function [A  Qp] = qrs(A, nit)
%% [A  Qp] = qrs(A, nit)
%% very simple classical QR algorithm 
%% with shifts. 
%%  
Qp = eye(size(A));
n = size(A,1) ;
t = 0.0;
for i=1:nit 
  A = A - t * eye(n) ;
  [Q, R] = qr(A);
  A = R*Q + t*eye(n)
  Qp = Qp*Q;
  t = A(n,n);
  pause 
end
