function [ITER,B,T,flg] = BLPRevisedSimplex(A,B,L,U,l,u,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
%
% flg = 0: convergence
% flg = 1: LP unbounded below
% flg = 2: LP degenerate
%
simplex = 1;
ITER    = 0;
[m,n]   = size(A);
x       = zeros(n,1);
x(L)    = l(L);
x(U)    = u(U);
x(B)    = T(1:m,2:m+1)*(b -A(:,L)*x(L) - A(:,U)*x(U));
flg     = 0;
obj     = c'*x;
ctol    = 1e-13;
while (simplex == 1)
%
% determine the next s and r values.
%
   y        = T(end,2:end)';
   x(L)    = l(L);
   x(U)    = u(U);
   x(B)    = T(1:m,2:m+1)*(b -A(:,L)*x(L) - A(:,U)*x(U));
   t0      = x(B);
%
% first look for positive components in c(U)'-y'*A(:,U)
%
   sflg = 1;
   if (length(U) > 0)
       ff = ['In U branch ITER = ',num2str(ITER)];
       disp(ff);
       [Y,I] = sort(c(U)'-y'*A(:,U));
       mask = find(Y > ctol);
       if (length(mask) >= 1)
%
% found positive components. try obj reduction.
%
           for sk = length(mask):-1:1
%
% loop over all possible s choices to reduce
% chance of non-convergence due to degeneracy.
%
              s    = U(I(sk));
              zmin = Y(sk);
              t    = T(1:end-1,2:end)*A(:,s);
              [r,BUcase] = BURevisedgetr(n,s,B,T,t,t0,l,u);
              ff = ['sk = ',num2str(sk), ' BUcase = ', num2str(BUcase)];
              disf(ff); 
              if (BUcase < 0)
                  disp('Failure in BURevisedgetr');
                  simplex = 0;
                  flg     = 1;
                  continue;
              end
              Unew = setdiff(U,s);
              Lnew = L;
              Bnew = B;
              if (BUcase == 0)
                  Lnew = [Lnew;s];
                  sflg = 0;
                  break;
              end
              if (BUcase == 1)
                  Unew = [Unew;B(r)];                  
                  [Tnew,Bnew,flg] = RevisedSimplexTableau(B,r,s,t,zmin,T); 
              end
              if (BUcase == 2)
                  Lnew = [Lnew;B(r)];
                  [Tnew,Bnew,flg] = RevisedSimplexTableau(B,r,s,t,zmin,T); 
              end
              xnew = zeros(n,1);
              xnew(Lnew) = l(Lnew);
              xnew(Unew)    = u(Unew);
              xnew(Bnew)    = Tnew(1:m,2:m+1)*(b -A(:,Lnew)*xnew(Lnew) - A(:,Unew)*x(Unew));
              objnew       = c'*xnew;
              if (flg == 0 & objnew-obj < -ctol)
%
% success. update the revised simplex tableau.
%
                  sflg = 0;
                  B    = Bnew;
                  L    = Lnew;
                  U    = Unew;
                  T    = Tnew;
                  obj  = objnew;
                  ITER = ITER + 1;
                  f = ['Iteration ', num2str(ITER), ' Obj ', num2str(obj)];
                  disp(f);
                  break;
             end
         end
     end
     if (sflg == 1 & length(L) > 0)
       disp('In L branch');
       [Y,I] = sort(c(L)'-y'*A(:,L));
       mask = find(Y <-ctol);
       if (length(mask) >= 1)
%
% found positive components. try obj reduction.
%
           sflg = 1;
           for sk = 1:length(mask)
%
% loop over all possible s choices to reduce
% chance of non-convergence due to degeneracy.
%
              s    = L(I(sk));
              zmin = Y(sk);
              t    = T(1:end-1,2:end)*A(:,s);
              [r,BLcase] = BLRevisedgetr(n,s,B,T,t,t0,l,u);
              if (BLcase < 0)
                  disp('Failure in BLRevisedgetr');
                  simplex = 0;
                  flg     = 1;
                  continue;
              end
              Lnew = setdiff(L,s);
              Unew = U;
              Bnew = B;
              if (BLcase == 0)
                  Unew = [Unew;s];
                  sflg = 0;
                  break;
              end
              if (BLcase == 1)
                  Unew = [Unew;B(r)];                  
                  [Tnew,Bnew,flg] = RevisedSimplexTableau(B,r,s,t,zmin,T); 
              end
              if (BLcase == 2)
                  Lnew = [Lnew;B(r)];
                  [Tnew,Bnew,flg] = RevisedSimplexTableau(B,r,s,t,zmin,T); 
              end
              xnew = zeros(n,1);
              xnew(Lnew) = l(Lnew);
              xnew(Unew) = u(Unew);
              xnew(Bnew) = Tnew(1:m,2:m+1)*(b -A(:,Lnew)*xnew(Lnew) - A(:,Unew)*x(Unew));
              objnew     = c'*xnew;
              if (flg == 0 & objnew-obj < -ctol)
%
% success. update the revised simplex tableau.
%
                  sflg = 0;
                  B    = Bnew;
                  L    = Lnew;
                  U    = Unew;
                  T    = Tnew;
                  obj  = objnew;
                  ITER = ITER + 1;
                  f = ['Iteration ', num2str(ITER), ' Obj ', num2str(obj)];
                  disp(f);
                  break;
             end
         end
     end
    if (sflg == 1)
%
%  none of the s choices was good enough to avoid degeneracy. Give up.
%
        disp('LP is degenerate');
        simplex = 0;
        flg     = 2;
%%%        disp(T(1:end-1,1));
        continue;
    end
end