function t = diagonalize(t,e,l,tol)
%
%  returns a diagonalized tableau after e has entered and l
%    has left the basis.
%
%  on entry:
%    t         linear programming problem in standard format;
%    e         variable entering the basis is column index;
%    l         variable leaving the basis is row (-1) index;
%    tol       tolerance used to decide whether number is zero.
%
%  on return:
%    t         linear programming problem in standard format,
%              with t(l+1,e) = 1.
%
nr = size(t,1);           % number of rows;
nc = size(t,2);           % number of columns;
p = t(l+1,e);             % pivot
for j=1:nc
  t(l+1,j) = t(l+1,j)/p;  % divide (l+1)-th row by pivot
end;
for i=1:nr                % make zeros
  if ((i~=l+1) & (abs(t(i,e)) > tol))
    p = t(i,e);
    for j=1:nc
      t(i,j) = t(i,j) - p*t(l+1,j);
    end;
  end;
end;