Eigenvalue decomposition derivatives needed

[riclarsson]

Hi,

This is somewhat of an open issue. An eigenvalue decomposition is necessary for line mixing ECS computations to be effective. This is done. We also need partial derivatives w.r.t. user input to fit with the rest of ARTS. I would like these derivatives to be analytical but I do not know how to take the partial derivatives of an eigenvalue decomposition. I need help here.

The specific function has been marked "FIXME: (Added 2021-01-19; Richard Larsson)" and is located in linemixing.cc at lines 13-58 at the merging of #281 . I can add computations of dW, dpop, and ddip if someone knows how to perform the required computations.