spherical.recursions

rotate

rotate(modes, R)

Source: spherical/recursions/__init__.py

Rotate Modes object by rotor(s) Compute fₗₘ = Σₙ fₗₙ 𝔇ˡₙₘ(R), where f is a (possibly spin-weighted) function, fₗₙ are its mode weights in the current frame, and fₗₘ are its mode weights in the rotated frame. fₗₘ = Σₙ fₗₙ 𝔇ˡₙₘ(R) = Σₙ fₗₙ dˡₙₘ(R) exp[iϕₐ(m-n)+iϕₛ(m+n)] = Σₙ fₗₙ dˡₙₘ(R) exp[i(ϕₛ+ϕₐ)m+i(ϕₛ-ϕₐ)n] = exp[i(ϕₛ+ϕₐ)m] Σₙ fₗₙ dˡₙₘ(R) exp[i(ϕₛ-ϕₐ)n] = zₚᵐ Σₙ fₗₙ dˡₙₘ(R) zₘⁿ = zₚᵐ {fₗ₀ dˡ₀ₘ(R) + Σₚₙ [fₗₙ dˡₙₘ(R) zₘⁿ + fₗ₋ₙ dˡ₋ₙₘ(R) / zₘⁿ]} = zₚᵐ {fₗ₀ ϵ₋ₘ Hˡ₀ₘ(R) + Σₚₙ [fₗₙ ϵₙ ϵ₋ₘ Hˡₙₘ(R) zₘⁿ + fₗ₋ₙ ϵ₋ₙ ϵ₋ₘ Hˡ₋ₙₘ(R) / zₘⁿ]} = ϵ₋ₘ zₚᵐ {fₗ₀ Hˡ₀ₘ(R) + Σₚₙ [fₗₙ (-1)ⁿ Hˡₙₘ(R) zₘⁿ + fₗ₋ₙ Hˡ₋ₙₘ(R) / zₘⁿ]} Here, n ranges over [-l, l] and pn ranges over [1, l].

Parameters

• modes: Modes

  SWSH modes to rotate

• R: quaternionic.array

  Its shape must satifsy R.shape[:-1] == modes.shape[:-1]