156 lines
4.4 KiB
Julia
156 lines
4.4 KiB
Julia
using ArgParse
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using SCS
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using Nemo
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if VERSION >= v"0.6.0"
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import Nemo.Generic.perm
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end
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addprocs(2)
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using PropertyT
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using Groups
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###############################################################################
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#
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# Action of WreathProductElems on AutGroupElem
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#
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###############################################################################
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function AutFG_emb(A::AutGroup, g::WreathProductElem)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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powers = [(elt == parent(elt)() ? 0: 1) for elt in g.n.elts]
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elt = reduce(*, [A(Groups.flip_autsymbol(i))^pow for (i,pow) in enumerate(powers)])
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Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
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return elt
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end
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function AutFG_emb(A::AutGroup, p::perm)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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return A(Groups.perm_autsymbol(p))
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end
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function (g::WreathProductElem)(a::AutGroupElem)
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g = AutFG_emb(parent(a),g)
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return g*a*g^-1
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end
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function (p::perm)(a::AutGroupElem)
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g = AutFG_emb(parent(a),p)
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return g*a*g^-1
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end
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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 SAutFN_generating_set(N::Int)
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SAutFN = AutGroup(FreeGroup(N), special=true)
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S = gens(SAutFN);
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S = [S; [inv(s) for s in S]]
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return SAutFN, 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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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 = 100000
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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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end
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return parse_args(settings)
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end
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###############################################################################
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#
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# main
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#
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###############################################################################
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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 = 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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dirname = "oSAutF$(N)_r$radius"
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isdir(dirname) || mkdir(dirname)
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logger = PropertyT.setup_logging(joinpath(dirname, "$(upper_bound)"))
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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 = SAutFN_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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AutS = WreathProduct(FiniteField(2,1, "a")[1], PermutationGroup(N))
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# AutS = PermutationGroup(N)
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
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sett = Settings(dirname, N, G, S, AutS, radius, solver, upper_bound, tol)
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PropertyT.check_property_T(sett)
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end
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main()
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