kalmar/PropertyT.jl
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reduce code duplication

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kalmarek 2018-01-02 03:22:46 +01:00
parent 955c8fc49e
commit f478081d4e
2 changed files with 29 additions and 45 deletions
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27
src/Orbit-wise.jl
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@ -243,32 +243,11 @@ function check_property_T(sett::Settings)
info(sett.logger, "maximum(P) = $(maximum(P))")
info(sett.logger, "minimum(P) = $(minimum(P))")
if λ > 0
pm_fname = filename(prepath(sett), :pm)
Δ_fname = filename(prepath(sett), :Δ)
RG = GroupRing(sett.G, load(pm_fname, "pm"))
Δ = GroupRingElem(load(Δ_fname, "Δ")[:, 1], RG)
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!")
# @assert P == Symmetric(P)
@logtime LOGGER Q = real(sqrtm(Symmetric(P)))
sgap = distance_to_positive_cone(Δ, λ, Q, 2*sett.radius, LOGGER)
if isa(sgap, Interval)
sgap = sgap.lo
end
if sgap > 0
info(LOGGER, "λ ≥ $(Float64(trunc(sgap,12)))")
Kazhdan_κ = PropertyT.Kazhdan_from_sgap(sgap, length(sett.S))
Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
info(LOGGER, "κ($(sett.name), S) ≥ $Kazhdan_κ: Group HAS property (T)!")
return true
else
sgap = Float64(trunc(sgap, 12))
info(LOGGER, "λ($(sett.name), S) ≥ $sgap: Group may NOT HAVE property (T)!")
return false
end
if λ > 0
return check_λ(sett.name, sett.S, λ, P, sett.radius, sett.logger)
end
info(sett.logger, "κ($(sett.name), S) ≥ $λ < 0: Tells us nothing about property (T)")
return false

47
src/PropertyT.jl
View File

@ -171,6 +171,28 @@ end
Kazhdan_from_sgap(λ,N) = sqrt(2*λ/N)
function check_λ(name, S, λ, P, radius, logger)
RG = GroupRing(parent(first(S)), load(filename(name, :pm), "pm"))
Δ = GroupRingElem(load(filename(name, :Δ), "Δ")[:, 1], RG)
@logtime logger Q = real(sqrtm(Symmetric(P)))
sgap = check_distance_to_cone(Δ, λ, Q, 2*radius, logger)
if sgap > 0
info(logger, "λ ≥ $(Float64(trunc(sgap,12)))")
Kazhdan_κ = Kazhdan_from_sgap(sgap, length(S))
Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
return true
else
sgap = Float64(trunc(sgap, 12))
info(logger, "λ($name, S) ≥ $sgap: Group may NOT HAVE property (T)!")
return false
end
end
function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
isdir(name) || mkdir(name)
@ -203,28 +225,11 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
info(LOGGER, "maximum(P) = $(maximum(P))")
info(LOGGER, "minimum(P) = $(minimum(P))")
isapprox(eigvals(P), abs.(eigvals(P)), atol=tol) ||
warn("The solution matrix doesn't seem to be positive definite!")
if λ > 0
RG = GroupRing(parent(first(S)), load(filename(name, :pm), "pm"))
Δ = GroupRingElem(load(filename(name, :Δ), "Δ")[:, 1], RG)
isapprox(eigvals(P), abs(eigvals(P)), atol=tol) ||
warn("The solution matrix doesn't seem to be positive definite!")
@logtime LOGGER Q = real(sqrtm(Symmetric(P)))
sgap = check_distance_to_cone(Δ, λ, Q, 2*radius, LOGGER)
if sgap > 0
info(LOGGER, "λ ≥ $(Float64(trunc(sgap,12)))")
Kazhdan_κ = Kazhdan_from_sgap(sgap, length(S))
Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
info(LOGGER, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
return true
else
sgap = Float64(trunc(sgap, 12))
info(LOGGER, "λ($name, S) ≥ $sgap: Group may NOT HAVE property (T)!")
return false
end
return check_λ(name, S, λ, P, radius, logger)
end
info(LOGGER, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
return false