73 lines
2.4 KiB
Julia
73 lines
2.4 KiB
Julia
using DelimitedFiles, LinearAlgebra
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function calculate_all_data(N::Int)
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ks = -N÷2:N÷2-1
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lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
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labels = reshape(collect(1:N^3), (N, N, N))
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unique_i = collect(1:N^3)
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multiplicity = fill(1, length(unique_i))
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unique_point = transpose(lattice)
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return unique_i, unique_point, multiplicity, labels
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end
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function calculate_A1_data(N::Int)
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rotations = readdlm("rotations.mat", ',', Int, '\n')
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rotations = reshape(rotations, (24, 3, 3))
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ks = -N÷2:N÷2-1
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lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
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labels = reshape(collect(1:N^3), (N, N, N))
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for r in 1:24
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rotated_lattice = Matrix(rotations[r, :, :]) * lattice
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for index in 1:N^3
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rotated_lattice_point = rotated_lattice[:, index]
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(i, j, k) = mod1.(rotated_lattice_point .+ (N÷2 + 1), N)
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old_label = max(labels[index], labels[i, j, k])
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new_label = min(labels[index], labels[i, j, k])
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if old_label != new_label
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for o in findall(isequal(old_label), labels)
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labels[o] = new_label
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end
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end
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end
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end
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unique_i = unique(labels)
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multiplicity = [count(labels.==i) for i in unique_i]
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unique_point = transpose(lattice[:, unique_i])
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return unique_i, unique_point, multiplicity, labels
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end
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function sym_reduce(s, K_partial)
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I = one(K_partial)
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K_partial_x1 = kron(kron(K_partial, I), I)
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K_partial_y1 = kron(kron(I, K_partial), I)
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K_partial_z1 = kron(kron(I, I), K_partial)
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K_partial_x2 = kron(kron(K_partial, I), I)
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K_partial_y2 = kron(kron(I, K_partial), I)
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K_partial_z2 = kron(kron(I, I), K_partial)
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for (i, label) in enumerate(s.labels)
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if i != label
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K_partial_x2[:, label] .+= K_partial_x2[:, i]
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K_partial_y2[:, label] .+= K_partial_y2[:, i]
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K_partial_z2[:, label] .+= K_partial_z2[:, i]
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end
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end
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K_partial_x1 = K_partial_x1[s.unique_i, :]
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K_partial_y1 = K_partial_y1[s.unique_i, :]
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K_partial_z1 = K_partial_z1[s.unique_i, :]
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K_partial_x2 = K_partial_x2[:, s.unique_i]
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K_partial_y2 = K_partial_y2[:, s.unique_i]
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K_partial_z2 = K_partial_z2[:, s.unique_i]
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return (K_partial_x1, K_partial_y1, K_partial_z1), (K_partial_x2, K_partial_y2, K_partial_z2)
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end |