% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc;

A = [ 2, 3, 1, 1, 0; 1, 2, 3, 0, 1 ];
[m,n] = size(A); 

% Solve each system one at a time: 
%
all_perms = perms(1:n);
nonzero_variables = unique( sort( all_perms(:,[1,2]), 2 ), 'rows' );
basic_feasable_solutions = [];
for ii=1:size( nonzero_variables, 1 )
  var1 = nonzero_variables(ii,1);
  var2 = nonzero_variables(ii,2);
  sprintf('var1= %5d; var2= %5d\n',var1,var2); % print the nonzero variables 
  sol = ( A(:,[var1,var2]) \ [ 4; 5 ] ).' % print the solution 
  full_sol = zeros( n, 1 );
  full_sol(var1) = sol(1); full_sol(var2) = sol(2);
  if( sum(sol>0)==m ) % this is a feasable solution 
    basic_feasable_solutions = [ basic_feasable_solutions, full_sol ] ;
  end
end

% Print all feasable solutions: 
basic_feasable_solutions

% Evaluate the objective function at these basic feasable solutions: 
basic_feasable_solutions.' * [ 3; 2; -1; 0; 0 ]