add check_positivity.jl
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using AbstractAlgebra
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using Groups
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using GroupRings
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using PropertyT
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using SCS
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solver(tol, iterations) =
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SCSSolver(linearsolver=SCS.Direct,
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eps=tol, max_iters=iterations,
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alpha=1.95, acceleration_lookback=1)
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include("../main.jl")
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using PropertyTGroups
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args = Dict("SAut" => 5, "upper-bound" => 10.0, "radius" => 2, "nosymmetry"=>false, "tol"=>1e-10, "iterations" =>200000, "repetitions"=>5)
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Gr = PropertyTGroups.PropertyTGroup(args)
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sett = PropertyT.Settings(Gr, args,
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solver(args["tol"], args["iterations"]))
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@show sett
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fullpath = PropertyT.fullpath(sett)
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isdir(fullpath) || mkpath(fullpath)
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# setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
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function (p::perm)(A::GroupRingElem)
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RG = parent(A)
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T = eltype(A.coeffs)
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result = zero(RG, T)
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for (idx, c) in enumerate(A.coeffs)
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if c!= zero(T)
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result[p(RG.basis[idx])] = c
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end
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end
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return result
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end
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function small_generating_set(RG::GroupRing{AutGroup{N}}, n) where N
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing]
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lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing]
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gen_set = RG.group.([rmuls; lmuls])
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return [gen_set; inv.(gen_set)]
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end
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function computeX(RG::GroupRing{AutGroup{N}}) where N
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Tn = small_generating_set(RG, N-1)
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ℤ = Int64
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Δn = length(Tn)*one(RG, ℤ) - RG(Tn, ℤ);
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Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
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@time X = sum(σ(Δn)*sum(τ(Δn) for τ ∈ Alt_N if τ ≠ σ) for σ in Alt_N);
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return X
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end
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function Sq(RG::GroupRing{AutGroup{N}}) where N
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T2 = small_generating_set(RG, 2)
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ℤ = Int64
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Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
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Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
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elt = sum(σ(Δ₂)^2 for σ in Alt_N)
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return elt
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end
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function Adj(RG::GroupRing{AutGroup{N}}) where N
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T2 = small_generating_set(RG, 2)
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ℤ = Int64
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Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
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Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
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adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
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adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 1]
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@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
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# return RG(elt.coeffs÷factorial(N-2)^2)
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return elt
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end
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function Op(RG::GroupRing{AutGroup{N}}) where N
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T2 = small_generating_set(RG, 2)
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ℤ = Int64
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Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
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Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
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adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
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adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 0]
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@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
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# return RG(elt.coeffs÷factorial(N-2)^2)
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return elt
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end
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const ELT_FILE = joinpath(dirname(PropertyT.filename(sett, :Δ)), "SqAdjOp_coeffs.jld")
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const WARMSTART_FILE = PropertyT.filename(sett, :warmstart)
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if isfile(PropertyT.filename(sett,:Δ)) && isfile(ELT_FILE) &&
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isfile(PropertyT.filename(sett, :OrbitData))
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# cached
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Δ = PropertyT.loadGRElem(PropertyT.filename(sett,:Δ), sett.G)
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RG = parent(Δ)
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orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
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sq_c, adj_c, op_c = load(ELT_FILE, "Sq", "Adj", "Op")
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# elt = ELT_FILE, sett.G)
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sq = GroupRingElem(sq_c, RG)
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adj = GroupRingElem(adj_c, RG)
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op = GroupRingElem(op_c, RG);
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else
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info("Compute Laplacian")
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Δ = PropertyT.Laplacian(sett.S, sett.radius)
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RG = parent(Δ)
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info("Compute Sq, Adj, Op")
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@time sq, adj, op = Sq(RG), Adj(RG), Op(RG)
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PropertyT.saveGRElem(PropertyT.filename(sett, :Δ), Δ)
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save(ELT_FILE, "Sq", sq.coeffs, "Adj", adj.coeffs, "Op", op.coeffs)
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info("Compute OrbitData")
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if !isfile(PropertyT.filename(sett, :OrbitData))
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orbit_data = PropertyT.OrbitData(parent(Y), sett.autS)
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save(PropertyT.filename(sett, :OrbitData), "OrbitData", orbit_data)
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else
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orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
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end
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end;
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orbit_data = PropertyT.decimate(orbit_data);
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elt = adj+3op;
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SDP_problem, varλ, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=sett.upper_bound)
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begin
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using SCS
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scs_solver = SCS.SCSSolver(linearsolver=SCS.Direct,
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eps=sett.tol,
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max_iters=args["iterations"],
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alpha=1.95,
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acceleration_lookback=1)
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JuMP.setsolver(SDP_problem, scs_solver)
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end
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λ = Ps = nothing
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ws = PropertyT.warmstart(sett)
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using ProgressMeter
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@showprogress "Running SDP optimization step... " for i in 1:args["repetitions"]
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# while true
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λ, Ps, ws = PropertyT.solve(PropertyT.filename(sett, :solverlog),
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SDP_problem, varλ, varP, ws);
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if all((!isnan).(ws[1]))
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save(WARMSTART_FILE, "warmstart", ws, "λ", λ, "Ps", Ps)
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save(WARMSTART_FILE[1:end-4]*"_$(now()).jld", "warmstart", ws, "λ", λ, "Ps", Ps)
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else
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warn("No valid solution was saved!")
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end
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end
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function check_SOS_precision(Q::Matrix, eoi::GroupRingElem)
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RG = parent(eoi)
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@time sos = PropertyT.compute_SOS(RG, Q);
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residue = eoi - sos
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return norm(residue, 1)
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end
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info("Reconstructing P...")
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@time P = PropertyT.reconstruct(Ps, orbit_data);
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save(PropertyT.filename(sett, :solution), "λ", λ, "P", P)
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addprocs(4)
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@everywhere using PropertyT
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@time const Q = real(sqrtm(P));
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const EOI = elt - λ*Δ;
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@show λ - 2^3*check_SOS_precision(Q, EOI);
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using IntervalArithmetic
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Qint = PropertyT.augIdproj(Q);
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@assert all([zero(eltype(Q)) in sum(view(Qint, :, i)) for i in 1:size(Qint, 2)])
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EOIint = GroupRingElem([@interval(c) for c in EOI.coeffs], parent(Δ));
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b_int = check_SOS_precision(Qint, EOIint)
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@show @interval(λ) - 2^3*b_int;
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