mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-13 14:00:27 +01:00
84 lines
2.0 KiB
Julia
84 lines
2.0 KiB
Julia
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using LinearAlgebra
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using MKL_jll
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BLAS.set_num_threads(4)
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ENV["OMP_NUM_THREADS"] = 4
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using Groups
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import Groups.MatrixGroups
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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using PropertyT
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using PropertyT.SymbolicWedderburn
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using PropertyT.PermutationGroups
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using PropertyT.StarAlgebras
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include(joinpath(@__DIR__, "argparse.jl"))
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include(joinpath(@__DIR__, "utils.jl"))
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const N = parsed_args["N"]
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const HALFRADIUS = parsed_args["halfradius"]
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const UPPER_BOUND = parsed_args["upper_bound"]
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const GENUS = 2N
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G = MatrixGroups.SymplecticGroup{GENUS}(Int8)
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@info "Running Δ² - λ·Δ sum of squares decomposition for " G
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@info "computing group algebra structure"
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RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
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@info "computing WedderburnDecomposition"
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wd = let RG = RG, N = N
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G = StarAlgebras.object(RG)
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P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
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Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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act = PropertyT.action_by_conjugation(G, Σ)
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wdfl = @time SymbolicWedderburn.WedderburnDecomposition(
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Float64,
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Σ,
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act,
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basis(RG),
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StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
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)
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end
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@info wd
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Δ = RG(length(S)) - sum(RG(s) for s in S)
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elt = Δ^2
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unit = Δ
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@info "defining optimization problem"
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@time model, varP = PropertyT.sos_problem_primal(
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elt,
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unit,
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wd;
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upper_bound = UPPER_BOUND,
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augmented = true,
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show_progress = true,
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)
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solve_in_loop(
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model,
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wd,
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varP;
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logdir = "./log/Sp($N,Z)/r=$HALFRADIUS/Δ²-$(UPPER_BOUND)Δ",
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optimizer = scs_optimizer(;
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linear_solver = SCS.MKLDirectSolver,
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eps = 1e-10,
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max_iters = 50_000,
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accel = 50,
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alpha = 1.95,
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),
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data = (elt = elt, unit = unit, halfradius = HALFRADIUS),
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)
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if certified && λ > 0
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Κ(λ, S) = round(sqrt(2λ / length(S)), Base.RoundDown; digits = 5)
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@info "Certified result: $G has property (T):" N λ Κ(λ, S)
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else
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@info "Could NOT certify the result:" certified λ
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end
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