mirror of
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move application specific code to 1712.07167.jl
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src/1712.07167.jl
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248
src/1712.07167.jl
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@ -0,0 +1,248 @@
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###############################################################################
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#
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# Settings and filenames
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#
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###############################################################################
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struct Symmetrize end
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struct Naive end
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abstract type PropertyTSettings end
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struct SolverSettings
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sdpsolver::AbstractMathProgSolver
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upper_bound::Float64
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warmstart::Bool
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SolverSettings(sol, ub, ws=true) = new(sol, upper_bound, ws)
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end
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struct Naive <: PropertyTSettings
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name::String
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G::Group
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S::Vector{GroupElem}
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radius::Int
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solver::SolverSettings
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end
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struct Symmetrized <: PropertyTSettings
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name::String
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G::Group
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S::Vector{GroupElem}
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autS::Group
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radius::Int
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solver::SolverSettings
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end
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function Settings(name::String,
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G::Group, S::Vector{GEl}, r::Integer,
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sol::Solver, ub, ws=true) where {GEl<:GroupElem, Solver<:AbstractMathProgSolver}
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sol_sett = SolverSettings(sol, ub, ws)
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return Naive(name, G, S, r, sol_sett)
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end
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function Settings(name::String,
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G::Group, S::Vector{GEl}, autS::Group, r::Integer,
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sol::Solver, ub, ws=true) where {GEl<:GroupElem, Solver<:AbstractMathProgSolver}
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sol_sett = SolverSettings(sol, ub, ws)
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return Symmetrized(name, G, S, autS, r, sol_sett)
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end
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prefix(s::Naive) = s.name
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prefix(s::Symmetrized) = "o"*s.name
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suffix(s::PropertyTSettings) = "$(s.upper_bound)"
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prepath(s::PropertyTSettings) = prefix(s)
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fullpath(s::PropertyTSettings) = joinpath(prefix(s), suffix(s))
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filename(sett::PropertyTSettings, s::Symbol) = filename(sett, Val{s})
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filename(sett::PropertyTSettings, ::Type{Val{:fulllog}}) =
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joinpath(fullpath(sett), "full_$(string(now())).log")
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filename(sett::PropertyTSettings, ::Type{Val{:solverlog}}) =
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joinpath(fullpath(sett), "solver_$(string(now())).log")
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filename(sett::PropertyTSettings, ::Type{Val{:Δ}}) =
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joinpath(prepath(sett), "delta.jld")
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filename(sett::PropertyTSettings, ::Type{Val{:OrbitData}}) =
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joinpath(prepath(sett), "OrbitData.jld")
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filename(sett::PropertyTSettings, ::Type{Val{:warmstart}}) =
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joinpath(fullpath(sett), "warmstart.jld")
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filename(sett::PropertyTSettings, ::Type{Val{:solution}}) =
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joinpath(fullpath(sett), "solution.jld")
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###############################################################################
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#
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# λandP
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#
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###############################################################################
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function warmstart(sett::PropertyTSettings)
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if sett.solver.warmstart && isfile(filename(sett, :warmstart))
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ws = load(filename(sett, :warmstart), "warmstart")
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else
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ws = nothing
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end
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return ws
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end
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function computeλandP(sett::Naive, Δ::GroupRingElem;
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solverlog=tempname()*".log")
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info("Creating SDP problem...")
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SDP_problem, varλ, varP = SOS_problem(Δ^2, Δ, upper_bound=sett.solver.upper_bound)
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JuMP.setsolver(SDP_problem, sett.solver.sdpsolver)
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info(Base.repr(SDP_problem))
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ws = warmstart(sett)
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@time status, (λ, P, ws) = PropertyT.solve(solverlog, SDP_problem, varλ, varP, ws)
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@show status
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save(filename(sett, :warmstart), "warmstart", ws, "P", P, "λ", λ)
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return λ, P
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end
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function computeλandP(sett::Symmetrized, Δ::GroupRingElem;
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solverlog=tempname()*".log")
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if !isfile(filename(sett, :OrbitData))
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isdefined(parent(Δ), :basis) || throw("You need to define basis of Group Ring to compute orbit decomposition!")
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orbit_data = OrbitData(parent(Δ), sett.autS)
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save(filename(sett, :OrbitData), "OrbitData", orbit_data)
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end
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orbit_data = load(filename(sett, :OrbitData), "OrbitData")
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orbit_data = decimate(orbit_data)
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info("Creating SDP problem...")
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SDP_problem, varλ, varP = SOS_problem(Δ^2, Δ, orbit_data, upper_bound=sett.solver.upper_bound)
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JuMP.setsolver(SDP_problem, sett.solver.sdpsolver)
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info(Base.repr(SDP_problem))
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ws = warmstart(sett)
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@time status, (λ, Ps, ws) = PropertyT.solve(solverlog, SDP_problem, varλ, varP, ws)
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@show status
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save(filename(sett, :warmstart), "warmstart", ws, "Ps", Ps, "λ", λ)
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info("Reconstructing P...")
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@time P = reconstruct(Ps, orbit_data)
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return λ, P
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end
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###############################################################################
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#
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# Checking solution
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#
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###############################################################################
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function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
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@info("------------------------------------------------------------")
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@info("Checking in floating-point arithmetic...")
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@info("λ = $λ")
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eoi = Δ^2-λ*Δ
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@time residual = eoi - compute_SOS(parent(eoi), augIdproj(Q))
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@info("ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", aug(residual)))")
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L1_norm = norm(residual,1)
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@info("‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", L1_norm))")
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distance = λ - 2.0^(2ceil(log2(R)))*L1_norm
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@info("Floating point distance (to positive cone) ≈")
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@info("$(@sprintf("%.10f", distance))")
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@info("")
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if distance ≤ 0
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return distance
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end
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@info("------------------------------------------------------------")
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@info("Checking in interval arithmetic...")
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@info("λ ∈ $λ")
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λ = @interval(λ)
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eoi = Δ^2 - λ*Δ
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@info("Projecting columns of Q to the augmentation ideal...")
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@time Q, check = augIdproj(Interval, Q)
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@info("Checking that sum of every column contains 0.0... ")
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@info((check? "They do." : "FAILED!"))
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check || @warn("The following numbers are meaningless!")
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@time residual = eoi - compute_SOS(parent(eoi), Q)
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@info("ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ∈ $(aug(residual))")
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L1_norm = norm(residual,1)
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@info("‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)")
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distance = λ - 2.0^(2ceil(log2(R)))*L1_norm
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@info("Interval distance (to positive cone) ∈")
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@info("$(distance)")
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@info("")
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return distance.lo
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end
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###############################################################################
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#
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# Interpreting the numerical results
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#
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###############################################################################
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Kazhdan(λ::Number, N::Integer) = sqrt(2*λ/N)
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function interpret_results(sett::PropertyTSettings, sgap::Number)
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if sgap > 0
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Kazhdan_κ = Kazhdan(sgap, length(sett.S))
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if Kazhdan_κ > 0
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info("κ($(sett.name), S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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end
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end
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info("λ($(sett.name), S) ≥ $sgap < 0: Tells us nothing about property (T)")
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return false
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end
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function check_property_T(sett::PropertyTSettings)
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fp = PropertyT.fullpath(sett)
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isdir(fp) || mkpath(fp)
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if isfile(filename(sett,:Δ))
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# cached
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Δ = loadLaplacian(filename(sett,:Δ), sett.G)
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else
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# compute
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Δ = Laplacian(sett.S, sett.radius)
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saveLaplacian(filename(sett, :Δ), Δ)
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end
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if !sett.warmstart && isfile(filename(sett, :solution))
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λ, P = load(filename(sett, :solution), "λ", "P")
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else
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λ, P = computeλandP(sett, Δ,
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solverlog=filename(sett, :solverlog))
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save(filename(sett, :solution), "λ", λ, "P", P)
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if λ < 0
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warn("Solver did not produce a valid solution!")
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end
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end
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info("λ = $λ")
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info("sum(P) = $(sum(P))")
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info("maximum(P) = $(maximum(P))")
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info("minimum(P) = $(minimum(P))")
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isapprox(eigvals(P), abs.(eigvals(P)), atol=sett.tol) ||
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warn("The solution matrix doesn't seem to be positive definite!")
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@time Q = real(sqrtm((P+P')/2))
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sgap = distance_to_positive_cone(Δ, λ, Q, wlen=2*sett.radius)
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return interpret_results(sett, sgap)
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end
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116
src/PropertyT.jl
116
src/PropertyT.jl
@ -12,126 +12,10 @@ using JuMP
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import MathProgBase.SolverInterface.AbstractMathProgSolver
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import MathProgBase.SolverInterface.AbstractMathProgSolver
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###############################################################################
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#
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# Settings and filenames
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#
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###############################################################################
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struct Symmetrize end
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struct Naive end
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struct Settings{T, GEl<:GroupElem}
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name::String
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G::Group
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S::Vector{GEl}
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radius::Int
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solver::AbstractMathProgSolver
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upper_bound::Float64
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tol::Float64
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warmstart::Bool
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autS::Group
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function Settings(name::String,
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G::Group, S::Vector{GEl}, r::Int,
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sol::Sol, ub, tol, ws) where {GEl<:GroupElem, Sol<:AbstractMathProgSolver}
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return new{Naive, GEl}(name, G, S, r, sol, ub, tol, ws)
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end
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function Settings(name::String,
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G::Group, S::Vector{GEl}, r::Int,
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sol::Sol, ub, tol, ws, autS) where {GEl<:GroupElem, Sol<:AbstractMathProgSolver}
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return new{Symmetrize, GEl}(name, G, S, r, sol, ub, tol, ws, autS)
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end
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end
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prefix(s::Settings{Naive}) = s.name
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prefix(s::Settings{Symmetrize}) = "o"*s.name
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suffix(s::Settings) = "$(s.upper_bound)"
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prepath(s::Settings) = prefix(s)
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fullpath(s::Settings) = joinpath(prefix(s), suffix(s))
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filename(sett::Settings, s::Symbol) = filename(sett, Val{s})
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filename(sett::Settings, ::Type{Val{:fulllog}}) =
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joinpath(fullpath(sett), "full_$(string(now())).log")
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filename(sett::Settings, ::Type{Val{:solverlog}}) =
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joinpath(fullpath(sett), "solver_$(string(now())).log")
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filename(sett::Settings, ::Type{Val{:Δ}}) =
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joinpath(prepath(sett), "delta.jld")
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filename(sett::Settings, ::Type{Val{:OrbitData}}) =
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joinpath(prepath(sett), "OrbitData.jld")
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filename(sett::Settings, ::Type{Val{:warmstart}}) =
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joinpath(fullpath(sett), "warmstart.jld")
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filename(sett::Settings, ::Type{Val{:solution}}) =
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joinpath(fullpath(sett), "solution.jld")
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function check_property_T(sett::Settings)
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fp = PropertyT.fullpath(sett)
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isdir(fp) || mkpath(fp)
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if isfile(filename(sett,:Δ))
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# cached
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Δ = loadLaplacian(filename(sett,:Δ), sett.G)
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else
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# compute
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Δ = Laplacian(sett.S, sett.radius)
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saveLaplacian(filename(sett, :Δ), Δ)
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end
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if !sett.warmstart && isfile(filename(sett, :solution))
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λ, P = load(filename(sett, :solution), "λ", "P")
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else
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λ, P = computeλandP(sett, Δ,
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solverlog=filename(sett, :solverlog))
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save(filename(sett, :solution), "λ", λ, "P", P)
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if λ < 0
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warn("Solver did not produce a valid solution!")
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end
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end
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info("λ = $λ")
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info("sum(P) = $(sum(P))")
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info("maximum(P) = $(maximum(P))")
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info("minimum(P) = $(minimum(P))")
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isapprox(eigvals(P), abs.(eigvals(P)), atol=sett.tol) ||
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warn("The solution matrix doesn't seem to be positive definite!")
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@time Q = real(sqrtm((P+P')/2))
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sgap = distance_to_cone(Δ, λ, Q, wlen=2*sett.radius)
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return interpret_results(sett, sgap)
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end
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Kazhdan(λ::Number, N::Integer) = sqrt(2*λ/N)
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function interpret_results(sett::Settings, sgap::Number)
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if sgap > 0
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Kazhdan_κ = Kazhdan(sgap, length(sett.S))
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if Kazhdan_κ > 0
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info("κ($(sett.name), S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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end
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end
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info("λ($(sett.name), S) ≥ $sgap < 0: Tells us nothing about property (T)")
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return false
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end
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include("laplacians.jl")
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include("laplacians.jl")
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include("RGprojections.jl")
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include("RGprojections.jl")
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include("orbitdata.jl")
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include("orbitdata.jl")
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include("sos_sdps.jl")
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include("sos_sdps.jl")
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include("checksolution.jl")
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include("checksolution.jl")
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||||||
end # module Property(T)
|
end # module Property(T)
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|||||||
@ -28,52 +28,5 @@ function augIdproj(Q::AbstractArray{T,2}) where {T<:Real}
|
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return result
|
return result
|
||||||
end
|
end
|
||||||
|
|
||||||
function distance_to_cone(Δ::GroupRingElem, λ, Q; wlen::Int=4)
|
|
||||||
info("------------------------------------------------------------")
|
|
||||||
info("Checking in floating-point arithmetic...")
|
|
||||||
info("λ = $λ")
|
|
||||||
@time sos = compute_SOS(parent(Δ), Q)
|
|
||||||
residue = Δ^2-λ*Δ - sos
|
|
||||||
info("ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", aug(residue)))")
|
|
||||||
L1_norm = norm(residue,1)
|
|
||||||
info("‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", L1_norm))")
|
|
||||||
|
|
||||||
distance = λ - 2^(wlen-1)*L1_norm
|
|
||||||
|
|
||||||
info("Floating point distance (to positive cone) ≈")
|
|
||||||
info("$(@sprintf("%.10f", distance))")
|
|
||||||
info("")
|
|
||||||
|
|
||||||
if distance ≤ 0
|
|
||||||
return distance
|
|
||||||
end
|
end
|
||||||
|
|
||||||
info("------------------------------------------------------------")
|
|
||||||
info("Checking in interval arithmetic...")
|
|
||||||
info("λ ∈ $λ")
|
|
||||||
|
|
||||||
λ = @interval(λ)
|
|
||||||
eoi = Δ^2 - λ*Δ
|
|
||||||
info("Projecting columns of Q to the augmentation ideal...")
|
|
||||||
T = eltype(Q)
|
|
||||||
@time Q = augIdproj(Q)
|
|
||||||
|
|
||||||
info("Checking that sum of every column contains 0.0... ")
|
|
||||||
check = all([zero(T) in sum(view(Q, :, i)) for i in 1:size(Q, 2)])
|
|
||||||
info((check? "They do." : "FAILED!"))
|
|
||||||
|
|
||||||
@assert check
|
|
||||||
|
|
||||||
@time sos = compute_SOS(parent(Δ), Q)
|
|
||||||
residue = Δ^2-λ*Δ - sos
|
|
||||||
info("ɛ(∑ξᵢ*ξᵢ) ∈ $(aug(residue))")
|
|
||||||
L1_norm = norm(residue,1)
|
|
||||||
info("‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)")
|
|
||||||
|
|
||||||
distance = λ - 2^(wlen-1)*L1_norm
|
|
||||||
info("The Augmentation-projected distance (to positive cone) ∈")
|
|
||||||
info("$(distance)")
|
|
||||||
info("")
|
|
||||||
|
|
||||||
return distance.lo
|
|
||||||
end
|
end
|
||||||
|
|||||||
@ -61,61 +61,3 @@ function loadGRElem(fname::String, G::Group)
|
|||||||
end
|
end
|
||||||
return Δ
|
return Δ
|
||||||
end
|
end
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# λandP
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function computeλandP(sett::Settings{Naive}, Δ::GroupRingElem;
|
|
||||||
solverlog=tempname()*".log")
|
|
||||||
|
|
||||||
info("Creating SDP problem...")
|
|
||||||
SDP_problem, varλ, varP = SOS_problem(Δ^2, Δ, upper_bound=sett.upper_bound)
|
|
||||||
JuMP.setsolver(SDP_problem, sett.solver)
|
|
||||||
info(Base.repr(SDP_problem))
|
|
||||||
|
|
||||||
ws = warmstart(sett)
|
|
||||||
@time status, (λ, P, ws) = PropertyT.solve(solverlog, SDP_problem, varλ, varP, ws)
|
|
||||||
save(filename(sett, :warmstart), "warmstart", ws)
|
|
||||||
|
|
||||||
return λ, P
|
|
||||||
end
|
|
||||||
|
|
||||||
function computeλandP(sett::Settings{Symmetrize}, Δ::GroupRingElem;
|
|
||||||
solverlog=tempname()*".log")
|
|
||||||
|
|
||||||
if isfile(filename(sett, :OrbitData))
|
|
||||||
orbit_data = load(filename(sett, :OrbitData), "OrbitData")
|
|
||||||
else
|
|
||||||
isdefined(parent(Δ), :basis) || throw("You need to define basis of Group Ring to compute orbit decomposition!")
|
|
||||||
orbit_data = OrbitData(parent(Δ), sett.autS)
|
|
||||||
save(filename(sett, :OrbitData), "OrbitData", orbit_data)
|
|
||||||
end
|
|
||||||
orbit_data = decimate(orbit_data)
|
|
||||||
|
|
||||||
info("Creating SDP problem...")
|
|
||||||
|
|
||||||
SDP_problem, varλ, varP = SOS_problem(Δ^2, Δ, orbit_data, upper_bound=sett.upper_bound)
|
|
||||||
JuMP.setsolver(SDP_problem, sett.solver)
|
|
||||||
info(Base.repr(SDP_problem))
|
|
||||||
|
|
||||||
ws = warmstart(sett)
|
|
||||||
@time status, (λ, Ps, ws) = PropertyT.solve(solverlog, SDP_problem, varλ, varP, ws)
|
|
||||||
save(filename(sett, :warmstart), "warmstart", ws, "Ps", Ps, "λ", λ)
|
|
||||||
|
|
||||||
info("Reconstructing P...")
|
|
||||||
@time P = reconstruct(Ps, orbit_data)
|
|
||||||
|
|
||||||
return λ, P
|
|
||||||
end
|
|
||||||
|
|
||||||
function warmstart(sett::Settings)
|
|
||||||
if sett.warmstart && isfile(filename(sett, :warmstart))
|
|
||||||
ws = load(filename(sett, :warmstart), "warmstart")
|
|
||||||
else
|
|
||||||
ws = nothing
|
|
||||||
end
|
|
||||||
return ws
|
|
||||||
end
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user