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 * Copyright (c) 2005, DoodleProject
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package jhplot.math.num.integration;

import jhplot.math.num.ConvergenceException;
import jhplot.math.num.Function;
import jhplot.math.num.IterativeMethod;
import jhplot.math.num.NumericException;
import jhplot.math.num.integration.TrapezoidalIntegrator;

/**
 * 

 * The extended Simpson's rule for numerically integrating functions.
 * 
 * 

 * For example, to evaluate definite integrals for sine, first a
 * {@link jhplot.math.num.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
 * {@link #integrate} 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:
 * 

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

 * 
 * @version $Revision: 1.2 $ $Date: 2007/10/25 04:44:16 $
 * @since 1.1
 */
public class SimpsonsIntegrator extends IterativeMethod {

    /** the target function. */
    private Function function;

    /**
     * Create an integrator for the given function.
     * 
     * @param f the target function.
     */
    public SimpsonsIntegrator(Function f) {
        this(f, 100, 1.0e-10);
    }

    /**
     * Create an integrator for the given function.
     * 
     * @param f the target function.
     * @param iterations maximum number of iterations.
     * @param error maximum relative error.
     */
    public SimpsonsIntegrator(Function f, int iterations, double error) {
        super(iterations, error);
        setFunction(f);
    }

    /**
     * Access the target function.
     * 
     * @return the target function.
     */
    public Function getFunction() {
        return function;
    }

    /**
     * Evaluate the definite integral from a to b.
     * 
     * @param a the lower limit of integration.
     * @param b the upper limit of integration.
     * @return the definite integral from a to b.
     * @throws NumericException if the integral can not be evaluated.
     */
    public double integrate(double a, double b) throws NumericException {
        TrapezoidalIntegrator.IterativeState state = new TrapezoidalIntegrator.IterativeState(
            function, a, b);

        double sumTrapezoidal = state.getResult();
        double sumTrapezoidalNext = sumTrapezoidal;
        double error = Double.MAX_VALUE;
        double sumSimpons = sumTrapezoidal;
        do {
            state.iterate();
            sumTrapezoidalNext = state.getResult();
            double sumSimponsNext = (4.0 * sumTrapezoidalNext / 3.0)
                - (sumTrapezoidal / 3.0);
            error = Math.abs(sumSimponsNext / sumSimpons - 1.0);
            sumTrapezoidal = sumTrapezoidalNext;
            sumSimpons = sumSimponsNext;
        } while (state.getIterations() < getMaximumIterations()
            && error > getMaximumRelativeError());

        if (state.getIterations() >= getMaximumIterations()) {
            throw new ConvergenceException(
                "Simpson's integration failed to converge.");
        }

        return sumSimpons;
    }

    /**
     * Modify the target function.
     * 
     * @param f the new target function.
     */
    public void setFunction(Function f) {
        if (f == null) {
            throw new IllegalArgumentException("Function can not be null.");
        }
        this.function = f;
    }
}