Support plotting on disks

Author: dlfivefifty

Project.toml

@@ -18,6 +18,7 @@ InfiniteLinearAlgebra = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
 LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
 LazyBandedMatrices = "d7e5e226-e90b-4449-9968-0f923699bf6f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 QuasiArrays = "c4ea9172-b204-11e9-377d-29865faadc5c"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

examples/diskhelmholtz.jl

@@ -1,20 +1,45 @@
-using MultivariateOrthogonalPolynomials, FastTransforms, BlockBandedMatrices, Plots
+using MultivariateOrthogonalPolynomials, FastTransforms, BlockBandedMatrices, WGLMakie
+import MultivariateOrthogonalPolynomials: ZernikeITransform, grid
+
+Z = Zernike()[:,Block.(Base.OneTo(10))]
+G = grid(Z)
+
+contourf(first.(G), last.(G), ones(size(G)...))
+
+
+scatter(vec(first.(G)), vec(last.(G)))
+G[1,1].θ
 
 WZ = Weighted(Zernike(1))
 xy = axes(WZ,1)
 x,y = first.(xy),last.(xy)
-u = Zernike(1) \ @. exp(x*cos(y))
+f = Zernike(1) \ @. exp(x*cos(y))
 
 N = 50
 KR = Block.(Base.OneTo(N))
-Δ = BandedBlockBandedMatrix((Zernike(1) \ (Laplacian(xy) * WZ))[KR,KR],(0,0),(0,0))
+Δ = (Zernike(1) \ (Laplacian(xy) * WZ))[KR,KR]
 C = (Zernike(1) \ WZ)[KR,KR]
 k = 5
 L = Δ - k^2 * C
 
-v = (L \ u[KR])
+v = f[KR]
+@time u = (L \ v);
+
+g = MultivariateOrthogonalPolynomials.grid(Zernike(1)[:,KR])
+U = ZernikeITransform{Float64}(N, 0, 1) * u
+
+plot(first.(g), last.(g), U)
+
+
+
+F = factorize(Zernike(1)[:,KR]).plan
+F \ u
+u
+
+
+F*u
+
 
-F = factorize(Zernike(1)[:,KR])
 F.plan \ v
 F |> typeof |> fieldnames
 

src/disk.jl

@@ -184,12 +184,24 @@ struct ZernikeTransform{T} <: Plan{T}
     analysis::FastTransforms.FTPlan{T,2,FastTransforms.DISKANALYSIS}
 end
 
+struct ZernikeITransform{T} <: Plan{T}
+    N::Int
+    disk2cxf::FastTransforms.FTPlan{T,2,FastTransforms.DISK}
+    synthesis::FastTransforms.FTPlan{T,2,FastTransforms.DISKSYNTHESIS}
+end
+
 function ZernikeTransform{T}(N::Int, a::Number, b::Number) where T<:Real
     Ñ = N ÷ 2 + 1
     ZernikeTransform{T}(N, plan_disk2cxf(T, Ñ, a, b), plan_disk_analysis(T, Ñ, 4Ñ-3))
 end
+function ZernikeITransform{T}(N::Int, a::Number, b::Number) where T<:Real
+    Ñ = N ÷ 2 + 1
+    ZernikeITransform{T}(N, plan_disk2cxf(T, Ñ, a, b), plan_disk_synthesis(T, Ñ, 4Ñ-3))
+end
+
+
 *(P::ZernikeTransform{T}, f::Matrix{T}) where T = DiskTrav(P.disk2cxf \ (P.analysis * f))[Block.(1:P.N)]
-\(P::ZernikeTransform, f::AbstractVector) = P.analysis \ (P.disk2cxf * DiskTrav(f).matrix)
+*(P::ZernikeITransform, f::AbstractVector) = P.synthesis * (P.disk2cxf * DiskTrav(f).matrix)
 
 factorize(S::FiniteZernike{T}) where T = TransformFactorization(grid(S), ZernikeTransform{T}(blocksize(S,2), parent(S).a, parent(S).b))