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unify AutFN and AutFN_orbit

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kalmarek 2017-09-10 16:20:36 +02:00
parent fa3fffa202
commit 82da35efdd
2 changed files with 64 additions and 36 deletions
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67
AutFN.jl
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@ -17,6 +17,27 @@ Moreover, due to work of Potapchik and Rapinchuk [1] every real representation o
We need a different approach: Here we actually compute in Aut(𝔽₄) We need a different approach: Here we actually compute in Aut(𝔽₄)
=# =#
###############################################################################
#
# Generating set
#
###############################################################################
function SOutFN_generating_set(N::Int)
SOutFN = AutGroup(FreeGroup(N), special=true, outer=true)
S = gens(SOutFN);
S = [S; [inv(s) for s in S]]
return SOutFN, unique(S)
end
###############################################################################
#
# Parsing command line
#
###############################################################################
function cpuinfo_physicalcores() function cpuinfo_physicalcores()
maxcore = -1 maxcore = -1
for line in eachline("/proc/cpuinfo") for line in eachline("/proc/cpuinfo")
@ -33,15 +54,15 @@ function parse_commandline()
@add_arg_table s begin @add_arg_table s begin
"--tol" "--tol"
help = "set numerical tolerance for the SDP solver (default: 1e-5)" help = "set numerical tolerance for the SDP solver"
arg_type = Float64 arg_type = Float64
default = 1e-5 default = 1e-6
"--iterations" "--iterations"
help = "set maximal number of iterations for the SDP solver (default: 20000)" help = "set maximal number of iterations for the SDP solver"
arg_type = Int arg_type = Int
default = 20000 default = 20000
"--upper-bound" "--upper-bound"
help = "Set an upper bound for the spectral gap (default: Inf)" help = "Set an upper bound for the spectral gap"
arg_type = Float64 arg_type = Float64
default = Inf default = Inf
"--cpus" "--cpus"
@ -49,7 +70,7 @@ function parse_commandline()
arg_type = Int arg_type = Int
required = false required = false
"-N" "-N"
help = "Consider automorphisms of free group on N generators (default: N=3)" help = "Consider automorphisms of free group on N generators"
arg_type = Int arg_type = Int
default = 2 default = 2
end end
@ -57,14 +78,6 @@ function parse_commandline()
return parse_args(s) return parse_args(s)
end end
# const name = "SYM$N"
# const upper_bound=factorial(N)-TOL^(1/5)
# S() = generating_set_of_Sym(N)
# name = "AutF$N"
# S() = generating_set_of_AutF(N)
function main() function main()
parsed_args = parse_commandline() parsed_args = parse_commandline()
@ -76,32 +89,30 @@ function main()
Blas.set_num_threads(parsed_args["cpus"]) Blas.set_num_threads(parsed_args["cpus"])
end end
N = parsed_args["N"]
radius = 2
tol = parsed_args["tol"] tol = parsed_args["tol"]
iterations = parsed_args["iterations"] iterations = parsed_args["iterations"]
# solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
N = parsed_args["N"]
upper_bound = parsed_args["upper-bound"] upper_bound = parsed_args["upper-bound"]
radius=2
name = "SOutF$N" dirname = "SOutF$(N)_$(upper_bound)_r=$radius"
name = "$(name)_$(upper_bound)_r=$radius"
logger = PropertyT.setup_logging(name) logger = PropertyT.setup_logging(dirname)
info(logger, "Group: $name") info(logger, "Group: $dirname")
info(logger, "Iterations: $iterations") info(logger, "Iterations: $iterations")
info(logger, "Precision: $tol") info(logger, "Precision: $tol")
info(logger, "Upper bound: $upper_bound") info(logger, "Upper bound: $upper_bound")
AutFN = AutGroup(FreeGroup(N), special=true, outer=true) G, S = SOutFN_generating_set(N)
S = gens(AutFN); info(logger, G)
S = unique([S; [inv(s) for s in S]]) info(logger, "Symmetric generating set of size $(length(S))")
Id = AutFN() info(logger, S)
Id = G()
@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, 2) solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
@time PropertyT.check_property_T(dirname, S, Id, solver, upper_bound, tol, 2)
return 0 return 0
end end

33
AutFN_orbit.jl
View File

@ -58,20 +58,31 @@ end
# #
############################################################################### ###############################################################################
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() function parse_commandline()
settings = ArgParseSettings() settings = ArgParseSettings()
@add_arg_table settings begin @add_arg_table settings begin
"--tol" "--tol"
help = "set numerical tolerance for the SDP solver (default: 1e-5)" help = "set numerical tolerance for the SDP solver"
arg_type = Float64 arg_type = Float64
default = 1e-5 default = 1e-14
"--iterations" "--iterations"
help = "set maximal number of iterations for the SDP solver (default: 20000)" help = "set maximal number of iterations for the SDP solver (default: 20000)"
arg_type = Int arg_type = Int
default = 20000 default = 100000
"--upper-bound" "--upper-bound"
help = "Set an upper bound for the spectral gap (default: Inf)" help = "Set an upper bound for the spectral gap"
arg_type = Float64 arg_type = Float64
default = Inf default = Inf
"--cpus" "--cpus"
@ -79,11 +90,11 @@ function parse_commandline()
arg_type = Int arg_type = Int
required = false required = false
"-N" "-N"
help = "Consider automorphisms of free group on N generators (default: N=2)" help = "Consider automorphisms of free group on N generators"
arg_type = Int arg_type = Int
default = 2 default = 2
"--radius" "--radius"
help = "Find the decomposition over B_r(e,S)" help = "Radius of ball B_r(e,S) to find solution over"
arg_type = Int arg_type = Int
default = 2 default = 2
end end
@ -100,6 +111,13 @@ end
function main() function main()
parsed_args = parse_commandline() 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"] N = parsed_args["N"]
radius = parsed_args["radius"] radius = parsed_args["radius"]
tol = parsed_args["tol"] tol = parsed_args["tol"]
@ -108,7 +126,6 @@ function main()
dirname = "oSOutF$(N)_$(upper_bound)_r=$radius" dirname = "oSOutF$(N)_$(upper_bound)_r=$radius"
isdir(dirname) || mkdir(dirname)
logger = PropertyT.setup_logging(dirname) logger = PropertyT.setup_logging(dirname)
info(logger, "Group: $dirname") info(logger, "Group: $dirname")
@ -123,7 +140,7 @@ function main()
AutS = WreathProduct(FiniteField(2,1, "a")[1], PermutationGroup(N)) AutS = WreathProduct(FiniteField(2,1, "a")[1], PermutationGroup(N))
# AutS = PermutationGroup(N) # AutS = PermutationGroup(N)
solver = SCS.SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Direct) solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
sett = Settings(dirname, N, G, S, AutS, radius, solver, upper_bound, tol) sett = Settings(dirname, N, G, S, AutS, radius, solver, upper_bound, tol)