Extend normalizedspace for PolynomialSpace (#242)

* Add normalized

* map normalized

* Extend normalizedspace from ApproxFunBase

* Extend normalizedspace for NormalizedPolynomialSpace

Author: jishnub

Project.toml

@@ -20,7 +20,7 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
-ApproxFunBase = "0.8.16"
+ApproxFunBase = "0.8.21"
 ApproxFunBaseTest = "0.1"
 Aqua = "0.5"
 BandedMatrices = "0.16, 0.17"

src/ApproxFunOrthogonalPolynomials.jl

@@ -44,7 +44,7 @@ import ApproxFunBase: Fun, SubSpace, WeightSpace, NoSpace, HeavisideSpace,
                     ℓ⁰, recα, recβ, recγ, ℵ₀, ∞, RectDomain,
                     assert_integer, supportsinplacetransform, ContinuousSpace, SpecialEvalPtType,
                     isleftendpoint, isrightendpoint, evaluation_point, boundaryfn, ldiffbc, rdiffbc,
-                    LeftEndPoint, RightEndPoint
+                    LeftEndPoint, RightEndPoint, normalizedspace
 
 import DomainSets: Domain, indomain, UnionDomain, FullSpace, Point,
             Interval, ChebyshevInterval, boundary, rightendpoint, leftendpoint,

src/Spaces/PolynomialSpace.jl

@@ -443,6 +443,9 @@ setdomain(NS::NormalizedPolynomialSpace, d::Domain) = NormalizedPolynomialSpace(
 
 NormalizedPolynomialSpace(space::PolynomialSpace{D,R}) where {D,R} = NormalizedPolynomialSpace{typeof(space),D,R}(space)
 
+normalizedspace(S::PolynomialSpace) = NormalizedPolynomialSpace(S)
+normalizedspace(S::NormalizedPolynomialSpace) = S
+
 supportsinplacetransform(N::NormalizedPolynomialSpace) = supportsinplacetransform(N.space)
 
 function Conversion(L::NormalizedPolynomialSpace{S}, M::S) where S<:PolynomialSpace

test/ChebyshevTest.jl

@@ -441,4 +441,18 @@ using ApproxFunOrthogonalPolynomials: forwardrecurrence
         blk = @inferred ApproxFunBase.block(s, 2)
         @test Int(blk) == 1
     end
+
+    @testset "PiecewiseSpace" begin
+        d = Segment(-1..0) ∪ Segment(0..1)
+        S = PiecewiseSpace(Chebyshev.(components(d)))
+        NS = normalizedspace(S)
+        @test domain(NS) == domain(S)
+        @test NS isa PiecewiseSpace{<:NTuple{<:Any,NormalizedChebyshev}}
+        f = Fun(S)
+        g = Conversion(S, NS) * f
+        @test g(0.4) ≈ 0.4
+        @test g(-0.4) ≈ -0.4
+
+        @test normalizedspace(NS) == NS
+    end
 end