mirror of
https://github.com/kalmarek/PropertyT.jl.git
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kalmar
a696205d6e
No need to include the whole property(T).jl @everywhere; this usually takes a lot of time
123 lines
3.4 KiB
Julia
123 lines
3.4 KiB
Julia
using JLD
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using JuMP
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import SCS: SCSSolver
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import Mosek: MosekSolver
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using Groups
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using ProgressMeter
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function SL₃ℤ_generatingset()
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function E(i::Int, j::Int, N::Int=3)
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@assert i≠j
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k = eye(N)
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k[i,j] = 1
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return k
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end
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S = [E(1,2), E(1,3), E(2,3)];
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S = vcat(S, [x' for x in S]);
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S = vcat(S, [inv(x) for x in S]);
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return S
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end
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function prepare_Δ_sdp_constraints(identity, S)
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@show length(S)
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B₁ = vcat([identity], S)
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B₂ = products(B₁, B₁);
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B₃ = products(B₁, B₂);
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B₄ = products(B₁, B₃);
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@assert B₄[1:length(B₂)] == B₂
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product_matrix = create_product_matrix(B₄,length(B₂));
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sdp_constraints = constraints_from_pm(product_matrix, length(B₄))
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L_coeff = splaplacian_coeff(S, B₂, length(B₄));
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Δ = GroupAlgebraElement(L_coeff, product_matrix)
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return Δ, sdp_constraints
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end
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function load_Δ_sdp_constraints(name::String;cached=true)
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pm_filename = "$name.product_matrix.jld"
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Δ_coeff_filename = "$name.delta.coefficients.jld"
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f₁ = isfile(pm_filename)
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f₂ = isfile(Δ_coeff_filename)
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if cached && f₁ && f₂
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println("Loading precomputed pm, Δ, sdp_constraints...")
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product_matrix = load(pm_filename, "pm")
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L = load(Δ_coeff_filename, "Δ")[:, 1]
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Δ = GroupAlgebraElement(L, Array{Int,2}(product_matrix))
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sdp_constraints = constraints_from_pm(product_matrix)
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else
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println("Computing pm, Δ, sdp_constraints...")
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ID = eye(Int, 3)
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S = SL₃ℤ_generatingset()
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Δ, sdp_constraints = prepare_Δ_sdp_constraints(ID, S)
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save(pm_filename, "pm", Δ.product_matrix)
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save(Δ_coeff_filename, "Δ", Δ.coefficients)
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end
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return Δ, sdp_constraints
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end
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function compute_κ_A(name::String, Δ, sdp_constraints;
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cached = true,
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tol = 1e-7,
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verbose = false,
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# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=!verbose))
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solver = SCSSolver(eps=tol, max_iters=20000, cg_rate=3, verbose=verbose))
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f₁ = isfile("$name.kappa")
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f₂ = isfile("$name.SDPmatrixA")
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if cached && f₁ && f₂
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println("Loading precomputed κ, A...")
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A = readdlm("$name.SDPmatrixA")
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κ = readdlm("$name.kappa")[1]
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else
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println("Solving SDP problem maximizing κ...")
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κ, A = solve_SDP(sdp_constraints, Δ, solver, verbose=verbose)
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# writedlm("$name.kappa", kappa)
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# writedlm("$name.SDPmatrixA", A)
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end
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return κ, A
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end
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function main()
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const NAME = "SL3Z"
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const VERBOSE = true
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const TOL=1e-7
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const Δ, sdp_constraints = load_Δ_sdp_constraints(NAME)
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const κ, A = compute_κ_A(NAME, Δ, sdp_constraints, cached=false, verbose=VERBOSE)
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if maximum(A) < 1e-2
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warn("Solver might not solved the problem successfully and the positive solution is due to floating-point error, proceeding anyway...")
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end
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if κ > 0
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@assert A == Symmetric(A)
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const A_sqrt = real(sqrtm(A))
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T = ℚ_distance_to_positive_cone(Δ, κ, A, tol=TOL, verbose=VERBOSE)
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if T < 0
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println("$NAME HAS property (T)!")
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else
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println("$NAME may NOT HAVE property (T)!")
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end
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else
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println("$κ < 0: $NAME may NOT HAVE property (T)!")
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end
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end
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@everywhere push!(LOAD_PATH, "./")
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using GroupAlgebras
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include("property(T).jl")
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main()
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