Optimize identity Fun in Ultraspherical (#163)

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.5.19"
+version = "0.5.20"
 
 [deps]
 ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
@@ -19,7 +19,7 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
-ApproxFunBase = "0.7.43"
+ApproxFunBase = "0.7.50"
 ApproxFunBaseTest = "0.1"
 Aqua = "0.5"
 BandedMatrices = "0.16, 0.17"

src/Spaces/Chebyshev/Chebyshev.jl

@@ -36,15 +36,18 @@ end
 normalization(::Type{T}, sp::Chebyshev, k::Int) where T = T(π)/(2-FastTransforms.δ(k,0))
 
 Space(d::SegmentDomain) = Chebyshev(d)
+_norm(x) = norm(x)
+_norm(x::Real) = abs(x) # this preserves integers, whereas norm returns a float
 function Space(d::AbstractInterval)
     a,b = endpoints(d)
-    if isinf(norm(a)) && isinf(norm(b))
-        Chebyshev(Line(d))
-    elseif isinf(norm(a)) || isinf(norm(b))
-        Chebyshev(Ray(d))
+    d2 = if isinf(_norm(a)) && isinf(_norm(b))
+        Line(d)
+    elseif isinf(_norm(a)) || isinf(_norm(b))
+        Ray(d)
     else
-        Chebyshev(d)
+        d
     end
+    Chebyshev(d2)
 end
 
 

src/Spaces/IntervalSpace.jl

@@ -1,14 +1,5 @@
 Space(d::IntervalOrSegment) = Chebyshev(d)
 Space(d::FullSpace{<:Real}) = Chebyshev(Line())
 
-Fun(::typeof(identity), d::IntervalOrSegment{T}) where {T<:Number} =
+Fun(::typeof(identity), d::IntervalOrSegment{<:Number}) =
     Fun(Chebyshev(d), [mean(d), complexlength(d)/2])
-
-
-## Calculus
-
-
-
-# the default domain space is higher to avoid negative ultraspherical spaces
-Integral(d::IntervalOrSegment,n::Integer) = Integral(Ultraspherical(1,d),n)
-

src/Spaces/Ultraspherical/Ultraspherical.jl

@@ -100,7 +100,7 @@ plan_itransform!(sp::Ultraspherical,cfs::AbstractVector) = UltrasphericalIPlan(o
 #domain(S) may be any domain
 
 ones(::Type{T},S::Ultraspherical) where {T<:Number} = Fun(S,fill(one(T),1))
-ones(S::Ultraspherical) = Fun(S,fill(1.0,1))
+ones(S::Ultraspherical) = ones(Float64, S)
 
 
 
@@ -118,7 +118,11 @@ Base.last(f::Fun{Ultraspherical{Int,D,R}}) where {D,R} = reduce(+,coefficients(f
 Base.first(f::Fun{Ultraspherical{O,D,R}}) where {O,D,R} = f(leftendpoint(domain(f)))
 Base.last(f::Fun{Ultraspherical{O,D,R}}) where {O,D,R} = f(rightendpoint(domain(f)))
 
-Fun(::typeof(identity), d::Ultraspherical) = Fun(Fun(identity, domain(d)),d)
+function Fun(::typeof(identity), s::Ultraspherical)
+    d = domain(s)
+    m = order(s)
+    Fun(s, [mean(d), complexlength(d)/4m])
+end
 
 
 ## Calculus

test/UltrasphericalTest.jl

@@ -9,6 +9,18 @@ using ApproxFunBaseTest: testbandedbelowoperator, testbandedoperator, testspace,
 using ApproxFunOrthogonalPolynomials: jacobip
 
 @testset "Ultraspherical" begin
+    @testset "identity fun" begin
+        for d in (ChebyshevInterval(), 3..4, Segment(2, 5), Segment(1, 4im)), order in (1, 2, 0.5)
+            s = Ultraspherical(order, d)
+            f = Fun(s)
+            xl = leftendpoint(domain(s))
+            xr = rightendpoint(domain(s))
+            xm = (xl + xr)/2
+            @test f(xl) ≈ xl
+            @test f(xr) ≈ xr
+            @test f(xm) ≈ xm
+        end
+    end
     @testset "Conversion" begin
         # Tests whether invalid/unimplemented arguments correctly throws ArgumentError
         @test_throws ArgumentError Conversion(Ultraspherical(2), Ultraspherical(1))