scale coefficients correctly

Author: jishnub

src/Spaces/Jacobi/Jacobi.jl

@@ -134,16 +134,16 @@ 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))
 
-_chebyintervalcoeff(J) = [(J.b-J.a)/(2+J.a+J.b), 2.0/(2+J.a+J.b)]
-_Fun(J::Jacobi, ::ChebyshevInterval) = Fun(J, _chebyintervalcoeff(J))
+_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 = _chebyintervalcoeff(J) .* scale
+    coeffs = _unscaledcoeff(J) .* scale
     coeffs[1] += leftendpoint(d)
     Fun(J, coeffs)
 end
 function _Fun(J::Jacobi, d)
-    complexlength(d)/2*(Fun(J,_chebyintervalcoeff(J)))+leftendpoint(d)
+    complexlength(d)/2*(Fun(J,_unscaledcoeff(J)))+leftendpoint(d)
 end
 
 function Fun(::typeof(identity), J::Jacobi)

test/JacobiTest.jl

@@ -55,13 +55,25 @@ 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
+    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.))