102 lines
3.0 KiB
Julia
102 lines
3.0 KiB
Julia
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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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 = 50000
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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.jld 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(s)
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end
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const PARSEDARGS = parse_commandline()
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include("CPUselect.jl")
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set_parallel_mthread(PARSEDARGS, workers=true)
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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(Fₙ) becomes trivial under the representation
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Aut(Fₙ) → GLₙ(ℤ)⋉ℤⁿ → GL_(n+1)(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 (S)Aut(𝔽ₙ)
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=#
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using Nemo
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using 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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include("groups/autfreegroup.jl")
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function main(GROUP, parsed_args)
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radius = parsed_args["radius"]
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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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warm = parsed_args["warmstart"]
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name, N = GROUP.groupname(parsed_args)
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G, S = GROUP.generatingset(parsed_args)
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name = "$(name)_r$radius"
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isdir(name) || mkdir(name)
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logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"))
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info(logger, "Group: $name")
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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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info(logger, G)
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info(logger, "Symmetric generating set of size $(length(S))")
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info(logger, "Threads: $(Threads.nthreads())")
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info(logger, "Workers: $(workers())")
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Id = G()
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)
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PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius, warm)
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return 0
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end
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main(SpecialAutomorphisms, PARSEDARGS)
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