99 lines
2.2 KiB
Julia
99 lines
2.2 KiB
Julia
using LinearAlgebra
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BLAS.set_num_threads(4)
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ENV["OMP_NUM_THREADS"] = 4
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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using SCS_MKL_jll
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using Groups
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import Groups.MatrixGroups
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using PropertyT
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import PropertyT.SW as SW
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using PropertyT.PG
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using PropertyT.SA
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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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include(joinpath(@__DIR__, "./G₂_gens.jl"))
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G, roots, Weyl = G₂_roots_weyl()
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@info "Running Adj² - λ·Δ sum of squares decomposition for G₂"
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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 Σ = Weyl, RG = RG
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act = PropertyT.AlphabetPermutation{eltype(Σ),Int64}(
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Dict(g => PermutationGroups.AP.perm(g) for g in Σ),
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)
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@time SW.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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semisimple = false,
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)
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end
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@info wd
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function desubscriptify(symbol::Symbol)
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digits = [
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Int(l) - 0x2080 for
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l in reverse(string(symbol)) if 0 ≤ Int(l) - 0x2080 ≤ 9
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]
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res = 0
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for (i, d) in enumerate(digits)
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res += 10^(i - 1) * d
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end
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return res
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end
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function PropertyT.grading(g::MatrixGroups.MatrixElt, roots = roots)
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id = desubscriptify(g.id)
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return roots[id]
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end
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Δ = RG(length(S)) - sum(RG(s) for s in S)
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Δs = PropertyT.laplacians(
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RG,
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S,
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x -> (gx = PropertyT.grading(x); Set([gx, -gx])),
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)
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elt = PropertyT.Adj(Δs)
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@assert elt == Δ^2 - PropertyT.Sq(Δs)
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unit = Δ
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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/G2/r=$HALFRADIUS/Adj-$(UPPER_BOUND)Δ",
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optimizer = scs_optimizer(;
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linear_solver = SCS.MKLDirectSolver,
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eps = 1e-9,
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max_iters = 100_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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