type-stability in Fun(identity, ::Jacobi) (#82)

* type-stability in Fun(identity, ::Jacobi)

* split default coeffs to separate function

* Fun for Interval

* scale coefficients correctly

* add tests against Legendre()

* version bump to v0.4.12

Author: jishnub

.github/workflows/ci.yml

@@ -2,6 +2,11 @@ name: CI
 on:
   - push
   - pull_request
+
+concurrency:
+  group: build-${{ github.event.pull_request.number || github.ref }}
+  cancel-in-progress: true
+
 jobs:
   test:
     name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.4.11"
+version = "0.4.12"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Spaces/Jacobi/Jacobi.jl

@@ -134,11 +134,20 @@ one(S::Jacobi) = Fun(S,fill(one(Float64),1))
 zeros(::Type{T},S::Jacobi) where {T<:Number} = Fun(S,zeros(T,1))
 zeros(S::Jacobi) = Fun(S,zeros(prectype(S),1))
 
-Fun(::typeof(identity), J::Jacobi{<:ChebyshevInterval}) =
-    Fun(J,[(J.b-J.a)/(2+J.a+J.b),2.0/(2+J.a+J.b)])
+_Fun(J::Jacobi, ::ChebyshevInterval) = Fun(J, [(J.b-J.a)/(2+J.a+J.b),2.0/(2+J.a+J.b)])
+_unscaledcoeff(J) = [2.0*(J.b + 1)/(2+J.a+J.b), 2.0/(2+J.a+J.b)]
+function _Fun(J::Jacobi, d::Interval)
+    scale = complexlength(d)/2
+    coeffs = _unscaledcoeff(J) .* scale
+    coeffs[1] += leftendpoint(d)
+    Fun(J, coeffs)
+end
+function _Fun(J::Jacobi, d)
+    complexlength(d)/2*(Fun(J,_unscaledcoeff(J)))+leftendpoint(d)
+end
+
 function Fun(::typeof(identity), J::Jacobi)
-    d=domain(J)
-    complexlength(d)/2*(Fun(J,[2.0*(J.b + 1)/(2+J.a+J.b),2.0/(2+J.a+J.b)]))+leftendpoint(d)
+    _Fun(J, domain(J))
 end
 
 

test/JacobiTest.jl

@@ -55,13 +55,29 @@ import ApproxFunOrthogonalPolynomials: jacobip
         @time testbandedoperator(D)
     end
 
+    @testset "identity Fun for interval domains" begin
+        for d in [1..2, -1..1, 10..20], s in Any[Legendre(d), Jacobi(1, 2, d), Jacobi(1.2, 2.3, d)]
+            f = Fun(identity, s)
+            g = Fun(x->x, s)
+            @test coefficients(f) ≈ coefficients(g)
+        end
+        f = Fun(identity, Legendre(-1..1))
+        g = Fun(identity, Legendre())
+        @test coefficients(f) ≈ coefficients(g)
+        @test f(0.2) ≈ g(0.2) ≈ 0.2
+    end
 
     @testset "Jacobi multiplication" begin
         x=Fun(identity,Jacobi(0.,0.))
         f=Fun(exp,Jacobi(0.,0.))
 
         @test (x*f)(.1) ≈ .1exp(.1)
 
+        x=Fun(identity,Jacobi(0.,0., 1..2))
+        f=Fun(exp,Jacobi(0.,0., 1..2))
+
+        @test (x*f)(1.1) ≈ 1.1exp(1.1)
+
         x=Fun(identity,Jacobi(12.324,0.123))
         f=Fun(exp,Jacobi(0.,0.))