Support different initialisations in NormalizationConstant (#16)

* Support different initialisations in NormalizationConstant

* v0.2.2

* Update test_hermite.jl

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "ClassicalOrthogonalPolynomials"
 uuid = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.2.1"
+version = "0.2.2"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

src/normalized.jl

@@ -1,16 +1,23 @@
+"""
+   NormalizationConstant
+
+gives the normalization constants so that the jacobi matrix is symmetric,
+that is, so we have orthonormal OPs:
+
+    Q == P*NormalizationConstant(P)
+"""
+
 
 mutable struct NormalizationConstant{T, PP<:AbstractQuasiMatrix{T}} <: AbstractCachedVector{T}
     P::PP # OPs
     data::Vector{T}
     datasize::Tuple{Int}
 
-    function NormalizationConstant{T, PP}(P::PP) where {T,PP<:AbstractQuasiMatrix{T}}
-        μ = inv(sqrt(sum(orthogonalityweight(P))))
-        new{T, PP}(P, [μ], (1,))
-    end
+    NormalizationConstant{T, PP}(μ, P::PP) where {T,PP<:AbstractQuasiMatrix{T}} = new{T, PP}(P, T[μ], (1,))
 end
 
-NormalizationConstant(P::AbstractQuasiMatrix{T}) where T = NormalizationConstant{T,typeof(P)}(P)
+NormalizationConstant(μ, P::AbstractQuasiMatrix{T}) where T = NormalizationConstant{T,typeof(P)}(μ, P)
+NormalizationConstant(P::AbstractQuasiMatrix) = NormalizationConstant(inv(sqrt(sum(orthogonalityweight(P)))), P)
 
 size(K::NormalizationConstant) = (ℵ₀,)
 

test/test_hermite.jl

@@ -4,13 +4,20 @@ import DomainSets: ℝ
 
 @testset "Hermite" begin
     H = Hermite()
+    w = HermiteWeight()
+    
     @test axes(H) == (Inclusion(ℝ), oneto(∞))
     x = axes(H,1)
     @test H[0.1,1:4] ≈ [1,2*0.1,4*0.1^2-2,8*0.1^3-12*0.1]
+    @test w[0.1] ≈ exp(-0.1^2)
 
     X = jacobimatrix(H)
     @test 0.1 * H[0.1,1:10]' ≈ H[0.1,1:11]'*X[1:11,1:10]
 
+    @test (H'*(w .* H))[1,1] ≈ sqrt(π)
+    @test (H'*(w .* H))[2,2] ≈ 2sqrt(π)
+    @test (H'*(w .* H))[3,3] ≈ 8sqrt(π)
+
     D = Derivative(x)
     @test (D*H)[0.1,1:4] ≈ [0,2,8*0.1,24*0.1^2-12]
 end