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rewrite scripts for G2
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@ -1,29 +1,34 @@
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using LinearAlgebra
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BLAS.set_num_threads(1)
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ENV["OMP_NUM_THREADS"] = 4
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BLAS.set_num_threads(8)
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using MKL_jll
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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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 SymbolicWedderburn
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using SymbolicWedderburn.StarAlgebras
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using PermutationGroups
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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__, "G₂_gens.jl"))
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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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const HALFRADIUS = 2
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const UPPER_BOUND = Inf
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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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Δ = RG(length(S)) - sum(RG(s) for s in S)
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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.perm(g) for g in Σ),
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@ -38,57 +43,7 @@ wd = let Σ = Weyl, RG = RG
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semisimple = false,
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)
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end
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elt = Δ^2
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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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warm = nothing
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begin
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@time status, warm = PropertyT.solve(
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model,
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scs_optimizer(;
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linear_solver = SCS.MKLDirectSolver,
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eps = 1e-10,
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max_iters = 20_000,
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accel = 50,
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alpha = 1.95,
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),
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warm,
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)
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@info "reconstructing the solution"
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Q = @time begin
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wd = wd
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Ps = [JuMP.value.(P) for P in varP]
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if any(any(isnan, P) for P in Ps)
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throw("solver was probably interrupted, no valid solution available")
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end
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Qs = real.(sqrt.(Ps))
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PropertyT.reconstruct(Qs, wd)
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end
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P = Q' * Q
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@info "certifying the solution"
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@time certified, λ = PropertyT.certify_solution(
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elt,
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unit,
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JuMP.objective_value(model),
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Q;
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halfradius = HALFRADIUS,
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augmented = true,
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)
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end
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### grading below
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@info wd
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function desubscriptify(symbol::Symbol)
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digits = [
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@ -107,6 +62,7 @@ function PropertyT.grading(g::MatrixGroups.MatrixElt, roots = roots)
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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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@ -114,7 +70,7 @@ end
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)
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elt = PropertyT.Adj(Δs)
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elt == Δ^2 - PropertyT.Sq(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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@ -123,57 +79,21 @@ unit = Δ
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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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warm = nothing
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begin
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@time status, warm = PropertyT.solve(
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model,
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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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warm,
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)
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@info "reconstructing the solution"
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Q = @time begin
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wd = wd
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Ps = [JuMP.value.(P) for P in varP]
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if any(any(isnan, P) for P in Ps)
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throw("solver was probably interrupted, no valid solution available")
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end
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Qs = real.(sqrt.(Ps))
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PropertyT.reconstruct(Qs, wd)
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end
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P = Q' * Q
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@info "certifying the solution"
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@time certified, λ = PropertyT.certify_solution(
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elt,
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unit,
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JuMP.objective_value(model),
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Q;
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halfradius = HALFRADIUS,
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augmented = true,
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)
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end
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# Δ² - 1 / 1 · Sq → -0.8818044647162608
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# Δ² - 2 / 3 · Sq → -0.1031738
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# Δ² - 1 / 2 · Sq → 0.228296213895906
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# Δ² - 1 / 3 · Sq → 0.520
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# Δ² - 0 / 1 · Sq → 0.9676851592000731
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# Sq → 0.333423
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# vals = [
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# 1.0 -0.8818
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# 2/3 -0.1032
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# 1/2 0.2282
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# 1/3 0.520
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# 0 0.9677
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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-InfΔ",
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optimizer = scs_optimizer(;
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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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97
scripts/G₂_has_T.jl
Normal file
97
scripts/G₂_has_T.jl
Normal file
@ -0,0 +1,97 @@
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using LinearAlgebra
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BLAS.set_num_threads(8)
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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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include(joinpath(@__DIR__, "./G₂_gens.jl"))
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G, roots, Weyl = G₂_roots_weyl()
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@info "Running Δ² - 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.perm(g) for g in Σ),
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)
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@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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semisimple = false,
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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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@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 = false,
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)
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warm = nothing
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status = JuMP.OPTIMIZE_NOT_CALLED
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while status ≠ JuMP.OPTIMAL
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@time status, warm = PropertyT.solve(
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model,
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scs_optimizer(;
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eps = 1e-10,
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max_iters = 20_000,
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accel = 50,
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alpha = 1.95,
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),
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warm,
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)
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@info "reconstructing the solution"
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Q = @time let wd = wd, Ps = [JuMP.value.(P) for P in varP]
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Qs = real.(sqrt.(Ps))
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PropertyT.reconstruct(Qs, wd)
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end
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@info "certifying the solution"
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@time certified, λ = PropertyT.certify_solution(
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elt,
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unit,
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JuMP.objective_value(model),
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Q;
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halfradius = HALFRADIUS,
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augmented = true,
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)
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end
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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: G₂ 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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@ -68,19 +68,19 @@ function solve_in_loop(model::JuMP.Model, args...; logdir, optimizer, data)
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end
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if flag == true && certified_λ ≥ 0
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@info "Certification done with λ = $certified_λ"
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@info "Certification done with λ = $certified_λ" certified_λ rel_change status
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return certified_λ
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else
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rel_change =
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abs(certified_λ - old_lambda) /
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(abs(certified_λ) + abs(old_lambda))
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@info "Certification failed with λ = $λ" certified_λ rel_change
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@info "Certification failed with λ = $λ" certified_λ rel_change status
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end
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old_lambda = certified_λ
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if rel_change < 1e-9
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@info "No progress detected, breaking"
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@info "No progress detected, breaking" certified_λ rel_change status
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break
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end
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end
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