Add inverse chebyshev transform plan for Dual (#904)

* Add inverse chebyshev transform plan for Dual

* Test inverse Chebyshev transform for dual numbers

* Version bump to v0.13.23

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFun"
 uuid = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
-version = "0.13.22"
+version = "0.13.23"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

ext/ApproxFunDualNumbersExt.jl

@@ -5,9 +5,9 @@ using ApproxFun
 using ApproxFun: TransformPlan, ITransformPlan
 import ApproxFunBase: valsdomain_type_promote
 using DomainSets
-import FastTransforms: ChebyshevTransformPlan, plan_chebyshevtransform,
-                        plan_chebyshevtransform!, plan_ichebyshevtransform,
-                        plan_ichebyshevtransform!
+import FastTransforms: ChebyshevTransformPlan, IChebyshevTransformPlan,
+                        plan_chebyshevtransform, plan_chebyshevtransform!,
+                        plan_ichebyshevtransform, plan_ichebyshevtransform!
 
 # Dual number support. Should there be realpart and dualpart of Space and Domain?
 DualNumbers.realpart(f::Fun{S,T}) where {S,T<:Dual} = Fun(space(f),realpart.(coefficients(f)))
@@ -45,6 +45,7 @@ plan_ichebyshevtransform(v::AbstractVector{D}, ::Val{kind}) where {D<:Dual,kind}
 
 
 Base.:(*)(P::ChebyshevTransformPlan,v::AbstractVector{<:Dual}) = dual.(P*realpart.(v),P*dualpart.(v))
+Base.:(*)(P::IChebyshevTransformPlan,v::AbstractVector{<:Dual}) = dual.(P*realpart.(v),P*dualpart.(v))
 
 #TODO: Hardy{false}
 for (OP,TransPlan) in ((:plan_transform,:TransformPlan),(:plan_itransform,:ITransformPlan)),

test/ExtrasTest.jl

@@ -56,6 +56,9 @@ include(joinpath(@__DIR__, "testutils.jl"))
         f=Fun(x->exp(dual(x,1)),-1..1)
         @test coefficients(realpart(f)) == realpart.(coefficients(f))
         @test coefficients(dualpart(f)) == dualpart.(coefficients(f))
+
+        # Test inverse Chebyshev transform for dual numbers
+        @test all(absdual.(transform(space(f),values(f)) - coefficients(f)) .< 10eps())
     end
 
     @testset "Eig test #336" begin