function [t,inb,otb] = initialize(f,A,b)
%
%  returns an initial tableau corresponding to the problem
%      max f'*x subject to A*x <= b
%
%  on entry:
%    f         coefficients of the linear objective function;
%    A         coefficients of the linear inequalities;
%    b         right hand side vector of the constraints.
%
%  on return:
%    t         initial tableau;
%    inb       indices to variables in the basis,
%              inb(i) gives column for i-th unit vector;
%    otb       indices to variables outside the basis.
%
n = size(A,2);          % number of variables
m = size(A,1);          % number of constraints
inb = zeros(1,m);
otb = zeros(1,n);
t = zeros(m+1,n+m+1);
for j=1:n               % copy objective f and A in t
  t(1,j) = f(j);
  for i=1:m
    t(i+1,j) = A(i,j);
  end;
  otb(j) = j;           % original variables are outside the basis
end;
for i=1:m               % assign identity and b in t
  t(i+1,n+i) = 1;
  t(i+1,n+m+1) = b(i);
  inb(i) = n+i;         % all slack variables are in the basis
end;