使用Java中随机生成的数据进行pi的Monte Carlo计算

我正在开发一个程序,该程序根据表示图表上x,y坐标的随机生成的浮点数来计算pi.每个x,y坐标乘以2的幂,然后存储在两个单独的数组中.坐标均匀地分布在间隔为0.1的图形上.

程序将x,y坐标相加,如果它们小于1,则这些点位于直径1的圆内,如下图所示.

然后我用公式

π≈4 w / n

制定圆周率.其中,w是圆内点的计数,n是数组内x或y坐标的数量.

当我将n设置为最大10,000,000(数组的大小)时,它将生成最精确的pi(15-16位小数位)计算.但是,在将4GB RAM分配给运行配置并将n设置为100,000,000 pi后,最终为0.6710 …

我想知道为什么会这样吗？抱歉,这是一个愚蠢的问题.代码在下面.

import java.text.DecimalFormat;
import java.util.Random;

public class random_pi {

    public random_pi() {

        float x2_store[] = new float[10000000];
        float y2_store[] = new float[10000000];
        float w = 0;

        Random rand = new Random();
        DecimalFormat df2 = new DecimalFormat("#,###,###");

        for (int i = 0; i < x2_store.length; i  ) {
            float x2 = (float) Math.pow(rand.nextFloat(), 2);
            x2_store[i] = x2;
            float y2 = (float) Math.pow(rand.nextFloat(), 2);
            y2_store[i] = y2;
        }

        for (int i = 0; i < x2_store.length; i  ) {
            if (x2_store[i]   y2_store[i] < 1) {
                w  ;
            }
        }

        System.out.println("w: " w);
        float numerator = (4*w);
        System.out.printf("4*w: "   (numerator));
        System.out.println("\nn: "   df2.format(x2_store.length));
        float pi = numerator / x2_store.length;

        String fmt = String.format("%.20f", pi);
        System.out.println(fmt);

        String pi_string = Double.toString(Math.abs(pi));
        int intP = pi_string.indexOf('.');
        int decP = pi_string.length() - intP - 1;
        System.out.println("decimal places: "   decP);
    }

    public static void main(String[] args) {
        new random_pi();
    }
}

解决方法:

问题在这里：

float w = 0;
float numerator = (4*w);

浮点精度不够,请将其更改为int或double：

像这样的工作示例代码：

import java.text.DecimalFormat;
import java.util.Random;

public class random_pi {

    public random_pi() {

        float x2_store[] = new float[100000000];
        float y2_store[] = new float[100000000];
        int w = 0;

        Random rand = new Random();
        DecimalFormat df2 = new DecimalFormat("#,###,###");

        for (int i = 0; i < x2_store.length; i  ) {
            float x2 = (float) Math.pow(rand.nextFloat(), 2);
            x2_store[i] = x2;
            float y2 = (float) Math.pow(rand.nextFloat(), 2);
            y2_store[i] = y2;
        }

        for (int i = 0; i < x2_store.length; i  ) {
            if (x2_store[i]   y2_store[i] < 1) {
                w  ;
            }
        }

        System.out.println("w: " w);
        int numerator = (4*w);
        System.out.printf("4*w: "   (numerator));
        System.out.println("\nn: "   df2.format(x2_store.length));
        float pi = ((float)numerator) / x2_store.length;

        String fmt = String.format("%.20f", pi);
        System.out.println(fmt);

        String pi_string = Double.toString(Math.abs(pi));
        int intP = pi_string.indexOf('.');
        int decP = pi_string.length() - intP - 1;
        System.out.println("decimal places: "   decP);
    }

    public static void main(String[] args) {
        new random_pi();
    }
}

输出：

w: 78544041
4*w: 314176164
n: 100,000,000
3.14176154136657700000
decimal places: 15

而且您不需要存储结果,例如以下工作示例代码：

import java.text.DecimalFormat;
import java.util.Random;

public class pi {

    public pi() {
        double n=100000000; 
        double w = 0;

        Random rand = new Random();
        DecimalFormat df2 = new DecimalFormat("#,###,###");

        for (int i = 0; i < n; i  ) {
            double x = rand.nextFloat(); 
            double y = rand.nextFloat();  
            if ((x*x   y*y) < 1.0) w  ;
        }

        System.out.println("w: " w);//w: 7852372.0
        double numerator = (4*w);
        System.out.printf("4*w: "   (numerator));//4*w: 3.1409488E7
        System.out.println("\nn: "   df2.format(n));//n: 10,000,000
        double pi = numerator / n;

        final String fmt = String.format("%.20f", pi);
        System.out.println(fmt);//3.14094877243042000000

        String pi_string = Double.toString(Math.abs(pi));
        int intP = pi_string.indexOf('.');
        int decP = pi_string.length() - intP - 1;
        System.out.println("decimal places: "   decP);//decimal places: 14
    }

    public static void main(String[] args) {
        new random_pi();
    }
}

输出：

w: 78539606
4*w: 314158424
n: 100,000,000
3.14158439636230470000
decimal places: 16

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