%  Code: compLinSlvrs
%
%  This code compares GMRES with Precond GMRES
%
%  It is set up to solve the Sherman 2 problem from Harwell Bowing
%  collection (available from Matrix Market).  The banded 
%  matrix consiting of bands [-10:10] is used as a pre-conditioner.  
%
%  Assumes files sherman2.mtx  sherman2_rhs1.mtx 
%
%          from Matrix Market exist
%
%-------------------
%
%  D.C. Sorensen
%  30 Mar 01
%

 A = mmread('sherman2.mtx'); 
 b = mmread('sherman2_rhs1.mtx');

 h1 = 1;
 h2 = 2;
 h3 = 3;

%
%   Construct a preconditioner from the diagonals [-10:10] 
%
 d = [-10:10];
 B = spdiags(A,d); 
 [n,n] = size(A);
 M = spdiags(B,d,n,n);  

 figure(h1)
 clf
 spy(A)    
 hold

 disp('Strike Key')
 pause
      k = 150;
      tol = 100*sqrt(eps);
      [x,r] = Gmres(A,b,k,tol);
  

   figure(h2)
   clf
   semilogy(r)
   hold
   semilogy(r,'*')
   hold

   




 disp('Strike Key')
 pause

 figure(h1)
 clf
 spy(A)
 hold
 spy(M,'r')    
 hold

 disp('Strike Key')
 pause

 dtol = 1e-6;
 [L,U] = lu(M); 

%opts = struct('droptol',dtol,'milu',1,'udiag',1);
%[L,U] = luinc(A,opts); 


 spy(L,'r')
 hold
 spy(U)
 hold

 disp('Strike Key')
 pause

       
      k = 150;
      tol = 100*sqrt(eps);
      [x,r] = GmresP(A,L,U,b,k,tol);

    
  

   semilogy(r)
   hold
   semilogy(r,'*')
   hold