Support normalized Half Weighted lowering (#23)

* Support normalized Half Weighted lowering

* Update jacobi.jl

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "ClassicalOrthogonalPolynomials"
 uuid = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
 authors = ["Sheehan Olver <solver@mac.com>"]
-version = "0.3.1"
+version = "0.3.2"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

src/jacobi.jl

@@ -174,6 +174,12 @@ broadcasted(::LazyQuasiArrayStyle{2}, ::typeof(*), x::Inclusion, Q::HalfWeighted
 \(w_A::HalfWeighted, B::AbstractQuasiArray) = convert(WeightedOrthogonalPolynomial, w_A) \ B
 \(A::AbstractQuasiArray, w_B::HalfWeighted) = A \ convert(WeightedOrthogonalPolynomial, w_B)
 
+function \(A::AbstractQuasiArray, w_B::WeightedOrthogonalPolynomial{<:Any,<:Weight,<:Normalized})
+    w,B = w_B.args
+    B̃,D = arguments(ApplyLayout{typeof(*)}(), B)
+    (A \ (w .* B̃)) * D
+end
+
 axes(::AbstractJacobi{T}) where T = (Inclusion{T}(ChebyshevInterval{real(T)}()), oneto(∞))
 ==(P::Jacobi, Q::Jacobi) = P.a == Q.a && P.b == Q.b
 ==(P::Legendre, Q::Jacobi) = Jacobi(P) == Q

src/normalized.jl

@@ -178,6 +178,9 @@ abstract type AbstractWeighted{T} <: Basis{T} end
 
 MemoryLayout(::Type{<:AbstractWeighted}) = WeightedBasisLayout()
 ContinuumArrays.unweightedbasis(wP::AbstractWeighted) = wP.P
+\(w_A::AbstractWeighted, w_B::AbstractWeighted) = convert(WeightedOrthogonalPolynomial, w_A) \ convert(WeightedOrthogonalPolynomial, w_B)
+\(w_A::AbstractWeighted, B::AbstractQuasiArray) = convert(WeightedOrthogonalPolynomial, w_A) \ B
+\(A::AbstractQuasiArray, w_B::AbstractWeighted) = A \ convert(WeightedOrthogonalPolynomial, w_B)
 
 """
     Weighted(P)
@@ -200,9 +203,6 @@ convert(::Type{WeightedOrthogonalPolynomial}, P::Weighted) = weight(P) .* unweig
 getindex(Q::Weighted, x::Union{Number,AbstractVector}, jr::Union{Number,AbstractVector}) = weight(Q)[x] .* unweightedbasis(Q)[x,jr]
 broadcasted(::LazyQuasiArrayStyle{2}, ::typeof(*), x::Inclusion, Q::Weighted) = Q * (Q.P \ (x .* Q.P))
 
-\(w_A::Weighted, w_B::Weighted) = convert(WeightedOrthogonalPolynomial, w_A) \ convert(WeightedOrthogonalPolynomial, w_B)
-\(w_A::Weighted, B::AbstractQuasiArray) = convert(WeightedOrthogonalPolynomial, w_A) \ B
-\(A::AbstractQuasiArray, w_B::Weighted) = A \ convert(WeightedOrthogonalPolynomial, w_B)
 
 @simplify *(Ac::QuasiAdjoint{<:Any,<:Weighted}, wB::Weighted) = 
     convert(WeightedOrthogonalPolynomial, parent(Ac))' * convert(WeightedOrthogonalPolynomial, wB)

test/test_jacobi.jl

@@ -386,6 +386,14 @@ import ClassicalOrthogonalPolynomials: recurrencecoefficients, basis, MulQuasiMa
         @test convert(WeightedOrthogonalPolynomial, HalfWeighted{:a}(Normalized(Jacobi(0.1,0.2))))[0.1,1:10] ≈
             HalfWeighted{:a}(Normalized(Jacobi(0.1,0.2)))[0.1,1:10]
         @test convert(WeightedOrthogonalPolynomial, HalfWeighted{:b}(Normalized(Jacobi(0.1,0.2))))[0.1,1:10] ≈
-            HalfWeighted{:b}(Normalized(Jacobi(0.1,0.2)))[0.1,1:10]            
+            HalfWeighted{:b}(Normalized(Jacobi(0.1,0.2)))[0.1,1:10]
+
+        
+        L = Normalized(Jacobi(0, 0)) \ HalfWeighted{:a}(Normalized(Jacobi(1, 0)))
+        @test Normalized(Jacobi(0, 0))[0.1,1:11]'*L[1:11,1:10] ≈ HalfWeighted{:a}(Normalized(Jacobi(1, 0)))[0.1,1:10]'
+        L = Jacobi(0, 0) \ HalfWeighted{:a}(Normalized(Jacobi(1, 0)))
+        @test Jacobi(0, 0)[0.1,1:11]'*L[1:11,1:10] ≈ HalfWeighted{:a}(Normalized(Jacobi(1, 0)))[0.1,1:10]'
+        L = Normalized(Jacobi(0, 0)) \ HalfWeighted{:a}(Jacobi(1, 0))
+        @test Normalized(Jacobi(0, 0))[0.1,1:11]'*L[1:11,1:10] ≈ HalfWeighted{:a}(Jacobi(1, 0))[0.1,1:10]'
     end
 end