kalmar/PropertyT.jl
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Merge pull request #6 from kalmarek/enh/small_fixes

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Enh/small fixes
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kalmarek 2019-11-20 15:09:46 +01:00 committed by GitHub
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8 changed files with 99 additions and 75 deletions
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1
.travis.yml
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@ -14,6 +14,7 @@ matrix:
fast_finish: true
allow_failures:
- julia: nightly
- os: osx
addons:
apt:

36
Manifest.toml
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@ -23,9 +23,9 @@ version = "0.8.10"
[[BinaryProvider]]
deps = ["Libdl", "SHA"]
git-tree-sha1 = "29995a7b317bbd06be147e1974a3541ce2502dca"
git-tree-sha1 = "5b08ed6036d9d3f0ee6369410b830f8873d4024c"
uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
version = "0.5.7"
version = "0.5.8"
[[Blosc]]
deps = ["BinaryProvider", "CMakeWrapper", "Compat", "Libdl"]
@ -90,10 +90,10 @@ uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
version = "0.0.4"
[[DiffRules]]
deps = ["Random", "Test"]
git-tree-sha1 = "dc0869fb2f5b23466b32ea799bd82c76480167f7"
deps = ["NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "f734b5f6bc9c909027ef99f6d91d5d9e4b111eed"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "0.0.10"
version = "0.1.0"
[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
@ -118,13 +118,13 @@ version = "1.0.7"
[[ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "NaNMath", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "e2c81741a8be50de143ecddee942396894f47750"
git-tree-sha1 = "4407e7b76999eca2646abdb68203bd4302476168"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.4"
version = "0.10.6"
[[GroupRings]]
deps = ["AbstractAlgebra", "LinearAlgebra", "Markdown", "SparseArrays"]
git-tree-sha1 = "0953bbaa3ccd0b7e12585e705011f01ac8672c7c"
git-tree-sha1 = "8a9541783cff6911e35840770d0f004c0d2a13dd"
repo-rev = "master"
repo-url = "https://github.com/kalmarek/GroupRings.jl"
uuid = "0befed6a-bd73-11e8-1e41-a1190947c2f5"
@ -132,17 +132,17 @@ version = "0.3.0"
[[Groups]]
deps = ["AbstractAlgebra", "LinearAlgebra", "Markdown"]
git-tree-sha1 = "852339602ab880eb0e2a78f072ad386f3266f8a2"
git-tree-sha1 = "2487fd5e6106dabcafb835b694df08b4d22dde0e"
repo-rev = "master"
repo-url = "https://github.com/kalmarek/Groups.jl"
uuid = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
version = "0.2.3"
version = "0.3.0"
[[HDF5]]
deps = ["BinaryProvider", "Blosc", "CMakeWrapper", "Libdl", "Mmap"]
git-tree-sha1 = "c14a84878428b66222fccea6ed89cdafa7c22ae4"
git-tree-sha1 = "d3ea5532668bf9bdd5e8d5f16571e0b520cbbb9f"
uuid = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
version = "0.12.4"
version = "0.12.5"
[[InteractiveUtils]]
deps = ["Markdown"]
@ -197,9 +197,9 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
[[MathOptInterface]]
deps = ["BenchmarkTools", "LinearAlgebra", "OrderedCollections", "SparseArrays", "Test", "Unicode"]
git-tree-sha1 = "0d0e9987440b0b5c03f8df9cd30694f1acec81bb"
git-tree-sha1 = "78427dcc212e0c0ad9658049bc56a50303ad9737"
uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
version = "0.9.6"
version = "0.9.7"
[[MathProgBase]]
deps = ["Compat"]
@ -230,9 +230,9 @@ version = "0.12.0"
[[Parsers]]
deps = ["Dates", "Test"]
git-tree-sha1 = "ef0af6c8601db18c282d092ccbd2f01f3f0cd70b"
git-tree-sha1 = "a23968e107c0544aca91bfab6f7dd34de1206a54"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "0.3.7"
version = "0.3.9"
[[Pkg]]
deps = ["Dates", "LibGit2", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
@ -290,9 +290,9 @@ version = "0.8.0"
[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "1085ffbf5fd48fdba64ef8e902ca429c4e1212d3"
git-tree-sha1 = "5a3bcb6233adabde68ebc97be66e95dcb787424c"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "0.11.1"
version = "0.12.1"
[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]

5
Project.toml
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@ -1,7 +1,7 @@
name = "PropertyT"
uuid = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
authors = ["Marek Kaluba <kalmar@amu.edu.pl>"]
version = "0.3.0"
version = "0.3.1"
[deps]
AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
@ -18,8 +18,9 @@ Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[compat]
AbstractAlgebra = "^0.7.0"
GroupRings = "^0.3.0"
Groups = "^0.2.1"
Groups = "^0.3.0"
julia = "≥ 1.1.0"
[extras]

14
README.md
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@ -1 +1,15 @@
# Property(T)
[![Build Status](https://travis-ci.org/kalmarek/PropertyT.jl.svg?branch=master)](https://travis-ci.org/kalmarek/PropertyT.jl)
[![codecov](https://codecov.io/gh/kalmarek/PropertyT.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/kalmarek/PropertyT.jl)
This package is concerned with sum of squares decompositions in group rings of finitely presented groups.
Please have a look into [test](https://github.com/kalmarek/GroupRings.jl/blob/master/test/runtests.jl) directory to see how to use this package. For an example applications have a look at our papers:
[1703.09680](https://arxiv.org/abs/1703.09680), [1712.07167](https://arxiv.org/abs/1712.07167) and [1812.03456](https://arxiv.org/abs/1812.03456).
The package depends on
* [AbstractAlgebra](https://github.com/Nemocas/AbstractAlgebra.jl),
* [Groups](https://github.com/kalmarek/Groups.jl)
* [GroupRings](https://github.com/kalmarek/GroupRings.jl)
* [JuMP](https://github.com/JuliaOpt/JuMP.jl)
* [scs](https://github.com/JuliaOpt/SCS.jl) [solver](https://github.com/cvxgrp/scs)

80
src/1712.07167.jl
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@ -33,43 +33,43 @@ end
function Settings(name::String,
G::Union{Group, NCRing}, S::AbstractVector{El}, solver::JuMP.OptimizerFactory;
halfradius::Integer=2, upper_bound::Float64=1.0, force_compute=false) where El <: Union{GroupElem, NCRingElem}
halfradius=2, upper_bound=1.0, force_compute=false) where El <: Union{GroupElem, NCRingElem}
return Naive(name, G, S, halfradius, upper_bound, solver, force_compute)
end
function Settings(name::String,
G::Union{Group, NCRing}, S::AbstractVector{El}, autS::Group, solver::JuMP.OptimizerFactory;
halfradius::Integer=2, upper_bound::Float64=1.0, force_compute=false) where El <: Union{GroupElem, NCRingElem}
halfradius=2, upper_bound=1.0, force_compute=false) where El <: Union{GroupElem, NCRingElem}
return Symmetrized(name, G, S, autS, halfradius, upper_bound, solver, force_compute)
end
prefix(s::Naive) = s.name
prefix(s::Symmetrized) = "o"*s.name
suffix(s::Settings) = "$(s.upper_bound)"
prepath(s::Settings) = prefix(s)
fullpath(s::Settings) = joinpath(prefix(s), suffix(s))
prepath(s::Settings) = s.name
fullpath(s::Settings) = joinpath(prepath(s), suffix(s))
filename(sett::Settings, s::Symbol; kwargs...) = filename(sett, Val{s}; kwargs...)
filename(sett::Settings, ::Type{Val{:fulllog}}) =
joinpath(fullpath(sett), "full_$(string(now())).log")
filename(sett::Settings, ::Type{Val{:solverlog}}) =
joinpath(fullpath(sett), "solver_$(string(now())).log")
filename(sett::Settings, ::Type{Val{:fulllog}}; kwargs...) =
filename(fullpath(sett), "full", "log", suffix=Dates.now(); kwargs...)
filename(sett::Settings, ::Type{Val{:solverlog}}; kwargs...) =
filename(fullpath(sett), "solver", "log", suffix=Dates.now(); kwargs...)
filename(sett::Settings, ::Type{Val{:Δ}}) =
joinpath(prepath(sett), "delta.jld")
filename(sett::Settings, ::Type{Val{:OrbitData}}) =
joinpath(prepath(sett), "OrbitData.jld")
filename(sett::Settings, ::Type{Val{:Δ}}; kwargs...) =
filename(prepath(sett), "delta", "jld"; kwargs...)
filename(sett::Settings, ::Type{Val{:OrbitData}}; kwargs...) =
filename(prepath(sett), "OrbitData", "jld"; kwargs...)
filename(sett::Settings, ::Type{Val{:solution}}) =
joinpath(fullpath(sett), "solution.jld")
filename(sett::Settings, ::Type{Val{:solution}}; kwargs...) =
filename(fullpath(sett), "solution", "jld"; kwargs...)
function filename(sett::Settings, ::Type{Val{:warmstart}}; date=false)
if date
return joinpath(fullpath(sett), "warmstart_$(Dates.now()).jld")
else
return joinpath(fullpath(sett), "warmstart.jld")
end
function filename(sett::Settings, ::Type{Val{:warmstart}}; kwargs...)
filename(fullpath(sett), "warmstart", "jld"; kwargs...)
end
function filename(path::String, name, extension; prefix=nothing, suffix=nothing)
pre = isnothing(prefix) ? "" : "$(prefix)_"
suf = isnothing(suffix) ? "" : "_$(suffix)"
return joinpath(path, "$pre$name$suf.$extension")
end
###############################################################################
@ -109,13 +109,13 @@ function approximate_by_SOS(sett::Naive,
P = value.(SDP_problem[:P])
λ = value(SDP_problem[:λ])
if any(isnan.(P))
if any(isnan, P)
@warn "The solution seems to contain NaNs. Not overriding warmstart.jld"
else
save(filename(sett, :warmstart), "warmstart", (ws.primal, ws.dual, ws.slack), "P", P, "λ", λ)
end
save(filename(sett, :warmstart, date=true),
save(filename(sett, :warmstart, suffix=Dates.now()),
"warmstart", (ws.primal, ws.dual, ws.slack), "P", P, "λ", λ)
return λ, P
@ -155,13 +155,13 @@ function approximate_by_SOS(sett::Symmetrized,
λ = value(SDP_problem[:λ])
Ps = [value.(P) for P in varP]
if any(any(isnan.(P)) for P in Ps)
if any(any(isnan, P) for P in Ps)
@warn "The solution seems to contain NaNs. Not overriding warmstart.jld"
else
save(filename(sett, :warmstart), "warmstart", (ws.primal, ws.dual, ws.slack), "Ps", Ps, "λ", λ)
end
save(filename(sett, :warmstart, date=true),
save(filename(sett, :warmstart, suffix=Dates.now()),
"warmstart", (ws.primal, ws.dual, ws.slack), "Ps", Ps, "λ", λ)
@info "Reconstructing P..."
@ -208,7 +208,7 @@ function certify_SOS_decomposition(elt::GroupRingElem, orderunit::GroupRingElem,
@info("Projecting columns of Q to the augmentation ideal...")
@time Q, check = augIdproj(Interval, Q)
@info "Checking that sum of every column contains 0.0..." check_augmented=check
check || @warn("The following numbers are meaningless!")
check || @error("The following numbers are meaningless!")
@info("Computing sum of squares decomposition...")
@time residual = eoi - compute_SOS(parent(eoi), Q)
@ -222,7 +222,7 @@ 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)
@ -236,7 +236,8 @@ 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
@ -257,21 +258,24 @@ 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)

2
src/PropertyT.jl
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@ -17,8 +17,6 @@ import AbstractAlgebra: Group, NCRing
import MathProgBase.SolverInterface.AbstractMathProgSolver
AbstractAlgebra.one(G::Group) = G()
include("laplacians.jl")
include("RGprojections.jl")
include("orbitdata.jl")

28
test/1712.07167.jl
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@ -1,13 +1,15 @@
@testset "1712.07167 Examples" begin
@testset "oSL(3,Z)" begin
@testset "SL(3,Z)" begin
N = 3
G = MatrixAlgebra(zz, N)
S = PropertyT.generating_set(G)
autS = WreathProduct(PermGroup(2), PermGroup(N))
rm("oSL($N,Z)", recursive=true, force=true)
sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(2000, accel=20);
NAME = "SL($N,Z)_orbit"
rm(NAME, recursive=true, force=true)
sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000, accel=20);
upper_bound=0.27, force_compute=false)
@info sett
@ -20,7 +22,7 @@
@test λ == PropertyT.spectral_gap(sett)
@test PropertyT.check_property_T(sett) == false
sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(4000, accel=20);
sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(4000, accel=20);
upper_bound=0.27, force_compute=true)
@info sett
@ -36,7 +38,7 @@
##########
# Symmetrizing by PermGroup(3):
sett = PropertyT.Settings("SL($N,Z)", G, S, PermGroup(N), with_SCS(4000, accel=20, warm_start=false);
sett = PropertyT.Settings(NAME, G, S, PermGroup(N), with_SCS(4000, accel=20, warm_start=false);
upper_bound=0.27, force_compute=true)
@info sett
@ -46,14 +48,16 @@
@test PropertyT.interpret_results(sett, λ) == true
end
@testset "oSL(4,Z)" begin
@testset "SL(4,Z)" begin
N = 4
G = MatrixAlgebra(zz, N)
S = PropertyT.generating_set(G)
autS = WreathProduct(PermGroup(2), PermGroup(N))
rm("oSL($N,Z)", recursive=true, force=true)
sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(2000, accel=20);
NAME = "SL($N,Z)_orbit"
rm(NAME, recursive=true, force=true)
sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(2000, accel=20);
upper_bound=1.3, force_compute=false)
@info sett
@ -66,7 +70,7 @@
@test λ == PropertyT.spectral_gap(sett)
@test PropertyT.check_property_T(sett) == false
sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(15000, accel=20, warm_start=true);
sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(15000, accel=20, warm_start=true);
upper_bound=1.3, force_compute=true)
@info sett
@ -86,9 +90,11 @@
S = PropertyT.generating_set(G)
autS = WreathProduct(PermGroup(2), PermGroup(N))
rm("oSAut(F$N)", recursive=true, force=true)
NAME = "SAut(F$N)_orbit"
sett = PropertyT.Settings("SAut(F$N)", G, S, autS, with_SCS(1000);
rm(NAME, recursive=true, force=true)
sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000);
upper_bound=0.15)
@info sett

8
test/SOS_correctness.jl
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@ -27,17 +27,17 @@
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
#########################################################
NAME = "oSL(3,Z)"
NAME = "SL(3,Z)_orbit"
eoi, pm, Q = prepare(NAME, 0.27, 3*2*2)
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
@time sos_hpc = PropertyT.compute_SOS(pm, Q)
@test norm(sos_sqr - sos_hpc, 1) < 4e-12
@test norm(sos_sqr - sos_hpc, 1) < 5e-12
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
#########################################################
NAME = "oSL(4,Z)"
NAME = "SL(4,Z)_orbit"
eoi, pm, Q = prepare(NAME, 1.3, 4*3*2)
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
@ -47,7 +47,7 @@
@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
#########################################################
NAME = "oSAut(F3)"
NAME = "SAut(F3)_orbit"
eoi, pm, Q = prepare(NAME, 0.15, 4*3*2*2)
@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)