#include "stdio.h"
#include "math.h"
int qrtt(n,a,u,v,eps,jt)
int n,jt;
double a[],u[],v[],eps;
{ int m,it,i,j,k,l,ii,jj,kk,ll;
double b,c,w,g,xy,p,q,r,x,s,e,f,z,y;
it=0; m=n;
while (m!=0)
{ l=m-1;
while ((l>0)&&(fabs(a[l*n+l-1])>eps*
(fabs(a[(l-1)*n+l-1])+fabs(a[l*n+l])))) l=l-1;
ii=(m-1)*n+m-1; jj=(m-1)*n+m-2;
kk=(m-2)*n+m-1; ll=(m-2)*n+m-2;
if (l==m-1)
{ u[m-1]=a[(m-1)*n+m-1]; v[m-1]=0.0;
m=m-1; it=0;
}
else if (l==m-2)
{ b=-(a[ii]+a[ll]);
c=a[ii]*a[ll]-a[jj]*a[kk];
w=b*b-4.0*c;
y=sqrt(fabs(w));
if (w>0.0)
{ xy=1.0;
if (b<0.0) xy=-1.0;
u[m-1]=(-b-xy*y)/2.0;
u[m-2]=c/u[m-1];
v[m-1]=0.0; v[m-2]=0.0;
}
else
{ u[m-1]=-b/2.0; u[m-2]=u[m-1];
v[m-1]=y/2.0; v[m-2]=-v[m-1];
}
m=m-2; it=0;
}
else
{ if (it>=jt)
{ printf("fail\n");
return(-1);
}
it=it+1;
for (j=l+2; j<=m-1; j++)
a[j*n+j-2]=0.0;
for (j=l+3; j<=m-1; j++)
a[j*n+j-3]=0.0;
for (k=l; k<=m-2; k++)
{ if (k!=l)
{ p=a[k*n+k-1]; q=a[(k+1)*n+k-1];
r=0.0;
if (k!=m-2) r=a[(k+2)*n+k-1];
}
else
{ x=a[ii]+a[ll];
y=a[ll]*a[ii]-a[kk]*a[jj];
ii=l*n+l; jj=l*n+l+1;
kk=(l+1)*n+l; ll=(l+1)*n+l+1;
p=a[ii]*(a[ii]-x)+a[jj]*a[kk]+y;
q=a[kk]*(a[ii]+a[ll]-x);
r=a[kk]*a[(l+2)*n+l+1];
}
if ((fabs(p)+fabs(q)+fabs(r))!=0.0)
{ xy=1.0;
if (p<0.0) xy=-1.0;
s=xy*sqrt(p*p+q*q+r*r);
if (k!=l) a[k*n+k-1]=-s;
e=-q/s; f=-r/s; x=-p/s;
y=-x-f*r/(p+s);
g=e*r/(p+s);
z=-x-e*q/(p+s);
for (j=k; j<=m-1; j++)
{ ii=k*n+j; jj=(k+1)*n+j;
p=x*a[ii]+e*a[jj];
q=e*a[ii]+y*a[jj];
r=f*a[ii]+g*a[jj];
if (k!=m-2)
{ kk=(k+2)*n+j;
p=p+f*a[kk];
q=q+g*a[kk];
r=r+z*a[kk]; a[kk]=r;
}
a[jj]=q; a[ii]=p;
}
j=k+3;
if (j>=m-1) j=m-1;
for (i=l; i<=j; i++)
{ ii=i*n+k; jj=i*n+k+1;
p=x*a[ii]+e*a[jj];
q=e*a[ii]+y*a[jj];
r=f*a[ii]+g*a[jj];
if (k!=m-2)
{ kk=i*n+k+2;
p=p+f*a[kk];
q=q+g*a[kk];
r=r+z*a[kk]; a[kk]=r;
}
a[jj]=q; a[ii]=p;
}
}
}
}
}
return(1);
}
