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extract checking if lambda > 0 ... block to a separate function
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@ -248,18 +248,5 @@ function check_property_T(sett::Settings)
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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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if λ > 0
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RG = GroupRing(parent(first(sett.S)), load(filename(sett.name, :pm), "pm"))
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Δ = RG(load(filename(name, :Δ), "Δ")[:, 1])
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@logtime logger Q = real(sqrtm(Symmetric(P)))
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sgap = distance_to_cone(Δ, λ, Q, wlen=2*sett.radius, logger=sett.logger)
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Kazhdan_κ = Kazhdan(sgap, length(S))
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if Kazhdan_κ > 0
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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end
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end
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info(LOGGER, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
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return false
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return interpret_results(sett.name, sett.S, sett.radius, λ, P, sett.logger)
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end
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@ -157,15 +157,15 @@ Kazhdan(λ::Number,N::Integer) = sqrt(2*λ/N)
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function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius, warm::Bool=false)
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isdir(name) || mkdir(name)
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LOGGER = Memento.getlogger()
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logger = Memento.getlogger()
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if exists(filename(name, :pm)) && exists(filename(name, :Δ))
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# cached
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info(LOGGER, "Loading precomputed Δ...")
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info(logger, "Loading precomputed Δ...")
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Δ = Laplacian(name, parent(S[1]))
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else
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# compute
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Δ = Laplacian(S, Id, LOGGER, radius=radius)
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Δ = Laplacian(S, Id, logger, radius=radius)
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save(filename(name, :pm), "pm", parent(Δ).pm)
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save(filename(name, :Δ), "Δ", Δ.coeffs)
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end
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@ -177,39 +177,44 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius,
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cond2 = exists(filename(fullpath, :P))
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if !(warm) && cond1 && cond2
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info(LOGGER, "Loading precomputed λ, P...")
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info(logger, "Loading precomputed λ, P...")
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λ, P = λandP(fullpath)
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else
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info(LOGGER, "Creating SDP problem...")
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info(logger, "Creating SDP problem...")
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SDP_problem, varλ, varP = create_SDP_problem(Δ, constraints(parent(Δ).pm), upper_bound=upper_bound)
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JuMP.setsolver(SDP_problem, solver)
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info(LOGGER, Base.repr(SDP_problem))
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info(logger, Base.repr(SDP_problem))
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@logtime LOGGER λ, P = λandP(fullpath, SDP_problem, varλ, varP)
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@logtime logger λ, P = λandP(fullpath, SDP_problem, varλ, varP)
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end
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info(LOGGER, "λ = $λ")
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info(LOGGER, "sum(P) = $(sum(P))")
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info(LOGGER, "maximum(P) = $(maximum(P))")
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info(LOGGER, "minimum(P) = $(minimum(P))")
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info(logger, "λ = $λ")
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info(logger, "sum(P) = $(sum(P))")
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info(logger, "maximum(P) = $(maximum(P))")
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info(logger, "minimum(P) = $(minimum(P))")
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isapprox(eigvals(P), abs.(eigvals(P)), atol=tol) ||
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warn("The solution matrix doesn't seem to be positive definite!")
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if λ > 0
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return interpret_results(name, S, radius, λ, P, logger)
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end
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RG = GroupRing(parent(first(S)), load(filename(name, :pm), "pm"))
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Δ = RG(load(filename(name, :Δ), "Δ")[:, 1])
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@logtime logger Q = real(sqrtm(Symmetric(P)))
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function interpret_results(name, S, radius, λ, P, logger)
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sgap = distance_to_cone(Δ, λ, Q, wlen=2*radius, logger=LOGGER)
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RG = GroupRing(parent(first(S)), load(filename(name, :pm), "pm"))
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Δ = GroupRingElem(load(filename(name, :Δ), "Δ")[:, 1], RG)
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@logtime logger Q = real(sqrtm(Symmetric(P)))
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sgap = distance_to_cone(Δ, λ, Q, wlen=2*radius, logger=logger)
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if sgap > 0
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Kazhdan_κ = Kazhdan(sgap, length(S))
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if Kazhdan_κ > 0
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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end
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end
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info(LOGGER, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
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info(logger, "λ($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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