1. 程式人生 > >蒙特卡洛演算法求PI

蒙特卡洛演算法求PI

利用蒙特卡洛法隨機生成任意點,求出PI

原始碼:


import java.awt.*;
import java.util.LinkedList;
import javax.swing.*;

public class AlgoFrame extends JFrame{

    private int canvasWidth;
    private int canvasHeight;

    public AlgoFrame(String title, int canvasWidth, int canvasHeight){

        super(title);

        this.canvasWidth = canvasWidth;
        this.canvasHeight = canvasHeight;

        AlgoCanvas canvas = new AlgoCanvas();
        setContentPane(canvas);
        pack();

        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setResizable(false);

        setVisible(true);
    }

    public AlgoFrame(String title){

        this(title, 1024, 768);
    }

    public int getCanvasWidth(){return canvasWidth;}
    public int getCanvasHeight(){return canvasHeight;}

    // data
    private MonteCarloPiData data;
    public void render(MonteCarloPiData data){
        this.data = data;
        repaint();
    }

    private class AlgoCanvas extends JPanel{

        public AlgoCanvas(){
            // 雙快取
            super(true);
        }

        @Override
        public void paintComponent(Graphics g) {
            super.paintComponent(g);

            Graphics2D g2d = (Graphics2D)g;

            // 抗鋸齒
            RenderingHints hints = new RenderingHints(
                    RenderingHints.KEY_ANTIALIASING,
                    RenderingHints.VALUE_ANTIALIAS_ON);
            hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
            g2d.addRenderingHints(hints);

            // 具體繪製
            AlgoVisHelper.setStrokeWidth(g2d, 3);
            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
            Circle circle = data.getCircle();
            AlgoVisHelper.strokeCircle(g2d, circle.getX(), circle.getY(), circle.getR());

            for(int i = 0 ; i < data.getPointsNumber() ; i ++){
                Point p = data.getPoint(i);
                if(circle.contain(p))
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
                else
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);

                AlgoVisHelper.fillCircle(g2d, p.x, p.y, 3);
            }
        }

        @Override
        public Dimension getPreferredSize(){
            return new Dimension(canvasWidth, canvasHeight);
        }
    }
}


import javax.swing.*;
import java.awt.*;
import java.awt.geom.Ellipse2D;
import java.awt.geom.GeneralPath;
import java.awt.geom.Line2D;
import java.awt.geom.Rectangle2D;
import java.lang.InterruptedException;


public class AlgoVisHelper {

    private AlgoVisHelper(){}

    public static final Color Red = new Color(0xF44336);
    public static final Color Pink = new Color(0xE91E63);
    public static final Color Purple = new Color(0x9C27B0);
    public static final Color DeepPurple = new Color(0x673AB7);
    public static final Color Indigo = new Color(0x3F51B5);
    public static final Color Blue = new Color(0x2196F3);
    public static final Color LightBlue = new Color(0x03A9F4);
    public static final Color Cyan = new Color(0x00BCD4);
    public static final Color Teal = new Color(0x009688);
    public static final Color Green = new Color(0x4CAF50);
    public static final Color LightGreen = new Color(0x8BC34A);
    public static final Color Lime = new Color(0xCDDC39);
    public static final Color Yellow = new Color(0xFFEB3B);
    public static final Color Amber = new Color(0xFFC107);
    public static final Color Orange = new Color(0xFF9800);
    public static final Color DeepOrange = new Color(0xFF5722);
    public static final Color Brown = new Color(0x795548);
    public static final Color Grey = new Color(0x9E9E9E);
    public static final Color BlueGrey = new Color(0x607D8B);
    public static final Color Black = new Color(0x000000);
    public static final Color White = new Color(0xFFFFFF);


    public static void strokeCircle(Graphics2D g, int x, int y, int r){

        Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
        g.draw(circle);
    }

    public static void fillCircle(Graphics2D g, int x, int y, int r){

        Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
        g.fill(circle);
    }

    public static void strokeRectangle(Graphics2D g, int x, int y, int w, int h){

        Rectangle2D rectangle = new Rectangle2D.Double(x, y, w, h);
        g.draw(rectangle);
    }

    public static void fillRectangle(Graphics2D g, int x, int y, int w, int h){

        Rectangle2D rectangle = new Rectangle2D.Double(x, y, w, h);
        g.fill(rectangle);
    }

    public static void setColor(Graphics2D g, Color color){
        g.setColor(color);
    }

    public static void setStrokeWidth(Graphics2D g, int w){
        int strokeWidth = w;
        g.setStroke(new BasicStroke(strokeWidth, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
    }

    public static void pause(int t) {
        try {
            Thread.sleep(t);
        }
        catch (InterruptedException e) {
            System.out.println("Error sleeping");
        }
    }

    public static void putImage(Graphics2D g, int x, int y, String imageURL){

        ImageIcon icon = new ImageIcon(imageURL);
        Image image = icon.getImage();

        g.drawImage(image, x, y, null);
    }

    public static void drawText(Graphics2D g, String text, int centerx, int centery){

        if(text == null)
            throw new IllegalArgumentException("Text is null in drawText function!");

        FontMetrics metrics = g.getFontMetrics();
        int w = metrics.stringWidth(text);
        int h = metrics.getDescent();
        g.drawString(text, centerx - w/2, centery + h);
    }

}

    import java.awt.*;
    import java.util.LinkedList;
    import javax.swing.*;

    public class AlgoVisualizer {

        private static int DELAY = 40;

        private MonteCarloPiData data;
        private AlgoFrame frame;
        private int N;

        public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){

            if(sceneWidth != sceneHeight)
                throw new IllegalArgumentException("This demo must be run in a square window!");

            this.N = N;
            Circle circle = new Circle(sceneWidth/2, sceneHeight/2, sceneWidth/2);
            data = new MonteCarloPiData(circle);

            // 初始化檢視
            EventQueue.invokeLater(() -> {
                frame = new AlgoFrame("Monte Carlo", sceneWidth, sceneHeight);

                new Thread(() -> {
                    run();
                }).start();
            });
        }

        public void run(){

            for(int i = 0 ; i < N ; i ++){

                if( i % 100 == 0) {
                    frame.render(data);
                    AlgoVisHelper.pause(DELAY);
                    System.out.println(data.estimatePi());
                }

                int x = (int)(Math.random() * frame.getCanvasWidth());
                int y = (int)(Math.random() * frame.getCanvasHeight());
                data.addPoint(new Point(x, y));
            }

        }

        public static void main(String[] args) {

            int sceneWidth = 800;
            int sceneHeight = 800;
            int N = 200000;

            AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N);
        }
    }


import java.awt.*;

public class Circle {

    private int x, y, r;

    public Circle(int x, int y, int r){
        this.x = x;
        this.y = y;
        this.r = r;
    }

    public int getX(){ return x; }
    public int getY(){ return y; }
    public int getR(){ return r; }

    public boolean contain(Point p){
        return Math.pow(p.x - x, 2) + Math.pow(p.y - y, 2) <= r*r;
    }
}


import java.util.LinkedList;
import java.awt.*;

public class MonteCarloPiData {

    private Circle circle;
    private LinkedList<Point> points;
    private int insideCircle = 0;

    public MonteCarloPiData(Circle circle){
        this.circle = circle;
        points = new LinkedList<Point>();
    }

    public Circle getCircle(){
        return circle;
    }

    public int getPointsNumber(){
        return points.size();
    }

    public Point getPoint(int i){
        if(i < 0 || i >= points.size())
            throw new IllegalArgumentException("out of bound in getPoint!");

        return points.get(i);
    }

    public void addPoint(Point p){
        points.add(p);
        if(circle.contain(p))
            insideCircle ++;
    }

    public double estimatePi(){

        if(points.size() == 0)
            return 0.0;

        int circleArea = insideCircle;
        int squareArea = points.size();
        return (double)circleArea * 4 / squareArea;
    }
}
首先隨機生成20000個點,截圖如下:

 

在再後面添個0,如下:

由於電腦問題,跑了將近1分鐘,電量警告了。兩次對比,精度提高了。

凌晨1點了,該洗洗睡了。明日再戰......