Julia file used as an example for unicode glyphs

example.jl

1 ∈ [1, 2, 3]

f ∘ g(x)

function hom(v::SVector)
    push(v,1)
end

function T(𝛉::AbstractArray, 𝒞::Tuple{AbstractArray, Vararg{AbstractArray}}, 𝒟::Tuple{AbstractArray, Vararg{AbstractArray}})
    ⊗ = kron
    l = length(𝛉)
    𝐈ₗ = SMatrix{l,l}(1.0I)
    𝐈ₘ =  SMatrix{1,1}(1.0I)
    𝐓 = @SMatrix zeros(l,l)
    N = length(𝒟[1])
    ℳ, ℳʹ = 𝒟
    Λ₁, Λ₂ = 𝒞
    𝚲ₙ = @MMatrix zeros(4,4)
    𝐞₁ = @SMatrix [1.0; 0.0; 0.0]
    𝐞₂ = @SMatrix [0.0; 1.0; 0.0]
    for n = 1: N
        index = SVector(1,2)
        𝚲ₙ[1:2,1:2] .=  Λ₁[n][index,index]
        𝚲ₙ[3:4,3:4] .=  Λ₂[n][index,index]
        𝐦 = hom(ℳ[n])
        𝐦ʹ= hom(ℳʹ[n])
        𝐔ₙ = (𝐦 ⊗ 𝐦ʹ)
        ∂ₓ𝐮ₙ =  [(𝐞₁ ⊗ 𝐦ʹ) (𝐞₂ ⊗ 𝐦ʹ) (𝐦 ⊗ 𝐞₁) (𝐦 ⊗ 𝐞₂)]
        𝐁ₙ =  ∂ₓ𝐮ₙ * 𝚲ₙ * ∂ₓ𝐮ₙ'
        𝚺ₙ = 𝛉' * 𝐁ₙ * 𝛉
        𝚺ₙ⁻¹ = inv(𝚺ₙ)
        𝐓₁ = @SMatrix zeros(Float64,l,l)
        for k = 1:l
            𝐞ₖ = 𝐈ₗ[:,k]
            ∂𝐞ₖ𝚺ₙ = (𝐈ₘ ⊗ 𝐞ₖ') * 𝐁ₙ * (𝐈ₘ ⊗ 𝛉) + (𝐈ₘ ⊗ 𝛉') * 𝐁ₙ * (𝐈ₘ ⊗ 𝐞ₖ)
            # Accumulating the result in 𝐓₁ allocates memory, even though
            # the two terms in the summation are both SArrays.
            𝐓₁ = 𝐓₁ + 𝐔ₙ * 𝚺ₙ⁻¹ * (∂𝐞ₖ𝚺ₙ) * 𝚺ₙ⁻¹ * 𝐔ₙ' * 𝛉 * 𝐞ₖ'
        end
        𝐓 = 𝐓 + 𝐓₁
    end
    𝐓
end


# Some sample data
N = 300
ℳ = [@SVector rand(2) for i = 1:N]
ℳʹ = [@SVector rand(2) for i = 1:N]
Λ₁ =  [SMatrix{3,3}(Matrix(Diagonal([1.0,1.0,0.0]))) for i = 1:length(ℳ)]
Λ₂ =  [SMatrix{3,3}(Matrix(Diagonal([1.0,1.0,0.0]))) for i = 1:length(ℳ)]
F = @SMatrix rand(3,3)
𝒞 = (Λ₁,Λ₂)
𝒟 = (ℳ, ℳʹ)

T(vec(F),𝒞,𝒟)
@btime T(vec($F),$𝒞,$𝒟)