Algorithm 3 Adjoints ω

 ω_ik = 0

 for v ← basis, ν = len(v) do

  \({{{\Theta }}}_{i{\bf{v}}}={\sum }_{p}\partial {\mathcal{F}}/\partial {\varphi }_{i}^{(p)}\cdot {\tilde{{\bf{c}}}}_{{\mu }_{i}{\bf{v}}}^{(p)}\)

  compute dA_ivt, t = 1, …, ν (Alg. 4)

  for t ← 1, …, ν do

   \({\omega }_{i{v}_{t}}+\!={{{\Theta }}}_{i{\bf{v}}}\cdot {\rm{Re}}({d{\bf{A}}}_{i{\bf{v}}t})\)

  end for

 end for