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1712.07167
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.gitignore
vendored
17
.gitignore
vendored
@ -1,15 +1,8 @@
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Articles
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Higman
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MCG*
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notebooks
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Oldies
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oSAutF*
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oSL*
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SAutF*
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SL*_*
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*ipynb*
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*ipynb*
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*.gws
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*.gws
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*/*.jld
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*/*.log
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Old*
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.*
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.*
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tests*
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o*
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*.py
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*test*
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*.pyc
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118
AutFN.jl
Normal file
118
AutFN.jl
Normal file
@ -0,0 +1,118 @@
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using ArgParse
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using Nemo
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import SCS.SCSSolver
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using PropertyT
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using Groups
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Nemo.setpermstyle(:cycles)
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#=
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Note that the element
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α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
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which surely belongs to ball of radius 4 in Aut(F₄) becomes trivial under the representation
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Aut(F₄) → GL₄(ℤ)⋉ℤ⁴ → GL₅(ℂ).
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Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ(ℂ) (for m ≤ 2n-2) factors through GLₙ(ℤ)⋉ℤⁿ, so will have the same problem.
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We need a different approach: Here we actually compute in Aut(𝔽₄)
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=#
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###############################################################################
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#
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# Generating set
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#
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###############################################################################
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function SOutFN_generating_set(N::Int)
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SOutFN = AutGroup(FreeGroup(N), special=true, outer=true)
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S = gens(SOutFN);
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S = [S; [inv(s) for s in S]]
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return SOutFN, unique(S)
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end
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###############################################################################
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#
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# Parsing command line
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#
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###############################################################################
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function cpuinfo_physicalcores()
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maxcore = -1
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for line in eachline("/proc/cpuinfo")
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if startswith(line, "core id")
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maxcore = max(maxcore, parse(Int, split(line, ':')[2]))
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end
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end
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maxcore < 0 && error("failure to read core ids from /proc/cpuinfo")
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return maxcore + 1
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end
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function parse_commandline()
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s = ArgParseSettings()
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@add_arg_table s begin
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"--tol"
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help = "set numerical tolerance for the SDP solver"
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arg_type = Float64
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default = 1e-6
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"--iterations"
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help = "set maximal number of iterations for the SDP solver"
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arg_type = Int
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default = 20000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"-N"
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help = "Consider automorphisms of free group on N generators"
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arg_type = Int
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default = 2
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|
end
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|
return parse_args(s)
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end
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|
function main()
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parsed_args = parse_commandline()
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if parsed_args["cpus"] ≠ nothing
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|
if parsed_args["cpus"] > cpuinfo_physicalcores()
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|
warn("Number of specified cores exceeds the physical core cound. Performance will suffer.")
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end
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Blas.set_num_threads(parsed_args["cpus"])
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end
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N = parsed_args["N"]
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radius = 2
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tol = parsed_args["tol"]
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iterations = parsed_args["iterations"]
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upper_bound = parsed_args["upper-bound"]
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dirname = "SOutF$(N)_$(upper_bound)_r=$radius"
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logger = PropertyT.setup_logging(dirname)
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info(logger, "Group: $dirname")
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info(logger, "Iterations: $iterations")
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info(logger, "Precision: $tol")
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info(logger, "Upper bound: $upper_bound")
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G, S = SOutFN_generating_set(N)
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info(logger, G)
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info(logger, "Symmetric generating set of size $(length(S))")
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info(logger, S)
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Id = G()
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
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@time PropertyT.check_property_T(dirname, S, Id, solver, upper_bound, tol, 2)
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return 0
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end
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main()
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54
AutFN_orbit.jl
Normal file
54
AutFN_orbit.jl
Normal file
@ -0,0 +1,54 @@
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using ArgParse
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###############################################################################
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|
#
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|
# Parsing command line
|
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|
#
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|
###############################################################################
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function parse_commandline()
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settings = ArgParseSettings()
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@add_arg_table settings begin
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|
"--tol"
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help = "set numerical tolerance for the SDP solver"
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|
arg_type = Float64
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default = 1e-14
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"--iterations"
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|
help = "set maximal number of iterations for the SDP solver (default: 20000)"
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|
arg_type = Int
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default = 60000
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"--upper-bound"
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help = "Set an upper bound for the spectral gap"
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arg_type = Float64
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|
default = Inf
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"--cpus"
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help = "Set number of cpus used by solver (default: auto)"
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arg_type = Int
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required = false
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"-N"
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help = "Consider automorphisms of free group on N generators"
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arg_type = Int
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default = 2
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"--radius"
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help = "Radius of ball B_r(e,S) to find solution over"
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arg_type = Int
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|
default = 2
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|
"--warmstart"
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|
help = "Use warmstart.jl as the initial guess for SCS"
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action = :store_true
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|
end
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|
return parse_args(settings)
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|
end
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|
parsed_args = parse_commandline()
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|
include("CPUselect.jl")
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set_parallel_mthread(parsed_args, workers=true)
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include("SAutFNs.jl")
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include("Orbit.jl")
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main(SAutFNs, parsed_args)
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19
CPUselect.jl
19
CPUselect.jl
@ -9,10 +9,16 @@ function cpuinfo_physicalcores()
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return maxcore + 1
|
return maxcore + 1
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end
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end
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function set_parallel_mthread(N::Int, workers::Bool)
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function set_parallel_mthread(parsed_args; workers=false)
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if parsed_args["cpus"] == nothing
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N = cpuinfo_physicalcores()
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|
else
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|
N = parsed_args["cpus"]
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if N > cpuinfo_physicalcores()
|
if N > cpuinfo_physicalcores()
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warn("Number of specified cores exceeds the physical core count. Performance may suffer.")
|
warn("Number of specified cores exceeds the physical core count. Performance may suffer.")
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end
|
end
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|
end
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if workers
|
if workers
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addprocs(N)
|
addprocs(N)
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@ -22,14 +28,5 @@ function set_parallel_mthread(N::Int, workers::Bool)
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BLAS.set_num_threads(N)
|
BLAS.set_num_threads(N)
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info("Using $N threads in BLAS.")
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info("Using $N threads in BLAS.")
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end
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return N
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function set_parallel_mthread(parsed_args::Dict; workers=false)
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if parsed_args["cpus"] == nothing
|
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N = cpuinfo_physicalcores()
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else
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N = parsed_args["cpus"]
|
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end
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set_parallel_mthread(N, workers)
|
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end
|
end
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157
FPGroups_GAP.jl
157
FPGroups_GAP.jl
@ -1,157 +0,0 @@
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using JLD
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function GAP_code(group_code, dir, R; maxeqns=10_000, infolevel=2)
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code = """
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LogTo("$(dir)/GAP.log");
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RequirePackage("kbmag");
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SetInfoLevel(InfoRWS, $infolevel);
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MetricBalls := function(rws, R)
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local l, basis, sizes, i;
|
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l := EnumerateReducedWords(rws, 0, R);;
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SortBy(l, Length);
|
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sizes := [1..R];
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Apply(sizes, i -> Number(l, w -> Length(w) <= i));
|
|
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return [l, sizes];
|
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end;;
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|
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ProductMatrix := function(rws, basis, len)
|
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local result, dict, g, tmpList, t;
|
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result := [];
|
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dict := NewDictionary(basis[1], true);
|
|
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t := Runtime();
|
|
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for g in [1..Length(basis)] do;
|
|
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AddDictionary(dict, basis[g], g);
|
|
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od;
|
|
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Print("Creating dictionary: \t\t", StringTime(Runtime()-t), "\\n");
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|
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for g in basis{[1..len]} do;
|
|
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tmpList := List(Inverse(g)*basis{[1..len]}, w->ReducedForm(rws, w));
|
|
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#t := Runtime();
|
|
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tmpList := List(tmpList, x -> LookupDictionary(dict, x));
|
|
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#Print(Runtime()-t, "\\n");
|
|
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Assert(1, ForAll(tmpList, x -> x <> fail));
|
|
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Add(result, tmpList);
|
|
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od;
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|
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return result;
|
|
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end;;
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|
|
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SaveCSV := function(fname, pm)
|
|
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local file, i, j, k;
|
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file := OutputTextFile(fname, false);;
|
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for i in pm do;
|
|
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k := 1;
|
|
||||||
for j in i do;
|
|
||||||
if k < Length(i) then
|
|
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AppendTo(file, j, ", ");
|
|
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else
|
|
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AppendTo(file, j, "\\n");
|
|
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fi;
|
|
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k := k+1;
|
|
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od;
|
|
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od;
|
|
||||||
CloseStream(file);
|
|
||||||
end;;
|
|
||||||
|
|
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$group_code
|
|
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|
|
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# G:= SimplifiedFpGroup(G);
|
|
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RWS := KBMAGRewritingSystem(G);
|
|
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# ResetRewritingSystem(RWS);
|
|
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O:=OptionsRecordOfKBMAGRewritingSystem(RWS);;
|
|
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O.maxeqns := $maxeqns;
|
|
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O.maxstates := 1000*$maxeqns;
|
|
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#O.maxstoredlen := [100,100];
|
|
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|
|
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before := Runtimes();;
|
|
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KnuthBendix(RWS);
|
|
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after := Runtimes();;
|
|
||||||
delta := after.user_time_children - before.user_time_children;;
|
|
||||||
Print("Knuth-Bendix completion: \t", StringTime(delta), "\\n");
|
|
||||||
|
|
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t := Runtime();
|
|
||||||
res := MetricBalls(RWS,$(2*R));;
|
|
||||||
Print("Metric-Balls generation: \t", StringTime(Runtime()-t), "\\n");
|
|
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B := res[1];; sizes := res[2];;
|
|
||||||
Print("Sizes of generated Balls: \t", sizes, "\\n");
|
|
||||||
|
|
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t := Runtime();
|
|
||||||
pm := ProductMatrix(RWS, B, sizes[$R]);;
|
|
||||||
Print("Computing ProductMatrix: \t", StringTime(Runtime()-t), "\\n");
|
|
||||||
|
|
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S := EnumerateReducedWords(RWS, 1, 1);
|
|
||||||
S := List(S, s -> Position(B,s));
|
|
||||||
|
|
||||||
SaveCSV("$(dir)/pm.csv", pm);
|
|
||||||
SaveCSV("$(dir)/S.csv", [S]);
|
|
||||||
SaveCSV("$(dir)/sizes.csv", [sizes]);
|
|
||||||
|
|
||||||
Print("DONE!\\n");
|
|
||||||
|
|
||||||
quit;""";
|
|
||||||
return code
|
|
||||||
end
|
|
||||||
|
|
||||||
function GAP_groupcode(S, rels)
|
|
||||||
F = "FreeGroup("*join(["\"$v\""for v in S], ", ") *");"
|
|
||||||
m = match(r".*(\[.*\])$", string(rels))
|
|
||||||
rels = replace(m.captures[1], " ", "\n")
|
|
||||||
code = """
|
|
||||||
F := $F;
|
|
||||||
AssignGeneratorVariables(F);;
|
|
||||||
relations := $rels;;
|
|
||||||
G := F/relations;
|
|
||||||
"""
|
|
||||||
return code
|
|
||||||
end
|
|
||||||
|
|
||||||
function GAP_execute(gap_code, dir)
|
|
||||||
isdir(dir) || mkdir(dir)
|
|
||||||
GAP_file = joinpath(dir, "GAP_code.g")
|
|
||||||
@show dir
|
|
||||||
@show GAP_file;
|
|
||||||
|
|
||||||
open(GAP_file, "w") do io
|
|
||||||
write(io, gap_code)
|
|
||||||
end
|
|
||||||
run(pipeline(`cat $(GAP_file)`, `gap -q`))
|
|
||||||
end
|
|
||||||
|
|
||||||
function prepare_pm_delta_csv(name, group_code, R; maxeqns=10_000, infolevel=2)
|
|
||||||
info("Preparing multiplication table using GAP (via kbmag)")
|
|
||||||
gap_code = GAP_code(group_code, name, R, maxeqns=maxeqns, infolevel=infolevel)
|
|
||||||
GAP_execute(gap_code, name)
|
|
||||||
end
|
|
||||||
|
|
||||||
function prepare_pm_delta(name, group_code, R; maxeqns=100_000, infolevel=2)
|
|
||||||
|
|
||||||
pm_fname = joinpath(name, "pm.csv")
|
|
||||||
S_fname = joinpath(name, "S.csv")
|
|
||||||
sizes_fname = joinpath(name, "sizes.csv")
|
|
||||||
delta_fname = joinpath(name, "delta.jld")
|
|
||||||
|
|
||||||
if !isfile(pm_fname) || !isfile(S_fname) || !isfile(sizes_fname)
|
|
||||||
prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
|
|
||||||
end
|
|
||||||
|
|
||||||
if isfile(sizes_fname)
|
|
||||||
sizes = readcsv(sizes_fname, Int)[1,:]
|
|
||||||
if 2R > length(sizes)
|
|
||||||
prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
pm = readcsv(pm_fname, Int)
|
|
||||||
S = readcsv(S_fname, Int)[1,:]
|
|
||||||
sizes = readcsv(sizes_fname, Int)[1,:]
|
|
||||||
|
|
||||||
Δ = spzeros(sizes[2R])
|
|
||||||
Δ[S] .= -1
|
|
||||||
Δ[1] = length(S)
|
|
||||||
|
|
||||||
pm = pm[1:sizes[R], 1:sizes[R]]
|
|
||||||
|
|
||||||
save(joinpath(name, "pm.jld"), "pm", pm)
|
|
||||||
save(joinpath(name, "delta.jld"), "Δ", Δ)
|
|
||||||
|
|
||||||
end
|
|
||||||
53
Orbit.jl
Normal file
53
Orbit.jl
Normal file
@ -0,0 +1,53 @@
|
|||||||
|
using SCS.SCSSolver
|
||||||
|
# using Mosek
|
||||||
|
# using CSDP
|
||||||
|
# using SDPA
|
||||||
|
|
||||||
|
using Nemo
|
||||||
|
|
||||||
|
using PropertyT
|
||||||
|
using Groups
|
||||||
|
|
||||||
|
function main(GROUP, parsed_args)
|
||||||
|
|
||||||
|
radius = parsed_args["radius"]
|
||||||
|
tol = parsed_args["tol"]
|
||||||
|
iterations = parsed_args["iterations"]
|
||||||
|
upper_bound = parsed_args["upper-bound"]
|
||||||
|
warm = parsed_args["warmstart"]
|
||||||
|
|
||||||
|
name, N = GROUP.groupname(parsed_args)
|
||||||
|
G, S = GROUP.generatingset(parsed_args)
|
||||||
|
autS = GROUP.autS(parsed_args)
|
||||||
|
|
||||||
|
name = "$(name)_r$radius"
|
||||||
|
isdir(name) || mkdir(name)
|
||||||
|
|
||||||
|
logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"))
|
||||||
|
|
||||||
|
info(logger, "Group: $name")
|
||||||
|
info(logger, "Iterations: $iterations")
|
||||||
|
info(logger, "Precision: $tol")
|
||||||
|
info(logger, "Upper bound: $upper_bound")
|
||||||
|
info(logger, "Threads: $(Threads.nthreads())")
|
||||||
|
info(logger, "Workers: $(workers())")
|
||||||
|
info(logger, G)
|
||||||
|
info(logger, "Symmetric generating set of size $(length(S))")
|
||||||
|
# info(logger, S)
|
||||||
|
|
||||||
|
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.9, acceleration_lookback=1)
|
||||||
|
|
||||||
|
# solver = Mosek.MosekSolver(
|
||||||
|
# MSK_DPAR_INTPNT_CO_TOL_REL_GAP=tol,
|
||||||
|
# MSK_IPAR_INTPNT_MAX_ITERATIONS=iterations,
|
||||||
|
# QUIET=false)
|
||||||
|
|
||||||
|
# solver = CSDP.CSDPSolver(axtol=tol, atytol=tol, objtol=tol, minstepp=tol*10.0^-1, minstepd=tol*10.0^-1)
|
||||||
|
|
||||||
|
# solver = SDPA.SDPASolver(epsilonStar=tol, epsilonDash=tol)
|
||||||
|
|
||||||
|
|
||||||
|
sett = Settings(name, N, G, S, autS, radius, solver, upper_bound, tol, warm)
|
||||||
|
|
||||||
|
PropertyT.check_property_T(sett)
|
||||||
|
end
|
||||||
@ -1,10 +1,4 @@
|
|||||||
# DEPRECATED!
|
This repository contains code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
|
||||||
|
|
||||||
This repository has not been updated for a while!
|
|
||||||
If You are interested in replicating results for [1712.07167](https://arxiv.org/abs/1712.07167) please check [these instruction](https://kalmar.faculty.wmi.amu.edu.pl/post/1712.07176/)
|
|
||||||
Also [this notebook](https://nbviewer.jupyter.org/gist/kalmarek/03510181bc1e7c98615e86e1ec580b2a) could be of some help. If everything else fails the [zenodo dataset](https://zenodo.org/record/1133440) should contain the last-resort instructions.
|
|
||||||
|
|
||||||
This repository contains some legacy code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
|
|
||||||
|
|
||||||
# Installing
|
# Installing
|
||||||
To run the code You need `julia-v0.5` (should work on `v0.6`, but with warnings).
|
To run the code You need `julia-v0.5` (should work on `v0.6`, but with warnings).
|
||||||
|
|||||||
80
SAutFNs.jl
Normal file
80
SAutFNs.jl
Normal file
@ -0,0 +1,80 @@
|
|||||||
|
module SAutFNs
|
||||||
|
|
||||||
|
using Nemo
|
||||||
|
using Groups
|
||||||
|
|
||||||
|
if VERSION >= v"0.6.0"
|
||||||
|
import Nemo.Generic.perm
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Generating set
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function generatingset(N::Int)
|
||||||
|
|
||||||
|
SAutFN = AutGroup(FreeGroup(N), special=true)
|
||||||
|
S = gens(SAutFN);
|
||||||
|
S = [S; [inv(s) for s in S]]
|
||||||
|
|
||||||
|
return SAutFN, unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
function generatingset(parsed_args)
|
||||||
|
N = parsed_args["N"]
|
||||||
|
return generatingset(N)
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Action of WreathProductElems on AutGroupElem
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function AutFG_emb(A::AutGroup, g::WreathProductElem)
|
||||||
|
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
||||||
|
parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
||||||
|
powers = [(elt == parent(elt)() ? 0: 1) for elt in g.n.elts]
|
||||||
|
elt = reduce(*, [A(Groups.flip_autsymbol(i))^pow for (i,pow) in enumerate(powers)])
|
||||||
|
Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
|
||||||
|
return elt
|
||||||
|
end
|
||||||
|
|
||||||
|
function AutFG_emb(A::AutGroup, p::perm)
|
||||||
|
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
||||||
|
parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
||||||
|
return A(Groups.perm_autsymbol(p))
|
||||||
|
end
|
||||||
|
|
||||||
|
function (g::WreathProductElem)(a::AutGroupElem)
|
||||||
|
g = AutFG_emb(parent(a),g)
|
||||||
|
return g*a*g^-1
|
||||||
|
end
|
||||||
|
|
||||||
|
function (p::perm)(a::AutGroupElem)
|
||||||
|
g = AutFG_emb(parent(a),p)
|
||||||
|
return g*a*g^-1
|
||||||
|
end
|
||||||
|
|
||||||
|
autS(N::Int) = WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
||||||
|
|
||||||
|
function autS(parsed_args)
|
||||||
|
return autS(parsed_args["N"])
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Misc
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function groupname(parsed_args)
|
||||||
|
N = parsed_args["N"]
|
||||||
|
return groupname(N), N
|
||||||
|
end
|
||||||
|
|
||||||
|
groupname(N::Int) = "oSAutF$(N)"
|
||||||
|
|
||||||
|
end # of module SAutFNs
|
||||||
151
SL.jl
Normal file
151
SL.jl
Normal file
@ -0,0 +1,151 @@
|
|||||||
|
using ArgParse
|
||||||
|
|
||||||
|
using Nemo
|
||||||
|
import SCS.SCSSolver
|
||||||
|
using PropertyT
|
||||||
|
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Generating set
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
|
||||||
|
@assert i≠j
|
||||||
|
m = one(M)
|
||||||
|
m[i,j] = val
|
||||||
|
return m
|
||||||
|
end
|
||||||
|
|
||||||
|
function SLsize(n,p)
|
||||||
|
result = BigInt(1)
|
||||||
|
for k in 0:n-1
|
||||||
|
result *= p^n - p^k
|
||||||
|
end
|
||||||
|
return div(result, p-1)
|
||||||
|
end
|
||||||
|
|
||||||
|
function SL_generatingset(n::Int, X::Bool=false)
|
||||||
|
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||||
|
G = MatrixSpace(ZZ, n, n)
|
||||||
|
if X
|
||||||
|
S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]]
|
||||||
|
else
|
||||||
|
S = [E(i,j,G,v) for (i,j) in indexing for v in [1]]
|
||||||
|
end
|
||||||
|
S = vcat(S, [inv(x) for x in S])
|
||||||
|
return G, unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
function SL_generatingset(n::Int, p::Int, X::Bool=false)
|
||||||
|
p == 0 && return SL_generatingset(n, X)
|
||||||
|
(p > 1 && n > 1) || throw("Both n and p should be positive integers!")
|
||||||
|
info("Size(SL($n,$p)) = $(SLsize(n,p))")
|
||||||
|
F = ResidueRing(ZZ, p)
|
||||||
|
G = MatrixSpace(F, n, n)
|
||||||
|
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||||
|
S = [E(i, j, G) for (i,j) in indexing]
|
||||||
|
S = vcat(S, [inv(x) for x in S])
|
||||||
|
return G, unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Parsing command line
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function cpuinfo_physicalcores()
|
||||||
|
maxcore = -1
|
||||||
|
for line in eachline("/proc/cpuinfo")
|
||||||
|
if startswith(line, "core id")
|
||||||
|
maxcore = max(maxcore, parse(Int, split(line, ':')[2]))
|
||||||
|
end
|
||||||
|
end
|
||||||
|
maxcore < 0 && error("failure to read core ids from /proc/cpuinfo")
|
||||||
|
return maxcore + 1
|
||||||
|
end
|
||||||
|
|
||||||
|
function parse_commandline()
|
||||||
|
settings = ArgParseSettings()
|
||||||
|
|
||||||
|
@add_arg_table settings begin
|
||||||
|
"--tol"
|
||||||
|
help = "set numerical tolerance for the SDP solver"
|
||||||
|
arg_type = Float64
|
||||||
|
default = 1e-6
|
||||||
|
"--iterations"
|
||||||
|
help = "set maximal number of iterations for the SDP solver (default: 20000)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 50000
|
||||||
|
"--upper-bound"
|
||||||
|
help = "Set an upper bound for the spectral gap"
|
||||||
|
arg_type = Float64
|
||||||
|
default = Inf
|
||||||
|
"--cpus"
|
||||||
|
help = "Set number of cpus used by solver"
|
||||||
|
arg_type = Int
|
||||||
|
required = false
|
||||||
|
"-N"
|
||||||
|
help = "Consider elementary matrices EL(N)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 2
|
||||||
|
"-p"
|
||||||
|
help = "Matrices over field of p-elements (p=0 => over ZZ)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 0
|
||||||
|
"--radius"
|
||||||
|
help = "Radius of ball B_r(e,S) to find solution over"
|
||||||
|
arg_type = Int
|
||||||
|
default = 2
|
||||||
|
end
|
||||||
|
|
||||||
|
return parse_args(settings)
|
||||||
|
end
|
||||||
|
|
||||||
|
function main()
|
||||||
|
|
||||||
|
parsed_args = parse_commandline()
|
||||||
|
if parsed_args["cpus"] ≠ nothing
|
||||||
|
if parsed_args["cpus"] > cpuinfo_physicalcores()
|
||||||
|
warn("Number of specified cores exceeds the physical core cound. Performance will suffer.")
|
||||||
|
end
|
||||||
|
BLAS.set_num_threads(parsed_args["cpus"])
|
||||||
|
end
|
||||||
|
|
||||||
|
N = parsed_args["N"]
|
||||||
|
p = parsed_args["p"]
|
||||||
|
|
||||||
|
if p == 0
|
||||||
|
dirname = "SL$(N)Z"
|
||||||
|
else
|
||||||
|
dirname = "SL$(N)_$p"
|
||||||
|
end
|
||||||
|
|
||||||
|
radius = parsed_args["radius"]
|
||||||
|
tol = parsed_args["tol"]
|
||||||
|
iterations = parsed_args["iterations"]
|
||||||
|
upper_bound = parsed_args["upper-bound"]
|
||||||
|
|
||||||
|
dirname = "$(dirname)_$(upper_bound)_r=$radius"
|
||||||
|
|
||||||
|
logger = PropertyT.setup_logging(dirname)
|
||||||
|
|
||||||
|
info(logger, "Group: $dirname")
|
||||||
|
info(logger, "Iterations: $iterations")
|
||||||
|
info(logger, "Precision: $tol")
|
||||||
|
info(logger, "Upper bound: $upper_bound")
|
||||||
|
|
||||||
|
G, S = SL_generatingset(N, p)
|
||||||
|
info(logger, G)
|
||||||
|
info(logger, "Symmetric generating set of size $(length(S))")
|
||||||
|
Id = one(G)
|
||||||
|
|
||||||
|
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
|
||||||
|
|
||||||
|
@time PropertyT.check_property_T(dirname, S, Id, solver, upper_bound, tol, radius)
|
||||||
|
return 0
|
||||||
|
end
|
||||||
|
|
||||||
|
main()
|
||||||
124
SLNs.jl
Normal file
124
SLNs.jl
Normal file
@ -0,0 +1,124 @@
|
|||||||
|
module SLNs
|
||||||
|
|
||||||
|
using Nemo
|
||||||
|
using Groups
|
||||||
|
|
||||||
|
if VERSION >= v"0.6.0"
|
||||||
|
import Nemo.Generic.perm
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Generating set
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
|
||||||
|
@assert i≠j
|
||||||
|
m = one(M)
|
||||||
|
m[i,j] = val
|
||||||
|
return m
|
||||||
|
end
|
||||||
|
|
||||||
|
function SLsize(n,p)
|
||||||
|
result = BigInt(1)
|
||||||
|
for k in 0:n-1
|
||||||
|
result *= p^n - p^k
|
||||||
|
end
|
||||||
|
return div(result, p-1)
|
||||||
|
end
|
||||||
|
|
||||||
|
function generatingset(n::Int, X::Bool=false)
|
||||||
|
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||||
|
G = MatrixSpace(ZZ, n, n)
|
||||||
|
if X
|
||||||
|
S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]]
|
||||||
|
else
|
||||||
|
S = [E(i,j,G,v) for (i,j) in indexing for v in [1]]
|
||||||
|
end
|
||||||
|
S = vcat(S, [inv(x) for x in S])
|
||||||
|
return G, unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
function generatingset(n::Int, p::Int, X::Bool=false)
|
||||||
|
(p > 1 && n > 1) || throw("Both n and p should be positive integers!")
|
||||||
|
info("Size(SL($n,$p)) = $(SLsize(n,p))")
|
||||||
|
F = ResidueRing(ZZ, p)
|
||||||
|
G = MatrixSpace(F, n, n)
|
||||||
|
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||||
|
S = [E(i, j, G) for (i,j) in indexing]
|
||||||
|
S = vcat(S, [inv(x) for x in S])
|
||||||
|
return G, unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
function generatingset(parsed_args)
|
||||||
|
N = parsed_args["N"]
|
||||||
|
p = parsed_args["p"]
|
||||||
|
X = parsed_args["X"]
|
||||||
|
|
||||||
|
if p == 0
|
||||||
|
return generatingset(N, X)
|
||||||
|
else
|
||||||
|
return generatingset(N, p, X)
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Action of WreathProductElems on Nemo.MatElem
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function matrix_emb(MM::MatSpace, g::WreathProductElem)
|
||||||
|
parent(g).P.n == MM.cols == MM.rows || throw("No natural embedding of $(parent(g)) in ")
|
||||||
|
powers = [(elt == parent(elt)() ? 0: 1) for elt in g.n.elts]
|
||||||
|
elt = diagm([(-1)^(elt == parent(elt)() ? 0: 1) for elt in g.n.elts])
|
||||||
|
return MM(elt)*MM(Nemo.matrix_repr(g.p)')
|
||||||
|
end
|
||||||
|
|
||||||
|
function (g::WreathProductElem)(A::MatElem)
|
||||||
|
G = matrix_emb(parent(A), g)
|
||||||
|
inv_G = matrix_emb(parent(A), inv(g))
|
||||||
|
return G*A*inv_G
|
||||||
|
end
|
||||||
|
|
||||||
|
function (p::perm)(A::MatElem)
|
||||||
|
length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
|
||||||
|
R = parent(A)
|
||||||
|
return p*A*inv(p)
|
||||||
|
end
|
||||||
|
|
||||||
|
autS(N::Int) = WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
||||||
|
|
||||||
|
function autS(parsed_args)
|
||||||
|
return autS(parsed_args["N"])
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Misc
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function groupname(parsed_args)
|
||||||
|
N = parsed_args["N"]
|
||||||
|
p = parsed_args["p"]
|
||||||
|
X = parsed_args["X"]
|
||||||
|
|
||||||
|
return groupname(N, p, X), N
|
||||||
|
end
|
||||||
|
|
||||||
|
function groupname(N, p=0, X=false)
|
||||||
|
if p == 0
|
||||||
|
if X
|
||||||
|
name = "oSL$(N)Z⟨X⟩"
|
||||||
|
else
|
||||||
|
name = "oSL$(N)Z"
|
||||||
|
end
|
||||||
|
else
|
||||||
|
name = "oSL$(N)_$p"
|
||||||
|
end
|
||||||
|
return name
|
||||||
|
end
|
||||||
|
|
||||||
|
end # of module SLNs
|
||||||
61
SL_orbit.jl
Normal file
61
SL_orbit.jl
Normal file
@ -0,0 +1,61 @@
|
|||||||
|
using ArgParse
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Parsing command line
|
||||||
|
#
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
function parse_commandline()
|
||||||
|
settings = ArgParseSettings()
|
||||||
|
|
||||||
|
@add_arg_table settings begin
|
||||||
|
"--tol"
|
||||||
|
help = "set numerical tolerance for the SDP solver"
|
||||||
|
arg_type = Float64
|
||||||
|
default = 1e-14
|
||||||
|
"--iterations"
|
||||||
|
help = "set maximal number of iterations for the SDP solver (default: 20000)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 60000
|
||||||
|
"--upper-bound"
|
||||||
|
help = "Set an upper bound for the spectral gap"
|
||||||
|
arg_type = Float64
|
||||||
|
default = Inf
|
||||||
|
"--cpus"
|
||||||
|
help = "Set number of cpus used by solver"
|
||||||
|
arg_type = Int
|
||||||
|
required = false
|
||||||
|
"-N"
|
||||||
|
help = "Consider elementary matrices EL(N)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 2
|
||||||
|
"-p"
|
||||||
|
help = "Matrices over field of p-elements (p=0 => over ZZ)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 0
|
||||||
|
"--radius"
|
||||||
|
help = "Radius of ball B_r(e,S) to find solution over"
|
||||||
|
arg_type = Int
|
||||||
|
default = 2
|
||||||
|
"-X"
|
||||||
|
help = "Consider EL(N, ZZ⟨X⟩)"
|
||||||
|
action = :store_true
|
||||||
|
"--warmstart"
|
||||||
|
help = "Use warmstart.jl as the initial guess for SCS"
|
||||||
|
action = :store_true
|
||||||
|
end
|
||||||
|
|
||||||
|
return parse_args(settings)
|
||||||
|
end
|
||||||
|
|
||||||
|
parsed_args = parse_commandline()
|
||||||
|
|
||||||
|
include("CPUselect.jl")
|
||||||
|
|
||||||
|
set_parallel_mthread(parsed_args, workers=true)
|
||||||
|
|
||||||
|
include("SLNs.jl")
|
||||||
|
include("Orbit.jl")
|
||||||
|
|
||||||
|
main(SLNs, parsed_args)
|
||||||
@ -1,56 +0,0 @@
|
|||||||
module PropertyTGroups
|
|
||||||
|
|
||||||
using PropertyT
|
|
||||||
using AbstractAlgebra
|
|
||||||
using Nemo
|
|
||||||
using Groups
|
|
||||||
using GroupRings
|
|
||||||
|
|
||||||
export PropertyTGroup, SymmetrizedGroup, GAPGroup,
|
|
||||||
SpecialLinearGroup,
|
|
||||||
SpecialAutomorphismGroup,
|
|
||||||
HigmanGroup,
|
|
||||||
CapraceGroup,
|
|
||||||
MappingClassGroup
|
|
||||||
|
|
||||||
export PropertyTGroup
|
|
||||||
|
|
||||||
abstract type PropertyTGroup end
|
|
||||||
|
|
||||||
abstract type SymmetrizedGroup <: PropertyTGroup end
|
|
||||||
|
|
||||||
abstract type GAPGroup <: PropertyTGroup end
|
|
||||||
|
|
||||||
function PropertyTGroup(args)
|
|
||||||
if haskey(args, "SL")
|
|
||||||
G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
elseif haskey(args, "SAut")
|
|
||||||
G = PropertyTGroups.SpecialAutomorphismGroup(args)
|
|
||||||
elseif haskey(args, "MCG")
|
|
||||||
G = PropertyTGroups.MappingClassGroup(args)
|
|
||||||
elseif haskey(args, "Higman")
|
|
||||||
G = PropertyTGroups.HigmanGroup(args)
|
|
||||||
elseif haskey(args, "Caprace")
|
|
||||||
G = PropertyTGroups.CapraceGroup(args)
|
|
||||||
else
|
|
||||||
throw("You must provide one of --SL, --SAut, --MCG, --Higman, --Caprace")
|
|
||||||
end
|
|
||||||
return G
|
|
||||||
end
|
|
||||||
|
|
||||||
include("autfreegroup.jl")
|
|
||||||
include("speciallinear.jl")
|
|
||||||
|
|
||||||
Comm(x,y) = x*y*x^-1*y^-1
|
|
||||||
|
|
||||||
function generatingset(G::GAPGroup)
|
|
||||||
S = gens(group(G))
|
|
||||||
return unique([S; inv.(S)])
|
|
||||||
end
|
|
||||||
|
|
||||||
include("mappingclassgroup.jl")
|
|
||||||
include("higman.jl")
|
|
||||||
include("caprace.jl")
|
|
||||||
include("actions.jl")
|
|
||||||
|
|
||||||
end # of module PropertyTGroups
|
|
||||||
@ -1,92 +0,0 @@
|
|||||||
function (p::perm)(A::GroupRingElem)
|
|
||||||
RG = parent(A)
|
|
||||||
result = zero(RG, eltype(A.coeffs))
|
|
||||||
|
|
||||||
for (idx, c) in enumerate(A.coeffs)
|
|
||||||
if c!= zero(eltype(A.coeffs))
|
|
||||||
result[p(RG.basis[idx])] = c
|
|
||||||
end
|
|
||||||
end
|
|
||||||
return result
|
|
||||||
end
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Action of WreathProductElems on Nemo.MatElem
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function matrix_emb(n::DirectProductGroupElem, p::perm)
|
|
||||||
Id = parent(n.elts[1])()
|
|
||||||
elt = diagm([(-1)^(el == Id ? 0 : 1) for el in n.elts])
|
|
||||||
return elt[:, p.d]
|
|
||||||
end
|
|
||||||
|
|
||||||
function (g::WreathProductElem)(A::MatElem)
|
|
||||||
g_inv = inv(g)
|
|
||||||
G = matrix_emb(g.n, g_inv.p)
|
|
||||||
G_inv = matrix_emb(g_inv.n, g.p)
|
|
||||||
M = parent(A)
|
|
||||||
return M(G)*A*M(G_inv)
|
|
||||||
end
|
|
||||||
|
|
||||||
import Base.*
|
|
||||||
|
|
||||||
doc"""
|
|
||||||
*(x::AbstractAlgebra.MatElem, P::Generic.perm)
|
|
||||||
> Apply the pemutation $P$ to the rows of the matrix $x$ and return the result.
|
|
||||||
"""
|
|
||||||
function *(x::AbstractAlgebra.MatElem, P::Generic.perm)
|
|
||||||
z = similar(x)
|
|
||||||
m = rows(x)
|
|
||||||
n = cols(x)
|
|
||||||
for i = 1:m
|
|
||||||
for j = 1:n
|
|
||||||
z[i, j] = x[i,P[j]]
|
|
||||||
end
|
|
||||||
end
|
|
||||||
return z
|
|
||||||
end
|
|
||||||
|
|
||||||
function (p::perm)(A::MatElem)
|
|
||||||
length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
|
|
||||||
return p*A*inv(p)
|
|
||||||
end
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Action of WreathProductElems on AutGroupElem
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function AutFG_emb(A::AutGroup, g::WreathProductElem)
|
|
||||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
|
||||||
parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
|
||||||
elt = A()
|
|
||||||
Id = parent(g.n.elts[1])()
|
|
||||||
flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
|
|
||||||
Groups.r_multiply!(elt, flips, reduced=false)
|
|
||||||
Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
function AutFG_emb(A::AutGroup, p::perm)
|
|
||||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
|
||||||
parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(p)) into $A")
|
|
||||||
return A(Groups.perm_autsymbol(p))
|
|
||||||
end
|
|
||||||
|
|
||||||
function (g::WreathProductElem)(a::Groups.Automorphism)
|
|
||||||
A = parent(a)
|
|
||||||
g = AutFG_emb(A,g)
|
|
||||||
res = A()
|
|
||||||
Groups.r_multiply!(res, g.symbols, reduced=false)
|
|
||||||
Groups.r_multiply!(res, a.symbols, reduced=false)
|
|
||||||
Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
|
|
||||||
return res
|
|
||||||
end
|
|
||||||
|
|
||||||
function (p::perm)(a::Groups.Automorphism)
|
|
||||||
g = AutFG_emb(parent(a),p)
|
|
||||||
return g*a*inv(g)
|
|
||||||
end
|
|
||||||
@ -1,21 +0,0 @@
|
|||||||
struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
|
|
||||||
group::AutGroup
|
|
||||||
end
|
|
||||||
|
|
||||||
function SpecialAutomorphismGroup(args::Dict)
|
|
||||||
N = args["SAut"]
|
|
||||||
return SpecialAutomorphismGroup{N}(AutGroup(FreeGroup(N), special=true))
|
|
||||||
end
|
|
||||||
|
|
||||||
name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"
|
|
||||||
|
|
||||||
group(G::SpecialAutomorphismGroup) = G.group
|
|
||||||
|
|
||||||
function generatingset(G::SpecialAutomorphismGroup)
|
|
||||||
S = gens(group(G));
|
|
||||||
return unique([S; inv.(S)])
|
|
||||||
end
|
|
||||||
|
|
||||||
function autS(G::SpecialAutomorphismGroup{N}) where N
|
|
||||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
|
||||||
end
|
|
||||||
@ -1,35 +0,0 @@
|
|||||||
struct CapraceGroup <: GAPGroup end
|
|
||||||
|
|
||||||
name(G::CapraceGroup) = "CapraceGroup"
|
|
||||||
|
|
||||||
function group(G::CapraceGroup)
|
|
||||||
|
|
||||||
caprace_group = Groups.FPGroup(["x","y","z","t","r"])
|
|
||||||
|
|
||||||
x,y,z,t,r = gens(caprace_group)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
x^7,
|
|
||||||
y^7,
|
|
||||||
t^2,
|
|
||||||
r^73,
|
|
||||||
t*r*t*r,
|
|
||||||
Comm(x,y)*z^-1,
|
|
||||||
Comm(x,z),
|
|
||||||
Comm(y,z),
|
|
||||||
Comm(x^2*y*z^-1, t),
|
|
||||||
Comm(x*y*z^3, t*r),
|
|
||||||
Comm(x^3*y*z^2, t*r^17),
|
|
||||||
Comm(x, t*r^-34),
|
|
||||||
Comm(y, t*r^-32),
|
|
||||||
Comm(z, t*r^-29),
|
|
||||||
Comm(x^-2*y*z, t*r^-25),
|
|
||||||
Comm(x^-1*y*z^-3, t*r^-19),
|
|
||||||
Comm(x^-3*y*z^-2, t*r^-11)
|
|
||||||
];
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
|
|
||||||
Groups.add_rels!(caprace_group, Dict(rel => caprace_group() for rel in relations))
|
|
||||||
return caprace_group
|
|
||||||
end
|
|
||||||
@ -1,22 +0,0 @@
|
|||||||
struct HigmanGroup <: GAPGroup end
|
|
||||||
|
|
||||||
name(G::HigmanGroup) = "HigmanGroup"
|
|
||||||
|
|
||||||
function group(G::HigmanGroup)
|
|
||||||
|
|
||||||
higman_group = Groups.FPGroup(["a","b","c","d"]);
|
|
||||||
|
|
||||||
a,b,c,d = gens(higman_group)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
b*Comm(b,a),
|
|
||||||
c*Comm(c,b),
|
|
||||||
d*Comm(d,c),
|
|
||||||
a*Comm(a,d)
|
|
||||||
];
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
|
|
||||||
Groups.add_rels!(higman_group, Dict(rel => higman_group() for rel in relations))
|
|
||||||
return higman_group
|
|
||||||
end
|
|
||||||
@ -1,83 +0,0 @@
|
|||||||
struct MappingClassGroup{N} <: GAPGroup end
|
|
||||||
|
|
||||||
MappingClassGroup(args::Dict) = MappingClassGroup{args["MCG"]}()
|
|
||||||
|
|
||||||
name(G::MappingClassGroup{N}) where N = "MCG(N)"
|
|
||||||
|
|
||||||
function group(G::MappingClassGroup{N}) where N
|
|
||||||
|
|
||||||
if N < 2
|
|
||||||
throw("Genus must be at least 2!")
|
|
||||||
elseif N == 2
|
|
||||||
MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
|
|
||||||
S = gens(MCGroup)
|
|
||||||
|
|
||||||
n = length(S)
|
|
||||||
A = prod(reverse(S))*prod(S)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
[Comm(S[i], S[j]) for i in 1:n for j in 1:n if abs(i-j) > 1]...,
|
|
||||||
[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:G.n-1]...,
|
|
||||||
(S[1]*S[2]*S[3])^4*inv(S[5])^2,
|
|
||||||
Comm(A, S[1]),
|
|
||||||
A^2
|
|
||||||
]
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
|
|
||||||
return MCGroup
|
|
||||||
|
|
||||||
else
|
|
||||||
MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
|
|
||||||
S = gens(MCGroup)
|
|
||||||
|
|
||||||
a0 = S[1]
|
|
||||||
A = S[2:end]
|
|
||||||
k = length(A)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
|
|
||||||
[Comm(a0, A[i]) for i in 1:k if i != 4]...,
|
|
||||||
[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
|
|
||||||
A[4]*a0*A[4]*inv(a0*A[4]*a0)
|
|
||||||
]
|
|
||||||
|
|
||||||
# 3-chain relation
|
|
||||||
c = prod(reverse(A[1:4]))*prod(A[1:4])
|
|
||||||
b0 = c*a0*inv(c)
|
|
||||||
push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
|
|
||||||
|
|
||||||
# Lantern relation
|
|
||||||
b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
|
|
||||||
b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
|
|
||||||
u = inv(A[6]*A[5])*b1*(A[6]*A[5])
|
|
||||||
x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
|
|
||||||
b3 = x*a0*inv(x)
|
|
||||||
push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
|
|
||||||
|
|
||||||
# Hyperelliptic relation
|
|
||||||
X = prod(reverse(A))*prod(A)
|
|
||||||
|
|
||||||
function n(i::Int, b=b0)
|
|
||||||
if i == 1
|
|
||||||
return A[1]
|
|
||||||
elseif i == 2
|
|
||||||
return b
|
|
||||||
else
|
|
||||||
return w(i-2)*n(i-2)*w(i-2)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function w(i::Int)
|
|
||||||
(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
|
|
||||||
(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
|
|
||||||
end
|
|
||||||
|
|
||||||
# push!(relations, X*n(N)*inv(n(N)*X))
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
|
|
||||||
|
|
||||||
return MCGroup
|
|
||||||
end
|
|
||||||
end
|
|
||||||
@ -1,62 +0,0 @@
|
|||||||
struct SpecialLinearGroup{N} <: SymmetrizedGroup
|
|
||||||
group::AbstractAlgebra.Group
|
|
||||||
p::Int
|
|
||||||
X::Bool
|
|
||||||
end
|
|
||||||
|
|
||||||
function SpecialLinearGroup(args::Dict)
|
|
||||||
N = args["SL"]
|
|
||||||
p = args["p"]
|
|
||||||
X = args["X"]
|
|
||||||
|
|
||||||
if p == 0
|
|
||||||
G = MatrixSpace(Nemo.ZZ, N, N)
|
|
||||||
else
|
|
||||||
R = Nemo.NmodRing(UInt(p))
|
|
||||||
G = MatrixSpace(R, N, N)
|
|
||||||
end
|
|
||||||
return SpecialLinearGroup{N}(G, p, X)
|
|
||||||
end
|
|
||||||
|
|
||||||
function name(G::SpecialLinearGroup{N}) where N
|
|
||||||
if G.p == 0
|
|
||||||
R = (G.X ? "Z[x]" : "Z")
|
|
||||||
else
|
|
||||||
R = "F$(G.p)"
|
|
||||||
end
|
|
||||||
return SL($(G.N),$R)
|
|
||||||
end
|
|
||||||
|
|
||||||
group(G::SpecialLinearGroup) = G.group
|
|
||||||
|
|
||||||
function generatingset(G::SpecialLinearGroup{N}) where N
|
|
||||||
G.p > 0 && G.X && throw("SL(n, F_p[x]) not implemented")
|
|
||||||
SL = group(G)
|
|
||||||
return generatingset(SL, G.X)
|
|
||||||
end
|
|
||||||
|
|
||||||
# r is the injectivity radius of
|
|
||||||
# SL(n, Z[X]) -> SL(n, Z) induced by X -> 100
|
|
||||||
|
|
||||||
function generatingset(SL::MatSpace, X::Bool=false, r=5)
|
|
||||||
n = SL.cols
|
|
||||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
|
||||||
|
|
||||||
if !X
|
|
||||||
S = [E(idx[1],idx[2],SL) for idx in indexing]
|
|
||||||
else
|
|
||||||
S = [E(i,j,SL,v) for (i,j) in indexing for v in [1, 100*r]]
|
|
||||||
end
|
|
||||||
return unique([S; inv.(S)])
|
|
||||||
end
|
|
||||||
|
|
||||||
function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
|
|
||||||
@assert i≠j
|
|
||||||
m = one(M)
|
|
||||||
m[i,j] = val
|
|
||||||
return m
|
|
||||||
end
|
|
||||||
|
|
||||||
function autS(G::SpecialLinearGroup{N}) where N
|
|
||||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
|
||||||
end
|
|
||||||
58
logging.jl
58
logging.jl
@ -1,58 +0,0 @@
|
|||||||
using Memento
|
|
||||||
|
|
||||||
function setup_logging(filename::String, handlername::Symbol=:log)
|
|
||||||
isdir(dirname(filename)) || mkdir(dirname(filename))
|
|
||||||
logger = Memento.config!("info", fmt="{date}| {msg}")
|
|
||||||
handler = DefaultHandler(filename, DefaultFormatter("{date}| {msg}"))
|
|
||||||
logger.handlers[String(handlername)] = handler
|
|
||||||
return logger
|
|
||||||
end
|
|
||||||
|
|
||||||
macro logtime(logger, ex)
|
|
||||||
quote
|
|
||||||
local stats = Base.gc_num()
|
|
||||||
local elapsedtime = Base.time_ns()
|
|
||||||
local val = $(esc(ex))
|
|
||||||
elapsedtime = Base.time_ns() - elapsedtime
|
|
||||||
local diff = Base.GC_Diff(Base.gc_num(), stats)
|
|
||||||
local ts = time_string(elapsedtime,
|
|
||||||
diff.allocd,
|
|
||||||
diff.total_time,
|
|
||||||
Base.gc_alloc_count(diff)
|
|
||||||
)
|
|
||||||
$(esc(info))($(esc(logger)), ts)
|
|
||||||
val
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function time_string(elapsedtime, bytes, gctime, allocs)
|
|
||||||
str = @sprintf("%10.6f seconds", elapsedtime/1e9)
|
|
||||||
if bytes != 0 || allocs != 0
|
|
||||||
bytes, mb = Base.prettyprint_getunits(bytes, length(Base._mem_units), Int64(1024))
|
|
||||||
allocs, ma = Base.prettyprint_getunits(allocs, length(Base._cnt_units), Int64(1000))
|
|
||||||
if ma == 1
|
|
||||||
str*= @sprintf(" (%d%s allocation%s: ", allocs, Base._cnt_units[ma], allocs==1 ? "" : "s")
|
|
||||||
else
|
|
||||||
str*= @sprintf(" (%.2f%s allocations: ", allocs, Base._cnt_units[ma])
|
|
||||||
end
|
|
||||||
if mb == 1
|
|
||||||
str*= @sprintf("%d %s%s", bytes, Base._mem_units[mb], bytes==1 ? "" : "s")
|
|
||||||
else
|
|
||||||
str*= @sprintf("%.3f %s", bytes, Base._mem_units[mb])
|
|
||||||
end
|
|
||||||
if gctime > 0
|
|
||||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
|
||||||
end
|
|
||||||
str*=")"
|
|
||||||
elseif gctime > 0
|
|
||||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
|
||||||
end
|
|
||||||
return str
|
|
||||||
end
|
|
||||||
|
|
||||||
import Base: info, @time
|
|
||||||
|
|
||||||
Base.info(x) = info(getlogger(), x)
|
|
||||||
macro time(x)
|
|
||||||
return :(@logtime(getlogger(Main), $(esc(x))))
|
|
||||||
end
|
|
||||||
61
main.jl
61
main.jl
@ -1,61 +0,0 @@
|
|||||||
using PropertyT
|
|
||||||
|
|
||||||
include("FPGroups_GAP.jl")
|
|
||||||
|
|
||||||
include("groups/Allgroups.jl")
|
|
||||||
using PropertyTGroups
|
|
||||||
|
|
||||||
import PropertyT.Settings
|
|
||||||
|
|
||||||
function summarize(sett::PropertyT.Settings)
|
|
||||||
info("Threads: $(Threads.nthreads())")
|
|
||||||
info("Workers: $(workers())")
|
|
||||||
info("GroupDir: $(PropertyT.prepath(sett))")
|
|
||||||
info(string(sett.G))
|
|
||||||
info("with generating set of size $(length(sett.S))")
|
|
||||||
|
|
||||||
info("Radius: $(sett.radius)")
|
|
||||||
info("Precision: $(sett.tol)")
|
|
||||||
info("Upper bound: $(sett.upper_bound)")
|
|
||||||
info("Solver: $(sett.solver)")
|
|
||||||
end
|
|
||||||
|
|
||||||
function Settings(Gr::PropertyTGroup, args, solver)
|
|
||||||
r = get(args, "radius", 2)
|
|
||||||
gr_name = PropertyTGroups.name(Gr)*"_r$r"
|
|
||||||
G = PropertyTGroups.group(Gr)
|
|
||||||
S = PropertyTGroups.generatingset(Gr)
|
|
||||||
|
|
||||||
sol = solver
|
|
||||||
ub = get(args,"upper-bound", Inf)
|
|
||||||
tol = get(args,"tol", 1e-10)
|
|
||||||
ws = get(args, "warmstart", false)
|
|
||||||
|
|
||||||
if get(args, "nosymmetry", false)
|
|
||||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws)
|
|
||||||
else
|
|
||||||
autS = PropertyTGroups.autS(Gr)
|
|
||||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws, autS)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function main(::PropertyTGroup, sett::PropertyT.Settings)
|
|
||||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
|
||||||
|
|
||||||
summarize(sett)
|
|
||||||
|
|
||||||
return PropertyT.check_property_T(sett)
|
|
||||||
end
|
|
||||||
|
|
||||||
function main(::GAPGroup, sett::PropertyT.Settings)
|
|
||||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
|
||||||
|
|
||||||
summarize(sett)
|
|
||||||
|
|
||||||
S = [s for s in sett.S if s.symbols[1].pow == 1]
|
|
||||||
relations = [k*inv(v) for (k,v) in sett.G.rels]
|
|
||||||
|
|
||||||
prepare_pm_delta(PropertyT.prepath(sett), GAP_groupcode(S, relations), sett.radius)
|
|
||||||
|
|
||||||
return PropertyT.check_property_T(sett)
|
|
||||||
end
|
|
||||||
@ -1,197 +0,0 @@
|
|||||||
using AbstractAlgebra
|
|
||||||
using Groups
|
|
||||||
using GroupRings
|
|
||||||
using PropertyT
|
|
||||||
|
|
||||||
using SCS
|
|
||||||
solver(tol, iterations) =
|
|
||||||
SCSSolver(linearsolver=SCS.Direct,
|
|
||||||
eps=tol, max_iters=iterations,
|
|
||||||
alpha=1.95, acceleration_lookback=1)
|
|
||||||
|
|
||||||
include("../main.jl")
|
|
||||||
|
|
||||||
using PropertyTGroups
|
|
||||||
|
|
||||||
args = Dict("SAut" => 5, "upper-bound" => 50.0, "radius" => 2, "nosymmetry"=>false, "tol"=>1e-12, "iterations" =>200000, "warmstart" => true)
|
|
||||||
|
|
||||||
Gr = PropertyTGroups.PropertyTGroup(args)
|
|
||||||
sett = PropertyT.Settings(Gr, args,
|
|
||||||
solver(args["tol"], args["iterations"]))
|
|
||||||
|
|
||||||
@show sett
|
|
||||||
|
|
||||||
fullpath = PropertyT.fullpath(sett)
|
|
||||||
isdir(fullpath) || mkpath(fullpath)
|
|
||||||
# setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
|
||||||
|
|
||||||
function small_generating_set(RG::GroupRing{AutGroup{N}}, n) where N
|
|
||||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
|
||||||
|
|
||||||
rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing]
|
|
||||||
lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing]
|
|
||||||
gen_set = RG.group.([rmuls; lmuls])
|
|
||||||
|
|
||||||
return [gen_set; inv.(gen_set)]
|
|
||||||
end
|
|
||||||
|
|
||||||
function computeX(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
Tn = small_generating_set(RG, N-1)
|
|
||||||
|
|
||||||
ℤ = Int64
|
|
||||||
Δn = length(Tn)*one(RG, ℤ) - RG(Tn, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
|
|
||||||
@time X = sum(σ(Δn)*sum(τ(Δn) for τ ∈ Alt_N if τ ≠ σ) for σ in Alt_N);
|
|
||||||
return X
|
|
||||||
end
|
|
||||||
|
|
||||||
function Sq(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
T2 = small_generating_set(RG, 2)
|
|
||||||
ℤ = Int64
|
|
||||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
elt = sum(σ(Δ₂)^2 for σ in Alt_N)
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
function Adj(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
T2 = small_generating_set(RG, 2)
|
|
||||||
|
|
||||||
ℤ = Int64
|
|
||||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
|
|
||||||
adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
|
|
||||||
adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 1]
|
|
||||||
|
|
||||||
@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
|
|
||||||
# return RG(elt.coeffs÷factorial(N-2)^2)
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
function Op(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
T2 = small_generating_set(RG, 2)
|
|
||||||
|
|
||||||
ℤ = Int64
|
|
||||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
|
|
||||||
adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
|
|
||||||
adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 0]
|
|
||||||
|
|
||||||
@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
|
|
||||||
# return RG(elt.coeffs÷factorial(N-2)^2)
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
const ELT_FILE = joinpath(dirname(PropertyT.filename(sett, :Δ)), "SqAdjOp_coeffs.jld")
|
|
||||||
const WARMSTART_FILE = PropertyT.filename(sett, :warmstart)
|
|
||||||
|
|
||||||
if isfile(PropertyT.filename(sett,:Δ)) && isfile(ELT_FILE) &&
|
|
||||||
isfile(PropertyT.filename(sett, :OrbitData))
|
|
||||||
# cached
|
|
||||||
Δ = PropertyT.loadGRElem(PropertyT.filename(sett,:Δ), sett.G)
|
|
||||||
RG = parent(Δ)
|
|
||||||
orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
|
|
||||||
sq_c, adj_c, op_c = load(ELT_FILE, "Sq", "Adj", "Op")
|
|
||||||
# elt = ELT_FILE, sett.G)
|
|
||||||
sq = GroupRingElem(sq_c, RG)
|
|
||||||
adj = GroupRingElem(adj_c, RG)
|
|
||||||
op = GroupRingElem(op_c, RG);
|
|
||||||
else
|
|
||||||
info("Compute Laplacian")
|
|
||||||
Δ = PropertyT.Laplacian(sett.S, sett.radius)
|
|
||||||
RG = parent(Δ)
|
|
||||||
|
|
||||||
info("Compute Sq, Adj, Op")
|
|
||||||
@time sq, adj, op = Sq(RG), Adj(RG), Op(RG)
|
|
||||||
|
|
||||||
PropertyT.saveGRElem(PropertyT.filename(sett, :Δ), Δ)
|
|
||||||
save(ELT_FILE, "Sq", sq.coeffs, "Adj", adj.coeffs, "Op", op.coeffs)
|
|
||||||
|
|
||||||
info("Compute OrbitData")
|
|
||||||
if !isfile(PropertyT.filename(sett, :OrbitData))
|
|
||||||
orbit_data = PropertyT.OrbitData(parent(Y), sett.autS)
|
|
||||||
save(PropertyT.filename(sett, :OrbitData), "OrbitData", orbit_data)
|
|
||||||
else
|
|
||||||
orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
|
|
||||||
end
|
|
||||||
end;
|
|
||||||
|
|
||||||
orbit_data = PropertyT.decimate(orbit_data);
|
|
||||||
|
|
||||||
elt = adj+2op;
|
|
||||||
|
|
||||||
const SOLUTION_FILE = PropertyT.filename(sett, :solution)
|
|
||||||
|
|
||||||
if !isfile(SOLUTION_FILE)
|
|
||||||
|
|
||||||
SDP_problem, varλ, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=sett.upper_bound)
|
|
||||||
|
|
||||||
begin
|
|
||||||
using SCS
|
|
||||||
scs_solver = SCS.SCSSolver(linearsolver=SCS.Direct,
|
|
||||||
eps=sett.tol,
|
|
||||||
max_iters=args["iterations"],
|
|
||||||
alpha=1.95,
|
|
||||||
acceleration_lookback=1)
|
|
||||||
|
|
||||||
JuMP.setsolver(SDP_problem, scs_solver)
|
|
||||||
end
|
|
||||||
|
|
||||||
λ = Ps = nothing
|
|
||||||
ws = PropertyT.warmstart(sett)
|
|
||||||
|
|
||||||
# using ProgressMeter
|
|
||||||
|
|
||||||
# @showprogress "Running SDP optimization step... " for i in 1:args["repetitions"]
|
|
||||||
while true
|
|
||||||
λ, Ps, ws = PropertyT.solve(PropertyT.filename(sett, :solverlog),
|
|
||||||
SDP_problem, varλ, varP, ws);
|
|
||||||
|
|
||||||
if all((!isnan).(ws[1]))
|
|
||||||
save(WARMSTART_FILE, "warmstart", ws, "λ", λ, "Ps", Ps)
|
|
||||||
save(WARMSTART_FILE[1:end-4]*"_$(now()).jld", "warmstart", ws, "λ", λ, "Ps", Ps)
|
|
||||||
else
|
|
||||||
warn("No valid solution was saved!")
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
info("Reconstructing P...")
|
|
||||||
@time P = PropertyT.reconstruct(Ps, orbit_data);
|
|
||||||
save(SOLUTION_FILE, "λ", λ, "P", P)
|
|
||||||
end
|
|
||||||
|
|
||||||
P, λ = load(SOLUTION_FILE, "P", "λ")
|
|
||||||
@show λ;
|
|
||||||
|
|
||||||
@time const Q = real(sqrtm(P));
|
|
||||||
|
|
||||||
function SOS_residual(eoi::GroupRingElem, Q::Matrix)
|
|
||||||
RG = parent(eoi)
|
|
||||||
@time sos = PropertyT.compute_SOS(RG, Q);
|
|
||||||
return eoi - sos
|
|
||||||
end
|
|
||||||
|
|
||||||
info("Floating Point arithmetic:")
|
|
||||||
EOI = elt - λ*Δ
|
|
||||||
b = SOS_residual(EOI, Q)
|
|
||||||
@show norm(b, 1);
|
|
||||||
|
|
||||||
info("Interval arithmetic:")
|
|
||||||
using IntervalArithmetic
|
|
||||||
Qint = PropertyT.augIdproj(Q);
|
|
||||||
@assert all([zero(eltype(Q)) in sum(view(Qint, :, i)) for i in 1:size(Qint, 2)])
|
|
||||||
|
|
||||||
EOI_int = elt - @interval(λ)*Δ;
|
|
||||||
Q_int = PropertyT.augIdproj(Q);
|
|
||||||
@assert all([zero(eltype(Q)) in sum(view(Q_int, :, i)) for i in 1:size(Q_int, 2)])
|
|
||||||
b_int = SOS_residual(EOI_int, Q_int)
|
|
||||||
@show norm(b_int, 1);
|
|
||||||
|
|
||||||
info("λ is certified to be > ", (@interval(λ) - 2^2*norm(b_int,1)).lo)
|
|
||||||
108
run.jl
108
run.jl
@ -1,108 +0,0 @@
|
|||||||
using ArgParse
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Parsing command line
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function parse_commandline()
|
|
||||||
settings = ArgParseSettings()
|
|
||||||
|
|
||||||
@add_arg_table settings begin
|
|
||||||
"--tol"
|
|
||||||
help = "set numerical tolerance for the SDP solver"
|
|
||||||
arg_type = Float64
|
|
||||||
default = 1e-6
|
|
||||||
"--iterations"
|
|
||||||
help = "set maximal number of iterations for the SDP solver"
|
|
||||||
arg_type = Int
|
|
||||||
default = 50000
|
|
||||||
"--upper-bound"
|
|
||||||
help = "Set an upper bound for the spectral gap"
|
|
||||||
arg_type = Float64
|
|
||||||
default = Inf
|
|
||||||
"--cpus"
|
|
||||||
help = "Set number of cpus used by solver"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
"--radius"
|
|
||||||
help = "Radius of ball B_r(e,S) to find solution over"
|
|
||||||
arg_type = Int
|
|
||||||
default = 2
|
|
||||||
"--warmstart"
|
|
||||||
help = "Use warmstart.jld as the initial guess for SCS"
|
|
||||||
action = :store_true
|
|
||||||
"--nosymmetry"
|
|
||||||
help = "Don't use symmetries of the Laplacian"
|
|
||||||
action = :store_true
|
|
||||||
|
|
||||||
"--SL "
|
|
||||||
help = "GROUP: the group generated by elementary matrices of size n by n"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
"-p"
|
|
||||||
help = "Matrices over field of p-elements (p=0 => over ZZ) [only with --SL]"
|
|
||||||
arg_type = Int
|
|
||||||
default = 0
|
|
||||||
"-X"
|
|
||||||
help = "Consider EL(N, ZZ⟨X⟩) [only with --SL]"
|
|
||||||
action = :store_true
|
|
||||||
|
|
||||||
"--SAut"
|
|
||||||
help = "GROUP: the automorphisms group of the free group on N generators"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
|
|
||||||
"--MCG"
|
|
||||||
help = "GROUP: mapping class group of surface of genus N"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
|
|
||||||
"--Higman"
|
|
||||||
help = "GROUP: the Higman Group"
|
|
||||||
action = :store_true
|
|
||||||
|
|
||||||
"--Caprace"
|
|
||||||
help = "GROUP: for Caprace Group"
|
|
||||||
action = :store_true
|
|
||||||
end
|
|
||||||
return parse_args(settings)
|
|
||||||
end
|
|
||||||
|
|
||||||
const PARSEDARGS = parse_commandline()
|
|
||||||
|
|
||||||
set_parallel_mthread(PARSEDARGS, workers=false)
|
|
||||||
|
|
||||||
include("CPUselect.jl")
|
|
||||||
include("logging.jl")
|
|
||||||
include("main.jl")
|
|
||||||
|
|
||||||
using SCS.SCSSolver
|
|
||||||
# using Mosek
|
|
||||||
# using CSDP
|
|
||||||
# using SDPA
|
|
||||||
|
|
||||||
solver(tol, iterations) =
|
|
||||||
SCSSolver(linearsolver=SCS.Direct,
|
|
||||||
eps=tol, max_iters=iterations,
|
|
||||||
alpha=1.95, acceleration_lookback=1)
|
|
||||||
|
|
||||||
# Mosek.MosekSolver(
|
|
||||||
# MSK_DPAR_INTPNT_CO_TOL_REL_GAP=tol,
|
|
||||||
# MSK_IPAR_INTPNT_MAX_ITERATIONS=iterations,
|
|
||||||
# QUIET=false)
|
|
||||||
|
|
||||||
# CSDP.CSDPSolver(axtol=tol, atytol=tol, objtol=tol, minstepp=tol*10.0^-1, minstepd=tol*10.0^-1)
|
|
||||||
|
|
||||||
# SDPA.SDPASolver(epsilonStar=tol, epsilonDash=tol)
|
|
||||||
|
|
||||||
const Gr = PropertyTGroups.PropertyTGroup(PARSEDARGS)
|
|
||||||
const sett = PropertyT.Settings(Gr, PARSEDARGS,
|
|
||||||
solver(PARSEDARGS["tol"], PARSEDARGS["iterations"]))
|
|
||||||
|
|
||||||
fullpath = PropertyT.fullpath(sett)
|
|
||||||
isdir(fullpath) || mkpath(fullpath)
|
|
||||||
setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
|
||||||
|
|
||||||
main(Gr, sett)
|
|
||||||
222
runtests.jl
222
runtests.jl
@ -1,222 +0,0 @@
|
|||||||
using Base.Test
|
|
||||||
|
|
||||||
include("main.jl")
|
|
||||||
|
|
||||||
testdir = "tests_"*string(now())
|
|
||||||
mkdir(testdir)
|
|
||||||
include("logging.jl")
|
|
||||||
logger=setup_logging(joinpath(testdir, "tests.log"))
|
|
||||||
info(testdir)
|
|
||||||
|
|
||||||
cd(testdir)
|
|
||||||
|
|
||||||
# groupname = name(G)
|
|
||||||
# ub = PARSEDARGS["upper-bound"]
|
|
||||||
#
|
|
||||||
# fullpath = joinpath(groupname, string(ub))
|
|
||||||
# isdir(fullpath) || mkpath(fullpath)
|
|
||||||
|
|
||||||
separator(n=60) = info("\n"*("\n"*"="^n*"\n"^3)*"\n")
|
|
||||||
|
|
||||||
|
|
||||||
function SL_tests(args)
|
|
||||||
|
|
||||||
|
|
||||||
args["SL"] = 2
|
|
||||||
args["p"] = 3
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == true
|
|
||||||
separator()
|
|
||||||
|
|
||||||
let args = args
|
|
||||||
args["SL"] = 2
|
|
||||||
args["p"] = 5
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["warmstart"] = true
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["upper-bound"] = 0.1
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == true
|
|
||||||
separator()
|
|
||||||
end
|
|
||||||
|
|
||||||
args["SL"] = 2
|
|
||||||
args["p"] = 7
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["SL"] = 3
|
|
||||||
args["p"] = 7
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == true
|
|
||||||
separator()
|
|
||||||
|
|
||||||
# begin
|
|
||||||
# args["iterations"] = 25000
|
|
||||||
# args["N"] = 3
|
|
||||||
# args["p"] = 0
|
|
||||||
# args["upper-bound"] = Inf
|
|
||||||
#
|
|
||||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
# @test main(G) == false
|
|
||||||
# separator()
|
|
||||||
#
|
|
||||||
# args["warmstart"] = false
|
|
||||||
# args["upper-bound"] = 0.27
|
|
||||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
# @test main(G) == false
|
|
||||||
# separator()
|
|
||||||
#
|
|
||||||
# args["warmstart"] = true
|
|
||||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
# @test main(G) == true
|
|
||||||
# separator()
|
|
||||||
# end
|
|
||||||
|
|
||||||
return 0
|
|
||||||
end
|
|
||||||
|
|
||||||
function SAut_tests(args)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["warmstart"] = true
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["upper-bound"] = 0.1
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
return 0
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "Groups with(out) (T)" begin
|
|
||||||
|
|
||||||
@testset "GAPGroups" begin
|
|
||||||
args = Dict(
|
|
||||||
"Higman" => true,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"Caprace" => true,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"MCG" => 3,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "SLn's" begin
|
|
||||||
@testset "Non-Symmetrized" begin
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"SL" => 2,
|
|
||||||
"p" => 3,
|
|
||||||
"X" => false,
|
|
||||||
"iterations"=>50000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
SL_tests(args)
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "Symmetrized" begin
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"SL" => 2,
|
|
||||||
"p" => 3,
|
|
||||||
"X" => false,
|
|
||||||
"iterations"=>20000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>false,
|
|
||||||
)
|
|
||||||
|
|
||||||
SL_tests(args)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "SAutF_n's" begin
|
|
||||||
|
|
||||||
@testset "Non-Symmetrized" begin
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"SAut" => 2,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
SAut_tests(args)
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "Symmetrized" begin
|
|
||||||
args = Dict(
|
|
||||||
"SAut" => 3,
|
|
||||||
"iterations"=>500,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>false,
|
|
||||||
)
|
|
||||||
SAut_tests(args)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
|
|
||||||
end
|
|
||||||
Loading…
Reference in New Issue
Block a user