unify AutFN and AutFN_orbit
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AutFN.jl
67
AutFN.jl
@ -17,6 +17,27 @@ Moreover, due to work of Potapchik and Rapinchuk [1] every real representation o
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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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@ -33,15 +54,15 @@ function parse_commandline()
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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 (default: 1e-5)"
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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-5
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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 (default: 20000)"
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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 (default: Inf)"
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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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@ -49,7 +70,7 @@ function parse_commandline()
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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 (default: N=3)"
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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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@ -57,14 +78,6 @@ function parse_commandline()
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return parse_args(s)
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end
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# const name = "SYM$N"
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# const upper_bound=factorial(N)-TOL^(1/5)
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# S() = generating_set_of_Sym(N)
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# name = "AutF$N"
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# S() = generating_set_of_AutF(N)
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function main()
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parsed_args = parse_commandline()
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@ -76,32 +89,30 @@ function main()
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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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# solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
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solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
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N = parsed_args["N"]
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upper_bound = parsed_args["upper-bound"]
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radius=2
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name = "SOutF$N"
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name = "$(name)_$(upper_bound)_r=$radius"
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dirname = "SOutF$(N)_$(upper_bound)_r=$radius"
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logger = PropertyT.setup_logging(name)
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logger = PropertyT.setup_logging(dirname)
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info(logger, "Group: $name")
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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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AutFN = AutGroup(FreeGroup(N), special=true, outer=true)
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S = gens(AutFN);
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S = unique([S; [inv(s) for s in S]])
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Id = AutFN()
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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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@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, 2)
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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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@ -58,20 +58,31 @@ end
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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 (default: 1e-5)"
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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-5
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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 = 20000
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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 (default: Inf)"
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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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@ -79,11 +90,11 @@ function parse_commandline()
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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 (default: N=2)"
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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 = "Find the decomposition over B_r(e,S)"
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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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@ -100,6 +111,13 @@ 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 = parsed_args["radius"]
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tol = parsed_args["tol"]
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@ -108,7 +126,6 @@ function main()
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dirname = "oSOutF$(N)_$(upper_bound)_r=$radius"
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isdir(dirname) || mkdir(dirname)
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logger = PropertyT.setup_logging(dirname)
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info(logger, "Group: $dirname")
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@ -123,7 +140,7 @@ function main()
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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 = SCS.SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Direct)
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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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