import java.awt.*; import java.awt.event.*; import java.text.DecimalFormat; import java.applet.Applet; import javax.swing.JLabel; import javax.swing.JTextField; public class GaussNewton extends Applet implements ActionListener{ // variable set private static final long serialVersionUID = -1173026208646241820L; public static double r = 1.0; public static double k = 1.0; public static double c = 1.0; public static double[] s1 = new double[1000]; public static double[] s2 = new double[1000]; public static double[] s3 = new double[1000]; public static double[] se1 = new double[1000]; public static double[] k0 = new double[1000]; public static double[] r0 = new double[1000]; public static double[] c0 = new double[1000]; public static double[] dk = new double[1000]; public static double[] dr = new double[1000]; public static double[] dc = new double[1000]; public static double[] k3 = new double [3]; public static double[] k4 = new double [3]; public static double[] r3 = new double [3]; public static int[] xxxx = new int [1000]; public static int[] yyyy = new int [1000]; public static int[] xxxx1 = new int [1000]; public static int[] yyyy1 = new int [1000]; public static double[][] Matrix = new double[3][3]; public static double[][] MatrixL = new double[3][3]; public static double[][] MatrixU = new double[3][3]; public static double[][] MatrixU1 = new double[3][3]; JTextField yx = new JTextField("1.0"); JTextField yn = new JTextField("1.0"); JTextField yr = new JTextField("1.0"); JLabel label1 = new JLabel("The Example of The Gauss-Newton algorithm", JLabel.CENTER); JLabel label2 = new JLabel("The Growth Rate (0<r≤10⁸)",JLabel.CENTER); JLabel label3 = new JLabel("The Carrying Capacity (0<K≤10⁸)",JLabel.CENTER); JLabel label4 = new JLabel("The Integration Constant (-10⁸<λ≤10⁸)", JLabel.CENTER); public void init(){ label1.setPreferredSize(new Dimension(416,24)); label1.setFont(new Font("Serif",Font.BOLD,14)); add(label1); label2.setPreferredSize(new Dimension(260,23)); label2.setFont(new Font("Serif",Font.BOLD,11)); add(label2); yx.setPreferredSize(new Dimension(80,23)); add(yx); label3.setPreferredSize(new Dimension(260,23)); label3.setFont(new Font("Serif",Font.BOLD,11)); add(label3); yn.setPreferredSize(new Dimension(80,23)); add(yn); label4.setPreferredSize(new Dimension(260,23)); label4.setFont(new Font("Serif",Font.BOLD,11)); add(label4); yr.setPreferredSize(new Dimension(80,23)); add(yr); yx.addActionListener(this); yn.addActionListener(this); yr.addActionListener(this); } public void actionPerformed(ActionEvent e){ if(e.getSource()==yx){ r=Double.valueOf(yx.getText()).doubleValue(); if(r <= 0 || r > Math.pow(10.0,8)){ r = 1.0; } } if(e.getSource()==yn){ k = Double.valueOf(yn.getText()).doubleValue(); if(k <= 0 || k > Math.pow(10.0,8)){ k = 1.0; } } if(e.getSource()==yr){c = Double.valueOf(yr.getText()).doubleValue(); if(c < -Math.pow(10.0,8) || c > Math.pow(10.0,8)){c = 1.0;} } yx.setText(""+r); yn.setText(""+k); yr.setText(""+c); repaint(); } public void paint(Graphics g){ s1[0] = (Math.log(Math.abs(c))+Math.log(k)-Math.log(999))/r; s1[999] = (Math.log(Math.abs(c))+Math.log(k)+Math.log(999))/r; double aa=(s1[999]-s1[0])/999; s2[0]=function(k,r,c,s1[0]); s2[999]=function(k,r,c,s1[999]); for(int i=1;i<999;i++){ s1[i]=s1[i-1]+aa; } for(int i=1;i<999;i++){ s2[i]=function(k,r,c,s1[i]); } for(int i=0;i<1000;i++){ se1[i]=normal.sampleNormal(0,k/50); } for(int i=0;i<1000;i++){ s3[i]=s2[i]+se1[i]; } for(int i=0;i<3;i++){ for(int j=0;j<3;j++){ Matrix[i][j]=0; } } k0[0]=k; r0[0]=r; c0[0]=c; for(int h=0;h<999;h++){ for(int i=0;i<1000;i++){ dk[i] = (1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i]))-k0[h]*c0[h]*Math.exp(r0[h]*(-s1[i])))/Math.pow(1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i])),2); dr[i] = -Math.pow(k0[h],2)*(-s1[i])*c0[h]*Math.exp(r0[h]*(-s1[i]))/Math.pow(1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i])),2); dc[i] = -Math.pow(k0[h],2)*Math.exp(r0[h]*(-s1[i]))/Math.pow(1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i])),2); Matrix[0][0]=Matrix[0][0]+Math.pow(dk[i],2); Matrix[0][1]=Matrix[0][1]+dk[i]*dr[i]; Matrix[0][2]=Matrix[0][2]+dk[i]*dc[i]; Matrix[1][0]=Matrix[1][0]+dr[i]*dk[i]; Matrix[1][1]=Matrix[1][1]+Math.pow(dr[i],2); Matrix[1][2]=Matrix[1][2]+dr[i]*dc[i]; Matrix[2][0]=Matrix[2][0]+dc[i]*dk[i]; Matrix[2][1]=Matrix[2][1]+dc[i]*dr[i]; Matrix[2][2]=Matrix[2][2]+Math.pow(dc[i],2); } MatrixU[0][0]=Matrix[0][0]; MatrixU[0][1]=Matrix[0][1]; MatrixU[0][2]=Matrix[0][2]; MatrixU[1][0]=0; MatrixU[1][1]=Matrix[1][1]-Matrix[0][1]*Matrix[1][0]/Matrix[0][0]; MatrixU[1][2]=Matrix[1][2]-Matrix[0][2]*Matrix[1][0]/Matrix[0][0]; MatrixU[2][0]=0; MatrixU[2][1]=Matrix[2][1]-Matrix[0][1]*Matrix[2][0]/Matrix[0][0]; MatrixU[2][2]=Matrix[2][2]-Matrix[0][2]*Matrix[2][0]/Matrix[0][0]; MatrixU1[2][0]=0; MatrixU1[2][1]=0; MatrixU1[2][2]=MatrixU[2][2]-MatrixU[1][2]*MatrixU[2][1]/MatrixU[1][1]; MatrixL[0][0]=1; MatrixL[0][1]=0; MatrixL[0][2]=0; MatrixL[1][0]=Matrix[1][0]/Matrix[0][0]; MatrixL[1][1]=1; MatrixL[1][2]=0; MatrixL[2][0]=Matrix[2][0]/Matrix[0][0]; MatrixL[2][1]=MatrixU[2][1]/MatrixU[1][1]; MatrixL[2][2]=1; r3[0]=0; r3[1]=0; r3[2]=0; for(int i=0;i<1000;i++){ r3[0]=r3[0]-dk[i]*(k0[h]/(1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i])))-s3[i]); r3[1]=r3[1]-dr[i]*(k0[h]/(1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i])))-s3[i]); r3[2]=r3[2]-dc[i]*(k0[h]/(1+c0[h]*k0[h]*Math.exp(r0[h]*(-s1[i])))-s3[i]); } k4[0]=r3[0]; k4[1]=r3[1]-MatrixL[1][0]*k4[0]; k4[2]=r3[2]-MatrixL[2][0]*k4[0]-MatrixL[2][1]*k4[1]; k3[2]=k4[2]/MatrixU1[2][2]; k3[1]=(k4[1]-MatrixU[1][2]*k3[2])/MatrixU[1][1]; k3[0]=(k4[0]-MatrixU[0][1]*k3[1]-MatrixU[0][2]*k3[2])/MatrixU[0][0]; k0[h+1]=k0[h]+k3[0]; r0[h+1]=r0[h]+k3[1]; c0[h+1]=c0[h]+k3[2]; } double minss3 = s3[0]; double maxss3 = s3[0]; if(c>=0){ for(int i=0;i<1000;i++){ if(s3[i]>maxss3){ maxss3 = s3[i]; } } for(int i=0;i<1000;i++){ if(s3[i]maxss3){ maxss3 = s3[i]; } } for(int i=0;i<475;i++){ if(s3[i]=0){ for (int i=0;i<1000;i++){ g2.fillOval(xxxx[i], yyyy[i], 4, 4); } } if(c<0){ for (int i=0;i<475;i++){ g2.fillOval(xxxx[i], yyyy[i], 4, 4); } for (int i=525;i<1000;i++){ g2.fillOval(xxxx[i], yyyy[i], 4, 4); } } GradientPaint gp3 = new GradientPaint(33, 227, new Color(79,129,189), 33,418,new Color(65,105,225), true); g2.setPaint(gp3); BasicStroke BoldLine = new BasicStroke(2.8f); g2.setStroke(BoldLine); if(c>=0){ for (int i=1;i<1000;i++){ g2.drawLine(xxxx1[i-1], yyyy1[i-1], xxxx1[i], yyyy1[i]); } } if(c<0){ for (int i=1;i<475;i++){ g2.drawLine(xxxx1[i-1], yyyy1[i-1], xxxx1[i], yyyy1[i]); } for (int i=526;i<1000;i++){ g2.drawLine(xxxx1[i-1], yyyy1[i-1], xxxx1[i], yyyy1[i]); } } DecimalFormat df0 = new DecimalFormat("0.00"); DecimalFormat df1 = new DecimalFormat("0.000"); DecimalFormat df2 = new DecimalFormat("0.000000"); for(int i=0;i<5;i++){ g2.setFont(new Font ("Serif",Font.BOLD,12)); g2.setColor (new Color(0,0,0)); String subx = df1.format(s1[0+249*i]); g2.drawString(subx,14+88*i,488); } for(int i=1;i<5;i++){ g2.setFont(new Font ("Serif",Font.BOLD,12)); g2.setColor (new Color(0,0,0)); String suby = df0.format(maxss3/4*i); g2.drawString(suby,3,484-87*i); } g2.setFont(new Font ("Serif",Font.BOLD,12)); g2.setColor (new Color(0,0,0)); g2.drawString("n = 1000",280,367); g2.drawString("r",280,387); g2.drawString("*",290,386); g2.drawString(" =",293,387); g2.drawString(df2.format(r0[999]),315,387); g2.drawString("k",280,407); g2.drawString("*",290,407); g2.drawString(" =",293,407); g2.drawString(df2.format(k0[999]),315,407); g2.drawString("c",280,427); g2.drawString("*",290,427); g2.drawString(" =",293,427); g2.drawString(df2.format(c0[999]),315,427); g2.drawString("y",15,115); g2.drawString("x",340,488); } public static double function(double k,double r,double c,double x){ return k/(1+c*k*Math.exp(r*(-x))); } }