work on cone

Author: dlfivefifty

Project.toml

@@ -1,5 +1,6 @@
 name = "MultivariateOrthogonalPolynomials"
 uuid = "4f6956fd-4f93-5457-9149-7bfc4b2ce06d"
+version = "0.0.1"
 
 [deps]
 ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
@@ -17,25 +18,27 @@ InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
 Libdl = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 ApproxFun = "0.11"
-ApproxFunBase = "≥ 0.0.3"
+ApproxFunBase = "0.1"
 BandedMatrices = "0.9"
 BlockArrays = "0.8"
-DomainSets = "≥ 0.0.1"
+DomainSets = "0.0.2"
 FastGaussQuadrature = "≥ 0.3.0"
 FastTransforms = "≥ 0.4.1"
 FillArrays = "≥ 0.5"
-InfiniteArrays = "0.0.3"
+InfiniteArrays = "0.1"
 LazyArrays = "0.8"
 RecipesBase = "≥ 0.5.0"
 SpecialFunctions = "≥ 0.6.0"
 StaticArrays = "≥ 0.3.0"
-julia = "≥ 0.7.0"
+julia = "0.7, 1"

src/Cone/Cone.jl

@@ -58,31 +58,40 @@ function evaluate(cfs::AbstractVector, S::DuffyCone, txy::Vec{3})
     Fun(rectspace(S), cfs)(t,θ)
 end
 
-
-function _coefficients(triangleplan, v::AbstractVector{T}, ::DuffyCone, ::LegendreCone) where T
-    F = totensor(rectspace(DuffyCone()), v)
-    F = pad(F, :, 2size(F,1)-1)
+function duffy2legendrecone!(triangleplan, F::AbstractMatrix)
     Fc = F[:,1:2:end]
     c_execute_tri_lo2hi(triangleplan, Fc)
     F[:,1:2:end] .= Fc
     # ignore first column
     Fc[:,2:end] .= F[:,2:2:end]
     c_execute_tri_lo2hi(triangleplan, Fc)
     F[:,2:2:end] .= Fc[:,2:end]
-    fromtensor(LegendreCone(), F)
+    F
 end
 
-function _coefficients(triangleplan, v::AbstractVector{T}, ::LegendreCone,  ::DuffyCone) where T
-    F = totensor(LegendreCone(), v)
-    F = pad(F, :, 2size(F,1)-1)
+function legendre2duffycone!(triangleplan, F::AbstractMatrix)
     Fc = F[:,1:2:end]
     c_execute_tri_hi2lo(triangleplan, Fc)
     F[:,1:2:end] .= Fc
     # ignore first column
     Fc[:,2:end] .= F[:,2:2:end]
     c_execute_tri_hi2lo(triangleplan, Fc)
     F[:,2:2:end] .= Fc[:,2:end]
-    fromtensor(DuffyCone(), F)
+    F
+end
+
+function _coefficients(triangleplan, v::AbstractVector{T}, ::DuffyCone, ::LegendreCone) where T
+    F = totensor(rectspace(DuffyCone()), v)
+    F = pad(F, :, 2size(F,1)-1)
+    duffy2legendrecone!(triangleplan, F)
+    fromtensor(LegendreCone(), F)
+end
+
+function _coefficients(triangleplan, v::AbstractVector{T}, ::LegendreCone,  ::DuffyCone) where T
+    F = totensor(LegendreCone(), v)
+    F = pad(F, :, 2size(F,1)-1)
+    legendre2duffycone!(triangleplan, F)
+    fromtensor(rectspace(DuffyCone()), F)
 end
 
 function coefficients(cfs::AbstractVector{T}, CD::DuffyCone, ZD::LegendreCone) where T

test/test_cone.jl

@@ -1,5 +1,5 @@
 using ApproxFun, MultivariateOrthogonalPolynomials, Test
-import MultivariateOrthogonalPolynomials: rectspace, totensor
+import MultivariateOrthogonalPolynomials: rectspace, totensor, duffy2legendrecone!, legendre2duffycone!, c_plan_rottriangle, plan_transform
 
 @testset "DuffyCone" begin
     f = Fun((t,x,y) -> 1, DuffyCone(), 10)
@@ -26,28 +26,31 @@ import MultivariateOrthogonalPolynomials: rectspace, totensor
     @test g(t,x,y) ≈ f((t,x,y))
 end
 
-@testset "LegendreConePlan" begin
-    m,ℓ = (1,1)
-    f = (txy) -> ((t,x,y) = txy;  θ = atan(y,x); Fun(NormalizedJacobi(0,2m+1,Segment(1,0)),[zeros(ℓ);1])(t) * 2^m * t^m * cos(m*θ))
-    p = points(LegendreCone(), 10)
-    P = plan_transform(LegendreCone(), f.(p))
-    @test P.duffyplan*f.(p) ≈ Fun(f, DuffyCone()).coefficients[1:12]
-    coefficients(g, LegendreCone())
-    g = Fun(f, LegendreCone(), 20)
-    t,x,y = sqrt(0.1^2+0.2^2),0.1,0.2
-    @test g(t,x,y) ≈ f((t,x,y))
-end
-
 @testset "Legendre<>DuffyCone" begin
-    a = randn(10)
-    F = totensor(rectspace(DuffyCone()), a)
-
+    for k = 0:10
+        a = [zeros(k); 1.0; zeros(5)]
+        F = totensor(rectspace(DuffyCone()), a)
+        F = pad(F, :, 2size(F,1)-1)
+        T = eltype(a)
+        P = c_plan_rottriangle(size(F,1), zero(T), zero(T), zero(T))
+        @test legendre2duffycone!(P, duffy2legendrecone!(P, copy(F))) ≈ F
+
+        b = coefficients(a, LegendreCone(), DuffyCone())
+        @test a ≈ coefficients(b, DuffyCone(), LegendreCone())[1:length(a)]
+    end
+end
 
-    b = coefficients(a, LegendreCone(), DuffyCone())
 
-    coefficients(b, DuffyCone(), LegendreCone())
+@testset "LegendreConePlan" begin
+    for (m,ℓ) in ((0,0), (0,1), (0,2), (1,1), (1,2), (2,2))
+        f = (txy) -> ((t,x,y) = txy;  θ = atan(y,x); Fun(NormalizedJacobi(0,2m+1,Segment(1,0)),[zeros(ℓ);1])(t) * 2^m * t^m * cos(m*θ))
+        g = Fun(f, LegendreCone())
+        t,x,y = sqrt(0.1^2+0.2^2),0.1,0.2
+        @test g(t,x,y) ≈ f((t,x,y))
+    end
 end
 
+
 @testset "LegendreCone" begin
     f = Fun((t,x,y) -> 1, LegendreCone(), 10)
     @test f.coefficients ≈ [1; zeros(ncoefficients(f)-1)]
@@ -58,6 +61,5 @@ end
     f = Fun((t,x,y) -> 1+t+x+y, LegendreCone(), 10)
     @test f(sqrt(0.1^2+0.2^2),0.1,0.2) ≈ 1+sqrt(0.1^2+0.2^2)+0.1+0.2
 
-
     @time Fun((t,x,y) -> 1+t+x+y, LegendreCone(), 1000)
 end