%
% This is JEM modification to plot errors also.
%
%
% Matlab code qrplt.m
% For "Applied Numerical Linear Algebra",  Question 4.15
% Written by James Demmel, Oct 25, 1995
%                Modified, Jun  5, 1997
%
%  Plot the diagonal entries of a matrix undergoing unshifted QR iteration
%
%  Inputs:
%    a = matrix
%    m = number of QR iterations
%
%  Outputs:
%    n curves, one for each diagonal entry of a 
%
hold off
e=diag(a);
for i=1:m,
   [q,r]=qr(a);dd=diag(sign(diag(r)));r=dd*r;q=q*dd;a=r*q; ...
   e=[e,diag(a)];
end
clg
plot(e','k'),grid
title('plot of each diagonal matrix entry during QR iteration')
%
% MODIFIED STUFF FROM HERE
%
%  Column i+1 of the matrix e contains the ith estimate for the
%  eigenvalues, generated in the ith step through the loop.
%
%  The best estimate for the eigenvalues generated by the algorithm
%  should be contained in the last column of e, so we set  evals  to
%  be this estimate.
%  We put the estimates in a  n by (m+1)  matrix  evalsm  with each
%  column of evalsm being a copy of this best estimate for the eigenvalues.
%
evals=e(1:n,m+1)
evalsm=evals;
for i=1:m
  evalsm=[evalsm,evals];
end
evalsm;
%
%  The error is the absolute value of the difference between
%  the iterates (stored in e) and the best estimate of the eigenvalues
%  (stored in evalsm)
%
%  The (m+1)st column of error will be a column of zeroes, so we rescale
%  error to ignore it.
%
error=abs(e-evalsm);
error=error(1:n,1:m);
%
%  Calculate the log of this error and plot it out.
%
logerror=log(error);
plot(logerror','k'),grid
title('plot of log error of each diagonal matrix entry during QR iteration')