function [Tnew,Bnew,flg] = ExtendedSimplexTableau(B,r,s,T)
%
% This function updates an ExtendedSimplexTableau
% 
% Written by Ming Gu for Math 170
% March 2007
%
% On input: 
% B: current basis index
% T: current ExtendedTableau
% r: B(r)-th column is to LEAVE the index.
% s: s-th  column is to JOIN the index.
%

% On output: 
%
% flg:  flg == 0 indicates SUCCESS in updating,
%       flg == 1 indicates FAILURE in updating,
% Bnew: New basis index
% Tnew: New Tableau
%

%
% initialize flg.
%
flg     = 0;
%
% find dimensions of T.
%
[mt,nt] = size(T); 
%
% Set up Bnew
%
B     = B(:);
Bnew  = [B(1:r-1);s;B(r+1:mt-1)];
%
% Setup Tnew
%
Tnew         = zeros(mt,nt); 
if (T(r,s) == 0)
%
% This is indication of degeneracy. Quit.
%
    flg = 1;
    return;
end
%
% This is the normal case. Proceed. 
%
Tnew(1:mt-1,Bnew) = eye(mt-1);
Tnew(1:mt-1,B(r)) =-T(1:mt-1,s)/T(r,s);
Tnew(r,B(r))      = 1/T(r,s);
Bbar              = setdiff((1:nt)',[B;s]);
Temp              = T(r,Bbar)/T(r,s);
Tnew(1:mt-1,Bbar) = T(1:mt-1,Bbar) - T(1:mt-1,s)*Temp;
Tnew(r,Bbar)      = Temp;
theta0            = T(mt,s)/T(r,s);
n                 = nt - mt;
Tnew(mt,1:n)      = T(mt,1:n) - theta0*T(r,1:n);
Tnew(mt,n+1:end)  = T(mt,n+1:end) + theta0*T(r,n+1:end);