function [ITER,B,x,T,flg] = RevisedSimplex(A,B,c,T)
%
% This is the Simplex Method using the Revised Simplex Tableau.
% We assume the Tableau T has been initialized on input.
% Written by Ming Gu for Math 170
% March 2007
%

simplex = 1;
ITER    = 0;
[m,n]   = size(A);
x       = zeros(n,1);
x(B)    = T(1:m,1);
flg     = 0;
obj     = c'*x;
while (simplex == 1)
%
% determine the next s and r values.
%
   y        = T(end,2:end)';
   [zmin,s] = min(c-A'*y); 
   t        = T(1:end-1,2:end)*A(:,s);
   r = Revisedgetr(n,s,B,T,t);
   if (r < 1)
       disp('LP has no lower bound');
       simplex = 0;
       flg     = 1;
       continue;
   end
   ITER = ITER + 1;
   x       = zeros(n,1);
   x(B)    = T(1:m,1);
   f = ['Iteration ', num2str(ITER), ' Obj ', num2str(c'*x), '. Smallest component in c-A^T*y: ', ... 
         num2str(zmin), ' at s =', num2str(s), '. Component r = ', num2str(r), ' out of basis'];
   obj1 = c'*x;
%%   disp(f);
%
% update the revised simplex tableau.
%
   [T,B1,flg]=RevisedSimplexTableau(B,r,s,t,zmin,T);      
   if (flg == 1)
       disp('LP is degenerate');
       simplex = 0;
       continue;
   end
%
% check for convergence.
%
   FF  = setdiff(B1,B);
   if (length(FF) == 0 | (abs(obj1-obj) < 1e-14 & ITER  > 1))
       disp('Simplex Method has converged');
       simplex = 0;
       continue;
   end
   B   = B1;
   obj = obj1;
end