To Do

[moble]

• Next version update

  • Update interface, to allow passing dworkspace, etc., as individual
    arguments. For example, the current signature

    D!(𝔇, R::AbstractQuaternion, ℓₘₐₓ, H_rec_coeffs, eⁱᵐᵅ, eⁱᵐᵞ)
    

    could become

    D!(𝔇, R::AbstractQuaternion, Dworkspace)
    

    Note that this would require including ℓₘₐₓ among the returned quantities of Dprep.

    Be careful to keep backwards compatibility.

  • Add d_matrices, D_matrices, and sYlm_values functions, with docs noting
    that these may be slower if they are to be called repeatedly. Maybe rename ALFcompute?

  • Consider removing storage of coefficients for d!, D!, and Y!, and maybe
    even complex powers.

  • Improve docs for new interface, with lots of examples. (Note the usual Divio structure.)

    • Transformations
      • SSHT
        • SSHTDirect
        • SSHTMinimal
        • SSHTRS
      • map2salm / salm2map
    • Computations
      • ALFcompute!
      • d!, d_matrices
      • D!, D_matrices
      • Y!, sYlm_values, ₛ𝐘
    • Storage-access iterators
      • Diterator
      • Yiterator
      • diterator
      • λiterator
    • Differential operators
      • Lz, L², L₊, L₋, R², Rz, R₊, R₋, ð, ð̄

  • Allow SSHT to be used either as a constructor or as a function

  • Bump minor version number

• Later

  • Optimize Hrecursion coefficients
    • Could probably remove a and b; if not, reduce b to single dimension as function of n-m
    • Get rid of alternating sign in c, allowing us to reduce m loop from -n:n to 0:n and use symmetry
  • Squeeze more performance out of core Hrecursion loops
    • The loops in steps 4 and 5 use up the majority of the time
    • They could be vectorized, because the output is not aliased over any of the inputs, and the current reuse via d7=d8, for example, could be eliminated
  • Improve operators
    • Add Lx, Ly
    • Add Li and LiLj
    • Look into using more generic sparse arrays — especially for products; maybe SparseMatricesCSR would be more performant for matrix multiplication? The builtin Bidiagonal?