%
%  This script will demonstrate some of the 
%
%   Unsymetric sparse matrix capabilities of Matlab
%
%
%  D.C. Sorensen
%  Last modified 3 Sep 04
%
   NZhistory = [];
%
%  read a matrix from matrix market
%

   echo on;
%  A = mmread('west2021.mtx');
%  A = mmread('bfw398a.mtx');
   A = mmread('add32.mtx');
%  A = mmread('memplus.mtx');

   echo off;

   [n,m] = size(A);
   disp('order of A ... n ='), disp(n)
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause



   norm(A-A',1)
   disp(' norm(A-A'',1) ')
   disp('  % Use one or inf norm for sparse A ')

   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause

%
%  -----------------------natural ordering-------------------------------------
%

   spy(A)
   title('Natural Ordering','Fontsize',15)
   disp(' spy(A) ')
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause

   [L,U,P] = lu(A);

   spy(L,'r')
   title('L Factor Fill in Red ','Fontsize',15)
   hold
   spy(U,'g')
   title('U Factor Fill in Green ','Fontsize',15)
   hold

   NonzerosLU = nnz(L) + nnz(U)
   NZhistory = [NZhistory , NonzerosLU];
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause



%
%  -----------------------colmmd ordering-------------------------------------
%
   p = colmmd(A);
   disp(' p = colmmd(A); ')

   spy(A(:,p))
   title('colmmd Ordering','Fontsize',15)
   disp(' spy(A(:,p)) ')
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause

   [L,U] = lu(A(:,p));

   spy(L,'r')
   title('L Factor Fill in Red ','Fontsize',15)
   hold
   spy(U,'g')
   title('U Factor Fill in Green ','Fontsize',15)
   hold

   NonzerosLU = nnz(L) + nnz(U)
   NZhistory = [NZhistory , NonzerosLU];
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause


%
%  -----------------------colmmd ordering with L U P Q  Umfpack-------------------------
%
   p = colmmd(A);
   disp(' p = colmmd(A); ')

   spy(A(:,p))
   title('colmmd Ordering','Fontsize',15)
   disp(' spy(A(:,p)) ')
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause

   [L,U,P,Q] = lu(A(:,p));

   spy(L,'r')
   title('L Factor Fill in Red ','Fontsize',15)
   hold
   spy(U,'g')
   title('U Factor Fill in Green ','Fontsize',15)
   hold
   disp(' UMfpack with colmmd ordering ')

   NonzerosLU = nnz(L) + nnz(U)
   NZhistory = [NZhistory , NonzerosLU];
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause


%
%  -----------------------natural ordering with L U P Q  Umfpack-------------------------
%


   [L,U,P,Q] = lu(A);

   spy(L,'r')
   title('L Factor Fill in Red ','Fontsize',15)
   hold
   spy(U,'g')
   title('U Factor Fill in Green ','Fontsize',15)
   hold
   disp(' UMfpack with natural ordering ')

   NonzerosLU = nnz(L) + nnz(U)
   NZhistory = [NZhistory , NonzerosLU];
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause

%
%  -----------------------colmmd ordering with L U  threshold-------------------------
%
   thresh = .1;
   p = colmmd(A);
   disp(' p = colmmd(A); ')

   [L,U,P] = lu(A(:,p),thresh);

   spy(L,'r')
   title('L Factor Fill in Red ','Fontsize',15)
   hold
   spy(U,'g')
   title('U Factor Fill in Green ','Fontsize',15)
   hold
   disp(sprintf(' Threshold pivoting,  thresh = %d',thresh))

   NonzerosLU = nnz(L) + nnz(U)
   NZhistory = [NZhistory , NonzerosLU];
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause


%
%  -----------------------colmmd ordering with Umfpack  threshold-------------------------
%
   thresh = .1;
   p = colmmd(A);
   disp(' p = colmmd(A); ')

   [L,U,P,Q] = lu(A(:,p),thresh);

   spy(L,'r')
   title('L Factor Fill in Red ','Fontsize',15)
   hold
   spy(U,'g')
   title('U Factor Fill in Green ','Fontsize',15)
   hold
   disp(sprintf(' UMF with Threshold pivoting,  thresh = %d',thresh))

   NonzerosLU = nnz(L) + nnz(U)
   NZhistory = [NZhistory , NonzerosLU];
   disp('  ')
   disp(' Strike a key ')
   disp('  ')
   pause


%
%  Display a comparision of fill in for various methods
%
   bar(NZhistory,.2)
   xlabel('  natural       mindeg      UMFpack  thresh   UMF thresh   ','Fontsize',20)
   ylabel(' Nonzeros in   L','fontsize',20)