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] 
using System;
using Imsl.Math;

public class HyperRectangleQuadratureEx1 : 
	HyperRectangleQuadrature.IFunction
{
	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;
	}

	public static void  Main(String[] args)
	{
		HyperRectangleQuadrature q = new HyperRectangleQuadrature(10);
		double result = q.Eval(new HyperRectangleQuadratureEx1());
		Console.Out.WriteLine("result = " + result);
	}
}

Output

result = 0.333125383208954
Link to C# source.