Disallow banded Ultraspherical conversion from n+1 to n (#308)

* Disallow banded Ultraspherical conversion from n+1 to n

* Add bandwidth test for HalfOddInt

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.6.45"
+version = "0.6.46"
 
 [deps]
 ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"

src/Spaces/Ultraspherical/UltrasphericalOperators.jl

@@ -174,7 +174,7 @@ function Conversion(A::Ultraspherical,B::Ultraspherical)
     if b==a
         return ConversionWrapper(Operator(I,A))
     elseif isapproxinteger(b-a) || isapproxhalfoddinteger(b-a)
-        if -1 ≤ b-a ≤ 1 && (a,b) ≠ (2,1)
+        if -0.5 ≤ b-a ≤ 1 # -0.5, 0.5 or 1
             return ConcreteConversion(A,B)
         elseif b-a > 1
             r = b:-1:a+1
@@ -251,6 +251,7 @@ end
 
 bandwidths(C::ConcreteConversion{<:Chebyshev,<:Ultraspherical{<:Integer}}) = 0,2  # order == 1
 bandwidths(C::ConcreteConversion{<:Ultraspherical{<:Integer},<:Ultraspherical{<:Integer}}) = 0,2
+bandwidths(C::ConcreteConversion{<:Ultraspherical{<:HalfOddInteger},<:Ultraspherical{<:HalfOddInteger}}) = 0,2
 
 function bandwidths(C::ConcreteConversion{<:Chebyshev,<:Ultraspherical})
     orderone = order(rangespace(C)) == 1

test/UltrasphericalTest.jl

@@ -38,6 +38,7 @@ include("testutils.jl")
     end
     @testset "Conversion" begin
         # Tests whether invalid/unimplemented arguments correctly throws ArgumentError
+        @test_throws ArgumentError Conversion(Ultraspherical(3), Ultraspherical(2))
         @test_throws ArgumentError Conversion(Ultraspherical(2), Ultraspherical(1))
         @test_throws ArgumentError Conversion(Ultraspherical(3), Ultraspherical(1.9))
 
@@ -140,14 +141,26 @@ include("testutils.jl")
         ff = x->x^2 +2x^3 + 3x^4
         for n1 in (0.5, 1)
             f = Fun(ff, Ultraspherical(n1))
-            for n2 in (2.5, 3)
+            for n2 in (1.5, 2.5, 3)
                 CLU = Conversion(Ultraspherical(n1), Ultraspherical(n2))
                 @test !isdiag(CLU)
                 g = CLU * f
-                @test g ≈ Fun(ff, Ultraspherical(n1))
+                @test g ≈ Fun(ff, Ultraspherical(n2))
             end
         end
 
+        for n1 in (0.5, half(Odd(1)), 1)
+            f = Fun(ff, Ultraspherical(n1))
+            for n2 in (1, 0.5, half(Odd(1)))
+                CLU = Conversion(Ultraspherical(n1), Ultraspherical(n2))
+                g = CLU * f
+                @test g ≈ Fun(ff, Ultraspherical(n2))
+            end
+        end
+
+        C = Conversion(Ultraspherical(half(Odd(1))), Ultraspherical(half(Odd(3))))
+        @test @inferred (C -> Val(bandwidths(C)))(C) == Val((0,2))
+
         @testset "Normalized" begin
             Tallowed = Union{
                 typeof(Conversion(Ultraspherical(1), NormalizedUltraspherical(1))),