example2_15.java

Java程序100例

import java.applet.*;
import java.awt.*;

public class Example2_15 extends Applet
{
  public void MHessenberg(double[][] a, double[][] Q,int n)
  {int i,j,k; double d,t;
    for(i=0;i<n;i++)
     {Q[i][i]=1;
      for(j=i+1;j<n;j++){Q[i][j]=0;Q[j][i]=0;}}
    for(k=0;k<=n-3;k++)
    {d=0;
     for(j=k+1;j<n;j++)
     {t=a[j][k];
      if (Math.abs(t)>Math.abs(d)){d=t;i=j;}
      }

     if(d!=0)
      {if(i!=(k+1))
       {for(j=k;j<n;j++)
        {t=a[i][j];a[i][j]=a[k+1][j];a[k+1][j]=t;}
        for(j=0;j<n;j++)
        {t=a[j][i];a[j][i]=a[j][k+1];a[j][k+1]=t;}
        for(j=0;j<n;j++)
	    {t=Q[j][i];Q[j][i]=Q[j][k+1];Q[j][k+1]=t;}
       }

	  for(i=k+2;i<n;i++)
	   {t=a[i][k]/d;a[i][k]=0;
	    for(j=k+1;j<n;j++)a[i][j]-=t*a[k+1][j];
	    for(j=0;j<n;j++)a[j][k+1]+=t*a[j][i];
	    for(j=0;j<n;j++)Q[j][k+1]+=t*Q[j][i];

	   }

	  }
    }

}

 public static void Mrcheng(double[][] a,double[][] b,double[][] c,int n,int m,int l)
   {int i,j,k;
    double[][] d=new double[n][l];
    for(i=0;i<n;i++)
     for(j=0;j<l;j++)
     { d[i][j]=0;
       for(k=0;k<m;k++)
       d[i][j]+=a[i][k]*b[k][j];
     }
    for(i=0;i<n;i++)
      for(j=0;j<l;j++)
        c[i][j]=d[i][j];

    }

 public void paint(Graphics g)
 {double[][] a={{1,6,-3,-1,7},{8,-15,18,5,4},{-2,11,9,15,20},{-13,2,21,30,-6},{17,22,-5,3,6}};
  double[][] Q=new double[5][5];
  double[][] b=new double[5][5];
  int i,j;double temp;boolean flag;
  for(i=0;i<5;i++)
    for(j=0;j<5;j++)b[i][j]=a[i][j];
  g.drawString("A=",10,10);
  for(i=0;i<5;i++)
  g.drawString(""+a[i][0]+"  "+a[i][1]+"  "+a[i][2]+"  "+a[i][3]+"  "+a[i][4],10,20+10*i);
  MHessenberg(a,Q,5);
  g.drawString("Hessenberg矩阵",10,70);
  for(i=0;i<5;i++)
  g.drawString(""+a[i][0]+"  "+a[i][1]+"  "+a[i][2]+"  "+a[i][3]+"  "+a[i][4],10,80+10*i);
  g.drawString("变换矩阵",10,130);
  for(i=0;i<5;i++)
  g.drawString(""+Q[i][0]+"  "+Q[i][1]+"  "+Q[i][2]+"  "+Q[i][3]+"  "+Q[i][4],10,140+10*i);
  Mrcheng(Q,a,a,5,5,5);Mrcheng(b,Q,b,5,5,5);
  g.drawString("AQ=",10,190);
  for(i=0;i<5;i++)
  g.drawString(""+b[i][0]+"  "+b[i][1]+"  "+b[i][2]+"  "+b[i][3]+"  "+b[i][4],10,200+10*i);
  g.drawString("QH=",10,250);
  for(i=0;i<5;i++)
  g.drawString(""+a[i][0]+"  "+a[i][1]+"  "+a[i][2]+"  "+a[i][3]+"  "+a[i][4],10,260+10*i);
  flag=true;
  for(i=0;i<5;i++)
    for(j=0;j<5;j++)
    {if(Math.abs(a[i][j]-b[i][j])>1e-7){flag=false;break;}}
 if(flag) g.drawString("对！",10,310);
 else g.drawString("不对",10,310);
}
}