Negative lower bandwidth for Jacobi derivative (#96)

Author: jishnub

src/Spaces/Jacobi/JacobiOperators.jl

@@ -107,7 +107,7 @@ end
 
 
 rangespace(D::ConcreteDerivative{J}) where {J<:Jacobi}=Jacobi(D.space.b+D.order,D.space.a+D.order,domain(D))
-bandwidths(D::ConcreteDerivative{J}) where {J<:Jacobi}=0,D.order
+bandwidths(D::ConcreteDerivative{J}) where {J<:Jacobi}=-D.order,D.order
 
 getindex(T::ConcreteDerivative{J},k::Integer,j::Integer) where {J<:Jacobi} =
     j==k+1 ? eltype(T)((k+1+T.space.a+T.space.b)/complexlength(domain(T))) : zero(eltype(T))

test/JacobiTest.jl

@@ -74,7 +74,8 @@ import ApproxFunOrthogonalPolynomials: jacobip
     @testset "Derivative" begin
         D=Derivative(Jacobi(0.,1.,Segment(1.,0.)))
         @time testbandedoperator(D)
-
+        # only one band should be populated
+        @test bandwidths(D, 1) == -bandwidths(D, 2)
 
         @testset for d in [-1..1, 0..1]
             f = Fun(x->x^2, Chebyshev(d))