% Testing program test_z.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.

clear all
% Read in data for Nachtegal, Reddy, & Trefeften (SIMAX 13(3) 1992).
load matdata
tol=1e-6;

% Use tridiagonal major part of matrix as factor for pre-conditioner.
K=n^2;
W = spalloc(K,K,3*K);
for j=2:K
    W(j-1,j) = A(j-1,j);
    W(j,j) = A(j,j);
    W(j,j-1) = A(j,j-1);
end
W(1,1) = A(1,1);
[L,U,P] = lu(W);
clear W;
z0 = zeros(K,1);
% Solve system with pre-conditioned GMRES algorithm
% as proposed by Kincaid and Hanson.

disp ' Solve Nachtegal, Reddy, & Trefeften problem using ILU principal tridigaonal preconditioners.'
disp ' To start try 75 inner GMRES iterations.  Use 0 as initial solution estimate.'

while 1
    [z0,sigma_sequence,iterations] = gmres_x(A,b,L,U,P,tol,z0);
% Plot the reshaped solution, as a surface.
%    x = reshape(z0,n,n);
%    surf(x)
   out=my_summary(n,z0,sigma_sequence,iterations,'test_z');
   m = input('Enter space for more computing or 0 to stop... ');
   if(m==0)
       break
   end
clear sigma_sequence;
% Start over at zero.  Otherwise this is likely already a solution.    
    z0 = zeros(K,1);
end