Realised Hermite and Stieltjes tests weren't being run... need to come back later and fix bugs

Author: dlfivefifty

Project.toml

@@ -36,7 +36,7 @@ FastGaussQuadrature = "0.4.3"
 FastTransforms = "0.11, 0.12"
 FillArrays = "0.11"
 InfiniteArrays = "0.10"
-InfiniteLinearAlgebra = "0.5.1"
+InfiniteLinearAlgebra = "0.5.2"
 IntervalSets = "0.5"
 LazyArrays = "0.20.6"
 LazyBandedMatrices = "0.5"

src/hermite.jl

@@ -18,6 +18,7 @@ axes(::Hermite{T}) where T = (Inclusion(ℝ), oneto(∞))
 # 1/2 * H_{n+1} + n H_{n-1} = x H_n 
 # x*[H_0 H_1 H_2 …] = [H_0 H_1 H_2 …] * [0    1; 1/2  0     2; 1/2   0  3; …]   
 jacobimatrix(H::Hermite{T}) where T = Tridiagonal(Fill(one(T)/2,∞), Zeros{T}(∞), one(T):∞)
+recurrencecoefficients(H::Hermite{T}) where T = Fill{T}(2,∞), Zeros{T}(∞), zero(T):2:∞
 
 @simplify function *(Ac::QuasiAdjoint{<:Any,<:Hermite}, B::WeightedBasis{<:Any,<:HermiteWeight,<:Hermite})  
     T = promote_type(eltype(Ac), eltype(B))

test/runtests.jl

@@ -31,10 +31,12 @@ include("test_chebyshev.jl")
 include("test_legendre.jl")
 include("test_ultraspherical.jl")
 include("test_jacobi.jl")
+include("test_hermite.jl")
 include("test_fourier.jl")
 include("test_odes.jl")
 include("test_normalized.jl")
 include("test_lanczos.jl")
+include("test_stieltjes.jl")
 
 @testset "Auto-diff" begin
     U = Ultraspherical(1)

test/test_hermite.jl

@@ -1,24 +1,15 @@
 using ClassicalOrthogonalPolynomials, ContinuumArrays, DomainSets, FillArrays, Test
-import ClassicalOrthogonalPolynomials: jacobimatrix
+import ClassicalOrthogonalPolynomials: jacobimatrix, oneto
 
 @testset "Hermite" begin
     H = Hermite()
     @test axes(H) == (Inclusion(ℝ), oneto(∞))
     x = axes(H,1)
-    X = jacobimatrix(H)
-
-    w = HermiteWeight()
-    wH = w.*H
-    M = H'* ( w.*H)
-    S = Diagonal(M.diag .^ (-1/2))
-    Si = Diagonal(M.diag .^ (1/2))
-    J = Si*X*S
+    @test H[0.1,1:4] ≈ [1,2*0.1,4*0.1^2-2,8*0.1^3-12*0.1]
 
-    (J - im*Eye(∞)) \ [1;zeros(∞)]
+    X = jacobimatrix(H)
+    @test 0.1 * H[0.1,1:10]' ≈ H[0.1,1:11]'*X[1:11,1:10]
 
-    @test H[0.1,1] === 1.0 # equivalent to H_0(0.1) == 1.0
     D = Derivative(x)
-    
-    h = 0.000001
-    @test (D*H)[0.1,1:5] ≈ (H[0.1+h,1:5] - H[0.1,1:5])/h atol=100h
+    @test (D*H)[0.1,1:4] ≈ [0,2,8*0.1,24*0.1^2-12]
 end

test/test_stieltjes.jl

@@ -10,20 +10,23 @@ import ClassicalOrthogonalPolynomials: Hilbert, StieltjesPoint
     @test S isa StieltjesPoint{ComplexF64,Float64,ChebyshevInterval{Float64}}
     f = wT * [[1,2,3]; zeros(∞)];
     J = T \ (x .* T)
-    @test π*((z*I-J) \ f.args[2])[1,1] ≈ (S*f)[1]
+    # TODO: fix LazyBandedMatrices.copy(M::Mul{Broadcast...}) to call simplify
+    @test_broken π*((z*I-J) \ f.args[2])[1,1] ≈ (S*f)[1]
+    @test π*((z*I-J) \ f.args[2])[1,1] ≈ (S*f.args[1]*f.args[2])[1]
 
     x = Inclusion(0..1)
     y = 2x .- 1
     wT2 = wT[y,:]
     S = inv.(z .- x')
     f = wT2 * [[1,2,3]; zeros(∞)];
 
-    @test (π/2*(((z-1/2)*I - J/2) \ f.args[2]))[1] ≈ (S*f)[1]
+    # TODO: fix LazyArrays ambiguity
+    @test_broken (π/2*(((z-1/2)*I - J/2) \ f.args[2]))[1] ≈ (S*f.args[1]*f.args[2])[1]
 end
 
 @testset "Hilbert" begin
-    wT = ChebyshevWeight() .* Chebyshev()
-    wU = UltrasphericalWeight(1) .*  Ultraspherical(1)
+    wT = ChebyshevTWeight() .* ChebyshevT()
+    wU = ChebyshevUWeight() .* ChebyshevU()
     x = axes(wT,1)
     H = inv.(x .- x')
     @test H isa Hilbert{Float64,ChebyshevInterval{Float64}}
@@ -43,7 +46,7 @@ end
     wT2 = wT[y,:]
     wU2 = wU[y,:]
     @test (Ultraspherical(1)[y,:]\(H*wT2))[1:10,1:10] == diagm(1 => fill(-π,9))
-    @test (Chebyshev()[y,:]\(H*wU2))[1:10,1:10] == diagm(-1 => fill(1.0π,9))
+    @test_broken (Chebyshev()[y,:]\(H*wU2))[1:10,1:10] == diagm(-1 => fill(1.0π,9))
 end
 
 @testset "Log kernel" begin