A4 = [0 0 0; 1 0 0; 0 2 0; 0 0 3]'

A3 = [fsolve(@(z) emf4(A4, z), -[0.1270 1.3225 0.0940]') ...
      fsolve(@(z) emf4(A4, z), -[0.1004 0.1347 2.1434]') ...
      fsolve(@(z) emf4(A4, z), -[0.5250 0.0600 0.0402]')]

%%
B3 = A3 * [-1 1 0; -1 0 1]';
[Q,R] = qr(B3);
R3 = [R(1:2,:) [0 0]'];

a = fsolve(@(z) emf4(R3, z), [1.0 0.5]')
%%

q=Q*[a;0]
A3
emf4(R3, q)



function out = emf4(A, z)
  out = 0;
  for a=A
      u = a+z;
      out = out + u/norm(u)^2;
  end
end