Hypercube Examples (Bravais Lattice)

Preamble

using LatticeTools
using Plots

mkpath("example_hypercube")

function draw_hypercube(hypercube::Hypercube, coordinates::AbstractMatrix{<:Integer})
    xlim = (minimum(coordinates[1,:]) - 3.5, maximum(coordinates[1,:]) + 3.5)
    ylim = (minimum(coordinates[2,:]) - 3.5, maximum(coordinates[2,:]) + 3.5)
    boundary = let
        r0 = [0,0]
        r1 = hypercube.shape_matrix[:,1]
        r2 = hypercube.shape_matrix[:,2]
        hcat(r0, r1, r1 .+ r2, r2, r0)
    end
    fig = plot(boundary[1,:], boundary[2,:], label="", size=(400, 400))
    for Ri in Iterators.product(-1:1, -1:1)
        alpha = (Ri == (0,0)) ? 1.0 : 0.1
        Rr = hypercube.shape_matrix * [Ri...]
        scatter!(coordinates[1,:] .+ Rr[1], coordinates[2,:] .+ Rr[2], aspect_ratio=1, markersize=12, xlim=xlim, ylim=ylim, markeralpha=alpha, label="")
        annotation = []
        for i in 1:size(coordinates, 2)
            x = coordinates[1,i] + Rr[1]
            y = coordinates[2,i] + Rr[2]
            if xlim[1] < x < xlim[2] && ylim[1] < y < ylim[2]
                push!(annotation, (x, y, text("$i", 8, :black, :center)))
            end
        end
        if !isempty(annotation)
            annotation = [annotation...]
            annotate!(annotation)
        end
    end
    fig
end

draw_hypercube (generic function with 1 method)

(4,-4) x (4,4)

size_matrix = [ 4 4; -4 4]
hypercube = Hypercube(size_matrix)
generator_translations = find_generators(hypercube)
coordinates = generate_coordinates(hypercube, generator_translations)
coordmat = hcat(coordinates...)
println("All elements")
for (i, c) in enumerate(coordinates)
    println("$i : $c")
end
println("Generator translations")
for (it, t) in enumerate(eachcol(generator_translations))
    println("t($it) = $t")
end
draw_hypercube(hypercube, coordmat)
savefig("example_hypercube/bravais_(4,-4)x(4,4).svg")

All elements
1 : [0, 0]
2 : [1, 0]
3 : [2, 0]
4 : [3, 0]
5 : [4, 0]
6 : [5, 0]
7 : [6, 0]
8 : [7, 0]
9 : [1, 1]
10 : [2, 1]
11 : [3, 1]
12 : [4, 1]
13 : [5, 1]
14 : [6, 1]
15 : [3, -3]
16 : [4, -3]
17 : [2, 2]
18 : [3, 2]
19 : [4, 2]
20 : [5, 2]
21 : [2, -2]
22 : [3, -2]
23 : [4, -2]
24 : [5, -2]
25 : [3, 3]
26 : [4, 3]
27 : [1, -1]
28 : [2, -1]
29 : [3, -1]
30 : [4, -1]
31 : [5, -1]
32 : [6, -1]
Generator translations
t(1) = [1, 0]
t(2) = [1, 1]
/home/runner/.julia/packages/GR/RlE5Y/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

(2,-2) x (2,4)

size_matrix = [ 2 2; -2 4]
hypercube = Hypercube(size_matrix)
generator_translations = find_generators(hypercube)
coordinates = generate_coordinates(hypercube, generator_translations)
coordmat = hcat(coordinates...)
draw_hypercube(hypercube, coordmat)
println("All elements")
for (i, c) in enumerate(coordinates)
    println("$i : $c")
end
println("Generator translations")
for (it, t) in enumerate(eachcol(generator_translations))
    println("t($it) = $t")
end
draw_hypercube(hypercube, coordmat)
savefig("example_hypercube/bravais_(2,-2)x(2,4).svg")

All elements
1 : [0, 0]
2 : [1, 0]
3 : [2, 0]
4 : [1, 2]
5 : [2, 2]
6 : [3, 2]
7 : [2, 1]
8 : [3, 1]
9 : [2, 3]
10 : [1, -1]
11 : [2, -1]
12 : [1, 1]
Generator translations
t(1) = [1, 0]
t(2) = [2, 1]
/home/runner/.julia/packages/GR/RlE5Y/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

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