diff --git a/SL.jl b/SL.jl index be6250b..4f2bc3a 100644 --- a/SL.jl +++ b/SL.jl @@ -5,41 +5,57 @@ import SCS.SCSSolver using PropertyT -function E(i::Int, j::Int, M::Nemo.MatSpace) +############################################################################### +# +# Generating set +# +############################################################################### + +function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring)) @assert i≠j m = one(M) - m[i,j] = m[1,1] + m[i,j] = val return m end -function SL_generatingset(n::Int) - indexing = [(i,j) for i in 1:n for j in 1:n if i≠j] - G = Nemo.MatrixSpace(Nemo.ZZ, n,n) - S = [E(i,j,G) for (i,j) in indexing]; - S = vcat(S, [transpose(x) for x in S]); - return unique(S) -end - function SLsize(n,p) - result = 1 + 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, p::Int) - p == 0 && return SL_generatingset(n) - (p > 1 && n > 0) || throw(ArgumentError("Both n and p should be positive integers!")) - println("Size(SL($n,$p)) = $(SLsize(n,p))") - F = Nemo.ResidueRing(Nemo.ZZ, p) - G = Nemo.MatrixSpace(F, n,n) +function SL_generatingset(n::Int, X::Bool=false) + indexing = [(i,j) for i in 1:n for j in 1:n if i≠j] + G = MatrixSpace(ZZ, n, n) + if X + S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]] + else + S = [E(i,j,G,v) for (i,j) in indexing for v in [1]] + end + S = vcat(S, [inv(x) for x in S]) + return G, unique(S) +end + +function SL_generatingset(n::Int, p::Int, X::Bool=false) + p == 0 && return SL_generatingset(n, X) + (p > 1 && n > 1) || throw("Both n and p should be positive integers!") + info("Size(SL($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, [transpose(x) for x in S]) - return unique(S) + 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") @@ -52,40 +68,40 @@ function cpuinfo_physicalcores() end function parse_commandline() - s = ArgParseSettings() + settings = ArgParseSettings() - @add_arg_table s begin + @add_arg_table settings begin "--tol" - help = "set numerical tolerance for the SDP solver (default: 1e-5)" + help = "set numerical tolerance for the SDP solver" arg_type = Float64 - default = 1e-5 + default = 1e-6 "--iterations" help = "set maximal number of iterations for the SDP solver (default: 20000)" arg_type = Int - default = 20000 + default = 50000 "--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 default = Inf "--cpus" - help = "Set number of cpus used by solver (default: auto)" + help = "Set number of cpus used by solver" arg_type = Int required = false "-N" - help = "Consider matrices of size N (default: N=3)" + help = "Consider elementary matrices EL(N)" arg_type = Int - default = 3 + default = 2 "-p" - help = "Matrices over filed of p-elements (default: p=0 => over ZZ)" + help = "Matrices over field of p-elements (p=0 => over ZZ)" arg_type = Int default = 0 "--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 default = 2 end - return parse_args(s) + return parse_args(settings) end function main() @@ -95,40 +111,40 @@ function main() 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"]) + BLAS.set_num_threads(parsed_args["cpus"]) end - tol = parsed_args["tol"] - iterations = parsed_args["iterations"] - - solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct) - N = parsed_args["N"] - upper_bound = parsed_args["upper-bound"] p = parsed_args["p"] if p == 0 - name = "SL$(N)Z" + dirname = "SL$(N)Z" else - name = "SL$(N)_$p" + dirname = "SL$(N)_$p" end - radius = parsed_args["radius"] +  radius = parsed_args["radius"] + tol = parsed_args["tol"] + iterations = parsed_args["iterations"] + upper_bound = parsed_args["upper-bound"] - name = "$(name)_$(upper_bound)_r=$radius" + dirname = "$(dirname)_$(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, "Precision: $tol") info(logger, "Upper bound: $upper_bound") - S = SL_generatingset(N, p) - S = unique([S; [inv(s) for s in S]]) - Id = one(parent(S[1])) + G, S = SL_generatingset(N, p) + info(logger, G) + info(logger, "Symmetric generating set of size $(length(S))") + Id = one(G) - @time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius) + 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