Overloads for Weighted Jacobi (#191)

* Overloads for Weighted Jacobi

* Update test_ultraspherical.jl

* Update test_ultraspherical.jl

Author: dlfivefifty

src/classical/jacobi.jl

@@ -377,9 +377,9 @@ function \(w_A::WeightedJacobi, w_B::WeightedJacobi)
 
     if wA == wB
         A \ B
-    elseif B.a == A.a && B.b == A.b+1 && wB.b == wA.b+1 && wB.a == wA.a
+    elseif B.a ≈ A.a && B.b ≈ A.b+1 && wB.b ≈ wA.b+1 && wB.a ≈ wA.a
         Bidiagonal(((2:2:∞) .+ 2A.b)./((2:2:∞) .+ (A.a+A.b)), (2:2:∞)./((2:2:∞) .+ (A.a+A.b)), :L)
-    elseif B.a == A.a+1 && B.b == A.b && wB.b == wA.b && wB.a == wA.a+1
+    elseif B.a ≈ A.a+1 && B.b ≈ A.b && wB.b ≈ wA.b && wB.a ≈ wA.a+1
         Bidiagonal(((2:2:∞) .+ 2A.a)./((2:2:∞) .+ (A.a+A.b)), -(2:2:∞)./((2:2:∞) .+ (A.a+A.b)), :L)
     elseif wB.a ≥ wA.a+1 && B.a > 0
         J = JacobiWeight(wB.a-1,wB.b) .* Jacobi(B.a-1,B.b)
@@ -405,6 +405,7 @@ end
 \(w_A::Weighted{<:Any,<:Jacobi}, w_B::WeightedJacobi) = convert(WeightedBasis,w_A) \ w_B
 \(A::Jacobi, w_B::Weighted{<:Any,<:Jacobi}) = A \ convert(WeightedBasis,w_B)
 
+\(w_A::Weighted{<:Any,<:Jacobi}, B::Legendre) = w_A \ Weighted(Jacobi(B))
 \(A::Legendre, wB::WeightedJacobi) = Jacobi(A) \ wB
 
 ##########

src/classical/ultraspherical.jl

@@ -183,6 +183,20 @@ function \(A::Jacobi, B::Ultraspherical)
     (A\B̃)*Diagonal(B[1,:]./B̃[1,:])
 end
 
+function \(wA::Weighted{<:Any,<:Ultraspherical}, wB::Weighted{<:Any,<:Jacobi})
+    A = wA.P
+    Ã = Jacobi(A)
+    Diagonal(Ã[1,:]./A[1,:]) * (Weighted(Ã)\wB)
+end
+
+function \(wA::Weighted{<:Any,<:Jacobi}, wB::Weighted{<:Any,<:Ultraspherical})
+    B = wB.P
+    B̃ = Jacobi(B)
+    (wA\Weighted(B̃))*Diagonal(B[1,:]./B̃[1,:])
+end
+
+
+
 function \(U::Ultraspherical{<:Any,<:Integer}, C::ChebyshevT)
     T = promote_type(eltype(U), eltype(C))
     (U\Ultraspherical{T}(1)) * (ChebyshevU{T}()\C)

test/test_ultraspherical.jl

@@ -177,4 +177,10 @@ using ClassicalOrthogonalPolynomials: grammatrix
         @test P[0.1,1:5] ≈ P̃[0.1,1:5] 
         @test (P \ Weighted(C))[1:10,1:10] ≈ (P \ Weighted(Jacobi(1,1)))[1:10,1:10] * (Jacobi(1,1) \ C)[1:10,1:10]
     end
+    @testset "Weighted(Jacobi) and Weighted(Ultraspherical)" begin
+        L = Weighted(Ultraspherical(1/2)) \ Weighted(Jacobi(1,0))
+        @test L[1:10,1:10] == (Legendre() \ Weighted(Jacobi(1,0)))[1:10,1:10]
+        L = Weighted(Jacobi(1,0)) \ Weighted(Ultraspherical(3/2))
+        @test L[1:10,1:10] == (Weighted(Jacobi(1,0)) \ Weighted(Jacobi(1,1)))[1:10,1:10] * (Jacobi(1,1) \ Ultraspherical(3/2))[1:10,1:10]
+    end
 end