Example: HyperRectangle Quadrature

This example evaluates the following multidimensional integral, with n =10.
\int_{a_{n-1}}^{b_{n-1}} \cdots \int_{a_0}^{b_0} \left[ \sum_{i=0}^n (-1)^i \prod_{j=0}^i x_j \right] \, dx_0 \ldots dx_{n-1} = \frac{1}{3}\left[ 1-\left(-\frac{1}{2}\right)^n\right] 

import com.imsl.math.*;

public class HyperRectangleQuadratureEx1 {

    public static void main(String args[]) {

        HyperRectangleQuadrature.Function fcn
                = new HyperRectangleQuadrature.Function() {
                    public double f(double x[]) {
                        int sign = 1;
                        double sum = 0.0;
                        for (int i = 0; i < x.length; i++) {
                            double prod = 1.0;
                            for (int j = 0; j <= i; j++) {
                                prod *= x[j];
                            }
                            sum += sign * prod;
                            sign = -sign;
                        }
                        return sum;
                    }
                };

        HyperRectangleQuadrature q = new HyperRectangleQuadrature(10);
        double result = q.eval(fcn);
        System.out.println("result = " + result);
    }
}

Output

result = 0.3331253832089543
Link to Java source.