java - Java 中的二重积分和期望值蒙特卡洛方法

Question

以下算法适用于一维情况，但我想修改它以处理二重积分。我该怎么做？

class doubleIntMonteCarlo
{
    private static double f(double x)
    {
        return 1 / Math.pow( x , 2 );
    }

    public static double doubleIntMonteCarlo(double a, double b, int n)
    {
        double xSum = 0D, ySum = 0D, sum = 0D;

        for (int i = 0; i < n; i++)
        {
            xSum = a + Math.random() * Math.abs( b - a );
            sum += f(xSum);
        }
        return Math.abs( b - a ) * sum / n;
    }
}

public class MonteCarloIntegration 
{
    public static void main(String[] args) 
    {
        System.out.println(doubleIntMonteCarlo.doubleIntMonteCarlo(10, 250, 100000));
    }
}

Answer 1

试试这个:

public static double doubleIntMonteCarlo(double a, double b, double c, double d, int n)
{
     double sum = 0D, xSum = 0D, ySum = 0D;

     for (int i = 0; i < n; i++)
     {
           xSum = a + Math.random() * Math.abs(b - a);
           ySum = c + Math.random() * Math.abs(d - c);
           sum += f(xSum, ySum);
     }
     return Math.abs(b - a) * Math.abs(d - c) * sum / n;
}