calculate nullspace of stochiometric matrix

Hello,

i try to calculate the nullspace of a stochiometric matrix with the algorithms lu, qr and svd. Standard is the null-command of matlab. i've got an example from a colleague but i did not understand every step and he is not there, so i cannot ask him. i think the lu-algorithm is wrong. can anyone find a mistake or way to make it better?

              case 'standard'
                  K = null(S.Stoich,'r');
                  [n,m] = size(K);
                  G = S.Stoich*K %check the result
              case 'lu'
                  A = S.Stoich;
                  [m,n] = size(A);
                  [L,U,Pr,Pc] = lu(sparse(A));
                  U = full(U);
                  r = rank(U);
                  Ui = U(1:r,1:r);
                  %Ue = pinv(Ui)
                  Ue = Ui*U(1:r,:); % =>Reduced Echelon-Form
                  K = full(Pc*[ -Ue(:,r+1:n); eye(n-r) ]);
                  G = Pr*A*Pc*K %check the result

              case 'qr'
                  A = S.Stoich;
                  [m,n] = size(A);
                  if rank(A)<m
                      [m,n] = size(A);
                      [Q,R,P] = qr(A);
                      r = rank(A); % ginge auch direkt aus QR-Zerlegung
                      Rb = R(1:r,1:r); % Basis-Anteil
                      Rn = R(1:r,r+1:n); % Null-Anteil
                      K = P*[ -inv(Rb)*Rn; eye(n-r) ];
                      %error('matrix must not be rank-deficient');
                  else
                      [Q,R] = qr(A');
                      K = Q(:,m+1:n);
                  end
                  G = A*K %check the result

              case 'svd'
                  A = S.Stoich;
                  % single value decomposition
                  [m,n] = size(A);
                  [U,s,V] = svd(A);
                  % numerische Rangbestimmung (alternativ: r=rank(A)):
                  tol = max(m,n)*s(1,1)*eps;
                  r = 0;
                  for i=1:min(size(s))
                      if s(i,i) >= tol, r = r+1; end
                  end
                  K = V(:,r+1:n);
                  G = A*K %check the result

Thank you