1+ export ChebyshevDisk, ZernikeDisk
2+
3+ struct ZernikeDisk{V,T} <: Space{Disk{V},T}
4+ domain:: Disk{V}
5+ end
6+
7+ ZernikeDisk (d:: Disk{V} ) where V = ZernikeDisk {V,complex(eltype(V))} (d)
8+ ZernikeDisk () = ZernikeDisk (Disk ())
9+
10+ spacescompatible (:: ZernikeDisk , :: ZernikeDisk ) = true
11+
12+ @containsconstants ZernikeDisk
13+
14+ points (K:: ZernikeDisk , n:: Integer ) =
15+ fromcanonical .(Ref (K), points (ChebyshevDisk (), n))
16+
17+ evaluate (cfs:: AbstractVector , Z:: ZernikeDisk , xy) =
18+ Fun (Fun (Z, cfs), ChebyshevDisk ())(xy)
19+
20+ Space (d:: Disk ) = ZernikeDisk (d)
21+
22+ struct ChebyshevDisk{V,T} <: Space{Disk{V},T}
23+ domain:: Disk{V}
24+ end
25+
26+ @containsconstants ChebyshevDisk
27+
28+ ChebyshevDisk (d:: Disk{V} ) where V = ChebyshevDisk {V,eltype(V)} (d)
29+ ChebyshevDisk () = ChebyshevDisk (Disk ())
30+
31+ rectspace (_) = Chebyshev () * Fourier ()
32+
33+ spacescompatible (K1:: ChebyshevDisk , K2:: ChebyshevDisk ) = domainscompatible (K1, K2)
34+
35+ function points (S:: ChebyshevDisk , N)
36+ pts = points (rectspace (S), N)
37+ polar .(pts)
38+ end
39+
40+ DiskTensorizer () = Tensorizer ((Ones {Int} (∞),Ones {Int} (∞)))
41+
42+ tensorizer (K:: ChebyshevDisk ) = DiskTensorizer ()
43+
44+ # we have each polynomial
45+ blocklengths (K:: ChebyshevDisk ) = 1 : ∞
46+
47+ for OP in (:block ,:blockstart ,:blockstop )
48+ @eval begin
49+ $ OP (s:: ChebyshevDisk ,M:: Block ) = $ OP (tensorizer (s),M)
50+ $ OP (s:: ChebyshevDisk ,M) = $ OP (tensorizer (s),M)
51+ end
52+ end
53+
54+
55+ plan_transform (S:: ChebyshevDisk , n:: AbstractVector ) =
56+ TransformPlan (S, plan_transform (rectspace (S),n), Val{false })
57+ plan_itransform (S:: ChebyshevDisk , n:: AbstractVector ) =
58+ ITransformPlan (S, plan_itransform (rectspace (S),n), Val{false })
59+
60+ # drop every other entry
61+ function checkerboard (A:: AbstractMatrix{T} ) where T
62+ m,n = size (A)
63+ C = zeros (T, (m+ 1 )÷ 2 , n)
64+ z = @view (A[1 : 2 : end ,1 ])
65+ e1,e2 = @view (A[1 : 2 : end ,4 : 4 : end ]),@view (A[1 : 2 : end ,5 : 4 : end ])
66+ o1,o2 = @view (A[2 : 2 : end ,2 : 4 : end ]),@view (A[2 : 2 : end ,3 : 4 : end ])
67+ C[1 : size (z,1 ),1 ] .= z
68+ C[1 : size (e1,1 ),4 : 4 : n] .= e1
69+ C[1 : size (e2,1 ),5 : 4 : n] .= e2
70+ C[1 : size (o1,1 ),2 : 4 : n] .= o1
71+ C[1 : size (o2,1 ),3 : 4 : n] .= o2
72+ C
73+ end
74+
75+ function icheckerboard (C:: AbstractMatrix{T} ) where T
76+ m,n = size (C)
77+ A = zeros (T, 2 * m, n)
78+ A[1 : 2 : end ,1 ] .= C[:,1 ]
79+ A[1 : 2 : end ,4 : 4 : end ] .= C[:,4 : 4 : end ]
80+ A[1 : 2 : end ,5 : 4 : end ] .= C[:,5 : 4 : end ]
81+ A[2 : 2 : end ,2 : 4 : end ] .= C[:,2 : 4 : end ]
82+ A[2 : 2 : end ,3 : 4 : end ] .= C[:,3 : 4 : end ]
83+ A
84+ end
85+
86+ torectcfs (S, v) = fromtensor (rectspace (S), icheckerboard (totensor (S, v)))
87+ fromrectcfs (S, v) = fromtensor (S, checkerboard (totensor (rectspace (S),v)))
88+
89+ * (P:: TransformPlan{<:Any,<:ChebyshevDisk} , v:: AbstractArray ) = fromrectcfs (P. space, P. plan* v)
90+ * (P:: ITransformPlan{<:Any,<:ChebyshevDisk} , v:: AbstractArray ) = P. plan* torectcfs (P. space, v)
91+
92+ evaluate (cfs:: AbstractVector , S:: ChebyshevDisk , x) = evaluate (torectcfs (S,cfs), rectspace (S), ipolar (x))
93+
94+
95+ function _coefficients (disk2cxf, v̂:: AbstractVector{T} , :: ChebyshevDisk , :: ZernikeDisk ) where T
96+ F = totensor (ChebyshevDisk (), v̂)
97+ F *= sqrt (convert (T,π))
98+ n = size (F,1 )
99+ F̌ = disk2cxf \ pad (F,n,4 n- 3 )
100+ trivec (F̌)
101+ end
102+
103+ function _coefficients (disk2cxf, v:: AbstractVector{T} , :: ZernikeDisk , :: ChebyshevDisk ) where T
104+ F̌ = tridevec (v)
105+ n = size (F̌,1 )
106+ F = disk2cxf * pad (F̌,n,4 n- 3 )
107+ F /= sqrt (convert (T,π))
108+ fromtensor (ChebyshevDisk (), F)
109+ end
110+
111+ function coefficients (cfs:: AbstractVector , CD:: ChebyshevDisk , ZD:: ZernikeDisk )
112+ c = totensor (ChebyshevDisk (), cfs) # TODO : wasteful
113+ n = size (c,1 )
114+ _coefficients (CDisk2CxfPlan (n), cfs, CD, ZD)
115+ end
116+
117+ function coefficients (cfs:: AbstractVector , ZD:: ZernikeDisk , CD:: ChebyshevDisk )
118+ c = tridevec (cfs) # TODO : wasteful
119+ n = size (c,1 )
120+ _coefficients (CDisk2CxfPlan (n), cfs, ZD, CD)
121+ end
122+
123+
124+ struct FastZernikeDiskTransformPlan{DUF,CHEB}
125+ cxfplan:: DUF
126+ disk2cxf:: CHEB
127+ end
128+
129+ function FastZernikeDiskTransformPlan (S:: ZernikeDisk , v:: AbstractVector{T} ) where T
130+ # n = floor(Integer,sqrt(2length(v)) + 1/2)
131+ # v = Array{T}(undef, sum(1:n))
132+ cxfplan = plan_transform (ChebyshevDisk (),v)
133+ c = totensor (ChebyshevDisk (), cxfplan* v) # TODO : wasteful
134+ n = size (c,1 )
135+ FastZernikeDiskTransformPlan (cxfplan, CDisk2CxfPlan (n))
136+ end
137+
138+ * (P:: FastZernikeDiskTransformPlan , v:: AbstractVector ) =
139+ _coefficients (P. disk2cxf, P. cxfplan* v, ChebyshevDisk (), ZernikeDisk ())
140+
141+ plan_transform (K:: ZernikeDisk , v:: AbstractVector ) = FastZernikeDiskTransformPlan (K, v)
142+
143+ struct FastZernikeDiskITransformPlan{DUF,CHEB}
144+ icxfplan:: DUF
145+ disk2cxf:: CHEB
146+ end
147+
148+ function FastZernikeDiskITransformPlan (S:: ZernikeDisk , v:: AbstractVector{T} ) where T
149+ # n = floor(Integer,sqrt(2length(v)) + 1/2)
150+ # v = Array{T}(undef, sum(1:n))
151+ FastZernikeDiskITransformPlan (plan_itransform (ChebyshevDisk (), v), CDisk2CxfPlan (n))
152+ end
153+
154+ function * (P:: FastZernikeDiskITransformPlan , v)
155+ # n = floor(Integer,sqrt(2length(v)) + 1/2)
156+ # v = pad(v, sum(1:n))
157+ F̌ = trinormalize! (tridevec (v))
158+ F = P. disk2cxf * F̌
159+ v̂ = trivec (transpose (F))
160+ P. icxfplan* v̂
161+ end
162+
163+
164+ plan_itransform (K:: ZernikeDisk , v:: AbstractVector ) = FastZernikeDiskITransformPlan (K, v)
165+ Base. sum (f:: Fun{<:ZernikeDisk} ) = Fun (f,ZernikeDisk ()). coefficients[1 ]/ π
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