% Testing program test_x.m for a version of gmres_x.m organized as suggested by
% R.J. Hanson and D.R. Kincaid,"Notes on GMRES Algorithm Organization",
% Technical Report TR-05-05, March 2005,
% Computer Sciences Department, University of Texas at Austin.
% Date = 18 April 2005.

disp ' Solve random problems with x = all ones as a solution'
disp ' To start try sytem size of 30, 15 subdiagonals, and 10 GMRES iterations.'

while 1
  rand('state',0);
  disp ' '
  n = input(' Enter system size here = ');

  % Create an n by n random matrix with a slight diagonal dominance.
  AA = rand(n,n);
  D = diag(AA);
  A = AA+diag(D+2*rand(n,1));
  % Use k diagonals for computing ILU preconditioners.

  k = input(' Enter number of sub- and super diagonals used for ILU factors = ');

  k = max(0,k); k = min(n-1,k);
  % Use x = all ones as a known solution.  Generate corresponding right hand
  % side.
  x = ones(n,1); b = A*x;

  %Create a matrix from A using k sub- and super-diagonals.
  C = A;
  for j=1:n-k
    C(k+j+1:n,j) = 0.; C(j,k+j+1:n) = 0.;
  end

  % Compute the row pivoted form of LU factorization of C.  These factors are
  % used as pre-conditioners.
  [L,U,P] = lu(C);

  tol = 1.E-4;
  Test_Case = 'test_x';

  [z0,sigma_sequence,iterations] = gmres_x(A,b,L,U,P,tol);
  out = my_summary(n,z0,sigma_sequence,iterations,'test_x');

  n = input('Enter space for more computing or 0 to stop... ');
  if(n==0)
    break
  end
  clear sigma_sequence;
end