add bespoke angularmomentum

Author: MikaelSlevinsky

src/rectdisk.jl

@@ -153,3 +153,38 @@ function jacobimatrix(::Val{2}, P::DunklXuDisk)
         ), (blockedrange(Fill(3, 3)), axes(n,1)))
     _BandedBlockBandedMatrix(dat, axes(k,1), (1,1), (1,1))
 end
+
+
+
+#########
+# AngularMomentum
+# Applies the partial derivative with respect to the last angular variable in the coordinate system.
+# For example, in polar coordinates (r, θ) in ℝ² or cylindrical coordinates (r, θ, z) in ℝ³, we apply ∂ / ∂θ = (x ∂ / ∂y - y ∂ / ∂x).
+# In spherical coordinates (ρ, θ, φ) in ℝ³, we apply ∂ / ∂φ = (x ∂ / ∂y - y ∂ / ∂x).
+#########
+
+struct AngularMomentum{T,Ax<:Inclusion} <: LazyQuasiMatrix{T}
+    axis::Ax
+end
+
+AngularMomentum{T}(axis::Inclusion) where T = AngularMomentum{T,typeof(axis)}(axis)
+AngularMomentum{T}(domain) where T = AngularMomentum{T}(Inclusion(domain))
+AngularMomentum(axis) = AngularMomentum{eltype(eltype(axis))}(axis)
+
+axes(A::AngularMomentum) = (A.axis, A.axis)
+==(a::AngularMomentum, b::AngularMomentum) = a.axis == b.axis
+copy(A::AngularMomentum) = AngularMomentum(copy(A.axis))
+
+^(A::AngularMomentum, k::Integer) = ApplyQuasiArray(^, A, k)
+
+@simplify function *(A::AngularMomentum, P::DunklXuDisk)
+    β = P.β
+    n = mortar(Fill.(oneto(∞),oneto(∞)))
+    k = mortar(Base.OneTo.(oneto(∞)))
+    dat = PseudoBlockArray(Vcat(
+        (2 .* (k .+ (β - 1)) .* (n .- k .+ 1) ./ (2k .+ (2β - 1)))', # n, k-1
+        (0 .* n)', # n, k
+        (-k .* (k .+ 2β) .* (n .+ k .+ 2β) ./ ((2k .+ (2β - 1)) .* (2k .+ 2β)))', # n, k+1
+        ), (blockedrange(Fill(3, 1)), axes(n,1)))
+    DunklXuDisk(β) * _BandedBlockBandedMatrix(dat, axes(k,1), (0,0), (1,1))
+end

test/test_rectdisk.jl

@@ -55,6 +55,12 @@ import MultivariateOrthogonalPolynomials: dunklxu_raising, dunklxu_lowering
 
         @test λ ≈ im*imag(λ)
 
+        ∂θ = AngularMomentum(P)
+
+        A = P \ (∂θ * P)
+
+        @test A[Block.(1:N), Block.(1:N)] ≈ C
+
         @testset "truncations" begin
             KR,JR = Block.(1:N),Block.(1:N)