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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;

/**
 * 

 * The extended trapezoidal 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 trapezoidal integrator is created with the above function:
 * 
 * 
 * TrapezoidalIntegrator integrator = new TrapezoidalIntegrator(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. "Trapezoidal Rule." From MathWorld--A Wolfram Web
 * Resource. 
 * http://mathworld.wolfram.com/TrapezoidalRule.html 
 * 
 * 

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

    /**
     * The internal state used during root finding.
     */
    static class IterativeState {

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

        /** The lower limit of integration. */
        private double a;

        /** The upper limit of integration. */
        private double b;

        /** The current iteration. */
        private int n;

        /** The current definite integral approximation. */
        private double s;

        /** The number of inner abscissa points in the evaluation. */
        private int k;

        /**
         * Create a state object for the given initial root approximation.
         * 
         * @param f the target function.
         * @param low the lower limit of integration.
         * @param up the upper limit of integration.
         * @throws NumericException if function cannot be evaluated
         *         at the limits of integration.
         */
        IterativeState(Function f, double low, double up)
            throws NumericException {
            super();
            this.a = low;
            this.b = up;
            this.function = f;
            double fa = f.evaluate(low);
            double fb = f.evaluate(up);
            s = (up - low) * (fa / 2.0 + fb / 2.0);
            n = 0;
            k = 2;
        }

        /**
         * Access the current iteration.
         * 
         * @return the current iteration.
         */
        public int getIterations() {
            return n;
        }

        /**
         * Perform the next iteration of finding a root. The current state is
         * updated with the newly compuated root data.
         * 
         * @throws NumericException if the function could not be evaluated.
         */
        public void iterate() throws NumericException {
            ++n;

            // compute function at next set of points
            double sn = 0.0;
            double h = (b - a) / k;
            for (int i = k - 1; i >= 1; i -= 2) {
                double x = a + (i * h);
                sn += function.evaluate(x);
            }
            sn = (0.5 * s) + (h * sn);

            k *= 2;
            s = sn;
        }

        /**
         * Access the result of this root finding.
         * 
         * @return the root.
         */
        public double getResult() {
            return s;
        }
    }

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

    /**
     * Create an integrator for the given function.
     * 
     * @param f the target function.
     */
    public TrapezoidalIntegrator(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 TrapezoidalIntegrator(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 {
        IterativeState state = new IterativeState(function, a, b);

        double s = state.getResult();
        double sn = s;
        double error = Double.MAX_VALUE;
        do {
            state.iterate();
            sn = state.getResult();
            error = Math.abs(sn / s - 1.0);
            s = sn;
        } while (state.getIterations() < getMaximumIterations()
            && error > getMaximumRelativeError());

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

        return s;
    }

    /**
     * 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;
    }
}