function D=qrbasic(A,tol,nmax)
%QRBASIC computes all the eigenvalues of a matrix A.
%  D=QRBASIC(A,TOL,NMAX) computes by QR iterations all
%  the eigenvalues of A within a tolerance TOL and a
%  maximum number of iteration NMAX. The convergence of
%  this method is not always guaranteed.
[n,m]=size(A);
if n ~= m, error('The matrix must be squared'); end
T = A; niter = 0; test = norm(tril(A,-1),inf);
while niter <= nmax & test >= tol
    [Q,R]=qr(T);    T = R*Q;
    niter = niter + 1;
    test = norm(tril(T,-1),inf);
end
if niter > nmax
  warning(['The method does not converge '...
           'in the maximum number of iterations']);
else
  fprintf(['The method converges in ' ...
           '%i iterations\n'],niter);
end
D = diag(T);
return