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package jhplot.math.num;


/**
 * 

 * This class provides the means to evaluate infinite power series (1). To
 * create a power series, authors subclass this class and provided a concrete
 * term method.
 * 
 * 

 * For example, this is the power series for the exponential function defined by
 * (2):
 * 
 * 
 * PowerSeries exponential = new PowerSeries() {
 *     public double getTerm(int n) {
 *         return 1.0 / factorial(n);
 *     }
 * 
 *     private double factorial(int n) {
 *         double p = 1.0;
 *         while(n > 1.0) {
 *             p *= n--;
 *         }
 *         return p;
 *     }
 * }
 * 
 * 
 * 

 * 

 * References:
 * 

 * 
 Eric W. Weisstein. "Power Series." From MathWorld--A Wolfram Web
 * Resource. 
 * http://mathworld.wolfram.com/PowerSeries.html 
 * 
 Exponential Function: Series Representation. 
 * http://functions.wolfram.com/01.03.06.0002.01 
 * 
 * 

 * 
 * @since 1.1
 * @version $Revision: 1.2 $ $Date: 2007/10/25 04:44:14 $
 */
public abstract class PowerSeries extends IterativeMethod {

    /** Index of the first term in this series. */
    private int firstIndex;

    /**
     * Default constructor.
     */
    protected PowerSeries() {
        this(100, 1.0e-15);
    }

    /**
     * Create a series with the given number of maximum iterations and maximum
     * relative error.
     * 
     * @param iterations maximum number of iterations.
     * @param error maximum relative error.
     */
    protected PowerSeries(int iterations, double error) {
        this(0, iterations, error);
    }

    /**
     * Create a series with the given first term index, number of maximum
     * iterations and maximum relative error.
     * 
     * @param index index of first term in this series.
     * @param iterations maximum number of iterations.
     * @param error maximum relative error.
     */
    protected PowerSeries(int index, int iterations, double error) {
        super(iterations, error);
        setFirstIndex(index);
    }

    /**
     * Evaluate this series at the given value.
     * 
     * @param x the point of evalutation.
     * @return the value of this series evaluated at x.
     * @throws NumericException if the series could not be evaluated.
     */
    public double evaluate(double x) throws NumericException {

        int n = getFirstIndex();
        double z = Math.pow(x, n);
        double t = getTerm(n) * z;
        double s = t;
        double sn = s;
        double error = Double.MAX_VALUE;

        do {
            ++n;
            z *= x;
            sn = s + (getTerm(n) * z);
            error = Math.abs(sn / s - 1.0);
            s = sn;
        } while (n < getMaximumIterations()
            && Math.abs(error) > getMaximumRelativeError());

        if (n >= getMaximumIterations()) {
            throw new ConvergenceException("Power series failed to converge.");
        }

        return s;
    }

    /**
     * Access the n-th term for this series.
     * 
     * @param n the term index.
     * @return the n-th series term.
     */
    protected abstract double getTerm(int n);

    /**
     * Access this first term index.
     * 
     * @return the first term index.
     */
    private int getFirstIndex() {
        return firstIndex;
    }

    /**
     * Modify the first term index.
     * 
     * @param index The new first term index.
     */
    private void setFirstIndex(int index) {
        this.firstIndex = index;
    }
}