kalmar/PropertyT.jl
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interpret_results for intervals

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kalmarek 2019-11-05 11:17:11 +01:00
parent f3ec2dd1b1
commit bfb08e69e4
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1 changed files with 15 additions and 11 deletions
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26
src/1712.07167.jl
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@ -224,7 +224,7 @@ function certify_SOS_decomposition(elt::GroupRingElem, orderunit::GroupRingElem,
"Interval aritmetic (certified) λ ∈"]
@info join(info_strs, "\n") certified_λ
return certified_λ.lo
return certified_λ
end
function spectral_gap(Δ::GroupRingElem, λ::Number, Q::AbstractMatrix; R::Int=2)
@ -238,7 +238,8 @@ end
#
###############################################################################
Kazhdan(λ::Number, N::Integer) = sqrt(2*λ/N)
Kazhdan_constant(λ::Number, N::Integer) = sqrt(2*λ/N)
Kazhdan_constant(λ::Interval, N::Integer) = IntervalArithmetic.inf(sqrt(2*λ/N))
function check_property_T(sett::Settings)
@info sett
@ -259,21 +260,24 @@ function Base.show(io::IO, sett::Settings)
print(io, join(info_strs, "\n"))
end
function interpret_results(sett::Settings, sgap::Number)
function interpret_results(name::String, sgap::Number, N::Integer)
if sgap > 0
Kazhdan_κ = Kazhdan(sgap, length(sett.S))
if Kazhdan_κ > 0
@info "κ($(sett.name), S) ≥ $Kazhdan_κ: Group HAS property (T)!"
return true
end
κ = Kazhdan_constant(sgap, N)
@info "κ($name, S) ≥ $κ: Group HAS property (T)!"
return true
end
info_strs = ["The certified lower bound on the spectral gap is negative:",
"λ($(sett.name), S) ≥ 0.0 > $sgap",
"This tells us nothing about property (T)"]
info_strs = [
"The certified lower bound on the spectral gap is negative:",
"λ($name, S) ≥ 0.0 > $sgap",
"This tells us nothing about property (T)",
]
@info join(info_strs, "\n")
return false
end
interpret_results(sett::Settings, sgap::Number) =
interpret_results(sett.name, sgap, length(sett.S))
function spectral_gap(sett::Settings)
fp = PropertyT.fullpath(sett)
isdir(fp) || mkpath(fp)