137 lines
3.6 KiB
Julia
137 lines
3.6 KiB
Julia
using ArgParse
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using Nemo
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using GroupRings
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using PropertyT
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import SCS.SCSSolver
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function E(i::Int, j::Int, M::Nemo.MatSpace)
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@assert i≠j
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m = one(M)
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m[i,j] = m[1,1]
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return m
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end
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function SL_generatingset(n::Int)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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G = Nemo.MatrixSpace(Nemo.ZZ, n,n)
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S = [E(i,j,G) for (i,j) in indexing];
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S = vcat(S, [transpose(x) for x in S]);
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return unique(S)
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end
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function SLsize(n,p)
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result = 1
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for k in 0:n-1
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result *= p^n - p^k
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end
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return div(result, p-1)
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end
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function SL_generatingset(n::Int, p::Int)
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p == 0 && return SL_generatingset(n)
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(p > 1 && n > 0) || throw(ArgumentError("Both n and p should be positive integers!"))
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println("Size(SL($n,$p)) = $(SLsize(n,p))")
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F = Nemo.ResidueRing(Nemo.ZZ, p)
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G = Nemo.MatrixSpace(F, n,n)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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S = [E(i, j, G) for (i,j) in indexing]
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S = vcat(S, [transpose(x) for x in S])
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return unique(S)
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end
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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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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 (default: 1e-5)"
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arg_type = Float64
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default = 1e-5
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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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"--upper-bound"
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help = "Set an upper bound for the spectral gap (default: Inf)"
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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 matrices of size N (default: N=3)"
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arg_type = Int
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default = 3
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"-p"
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help = "Matrices over filed of p-elements (default: p=0 => over ZZ)"
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arg_type = Int
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default = 0
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"--radius"
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help = "Find the decomposition over B_r(e,S)"
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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(s)
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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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tol = parsed_args["tol"]
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iterations = parsed_args["iterations"]
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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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p = parsed_args["p"]
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if p == 0
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name = "SL$(N)Z"
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else
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name = "SL$(N)_$p"
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end
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radius = parsed_args["radius"]
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name = "$(name)_$iterations-$(string(upper_bound))-r=$radius"
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logger = PropertyT.setup_logging(name)
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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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S = SL_generatingset(N, p)
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S = unique([S; [inv(s) for s in S]])
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Id = one(parent(S[1]))
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@time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius)
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return 0
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end
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main()
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