48 lines
2.0 KiB
Julia
48 lines
2.0 KiB
Julia
Float = Union{Float32,Float64}
|
|
|
|
"Eq (46): Partial derivative matrix element for 1 degree of freedom"
|
|
function ∂_1DOF(L::T, N::Int, k::Int, l::Int)::Complex{T} where {T<:Float}
|
|
if k == l
|
|
return -im * (π / L)
|
|
else
|
|
return (π / L) * (-1)^(k - l) * exp(-im * π * (k - l) / N) / sin(π * (k - l) / N)
|
|
end
|
|
end
|
|
|
|
"Which index (dimension of the multidimensional array) corresponds to this dimension and coordinate?"
|
|
which_index(n::Int, dim::Int, coord::Int)::Int = (dim - 1) * (n - 1) + coord
|
|
|
|
"k value of the given degree of freedom at the corresponding index, with coord=0 always returning 0"
|
|
get_k(n::Int, N::Int, i::CartesianIndex, dim::Int, coord::Int)::Int =
|
|
coord == 0 ? 0 : i[which_index(n, dim, coord)] - N ÷ 2 - 1
|
|
|
|
"k value of the DOF at the specified cubic image"
|
|
get_shifted_k(n::Int, N::Int, i::CartesianIndex, dim::Int, coord::Int, image::Vector{Int})::Int =
|
|
get_k(n, N, i, dim, coord) + N * image[dim]
|
|
|
|
"Difference of k values between two particles"
|
|
get_Δk(n::Int, N::Int, i::CartesianIndex, dim::Int, coord1::Int, coord2::Int, image::Vector{Int})::Int =
|
|
get_k(n, N, i, dim, coord1) - get_shifted_k(n, N, i, dim, coord2, image)
|
|
|
|
"Calculate diagonal elements of the V matrix"
|
|
function calculate_Vs(V_twobody::Function, d::Int, n::Int, N::Int, L::T, n_image::Int)::Array{T} where {T<:Float}
|
|
L²_over_N² = (L / N)^2
|
|
coords = n - 1
|
|
images = collect.(Iterators.product(fill(-n_image:n_image, d)...)) # TODO: Learn how to use tuples instead of vectors
|
|
Vs = zeros(T, fill(N, d * coords)...)
|
|
for image in images
|
|
Threads.@threads for i in CartesianIndices(Vs)
|
|
for coord1 in 1:coords
|
|
for coord2 in 0:coord1-1
|
|
Δk² = 0
|
|
for dim in 1:d
|
|
Δk² += get_Δk(n, N, i, dim, coord1, coord2, image)^2
|
|
end
|
|
Vs[i] += V_twobody(Δk² * L²_over_N²)
|
|
end
|
|
end
|
|
end
|
|
end
|
|
return Vs
|
|
end
|