GroupsWithPropertyT/MCG.jl
2018-01-04 10:47:00 +01:00

111 lines
2.9 KiB
Julia

using ArgParse
using JLD
using Nemo
import SCS.SCSSolver
using PropertyT
using Groups
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()
args = ArgParseSettings()
@add_arg_table args 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 (default: auto)"
arg_type = Int
required = false
"-N"
help = "Consider mapping class group of surface of genus N"
arg_type = Int
default = 2
"--radius"
help = "Radius of ball B_r(e,S) to find solution over"
arg_type = Int
default = 4
"--warmstart"
help = "Use warmstart.jl as the initial guess for SCS"
action = :store_true
end
return parse_args(args)
end
include("FPGroups_GAP.jl")
include("CPUselect.jl")
function main()
parsed_args = parse_commandline()
set_parallel_mthread(parsed_args)
tol = parsed_args["tol"]
iterations = parsed_args["iterations"]
upper_bound = parsed_args["upper-bound"]
radius = parsed_args["radius"]
N = parsed_args["N"]
prefix = "MCG($N)"
name = "$(prefix)"
isdir(name) || mkdir(name)
prepare_pm_delta(prefix, name, radius)
logger = PropertyT.setup_logging(name)
info(logger, "Group: $name")
info(logger, "Iterations: $iterations")
info(logger, "Precision: $tol")
info(logger, "Upper bound: $upper_bound")
MCGroup = Groups.FPGroup(["a1","a2","a3","a4", "a5"]);
S = Nemo.gens(MCGroup)
Comm(x,y) = x*y*x^-1*y^-1
k = length(S)
relations = [[Comm(S[i], S[j]) for i in 1:k for j in 1:k 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:k-1]...,
(S[1]*S[2]*S[3])^4*inv(S[5])^5,
Comm(prod(reverse(S))*prod(S), S[1]),
(prod(reverse(S))*prod(S))^2
];
relations = [relations; [inv(rel) for rel in relations]]
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
S = gens(MCGroup)
S = unique([S; [inv(s) for s in S]])
Id = MCGroup()
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.9, acceleration_lookback=1)
@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius)
return 0
end
main()