Use == for Integer in spacescompatible (#218)

* Use == for Integer in Jacobi spacescompatible

* consistent spacescompatible between Ultraspherical and Jacobi

* compare_orders in Laguerre

Author: jishnub

src/ApproxFunOrthogonalPolynomials.jl

@@ -121,6 +121,13 @@ convert_vector_or_svector(t::Tuple) = SVector(t)
 
 const TupleOrVector{T} = Union{Tuple{T,Vararg{T}},AbstractVector{<:T}}
 
+# If any of the orders is an Integer, use == for an exact comparison, else fall back to isapprox
+# We assume that Integer orders are deliberately chosen to be exact
+compare_op(::Integer, args...) = ==
+compare_op() = ≈
+compare_op(::Any, args...) = compare_op(args...)
+compare_orders(a::Number, b::Number) = compare_op(a, b)(a, b)
+
 include("bary.jl")
 
 

src/Spaces/Jacobi/Jacobi.jl

@@ -41,8 +41,8 @@ Base.promote_rule(::Type{Jacobi{D,R1,T1}},::Type{Jacobi{D,R2,T2}}) where {D,R1,R
 convert(::Type{Jacobi{D,R1,T1}},J::Jacobi{D,R2,T2}) where {D,R1,R2,T1,T2} =
     Jacobi{D,R1}(T1(J.b)::T1, T1(J.a)::T1, J.domain)::Jacobi{D,R1,T1}
 
-
-spacescompatible(a::Jacobi,b::Jacobi) = a.a ≈ b.a && a.b ≈ b.b && domainscompatible(a,b)
+compare_orders((Aa, Ba)::NTuple{2,Number}, (Ab, Bb)::NTuple{2,Number}) = compare_orders(Aa, Ba) && compare_orders(Ab, Bb)
+spacescompatible(a::Jacobi, b::Jacobi) = compare_orders((a.a, b.a), (a.b, b.b)) && domainscompatible(a,b)
 
 isapproxinteger_addhalf(a) = !isapproxinteger(a) && isapproxinteger(a+0.5)
 isapproxinteger_addhalf(::Integer) = false

src/Spaces/Laguerre/Laguerre.jl

@@ -35,7 +35,7 @@ const NormalizedLaguerre{T<:Real,D<:Ray} = NormalizedPolynomialSpace{Laguerre{T,
 NormalizedLaguerre(α) = NormalizedPolynomialSpace(Laguerre(α))
 NormalizedLaguerre() = NormalizedLaguerre(0)
 
-spacescompatible(A::Laguerre,B::Laguerre) = A.α ≈ B.α && B.domain == A.domain
+spacescompatible(A::Laguerre,B::Laguerre) = compare_orders(A.α, B.α) && B.domain == A.domain
 
 canonicaldomain(::Laguerre) = Ray()
 domain(d::Laguerre) = d.domain

src/Spaces/Ultraspherical/Ultraspherical.jl

@@ -128,7 +128,7 @@ end
 
 
 spacescompatible(a::Ultraspherical,b::Ultraspherical) =
-    order(a) == order(b) && domainscompatible(a,b)
+    compare_orders(order(a), order(b)) && domainscompatible(a,b)
 hasfasttransform(::Ultraspherical) = true
 
 

test/JacobiTest.jl

@@ -42,6 +42,15 @@ using Static
             @test ncoefficients(g) == 1
             @test coefficients(g)[1] == f(x)
         end
+
+        @testset "spacescompatible" begin
+            x = 1.0
+            y = 1.0 + eps(1.0)
+            Jx = Jacobi(x,x)
+            Jy = Jacobi(y,y)
+            @test ApproxFunBase.spacescompatible(Jx, Jy)
+            @test ApproxFunBase.spacescompatible(Ultraspherical(Jx), Ultraspherical(Jy))
+        end
     end
 
     @testset "Conversion" begin