Remove Hermite

src/sequence_spaces/special_operators/calculus.jl

@@ -1193,174 +1193,6 @@ function _nzval(ℐ::Integral, ::Chebyshev, ::Chebyshev, ::Type{T}, i, j) where
     end
 end
 
-# Hermite
-
-image(𝒟::Derivative, s::Hermite) = Hermite(order(s)+order(𝒟))
-
-_coeftype(::Derivative, ::Hermite, ::Type{T}) where {T} = float(T)
-
-function _apply!(c::Sequence{Hermite}, 𝒟::Derivative, a)
-    n = order(𝒟)
-    if n == 0
-        coefficients(c) .= coefficients(a)
-    elseif n == 1
-        real_CoefType = real(eltype(c))
-        order_a = order(a)
-        if order_a ≥ 1
-            @inbounds c[0] = - sqrt(convert(real_CoefType, ExactReal(1)) / ExactReal(2)) * a[1]
-        end
-        @inbounds for i ∈ 1:order_a+1
-            c[i] = sqrt(convert(real_CoefType, ExactReal(i)) / ExactReal(2)) * a[i-1]
-            if i+1 ≤ order_a
-                c[i] -= sqrt(convert(real_CoefType, ExactReal(i+1)) / ExactReal(2)) * a[i+1]
-            end
-        end
-    else # TODO: lift restriction
-        return throw(DomainError)
-    end
-    return c
-end
-
-function _apply!(C::AbstractArray{T}, 𝒟::Derivative, space::Hermite, A) where {T}
-    n = order(𝒟)
-    if n == 0
-        C .= A
-    elseif n == 1
-        real_T = real(T)
-        ord = order(space)
-        if ord ≥ 1
-            @inbounds selectdim(C, 1, 1) .= (-sqrt(convert(real_T, ExactReal(1)) / ExactReal(2))) .* selectdim(A, 1, i+1)
-        end
-        @inbounds for i ∈ 1:ord+1
-            Cᵢ = selectdim(C, 1, i+1)
-            Cᵢ .= (sqrt(convert(real_T, ExactReal(i)) / ExactReal(2))) .* selectdim(A, 1, i)
-            if i+1 ≤ ord
-                Cᵢ .-= (sqrt(convert(real_T, ExactReal(i+1)) / ExactReal(2))) .* selectdim(A, 1, i+2)
-            end
-        end
-    else # TODO: lift restriction
-        return throw(DomainError)
-    end
-    return C
-end
-
-function _apply(𝒟::Derivative, space::Hermite, ::Val{D}, A::AbstractArray{T,N}) where {D,T,N}
-    n = order(𝒟)
-    CoefType = _coeftype(𝒟, space, T)
-    if n == 0
-        return convert(Array{CoefType,N}, A)
-    elseif n == 1
-        real_CoefType = real(CoefType)
-        ord = order(space)
-        C = zeros(CoefType, ntuple(i -> i == D ? ord : size(A, i), Val(N)))
-        if ord ≥ 1
-            @inbounds selectdim(C, D, 1) .= (-sqrt(convert(real_CoefType, ExactReal(1)) / ExactReal(2))) .* selectdim(A, D, i+1)
-        end
-        @inbounds for i ∈ 1:ord+1
-            Cᵢ = selectdim(C, D, i+1)
-            Cᵢ .= (sqrt(convert(real_CoefType, ExactReal(i)) / ExactReal(2))) .* selectdim(A, D, i)
-            if i+1 ≤ ord
-                Cᵢ .-= (sqrt(convert(real_CoefType, ExactReal(i+1)) / ExactReal(2))) .* selectdim(A, D, i+2)
-            end
-        end
-        return C
-    else # TODO: lift restriction
-        return throw(DomainError)
-    end
-end
-
-function _nzind_domain(𝒟::Derivative, domain::Hermite, codomain::Hermite)
-    if order(𝒟) == 0
-        return collect(0:min(order(domain), order(codomain)))
-    elseif order(𝒟) == 1
-        len = 0
-        for j ∈ 0:order(domain)
-            if j == 0
-                len += 1 ≤ order(codomain)
-            else
-                len += (0 + (j+1 ≤ order(codomain))) + (j-1 ≤ order(codomain))
-            end
-        end
-        v = Vector{Int}(undef, len)
-        idx = 1
-        for j ∈ 0:order(domain)
-            if j == 0
-                if j+1 ≤ order(codomain)
-                    v[1] = 0
-                    idx += 1
-                end
-            else
-                idx2 = (idx-1 + (j+1 ≤ order(codomain))) + (j-1 ≤ order(codomain))
-                view(v, idx:idx2) .= j
-                idx = idx2 + 1
-            end
-        end
-        return v
-    else # TODO: lift restriction
-        return throw(DomainError)
-    end
-end
-
-function _nzind_codomain(𝒟::Derivative, domain::Hermite, codomain::Hermite)
-    if order(𝒟) == 0
-        return collect(0:min(order(domain), order(codomain)))
-    elseif order(𝒟) == 1
-        len = 0
-        for j ∈ 0:order(domain)
-            if j == 0
-                len += 1 ≤ order(codomain)
-            else
-                len += (0 + (j+1 ≤ order(codomain))) + (j-1 ≤ order(codomain))
-            end
-        end
-        v = Vector{Int}(undef, len)
-        idx = 1
-        for j ∈ 0:order(domain)
-            if j == 0
-                if 1 ≤ order(codomain)
-                    v[idx] = 1
-                    idx += 1
-                end
-            else
-                if j+1 ≤ order(codomain)
-                    v[idx] = j-1
-                    v[idx+1] = j+1
-                    idx += 2
-                elseif j-1 ≤ order(codomain)
-                    v[idx] = j-1
-                    idx += 1
-                end
-            end
-        end
-        return v
-    else # TODO: lift restriction
-        return throw(DomainError)
-    end
-end
-
-function _nzval(𝒟::Derivative, ::Hermite, ::Hermite, ::Type{T}, i, j) where {T}
-    n = order(𝒟)
-    if n == 0
-        return one(T)
-    elseif n == 1
-        if i == 0
-            if j == 1
-                return convert(T, -sqrt(convert(real(T), ExactReal(1)) / ExactReal(2)))
-            else
-                return zero(T)
-            end
-        else
-            if i+1 == j
-                return convert(T, -sqrt(convert(real(T), ExactReal(i+1)) / ExactReal(2)))
-            else # i == j+1
-                return convert(T, sqrt(convert(real(T), ExactReal(i)) / ExactReal(2)))
-            end
-        end
-    else # TODO: lift restriction
-        return throw(DomainError)
-    end
-end
-
 # Cartesian spaces
 
 for F ∈ (:Derivative, :Integral)