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

public class Example2_13 extends Applet
{
  public static void  MSymTri(double[][] a,double[][] Q,int n)
  {int i,j,k,l;
   double[] u=new double[n];
   double[] q=new double[n];
   double alpha,beta,temp;
   for(i=0;i<n;i++)
   {Q[i][i]=1;for(j=i+1;j<n;j++){Q[j][i]=0;Q[i][j]=0;}}

  for(k=0;k<n-2;k++)
  { l=n-k-1;
	alpha=0;
    for(j=0;j<l;j++)alpha+=a[l][j]*a[l][j];
    if(alpha==0)continue;
    alpha=Math.sqrt(alpha);
    if(a[l][l-1]<0)alpha*=-1;
    beta=(alpha+a[l][l-1])*alpha;
    for(i=0;i<l-1;i++)u[i]=a[l][i];
    u[l-1]=a[l][l-1]+alpha;
    for(i=l;i<n;i++)u[i]=0;
    for(i=0;i<=l;i++)
    {q[i]=0;
     for(j=0;j<l;j++)q[i]+=a[i][j]*u[j];
     q[i]/=beta;}
     temp=0;
     for(j=0;j<l;j++)temp+=u[j]*q[j];
     temp/=2*beta;
    for(i=0;i<l;i++)q[i]-=temp*u[i];
    for(i=0;i<l;i++)
      for(j=0;j<l;j++)
     {a[i][j]-=q[i]*u[j]+q[j]*u[i];}
    for(i=0;i<l-1;i++)a[l][i]=a[i][l]=0;
    a[l][l-1]=a[l-1][l]=-alpha;

     for(i=0;i<n;i++)
     {q[i]=0;
      for(j=0;j<l;j++)q[i]+=Q[i][j]*u[j];}

    for(i=0;i<n;i++)
      for(j=0;j<l;j++)
      Q[i][j]-=q[i]*u[j]/beta;
   }
}

 public static void cheng(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={{10,1,2,3,4},{1,9,-1,2,-3},{2,-1,7,3,-5},{3,2,3,12,-1},{4,-3,-5,-1,15}};
  double[][] Q=new double[5][5];
  int i,j;double temp;
  g.setColor(Color.blue);
  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);
  MSymTri(a,Q,5);
  g.drawString("三對角矩陣",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("變換矩陣",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);
  cheng(Q,a,a,5,5,5);
  for(i=0;i<5;i++)
   for(j=i+1;j<5;j++){temp=Q[i][j];Q[i][j]=Q[j][i];Q[j][i]=temp;}
  cheng(a,Q,a,5,5,5);
  g.drawString("QAQ=",10,190);
  for(i=0;i<5;i++)
  g.drawString(""+a[i][0]+"  "+a[i][1]+"  "+a[i][2]+"  "+a[i][3]+"  "+a[i][4],10,200+10*i);
 }
}