Extracting poloidal-toroidal coefficients of vector fields directly in dedalus

[Andrey Kononov]

Hi all! 

I compute EVP and get a vector field as an eigenfunction. I want to decompose it into poloidal-toroidal amplitudes following this notation: 

Right now I am integrating over a sphere for different radii (code attached) to acquire those coefficients, but I was wandering whether a more direct approach exists. As I understand, in dedalus vector fields on balls/shells are decomposed into spin-weighted spherical harmonics, which are connected to poloidal-toroidal decomposition by simple identites. So perhaps I can get those amplitudes from xi['c'] or something alike? 

Thank you!