package numbercruncher.mathutils;/** * Function integrator that implements * Simpson's algorithm with parabolas. */public class SimpsonsIntegrator implements Integrator{    /** the function to integrate */  private Evaluatable integrand;    /**     * Constructor.     * @param integrand the function to integrate     */    public SimpsonsIntegrator(Evaluatable integrand)    {        this.integrand = integrand;    }    /**     * Integrate the function from a to b using Simpson's algorithm,     * and return an approximation to the area.     * (Integrator implementation.)     * @param a the lower limit     * @param b the upper limit     * @param intervals the number of equal-width intervals     * @return an approximation to the area     */    public float integrate(float a, float b, int intervals)    {        if (b <= a) return 0;        float h         = (b - a)/intervals/2;  // interval width                                                //   (split in two)        float totalArea = 0;        // Compute the area using the current number of intervals.        for (int i = 0; i < intervals; ++i) {            float x1 = a + 2*i*h;            totalArea += areaOf(x1, h);        }        return totalArea;    }    /**     * Compute the area of the ith parabolic region.     * @param x1 the left bound of the region     * @param h the interval width     * @return the area of the region     */    private float areaOf(float x1, float h)    {        float x2   = x1 + h;               // middle        float x3   = x2 + h;               // right bound of the region        float y1   = integrand.at(x1);     // value at left bound        float y2   = integrand.at(x2);     // value at the middle        float y3   = integrand.at(x3);     // value at right bound        float area = h*(y1 + 4*y2+ y3)/3;  // area of the region        return area;    }}