% x = LinProg(f, AInEq, bInEq)
% x = LinProg(f, AInEq, bInEq,AEq, bEq)
% x = LinProg(f, AInEq, bInEq,AEq, bEq,debug)
% [x,fval] = LinProg(___)
% [x,fval,exitflag] = LinProg(___)
%This function implments the simplex matrix algorithm.
%It accepts row vector f defining the objective function as f*x
%It can accept only inequality constraints(as in x = LinProg(f, AInEq, bInEq)) ,
% or only equality constraints (as in x = LinProg(f, [], [], AEq, bEq).
% The debug defaults false if the use did not specify to see the stages
% during the solution process
%
%It runs both phase one and phase two automatically.
%
%The input is
%
%AInEq and bInEq: defined the inequality constrain AInEq*x <= bInEq
%
%AEq and bEq: defined the equality constrain AEq*x = bEq
%
%f: Vector. This is from minimize F(x) = fx. As defined in
% standard Matlab documentations.
%
%debug: flag. Set to true to see lots of internal steps.

%
% Version 7/16/2017( modification of original version by Nasser M. Abbasi)
% by Lateef A. Kareem
% Free for use.