jhplot.math.num.integration

Class SimpsonsIntegrator

java.lang.Object

jhplot.math.num.IterativeMethod

jhplot.math.num.integration.SimpsonsIntegrator

public class SimpsonsIntegrator
extends IterativeMethod

The extended Simpson's rule for numerically integrating functions.

For example, to evaluate definite integrals for sine, first a Function is defined:

 Function sine = new Function() {
    public double evaluate(double x) {
        return Math.sin(x);
    }}
 };
 

Then, a Simpson's integrator is created with the above function:

 SimpsonsIntegrator integrator = new SimpsonsIntegrator(sine);
 

Lastly, evaluating definite integrals is accomplished using the integrate(double, double) method:

 // integrate sine from 0 to Pi.
 double two = integrator.integrate(0.0, Math.PI);
 
 // integrate sine from Pi/2 to 2 Pi.
 double one = integrator.integrate(Math.PI / 2.0, Math.PI);
 

References:

1. Eric W. Weisstein. "Newton-Cotes Formulas." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Newton-CotesFormulas.html
2. Eric W. Weisstein. "Simpson's Rule." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SimpsonsRule.html

Since:

1.1

Nested Class Summary

Nested classes/interfaces inherited from class jhplot.math.num.IterativeMethod

IterativeMethod.IterativeState

Constructor Summary

Constructors

Constructor and Description
SimpsonsIntegrator(Function f) Create an integrator for the given function.
SimpsonsIntegrator(Function f, int iterations, double error) Create an integrator for the given function.

Method Summary

Modifier and Type	Method and Description
Function	getFunction() Access the target function.
double	integrate(double a, double b) Evaluate the definite integral from a to b.
void	setFunction(Function f) Modify the target function.

Methods inherited from class jhplot.math.num.IterativeMethod

getMaximumIterations, getMaximumRelativeError, iterate, setMaximumIterations, setMaximumRelativeError

Methods inherited from class java.lang.Object

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

Constructor Detail

SimpsonsIntegrator

public SimpsonsIntegrator(Function f)

Create an integrator for the given function.

Parameters:

f - the target function.

SimpsonsIntegrator

public SimpsonsIntegrator(Function f,
                          int iterations,
                          double error)

Create an integrator for the given function.

Parameters:

f - the target function.

iterations - maximum number of iterations.

error - maximum relative error.

Method Detail

getFunction

public Function getFunction()

Access the target function.

Returns:

the target function.

integrate

public double integrate(double a,
                        double b)
                 throws NumericException

Evaluate the definite integral from a to b.

Parameters:

a - the lower limit of integration.

b - the upper limit of integration.

Returns:

the definite integral from a to b.

Throws:

NumericException - if the integral can not be evaluated.

setFunction

public void setFunction(Function f)

Modify the target function.

Parameters:

f - the new target function.