defaultcoeff for int coeffs (#170)

Author: jishnub

src/Space.jl

@@ -310,7 +310,7 @@ _ldiv_coefficients!!(inplace::Val{false}) = ldiv_coefficients
 _Fun(v::AbstractVector, sp) = Fun(sp, v)
 _Fun(v, sp) = Fun(v, sp)
 _maybeconvert(inplace::Val{true}, f, v) = v
-_maybeconvert(inplace::Val{false}, f::AbstractVector, v) = strictconvert(Vector{eltype(f)}, v)
+_maybeconvert(inplace::Val{false}, f::AbstractVector, v) = strictconvert(Vector{float(eltype(f))}, v)
 function defaultcoefficients(f,a,b,inplace = Val(false))
     ct=conversion_type(a,b) # gives a space that has a banded conversion to both a and b
 

test/SpacesTest.jl

@@ -239,6 +239,18 @@ using StaticArrays
         v = @inferred coefficients(Float64[0,0,1], Chebyshev(), Ultraspherical(1))
         @test v ≈ [-0.5, 0, 0.5]
 
+        @testset "int coeffs" begin
+            f = Fun(Chebyshev(), [0,1])
+            @test f(0.4) ≈ 0.4
+            f = Fun(NormalizedChebyshev(), [0,1])
+            @test f(0.4) ≈ 0.4 * √(2/pi)
+
+            f = Fun(Chebyshev(), [1])
+            @test f(0.4) ≈ 1
+            f = Fun(NormalizedChebyshev(), [1])
+            @test f(0.4) ≈ √(1/pi)
+        end
+
         @testset "inplace transform" begin
             @testset for sp_c in Any[Legendre(), Chebyshev(), Jacobi(1,2), Jacobi(0.3, 2.3),
                     Ultraspherical(1), Ultraspherical(2)]