x), where f is a
UnivariateRealFunction. |
java.lang.Double |
evaluate(Vector x)
Evaluate the function f at x, where x is from the domain.
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double |
evaluate(Vector x,
double h)
Evaluate numerically the derivative of f at point x, f'(x), with step size h.
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public Ridders(UnivariateRealFunction f, int order, double rate, int discretization)
f - the UnivariateRealFunction to take derivative oforder - the order of differentiationrate - the rate at which the increment h decreases; rate should be a simple number such as 0.75, not like 0.66666666666...discretization - the number of points for extrapolationpublic Ridders(UnivariateRealFunction f, int order)
f - the UnivariateRealFunction to take derivative oforder - the order of the derivativepublic Ridders(RealScalarFunction f, int[] varidx, double rate, int discretization)
varidx = new int[]{1, 2} means
\[
f_{x_1,x_2} = {\partial^2 f \over \partial x_1 \partial x_2} = {\partial \over \partial x_2}{\partial \over \partial x_1}
\]
The indices count from 1 up to the number of variables of f,
i.e., the domain dimension of f.f - the multivariate function to take derivative ofvaridx - specify the variable indices, numbering from 1 up to the domain dimension of frate - rate should be a simple number, not like 0.66666666666...discretization - the number of points used for extrapolationpublic Ridders(RealScalarFunction f, int[] varidx)
varidx = new int[]{1, 2} means
\[
f_{x_1,x_2} = {\partial^2 f \over \partial x_1 \partial x_2} = {\partial \over \partial x_2}{\partial \over \partial x_1}
\]
The indices count from 1 up to the number of variables of f,
i.e., the domain dimension of f.f - the real multivariate function to take derivative ofvaridx - specify the variable indices, numbering from 1 up to the domain dimension of fpublic java.lang.Double evaluate(Vector x)
evaluate in interface Function<Vector,java.lang.Double>x - the point to evaluate the derivative of f atpublic double evaluate(double x)
UnivariateRealFunction.x - the point to evaluate the derivative of f atpublic double evaluate(Vector x, double h)
x - the point to evaluate f ath - the step sizepublic int dimensionOfDomain()
FunctiondimensionOfDomain in interface Function<Vector,java.lang.Double>public int dimensionOfRange()
FunctiondimensionOfRange in interface Function<Vector,java.lang.Double>