update SL.jl

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