kalmar/PropertyT.jl
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extract checking if lambda > 0 ... block to a separate function

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kalmarek 2018-08-15 19:10:38 +02:00
parent 2d62aa26f2
commit 0c2f5b1a9a
2 changed files with 23 additions and 31 deletions
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15
src/Orbit-wise.jl
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@ -248,18 +248,5 @@ function check_property_T(sett::Settings)
isapprox(eigvals(P), abs.(eigvals(P)), atol=sett.tol) || isapprox(eigvals(P), abs.(eigvals(P)), atol=sett.tol) ||
warn("The solution matrix doesn't seem to be positive definite!") warn("The solution matrix doesn't seem to be positive definite!")
if λ > 0 return interpret_results(sett.name, sett.S, sett.radius, λ, P, sett.logger)
RG = GroupRing(parent(first(sett.S)), load(filename(sett.name, :pm), "pm"))
Δ = RG(load(filename(name, :Δ), "Δ")[:, 1])
@logtime logger Q = real(sqrtm(Symmetric(P)))
sgap = distance_to_cone(Δ, λ, Q, wlen=2*sett.radius, logger=sett.logger)
Kazhdan_κ = Kazhdan(sgap, length(S))
if Kazhdan_κ > 0
info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
return true
end
end
info(LOGGER, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
return false
end end

35
src/PropertyT.jl
View File

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