GroupsWithPropertyT/SL.jl

using ArgParse

using Nemo
import SCS.SCSSolver
using PropertyT


###############################################################################
#
#  Generating set
#
###############################################################################

function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
    @assert i≠j
    m = one(M)
    m[i,j] = val
    return m
end

function SLsize(n,p)
    result = BigInt(1)
    for k in 0:n-1
        result *= p^n - p^k
    end
    return div(result, p-1)
end

function SL_generatingset(n::Int, X::Bool=false)
   indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
   G = MatrixSpace(ZZ, n, n)
   if X
      S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]]
   else
      S = [E(i,j,G,v) for (i,j) in indexing for v in [1]]
   end
   S = vcat(S, [inv(x) for x in S])
   return G, unique(S)
end

function SL_generatingset(n::Int, p::Int, X::Bool=false)
    p == 0 && return SL_generatingset(n, X)
    (p > 1 && n > 1) || throw("Both n and p should be positive integers!")
    info("Size(SL($n,$p)) = $(SLsize(n,p))")
    F = ResidueRing(ZZ, p)
    G = MatrixSpace(F, n, n)
    indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
    S = [E(i, j, G) for (i,j) in indexing]
    S = vcat(S, [inv(x) for x in S])
    return G, unique(S)
end

###############################################################################
#
#  Parsing command line
#
###############################################################################

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()
    settings = ArgParseSettings()

    @add_arg_table settings begin
        "--tol"
            help = "set numerical tolerance for the SDP solver"
            arg_type = Float64
            default = 1e-6
        "--iterations"
            help = "set maximal number of iterations for the SDP solver (default: 20000)"
            arg_type = Int
            default = 50000
        "--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"
            arg_type = Int
            required = false
        "-N"
            help = "Consider elementary matrices EL(N)"
            arg_type = Int
            default = 2
        "-p"
            help = "Matrices over field of p-elements (p=0 => over ZZ)"
            arg_type = Int
            default = 0
        "--radius"
            help = "Radius of ball B_r(e,S) to find solution over"
            arg_type = Int
            default = 2
    end

    return parse_args(settings)
end

function main()

    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"]
    p = parsed_args["p"]

    if p == 0
        dirname = "SL$(N)Z"
    else
        dirname = "SL$(N)_$p"
    end

    radius = parsed_args["radius"]
    tol = parsed_args["tol"]
    iterations = parsed_args["iterations"]
    upper_bound = parsed_args["upper-bound"]

    dirname = "$(dirname)_$(upper_bound)_r=$radius"

    logger = PropertyT.setup_logging(dirname)

    info(logger, "Group:       $dirname")
    info(logger, "Iterations:  $iterations")
    info(logger, "Precision:   $tol")
    info(logger, "Upper bound: $upper_bound")

    G, S = SL_generatingset(N, p)
    info(logger, G)
    info(logger, "Symmetric generating set of size $(length(S))")
    Id = one(G)

    solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)

    @time PropertyT.check_property_T(dirname, S, Id, solver, upper_bound, tol, radius)
    return 0
end

main()