make linear_combination work with SVector of coefficients

src/derivatives.jl

@@ -12,11 +12,11 @@ export 𝑑, ∂
 
 _one(::Type{T}) where {T<:Real} = one(T)
 
-_add(x::Real, y::Real) = x + y
+_add(x::T, y::T) where {T <: Union{Real,SVector}} = x + y
 
 _sub(x::Real, y::Real) = x - y
 
-_mul(x::Real, y::Real) = x * y
+_mul(x::Union{Real,SVector}, y::Real) = x * y
 
 _mul(x, y, z) = _mul(_mul(x, y), z)
 

src/generic_api.jl

@@ -106,6 +106,10 @@ $(SIGNATURES)
 
 Helper function for linear combinations of basis elements at `x`. Always checks that `θ`
 and `basis` have compatible dimensions.
+
+!!! NOTE
+    `x` and `θ` can be anything that supports `_mul(θ[i], b[i])` and `_add` on the
+    result of this.
 """
 @inline function _linear_combination(basis, θ, x)
     # an implementation of mapreduce, to work around

test/test_generic_api.jl

@@ -88,6 +88,15 @@ end
     @test transform_from(basis, t, x) == transform_from(domain(basis), t, x)
 end
 
+@testset "linear combination SVector passthrough" begin
+    N = 10
+    M = 3
+    basis = Chebyshev(InteriorGrid(), N) ∘ SemiInfRational(0.0, 1.0)
+    θ = rand(SVector{M,Float64}, N)
+    x = 2.0
+    @test linear_combination(basis, θ, x) ≡ SVector{M}(linear_combination(basis, map(x -> x[i], θ), x) for i in 1:M)
+end
+
 @testset "subset fallback" begin
     @test !is_subset_basis(Chebyshev(InteriorGrid(), 4), # just test the fallback method
                            smolyak_basis(Chebyshev, InteriorGrid(), SmolyakParameters(2, 2), 2))