ZernikeDIsk constructor

Author: dlfivefifty

src/Disk/Disk.jl

@@ -88,19 +88,19 @@ fromrectcfs(S, v) = fromtensor(S, checkerboard(totensor(rectspace(S),v)))
 evaluate(cfs::AbstractVector, S::ChebyshevDisk, x) = evaluate(torectcfs(S,cfs), rectspace(S), ipolar(x))
 
 
-function _coefficients(disk2cxf, v̂::AbstractVector, ::ChebyshevDisk, ::ZernikeDisk)
+function _coefficients(disk2cxf, v̂::AbstractVector{T}, ::ChebyshevDisk, ::ZernikeDisk) where T
     F = totensor(ChebyshevDisk(), v̂)
     F *= sqrt(convert(T,π))
     n = size(F,1)
     F̌ = disk2cxf \ pad(F,n,4n-3)
     trivec(F̌)
 end
 
-function _coefficients(disk2cxf, v::AbstractVector, ::ZernikeDisk,  ::ChebyshevDisk)
+function _coefficients(disk2cxf, v::AbstractVector{T}, ::ZernikeDisk,  ::ChebyshevDisk) where T
     F̌ = tridevec(v)
-    F̌ /= sqrt(convert(T,π))
-    n = size(F,1)
-    F = disk2cxf \ pad(F̌,n,4n-3)
+    n = size(F̌,1)
+    F = disk2cxf * pad(F̌,n,4n-3)
+    F /= sqrt(convert(T,π))
     fromtensor(ChebyshevDisk(), F)
 end
 
@@ -113,7 +113,7 @@ end
 function coefficients(cfs::AbstractVector, ZD::ZernikeDisk, CD::ChebyshevDisk)
     c = tridevec(cfs)            # TODO: wasteful
     n = size(c,1)
-    _coefficients(CDisk2CxfPlan(n), cfs, CD, ZD)
+    _coefficients(CDisk2CxfPlan(n), cfs, ZD, CD)
 end
 
 

test/test_disk.jl

@@ -1,10 +1,10 @@
-using Revise, ApproxFun, MultivariateOrthogonalPolynomials
+using Revise
+using  ApproxFun, MultivariateOrthogonalPolynomials
 import MultivariateOrthogonalPolynomials: checkerboard, icheckerboard, CDisk2CxfPlan
 import ApproxFunBase: totensor
 import ApproxFunOrthogonalPolynomials: jacobip
 
 
-
 function chebydiskeval(c::AbstractMatrix{T}, r, θ) where T
     ret = zero(T)
     for j = 1:2:size(c,2), k=1:size(c,1)
@@ -52,6 +52,7 @@ end
     P = CDisk2CxfPlan(n)
     d = P \ c
     @test d ≈ [1/sqrt(2)]
+    
     f = Fun((x,y) -> y, ChebyshevDisk()); n = 2;
     c = totensor(f.space, f.coefficients)
     c = pad(c, n, 4n-3)
@@ -80,7 +81,7 @@ end
         @test d[2,5] ≈ 1
     end
     @testset "different m and ℓ" begin
-        for (m,ℓ) in ((0,2), (1,1), (2,2), (2,6), (3,3))
+        for (m,ℓ) in ((0,0), (0,2), (1,1), (2,2), (2,6), (3,3))
             p1 = (r,θ) -> sqrt(2ℓ+2)*r^m*jacobip((ℓ-m)÷2, 0, m, 2r^2-1)*cos(m*θ)/sqrt(π)
             f = Fun((x,y) -> p1(sqrt(x^2+y^2), atan(y,x)), ChebyshevDisk());
             @test f(0.1*cos(0.2),0.1*sin(0.2)) ≈ p1(0.1,0.2)
@@ -99,3 +100,16 @@ end
     end
 end
 
+@testset "ChebyshevDisk-ZernikeDisk" begin
+    @test coefficients([sqrt(2/π)], ChebyshevDisk(), ZernikeDisk()) ≈ [1.0]
+    @test coefficients([1.0], ZernikeDisk(), ChebyshevDisk()) ≈ [sqrt(2/π)]
+end
+
+@testset "ZernikeDisk" begin
+    f = Fun((x,y) -> 1, ZernikeDisk(), 10)
+    @test f(0.1,0.2) ≈ 1.0
+    f = Fun((x,y) -> 1, ZernikeDisk())
+    @test f(0.1,0.2) ≈ 1.0
+    f = Fun((x,y) -> exp(x*cos(y-0.1)), ZernikeDisk())
+    @test f(0.1,0.2) ≈ exp(0.1*cos(0.1))
+end