Support broadcasting and operators

Author: dlfivefifty

src/ClassicalOrthogonalPolynomials.jl

@@ -15,8 +15,8 @@ import LazyArrays: MemoryLayout, Applied, ApplyStyle, flatten, _flatten, colsupp
                 AbstractCachedVector, AbstractCachedMatrix
 import ArrayLayouts: MatMulVecAdd, materialize!, _fill_lmul!, sublayout, sub_materialize, lmul!, ldiv!, ldiv, transposelayout, triangulardata,
                         subdiagonaldata, diagonaldata, supdiagonaldata
-import LazyBandedMatrices: SymTridiagonal, Bidiagonal, Tridiagonal
-import LinearAlgebra: pinv, factorize, qr, adjoint, transpose
+import LazyBandedMatrices: SymTridiagonal, Bidiagonal, Tridiagonal, AbstractLazyBandedLayout
+import LinearAlgebra: pinv, factorize, qr, adjoint, transpose, dot
 import BandedMatrices: AbstractBandedLayout, AbstractBandedMatrix, _BandedMatrix, bandeddata
 import FillArrays: AbstractFill, getindex_value
 

src/clenshaw.jl

@@ -263,7 +263,7 @@ bandwidths(M::Clenshaw) = (length(M.c)-1,length(M.c)-1)
 Base.array_summary(io::IO, C::Clenshaw{T}, inds::Tuple{Vararg{OneToInf{Int}}}) where T =
     print(io, Base.dims2string(length.(inds)), " Clenshaw{$T} with $(length(C.c)) degree polynomial")
 
-struct ClenshawLayout <: AbstractBandedLayout end
+struct ClenshawLayout <: AbstractLazyBandedLayout end
 MemoryLayout(::Type{<:Clenshaw}) = ClenshawLayout()
 sublayout(::ClenshawLayout, ::Type{<:NTuple{2,AbstractUnitRange{Int}}}) = ClenshawLayout()
 sub_materialize(::ClenshawLayout, V) = BandedMatrix(V)

test/test_odes.jl

@@ -170,4 +170,14 @@ import SemiseparableMatrices: VcatAlmostBandedLayout
         u = L \ [airyai(-ε^(-2/3)); airyai(ε^(2/3)); zeros(∞)]
         @test T[-0.1,:]'u ≈ airyai(-0.1*ε^(-2/3))
     end
+
+    @testset "combo operators" begin
+        T = Chebyshev()
+        C = Ultraspherical(2)
+        x = axes(T,1)
+        D = Derivative(x)
+        L = x .* D + cos.(x) .* D^2
+        M = C \ (L * T)
+        @test C[0.1,:]' * (M * (T \ exp.(x))) ≈ (0.1 + cos(0.1))*exp(0.1)
+    end
 end