A = [0.620405 + 0.956953i  0.480013 + 0.048806i  0.402627 + 0.338171i;
      0.589077 + 0.658457i  0.013205 + 0.279323i  0.229284 + 0.721929i;
      0.092758 + 0.345687i  0.928679 + 0.241052i  0.764536 + 0.832406i;
      0.912098 + 0.721024i  0.049018 + 0.269452i  0.730029 + 0.796517i;
      0.112849 + 0.603871i  0.486352 + 0.142337i  0.355646 + 0.151496i ];

 x = [0.20351 + 0.05401i;
      0.13141 + 0.43708i;
      0.29808 + 0.08789i;
      0.69821 + 0.38844i;
      0.74871 + 0.25821i ];

[Q,R] = qr(A);
[Q,R] = qrinsert(Q,R,3,x);
disp(norm(vec(Q'*Q - eye(5)),Inf) < 1e1*eps)
disp(norm(vec(triu(R)-R),Inf) == 0)
disp(norm(vec(Q*R - [A(:,1:2) x A(:,3)]),Inf) < norm(A)*1e1*eps)