import java.applet.*;
import java.awt.*;
public class Example2_10 extends Applet
{ public static void  QR(double[][] a,double[][] Q,int m,int n )
   {int i,j,k,l=Math.max(m,n);
    double[] t=new double[l];
    double alpha,beta;
    for(i=0;i<m;i++)
     for(j=0;j<m;j++)
      {if (i==j) Q[i][j]=1;
       else Q[i][j]=0; }

   for(k=0;k<Math.min(n,m);k++)
   { alpha=0;
     for(l=k;l<m;l++)alpha+=a[l][k]*a[l][k];
     alpha=Math.sqrt(alpha);
     if(alpha==0)continue;
     if(a[k][k]<0)alpha*=-1;
     beta=(alpha+a[k][k])*alpha;
     for(i=0;i<m;i++)
      {t[i]=Q[i][k]*alpha;
       for(l=k;l<m;l++)t[i]+=Q[i][l]*a[l][k];
      }
     for(i=0;i<m;i++)
     { Q[i][k]-=t[i]/alpha;
 	  for(j=k+1;j<m;j++)Q[i][j]-=(t[i]*a[j][k]/beta);}
     for(j=0;j<n;j++)
      {t[j]=alpha*a[k][j];
       for(l=k;l<m;l++)t[j]+=a[l][k]*a[l][j];
      }
    for(j=k+1;j<n;j++)a[k][j]-=t[j]/alpha;
    for(i=k+1;i<m;i++)
      for(j=k+1;j<n;j++)a[i][j]-=(a[i][k]*t[j]/beta);
    for(l=k+1;l<m;l++)a[l][k]=0;
    a[k][k]=-alpha;
    }
  }

  public void paint(Graphics g)
  {double[][] a={{1,1,-1},{2,1,0},{1,-1,0},{-1,2,1}};
   double[][] Q=new double[4][4];
   QR(a,Q,4,3);
   g.drawString("Q=",10,20);
   g.drawString(""+Q[0][0]+"  "+Q[0][1]+"  "+Q[0][2]+"  "+Q[0][3],10,40);
   g.drawString(""+Q[1][0]+"  "+Q[1][1]+"  "+Q[1][2]+"  "+Q[1][3],10,60);
   g.drawString(""+Q[2][0]+"  "+Q[2][1]+"  "+Q[2][2]+"  "+Q[2][3],10,80);
   g.drawString(""+Q[3][0]+"  "+Q[3][1]+"  "+Q[3][2]+"  "+Q[3][3],10,100);
   g.drawString("R=",10,120);
   g.drawString(""+a[0][0]+"  "+a[0][1]+"  "+a[0][2],10,140);
   g.drawString(""+a[1][0]+"  "+a[1][1]+"  "+a[1][2],10,160);
   g.drawString(""+a[2][0]+"  "+a[2][1]+"  "+a[2][2],10,180);
   g.drawString(""+a[3][0]+"  "+a[3][1]+"  "+a[3][2],10,200);
  }
}