function evals=QRalg(A,maxiter)

% This program implements the QR Algorithm for finding eigenvalues

[m n]=size(A);

if m~=n
    error('A must be square')
end

figure(1)
clf
spy(A)
%imagesc(A)
%colorbar
title('Original matrix A')
fprintf('\nHit any key to continue\n')
pause


if ~exist('maxiter','var')
    maxiter=10*n;
end

tic
% For problem 7, uncomment out this next line
%A=hess(A);


for i=1:maxiter
  [Q R]=qr(A);
  A=R*Q;           % Note that this means that Anew = Q'QRQ=Q'AQ
  if ~mod(i,n) | i==maxiter
      %imagesc(A)
      %colorbar
      spy(abs(A)>sqrt(eps))
      title(sprintf('Check for convergence at iter=%d: Is this matrix either upper-triangular or diagonal?',i))
      fprintf('\nCheck for convergence in figure(1); Hit any key to continue\n')
      pause
  end
end

evals=diag(A);
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