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master
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enh/cmd_li
15
.gitignore
vendored
15
.gitignore
vendored
@ -1,15 +1,4 @@
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Articles
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Higman
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MCG*
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notebooks
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Oldies
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oSAutF*
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oSL*
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SAutF*
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SL*_*
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*ipynb*
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*ipynb*
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*.gws
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*.gws
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.*
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*/*.jld
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tests*
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*/*.log
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*.py
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*.pyc
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120
AutF4.jl
Normal file
120
AutF4.jl
Normal file
@ -0,0 +1,120 @@
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using Combinatorics
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using JuMP
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import SCS: SCSSolver
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import Mosek: MosekSolver
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push!(LOAD_PATH, "./")
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using SemiDirectProduct
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using GroupAlgebras
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include("property(T).jl")
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const N = 4
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const VERBOSE = true
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function permutation_matrix(p::Vector{Int})
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n = length(p)
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sort(p) == collect(1:n) || throw(ArgumentError("Input array must be a permutation of 1:n"))
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A = eye(n)
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return A[p,:]
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end
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SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
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# const SymmetricGroup = [permutation_matrix(x) for x in SymmetricGroup_perms]
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function E(i, j; dim::Int=N)
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@assert i≠j
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k = eye(dim)
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k[i,j] = 1
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return k
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end
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function eltary_basis_vector(i; dim::Int=N)
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result = zeros(dim)
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if 0 < i ≤ dim
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result[i] = 1
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end
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return result
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end
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v(i; dim=N) = eltary_basis_vector(i,dim=dim)
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ϱ(i,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), v(j,dim=n))
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λ(i,j::Int,n=N) = SemiDirectProductElement(E(i,j,dim=n), -v(j,dim=n))
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function ɛ(i, n::Int=N)
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result = eye(n)
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result[i,i] = -1
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return SemiDirectProductElement(result)
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end
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σ(permutation::Vector{Int}) =
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SemiDirectProductElement(permutation_matrix(permutation))
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# Standard generating set: 103 elements
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function generatingset_ofAutF(n::Int=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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ϱs = [ϱ(ij...) for ij in indexing]
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λs = [λ(ij...) for ij in indexing]
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ɛs = [ɛ(i) for i in 1:N]
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σs = [σ(perm) for perm in SymmetricGroup(n)]
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S = vcat(ϱs, λs, ɛs, σs);
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S = unique(vcat(S, [inv(x) for x in S]));
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return S
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end
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#=
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Note that the element
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α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
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which surely belongs to ball of radius 4 in Aut(F₄) becomes trivial under the representation
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Aut(F₄) → GL₄(ℤ)⋉ℤ⁴ → GL₅(ℂ).
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Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ(ℂ) (for m ≤ 2n-2) factors through GLₙ(ℤ)⋉ℤⁿ, so will have the same problem.
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We need a different approach!
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=#
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const ID = eye(N+1)
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const S₁ = generatingset_ofAutF(N)
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matrix_S₁ = [matrix_repr(x) for x in S₁]
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const TOL=10.0^-7
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matrix_S₁[1:10,:][:,1]
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Δ, cm = prepare_Laplacian_and_constraints(matrix_S₁)
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#solver = SCSSolver(eps=TOL, max_iters=ITERATIONS, verbose=true);
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solver = MosekSolver(MSK_DPAR_INTPNT_CO_TOL_REL_GAP=TOL,
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# MSK_DPAR_INTPNT_CO_TOL_PFEAS=1e-15,
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# MSK_DPAR_INTPNT_CO_TOL_DFEAS=1e-15,
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# MSK_IPAR_PRESOLVE_USE=0,
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QUIET=!VERBOSE)
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# κ, A = solve_for_property_T(S₁, solver, verbose=VERBOSE)
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product_matrix = readdlm("SL₃Z.product_matrix", Int)
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L = readdlm("SL₃Z.Δ.coefficients")[:, 1]
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Δ = GroupAlgebraElement(L, product_matrix)
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A = readdlm("matrix.A.Mosek")
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κ = readdlm("kappa.Mosek")[1]
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# @show eigvals(A)
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@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
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@assert A == Symmetric(A)
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const A_sqrt = real(sqrtm(A))
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SOS_EOI_fp_L₁, Ω_fp_dist = check_solution(κ, A_sqrt, Δ)
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κ_rational = rationalize(BigInt, κ;)
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A_sqrt_rational = rationalize(BigInt, A_sqrt)
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Δ_rational = rationalize(BigInt, Δ)
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SOS_EOI_rat_L₁, Ω_rat_dist = check_solution(κ_rational, A_sqrt_rational, Δ_rational)
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177
AutFN.jl
Normal file
177
AutFN.jl
Normal file
@ -0,0 +1,177 @@
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using Groups
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using ProgressMeter
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#=
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Note that the element
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α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
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which surely belongs to ball of radius 4 in Aut(F₄) becomes trivial under the representation
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Aut(F₄) → GL₄(ℤ)⋉ℤ⁴ → GL₅(ℂ).
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Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ(ℂ) (for m ≤ 2n-2) factors through GLₙ(ℤ)⋉ℤⁿ, so will have the same problem.
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We need a different approach: Here we actually compute in Aut(𝔽₄)
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=#
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import Combinatorics.nthperm
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SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
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function generating_set_of_AutF(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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σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
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ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
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λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
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ɛs = [flip_AutSymbol(i) for i in 1:N];
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S = vcat(ϱs,λs)
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S = vcat(S..., σs..., ɛs)
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S = vcat(S..., [inv(g) for g in S])
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return Vector{AutWord}(unique(S))
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end
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function generating_set_of_OutF(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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ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
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λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
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ɛs = [flip_AutSymbol(i) for i in 1:N];
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S = ϱs
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push!(S, λs..., ɛs...)
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push!(S,[inv(g) for g in S]...)
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return Vector{AutWord}(unique(S))
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end
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function generating_set_of_Sym(N::Int)
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σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
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S = σs
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push!(S, [inv(s) for s in S]...)
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return Vector{AutWord}(unique(S))
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end
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function products(S1::Vector{AutWord}, S2::Vector{AutWord})
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result = Vector{AutWord}()
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seen = Set{Vector{FGWord}}()
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n = length(S1)
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p = Progress(n, 1, "Computing complete products...", 50)
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for (i,x) in enumerate(S1)
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for y in S2
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z::AutWord = x*y
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v::Vector{FGWord} = z(domain)
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if !in(v, seen)
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push!(seen, v)
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push!(result, z)
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end
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end
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next!(p)
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end
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return result
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end
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function products_images(S1::Vector{AutWord}, S2::Vector{AutWord})
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result = Vector{Vector{FGWord}}()
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seen = Set{Vector{FGWord}}()
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n = length(S1)
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p = Progress(n, 1, "Computing images of elts in B₄...", 50)
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for (i,x) in enumerate(S1)
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z = x(domain)
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for y in S2
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v = y(z)
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if !in(v, seen)
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push!(seen, v)
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push!(result, v)
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end
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end
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next!(p)
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end
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return result
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end
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function hashed_product{T}(image::T, B, images_dict::Dict{T, Int})
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n = size(B,1)
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column = zeros(Int,n)
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Threads.@threads for j in 1:n
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w = (B[j])(image)
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k = images_dict[w]
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k ≠ 0 || throw(ArgumentError(
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"($i,$j): $(x^-1)*$y don't seem to be supported on basis!"))
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column[j] = k
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end
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return column
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end
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function create_product_matrix(basis::Vector{AutWord}, images)
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n = length(basis)
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product_matrix = zeros(Int, (n, n));
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print("Creating hashtable of images...")
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@time images_dict = Dict{Vector{FGWord}, Int}(x => i
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for (i,x) in enumerate(images))
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p = Progress(n, 1, "Computing product matrix in basis...", 50)
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for i in 1:n
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z = (inv(basis[i]))(domain)
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product_matrix[i,:] = hashed_product(z, basis, images_dict)
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next!(p)
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end
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return product_matrix
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end
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function ΔandSDPconstraints(identity::AutWord, S::Vector{AutWord})
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println("Generating Balls of increasing radius...")
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@time B₁ = vcat([identity], S)
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@time B₂ = products(B₁,B₁);
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@show length(B₂)
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if length(B₂) != length(B₁)
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@time B₃ = products(B₁, B₂)
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@show length(B₃)
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if length(B₃) != length(B₂)
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@time B₄_images = products_images(B₁, B₃)
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else
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B₄_images = unique([f(domain) for f in B₃])
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|
end
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else
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B₃ = B₂
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B₄ = B₂
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B₄_images = unique([f(domain) for f in B₃])
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end
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@show length(B₄_images)
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# @assert length(B₄_images) == 3425657
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println("Creating product matrix...")
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@time pm = PropertyT.create_product_matrix(B₂, B₄_images)
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println("Creating sdp_constratints...")
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@time sdp_constraints = PropertyT.constraints_from_pm(pm)
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|
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L_coeff = PropertyT.splaplacian_coeff(S, B₂, length(B₄_images))
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Δ = PropertyT.GroupAlgebraElement(L_coeff, Array{Int,2}(pm))
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return Δ, sdp_constraints
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end
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using GroupAlgebras
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using PropertyT
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|
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|
const symbols = [FGSymbol("x₁",1), FGSymbol("x₂",1), FGSymbol("x₃",1), FGSymbol("x₄",1), FGSymbol("x₅",1), FGSymbol("x₆",1)]
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const TOL=1e-8
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const N = 4
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const domain = Vector{FGWord}(symbols[1:N])
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const ID = one(AutWord)
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# const name = "SYM$N"
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# const upper_bound=factorial(N)-TOL^(1/5)
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# S() = generating_set_of_Sym(N)
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# name = "AutF$N"
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# S() = generating_set_of_AutF(N)
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name = "OutF$N"
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S() = generating_set_of_OutF(N)
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const upper_bound=0.05
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BLAS.set_num_threads(4)
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@time check_property_T(name, ID, S; verbose=true, tol=TOL, upper_bound=upper_bound)
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35
CPUselect.jl
35
CPUselect.jl
@ -1,35 +0,0 @@
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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")
|
|
||||||
maxcore = max(maxcore, parse(Int, split(line, ':')[2]))
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|
||||||
end
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|
||||||
end
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|
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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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|
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end
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function set_parallel_mthread(N::Int, workers::Bool)
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if N > cpuinfo_physicalcores()
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|
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warn("Number of specified cores exceeds the physical core count. Performance may suffer.")
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|
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end
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|
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if workers
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|
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addprocs(N)
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|
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info("Using $N cpus in @parallel code.")
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|
||||||
end
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info("Using $(Threads.nthreads()) threads in @threads code.")
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|
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BLAS.set_num_threads(N)
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info("Using $N threads in BLAS.")
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|
||||||
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|
||||||
end
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|
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function set_parallel_mthread(parsed_args::Dict; workers=false)
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|
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if parsed_args["cpus"] == nothing
|
|
||||||
N = cpuinfo_physicalcores()
|
|
||||||
else
|
|
||||||
N = parsed_args["cpus"]
|
|
||||||
end
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|
||||||
|
|
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set_parallel_mthread(N, workers)
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|
||||||
end
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|
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157
FPGroups_GAP.jl
157
FPGroups_GAP.jl
@ -1,157 +0,0 @@
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using JLD
|
|
||||||
|
|
||||||
function GAP_code(group_code, dir, R; maxeqns=10_000, infolevel=2)
|
|
||||||
code = """
|
|
||||||
LogTo("$(dir)/GAP.log");
|
|
||||||
RequirePackage("kbmag");
|
|
||||||
SetInfoLevel(InfoRWS, $infolevel);
|
|
||||||
|
|
||||||
|
|
||||||
MetricBalls := function(rws, R)
|
|
||||||
local l, basis, sizes, i;
|
|
||||||
l := EnumerateReducedWords(rws, 0, R);;
|
|
||||||
SortBy(l, Length);
|
|
||||||
sizes := [1..R];
|
|
||||||
Apply(sizes, i -> Number(l, w -> Length(w) <= i));
|
|
||||||
return [l, sizes];
|
|
||||||
end;;
|
|
||||||
|
|
||||||
ProductMatrix := function(rws, basis, len)
|
|
||||||
local result, dict, g, tmpList, t;
|
|
||||||
result := [];
|
|
||||||
dict := NewDictionary(basis[1], true);
|
|
||||||
t := Runtime();
|
|
||||||
for g in [1..Length(basis)] do;
|
|
||||||
AddDictionary(dict, basis[g], g);
|
|
||||||
od;
|
|
||||||
Print("Creating dictionary: \t\t", StringTime(Runtime()-t), "\\n");
|
|
||||||
for g in basis{[1..len]} do;
|
|
||||||
tmpList := List(Inverse(g)*basis{[1..len]}, w->ReducedForm(rws, w));
|
|
||||||
#t := Runtime();
|
|
||||||
tmpList := List(tmpList, x -> LookupDictionary(dict, x));
|
|
||||||
#Print(Runtime()-t, "\\n");
|
|
||||||
Assert(1, ForAll(tmpList, x -> x <> fail));
|
|
||||||
Add(result, tmpList);
|
|
||||||
od;
|
|
||||||
return result;
|
|
||||||
end;;
|
|
||||||
|
|
||||||
SaveCSV := function(fname, pm)
|
|
||||||
local file, i, j, k;
|
|
||||||
file := OutputTextFile(fname, false);;
|
|
||||||
for i in pm do;
|
|
||||||
k := 1;
|
|
||||||
for j in i do;
|
|
||||||
if k < Length(i) then
|
|
||||||
AppendTo(file, j, ", ");
|
|
||||||
else
|
|
||||||
AppendTo(file, j, "\\n");
|
|
||||||
fi;
|
|
||||||
k := k+1;
|
|
||||||
od;
|
|
||||||
od;
|
|
||||||
CloseStream(file);
|
|
||||||
end;;
|
|
||||||
|
|
||||||
$group_code
|
|
||||||
|
|
||||||
# G:= SimplifiedFpGroup(G);
|
|
||||||
RWS := KBMAGRewritingSystem(G);
|
|
||||||
# ResetRewritingSystem(RWS);
|
|
||||||
O:=OptionsRecordOfKBMAGRewritingSystem(RWS);;
|
|
||||||
O.maxeqns := $maxeqns;
|
|
||||||
O.maxstates := 1000*$maxeqns;
|
|
||||||
#O.maxstoredlen := [100,100];
|
|
||||||
|
|
||||||
before := Runtimes();;
|
|
||||||
KnuthBendix(RWS);
|
|
||||||
after := Runtimes();;
|
|
||||||
delta := after.user_time_children - before.user_time_children;;
|
|
||||||
Print("Knuth-Bendix completion: \t", StringTime(delta), "\\n");
|
|
||||||
|
|
||||||
t := Runtime();
|
|
||||||
res := MetricBalls(RWS,$(2*R));;
|
|
||||||
Print("Metric-Balls generation: \t", StringTime(Runtime()-t), "\\n");
|
|
||||||
B := res[1];; sizes := res[2];;
|
|
||||||
Print("Sizes of generated Balls: \t", sizes, "\\n");
|
|
||||||
|
|
||||||
t := Runtime();
|
|
||||||
pm := ProductMatrix(RWS, B, sizes[$R]);;
|
|
||||||
Print("Computing ProductMatrix: \t", StringTime(Runtime()-t), "\\n");
|
|
||||||
|
|
||||||
S := EnumerateReducedWords(RWS, 1, 1);
|
|
||||||
S := List(S, s -> Position(B,s));
|
|
||||||
|
|
||||||
SaveCSV("$(dir)/pm.csv", pm);
|
|
||||||
SaveCSV("$(dir)/S.csv", [S]);
|
|
||||||
SaveCSV("$(dir)/sizes.csv", [sizes]);
|
|
||||||
|
|
||||||
Print("DONE!\\n");
|
|
||||||
|
|
||||||
quit;""";
|
|
||||||
return code
|
|
||||||
end
|
|
||||||
|
|
||||||
function GAP_groupcode(S, rels)
|
|
||||||
F = "FreeGroup("*join(["\"$v\""for v in S], ", ") *");"
|
|
||||||
m = match(r".*(\[.*\])$", string(rels))
|
|
||||||
rels = replace(m.captures[1], " ", "\n")
|
|
||||||
code = """
|
|
||||||
F := $F;
|
|
||||||
AssignGeneratorVariables(F);;
|
|
||||||
relations := $rels;;
|
|
||||||
G := F/relations;
|
|
||||||
"""
|
|
||||||
return code
|
|
||||||
end
|
|
||||||
|
|
||||||
function GAP_execute(gap_code, dir)
|
|
||||||
isdir(dir) || mkdir(dir)
|
|
||||||
GAP_file = joinpath(dir, "GAP_code.g")
|
|
||||||
@show dir
|
|
||||||
@show GAP_file;
|
|
||||||
|
|
||||||
open(GAP_file, "w") do io
|
|
||||||
write(io, gap_code)
|
|
||||||
end
|
|
||||||
run(pipeline(`cat $(GAP_file)`, `gap -q`))
|
|
||||||
end
|
|
||||||
|
|
||||||
function prepare_pm_delta_csv(name, group_code, R; maxeqns=10_000, infolevel=2)
|
|
||||||
info("Preparing multiplication table using GAP (via kbmag)")
|
|
||||||
gap_code = GAP_code(group_code, name, R, maxeqns=maxeqns, infolevel=infolevel)
|
|
||||||
GAP_execute(gap_code, name)
|
|
||||||
end
|
|
||||||
|
|
||||||
function prepare_pm_delta(name, group_code, R; maxeqns=100_000, infolevel=2)
|
|
||||||
|
|
||||||
pm_fname = joinpath(name, "pm.csv")
|
|
||||||
S_fname = joinpath(name, "S.csv")
|
|
||||||
sizes_fname = joinpath(name, "sizes.csv")
|
|
||||||
delta_fname = joinpath(name, "delta.jld")
|
|
||||||
|
|
||||||
if !isfile(pm_fname) || !isfile(S_fname) || !isfile(sizes_fname)
|
|
||||||
prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
|
|
||||||
end
|
|
||||||
|
|
||||||
if isfile(sizes_fname)
|
|
||||||
sizes = readcsv(sizes_fname, Int)[1,:]
|
|
||||||
if 2R > length(sizes)
|
|
||||||
prepare_pm_delta_csv(name, group_code, R, maxeqns=maxeqns, infolevel=infolevel)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
pm = readcsv(pm_fname, Int)
|
|
||||||
S = readcsv(S_fname, Int)[1,:]
|
|
||||||
sizes = readcsv(sizes_fname, Int)[1,:]
|
|
||||||
|
|
||||||
Δ = spzeros(sizes[2R])
|
|
||||||
Δ[S] .= -1
|
|
||||||
Δ[1] = length(S)
|
|
||||||
|
|
||||||
pm = pm[1:sizes[R], 1:sizes[R]]
|
|
||||||
|
|
||||||
save(joinpath(name, "pm.jld"), "pm", pm)
|
|
||||||
save(joinpath(name, "delta.jld"), "Δ", Δ)
|
|
||||||
|
|
||||||
end
|
|
||||||
634
LICENSE.md
634
LICENSE.md
@ -1,634 +0,0 @@
|
|||||||
> Copyright (c) 2017: Marek Kaluba.
|
|
||||||
> This program is free software: you can redistribute it and/or modify
|
|
||||||
> it under the terms of the GNU General Public License as published by
|
|
||||||
> the Free Software Foundation, either version 3 of the License, or
|
|
||||||
> (at your option) any later version.
|
|
||||||
>
|
|
||||||
> This program is distributed in the hope that it will be useful,
|
|
||||||
> but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
||||||
> MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
||||||
> GNU General Public License for more details.
|
|
||||||
>
|
|
||||||
>
|
|
||||||
> GNU GENERAL PUBLIC LICENSE
|
|
||||||
> Version 3, 29 June 2007
|
|
||||||
>
|
|
||||||
> Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
|
|
||||||
> Everyone is permitted to copy and distribute verbatim copies
|
|
||||||
> of this license document, but changing it is not allowed.
|
|
||||||
>
|
|
||||||
> Preamble
|
|
||||||
>
|
|
||||||
> The GNU General Public License is a free, copyleft license for
|
|
||||||
> software and other kinds of works.
|
|
||||||
>
|
|
||||||
> The licenses for most software and other practical works are designed
|
|
||||||
> to take away your freedom to share and change the works. By contrast,
|
|
||||||
> the GNU General Public License is intended to guarantee your freedom to
|
|
||||||
> share and change all versions of a program--to make sure it remains free
|
|
||||||
> software for all its users. We, the Free Software Foundation, use the
|
|
||||||
> GNU General Public License for most of our software; it applies also to
|
|
||||||
> any other work released this way by its authors. You can apply it to
|
|
||||||
> your programs, too.
|
|
||||||
>
|
|
||||||
> When we speak of free software, we are referring to freedom, not
|
|
||||||
> price. Our General Public Licenses are designed to make sure that you
|
|
||||||
> have the freedom to distribute copies of free software (and charge for
|
|
||||||
> them if you wish), that you receive source code or can get it if you
|
|
||||||
> want it, that you can change the software or use pieces of it in new
|
|
||||||
> free programs, and that you know you can do these things.
|
|
||||||
>
|
|
||||||
> To protect your rights, we need to prevent others from denying you
|
|
||||||
> these rights or asking you to surrender the rights. Therefore, you have
|
|
||||||
> certain responsibilities if you distribute copies of the software, or if
|
|
||||||
> you modify it: responsibilities to respect the freedom of others.
|
|
||||||
>
|
|
||||||
> For example, if you distribute copies of such a program, whether
|
|
||||||
> gratis or for a fee, you must pass on to the recipients the same
|
|
||||||
> freedoms that you received. You must make sure that they, too, receive
|
|
||||||
> or can get the source code. And you must show them these terms so they
|
|
||||||
> know their rights.
|
|
||||||
>
|
|
||||||
> Developers that use the GNU GPL protect your rights with two steps:
|
|
||||||
> (1) assert copyright on the software, and (2) offer you this License
|
|
||||||
> giving you legal permission to copy, distribute and/or modify it.
|
|
||||||
>
|
|
||||||
> For the developers' and authors' protection, the GPL clearly explains
|
|
||||||
> that there is no warranty for this free software. For both users' and
|
|
||||||
> authors' sake, the GPL requires that modified versions be marked as
|
|
||||||
> changed, so that their problems will not be attributed erroneously to
|
|
||||||
> authors of previous versions.
|
|
||||||
>
|
|
||||||
> Some devices are designed to deny users access to install or run
|
|
||||||
> modified versions of the software inside them, although the manufacturer
|
|
||||||
> can do so. This is fundamentally incompatible with the aim of
|
|
||||||
> protecting users' freedom to change the software. The systematic
|
|
||||||
> pattern of such abuse occurs in the area of products for individuals to
|
|
||||||
> use, which is precisely where it is most unacceptable. Therefore, we
|
|
||||||
> have designed this version of the GPL to prohibit the practice for those
|
|
||||||
> products. If such problems arise substantially in other domains, we
|
|
||||||
> stand ready to extend this provision to those domains in future versions
|
|
||||||
> of the GPL, as needed to protect the freedom of users.
|
|
||||||
>
|
|
||||||
> Finally, every program is threatened constantly by software patents.
|
|
||||||
> States should not allow patents to restrict development and use of
|
|
||||||
> software on general-purpose computers, but in those that do, we wish to
|
|
||||||
> avoid the special danger that patents applied to a free program could
|
|
||||||
> make it effectively proprietary. To prevent this, the GPL assures that
|
|
||||||
> patents cannot be used to render the program non-free.
|
|
||||||
>
|
|
||||||
> The precise terms and conditions for copying, distribution and
|
|
||||||
> modification follow.
|
|
||||||
>
|
|
||||||
> TERMS AND CONDITIONS
|
|
||||||
>
|
|
||||||
> 0. Definitions.
|
|
||||||
>
|
|
||||||
> "This License" refers to version 3 of the GNU General Public License.
|
|
||||||
>
|
|
||||||
> "Copyright" also means copyright-like laws that apply to other kinds of
|
|
||||||
> works, such as semiconductor masks.
|
|
||||||
>
|
|
||||||
> "The Program" refers to any copyrightable work licensed under this
|
|
||||||
> License. Each licensee is addressed as "you". "Licensees" and
|
|
||||||
> "recipients" may be individuals or organizations.
|
|
||||||
>
|
|
||||||
> To "modify" a work means to copy from or adapt all or part of the work
|
|
||||||
> in a fashion requiring copyright permission, other than the making of an
|
|
||||||
> exact copy. The resulting work is called a "modified version" of the
|
|
||||||
> earlier work or a work "based on" the earlier work.
|
|
||||||
>
|
|
||||||
> A "covered work" means either the unmodified Program or a work based
|
|
||||||
> on the Program.
|
|
||||||
>
|
|
||||||
> To "propagate" a work means to do anything with it that, without
|
|
||||||
> permission, would make you directly or secondarily liable for
|
|
||||||
> infringement under applicable copyright law, except executing it on a
|
|
||||||
> computer or modifying a private copy. Propagation includes copying,
|
|
||||||
> distribution (with or without modification), making available to the
|
|
||||||
> public, and in some countries other activities as well.
|
|
||||||
>
|
|
||||||
> To "convey" a work means any kind of propagation that enables other
|
|
||||||
> parties to make or receive copies. Mere interaction with a user through
|
|
||||||
> a computer network, with no transfer of a copy, is not conveying.
|
|
||||||
>
|
|
||||||
> An interactive user interface displays "Appropriate Legal Notices"
|
|
||||||
> to the extent that it includes a convenient and prominently visible
|
|
||||||
> feature that (1) displays an appropriate copyright notice, and (2)
|
|
||||||
> tells the user that there is no warranty for the work (except to the
|
|
||||||
> extent that warranties are provided), that licensees may convey the
|
|
||||||
> work under this License, and how to view a copy of this License. If
|
|
||||||
> the interface presents a list of user commands or options, such as a
|
|
||||||
> menu, a prominent item in the list meets this criterion.
|
|
||||||
>
|
|
||||||
> 1. Source Code.
|
|
||||||
>
|
|
||||||
> The "source code" for a work means the preferred form of the work
|
|
||||||
> for making modifications to it. "Object code" means any non-source
|
|
||||||
> form of a work.
|
|
||||||
>
|
|
||||||
> A "Standard Interface" means an interface that either is an official
|
|
||||||
> standard defined by a recognized standards body, or, in the case of
|
|
||||||
> interfaces specified for a particular programming language, one that
|
|
||||||
> is widely used among developers working in that language.
|
|
||||||
>
|
|
||||||
> The "System Libraries" of an executable work include anything, other
|
|
||||||
> than the work as a whole, that (a) is included in the normal form of
|
|
||||||
> packaging a Major Component, but which is not part of that Major
|
|
||||||
> Component, and (b) serves only to enable use of the work with that
|
|
||||||
> Major Component, or to implement a Standard Interface for which an
|
|
||||||
> implementation is available to the public in source code form. A
|
|
||||||
> "Major Component", in this context, means a major essential component
|
|
||||||
> (kernel, window system, and so on) of the specific operating system
|
|
||||||
> (if any) on which the executable work runs, or a compiler used to
|
|
||||||
> produce the work, or an object code interpreter used to run it.
|
|
||||||
>
|
|
||||||
> The "Corresponding Source" for a work in object code form means all
|
|
||||||
> the source code needed to generate, install, and (for an executable
|
|
||||||
> work) run the object code and to modify the work, including scripts to
|
|
||||||
> control those activities. However, it does not include the work's
|
|
||||||
> System Libraries, or general-purpose tools or generally available free
|
|
||||||
> programs which are used unmodified in performing those activities but
|
|
||||||
> which are not part of the work. For example, Corresponding Source
|
|
||||||
> includes interface definition files associated with source files for
|
|
||||||
> the work, and the source code for shared libraries and dynamically
|
|
||||||
> linked subprograms that the work is specifically designed to require,
|
|
||||||
> such as by intimate data communication or control flow between those
|
|
||||||
> subprograms and other parts of the work.
|
|
||||||
>
|
|
||||||
> The Corresponding Source need not include anything that users
|
|
||||||
> can regenerate automatically from other parts of the Corresponding
|
|
||||||
> Source.
|
|
||||||
>
|
|
||||||
> The Corresponding Source for a work in source code form is that
|
|
||||||
> same work.
|
|
||||||
>
|
|
||||||
> 2. Basic Permissions.
|
|
||||||
>
|
|
||||||
> All rights granted under this License are granted for the term of
|
|
||||||
> copyright on the Program, and are irrevocable provided the stated
|
|
||||||
> conditions are met. This License explicitly affirms your unlimited
|
|
||||||
> permission to run the unmodified Program. The output from running a
|
|
||||||
> covered work is covered by this License only if the output, given its
|
|
||||||
> content, constitutes a covered work. This License acknowledges your
|
|
||||||
> rights of fair use or other equivalent, as provided by copyright law.
|
|
||||||
>
|
|
||||||
> You may make, run and propagate covered works that you do not
|
|
||||||
> convey, without conditions so long as your license otherwise remains
|
|
||||||
> in force. You may convey covered works to others for the sole purpose
|
|
||||||
> of having them make modifications exclusively for you, or provide you
|
|
||||||
> with facilities for running those works, provided that you comply with
|
|
||||||
> the terms of this License in conveying all material for which you do
|
|
||||||
> not control copyright. Those thus making or running the covered works
|
|
||||||
> for you must do so exclusively on your behalf, under your direction
|
|
||||||
> and control, on terms that prohibit them from making any copies of
|
|
||||||
> your copyrighted material outside their relationship with you.
|
|
||||||
>
|
|
||||||
> Conveying under any other circumstances is permitted solely under
|
|
||||||
> the conditions stated below. Sublicensing is not allowed; section 10
|
|
||||||
> makes it unnecessary.
|
|
||||||
>
|
|
||||||
> 3. Protecting Users' Legal Rights From Anti-Circumvention Law.
|
|
||||||
>
|
|
||||||
> No covered work shall be deemed part of an effective technological
|
|
||||||
> measure under any applicable law fulfilling obligations under article
|
|
||||||
> 11 of the WIPO copyright treaty adopted on 20 December 1996, or
|
|
||||||
> similar laws prohibiting or restricting circumvention of such
|
|
||||||
> measures.
|
|
||||||
>
|
|
||||||
> When you convey a covered work, you waive any legal power to forbid
|
|
||||||
> circumvention of technological measures to the extent such circumvention
|
|
||||||
> is effected by exercising rights under this License with respect to
|
|
||||||
> the covered work, and you disclaim any intention to limit operation or
|
|
||||||
> modification of the work as a means of enforcing, against the work's
|
|
||||||
> users, your or third parties' legal rights to forbid circumvention of
|
|
||||||
> technological measures.
|
|
||||||
>
|
|
||||||
> 4. Conveying Verbatim Copies.
|
|
||||||
>
|
|
||||||
> You may convey verbatim copies of the Program's source code as you
|
|
||||||
> receive it, in any medium, provided that you conspicuously and
|
|
||||||
> appropriately publish on each copy an appropriate copyright notice;
|
|
||||||
> keep intact all notices stating that this License and any
|
|
||||||
> non-permissive terms added in accord with section 7 apply to the code;
|
|
||||||
> keep intact all notices of the absence of any warranty; and give all
|
|
||||||
> recipients a copy of this License along with the Program.
|
|
||||||
>
|
|
||||||
> You may charge any price or no price for each copy that you convey,
|
|
||||||
> and you may offer support or warranty protection for a fee.
|
|
||||||
>
|
|
||||||
> 5. Conveying Modified Source Versions.
|
|
||||||
>
|
|
||||||
> You may convey a work based on the Program, or the modifications to
|
|
||||||
> produce it from the Program, in the form of source code under the
|
|
||||||
> terms of section 4, provided that you also meet all of these conditions:
|
|
||||||
>
|
|
||||||
> a) The work must carry prominent notices stating that you modified
|
|
||||||
> it, and giving a relevant date.
|
|
||||||
>
|
|
||||||
> b) The work must carry prominent notices stating that it is
|
|
||||||
> released under this License and any conditions added under section
|
|
||||||
> 7. This requirement modifies the requirement in section 4 to
|
|
||||||
> "keep intact all notices".
|
|
||||||
>
|
|
||||||
> c) You must license the entire work, as a whole, under this
|
|
||||||
> License to anyone who comes into possession of a copy. This
|
|
||||||
> License will therefore apply, along with any applicable section 7
|
|
||||||
> additional terms, to the whole of the work, and all its parts,
|
|
||||||
> regardless of how they are packaged. This License gives no
|
|
||||||
> permission to license the work in any other way, but it does not
|
|
||||||
> invalidate such permission if you have separately received it.
|
|
||||||
>
|
|
||||||
> d) If the work has interactive user interfaces, each must display
|
|
||||||
> Appropriate Legal Notices; however, if the Program has interactive
|
|
||||||
> interfaces that do not display Appropriate Legal Notices, your
|
|
||||||
> work need not make them do so.
|
|
||||||
>
|
|
||||||
> A compilation of a covered work with other separate and independent
|
|
||||||
> works, which are not by their nature extensions of the covered work,
|
|
||||||
> and which are not combined with it such as to form a larger program,
|
|
||||||
> in or on a volume of a storage or distribution medium, is called an
|
|
||||||
> "aggregate" if the compilation and its resulting copyright are not
|
|
||||||
> used to limit the access or legal rights of the compilation's users
|
|
||||||
> beyond what the individual works permit. Inclusion of a covered work
|
|
||||||
> in an aggregate does not cause this License to apply to the other
|
|
||||||
> parts of the aggregate.
|
|
||||||
>
|
|
||||||
> 6. Conveying Non-Source Forms.
|
|
||||||
>
|
|
||||||
> You may convey a covered work in object code form under the terms
|
|
||||||
> of sections 4 and 5, provided that you also convey the
|
|
||||||
> machine-readable Corresponding Source under the terms of this License,
|
|
||||||
> in one of these ways:
|
|
||||||
>
|
|
||||||
> a) Convey the object code in, or embodied in, a physical product
|
|
||||||
> (including a physical distribution medium), accompanied by the
|
|
||||||
> Corresponding Source fixed on a durable physical medium
|
|
||||||
> customarily used for software interchange.
|
|
||||||
>
|
|
||||||
> b) Convey the object code in, or embodied in, a physical product
|
|
||||||
> (including a physical distribution medium), accompanied by a
|
|
||||||
> written offer, valid for at least three years and valid for as
|
|
||||||
> long as you offer spare parts or customer support for that product
|
|
||||||
> model, to give anyone who possesses the object code either (1) a
|
|
||||||
> copy of the Corresponding Source for all the software in the
|
|
||||||
> product that is covered by this License, on a durable physical
|
|
||||||
> medium customarily used for software interchange, for a price no
|
|
||||||
> more than your reasonable cost of physically performing this
|
|
||||||
> conveying of source, or (2) access to copy the
|
|
||||||
> Corresponding Source from a network server at no charge.
|
|
||||||
>
|
|
||||||
> c) Convey individual copies of the object code with a copy of the
|
|
||||||
> written offer to provide the Corresponding Source. This
|
|
||||||
> alternative is allowed only occasionally and noncommercially, and
|
|
||||||
> only if you received the object code with such an offer, in accord
|
|
||||||
> with subsection 6b.
|
|
||||||
>
|
|
||||||
> d) Convey the object code by offering access from a designated
|
|
||||||
> place (gratis or for a charge), and offer equivalent access to the
|
|
||||||
> Corresponding Source in the same way through the same place at no
|
|
||||||
> further charge. You need not require recipients to copy the
|
|
||||||
> Corresponding Source along with the object code. If the place to
|
|
||||||
> copy the object code is a network server, the Corresponding Source
|
|
||||||
> may be on a different server (operated by you or a third party)
|
|
||||||
> that supports equivalent copying facilities, provided you maintain
|
|
||||||
> clear directions next to the object code saying where to find the
|
|
||||||
> Corresponding Source. Regardless of what server hosts the
|
|
||||||
> Corresponding Source, you remain obligated to ensure that it is
|
|
||||||
> available for as long as needed to satisfy these requirements.
|
|
||||||
>
|
|
||||||
> e) Convey the object code using peer-to-peer transmission, provided
|
|
||||||
> you inform other peers where the object code and Corresponding
|
|
||||||
> Source of the work are being offered to the general public at no
|
|
||||||
> charge under subsection 6d.
|
|
||||||
>
|
|
||||||
> A separable portion of the object code, whose source code is excluded
|
|
||||||
> from the Corresponding Source as a System Library, need not be
|
|
||||||
> included in conveying the object code work.
|
|
||||||
>
|
|
||||||
> A "User Product" is either (1) a "consumer product", which means any
|
|
||||||
> tangible personal property which is normally used for personal, family,
|
|
||||||
> or household purposes, or (2) anything designed or sold for incorporation
|
|
||||||
> into a dwelling. In determining whether a product is a consumer product,
|
|
||||||
> doubtful cases shall be resolved in favor of coverage. For a particular
|
|
||||||
> product received by a particular user, "normally used" refers to a
|
|
||||||
> typical or common use of that class of product, regardless of the status
|
|
||||||
> of the particular user or of the way in which the particular user
|
|
||||||
> actually uses, or expects or is expected to use, the product. A product
|
|
||||||
> is a consumer product regardless of whether the product has substantial
|
|
||||||
> commercial, industrial or non-consumer uses, unless such uses represent
|
|
||||||
> the only significant mode of use of the product.
|
|
||||||
>
|
|
||||||
> "Installation Information" for a User Product means any methods,
|
|
||||||
> procedures, authorization keys, or other information required to install
|
|
||||||
> and execute modified versions of a covered work in that User Product from
|
|
||||||
> a modified version of its Corresponding Source. The information must
|
|
||||||
> suffice to ensure that the continued functioning of the modified object
|
|
||||||
> code is in no case prevented or interfered with solely because
|
|
||||||
> modification has been made.
|
|
||||||
>
|
|
||||||
> If you convey an object code work under this section in, or with, or
|
|
||||||
> specifically for use in, a User Product, and the conveying occurs as
|
|
||||||
> part of a transaction in which the right of possession and use of the
|
|
||||||
> User Product is transferred to the recipient in perpetuity or for a
|
|
||||||
> fixed term (regardless of how the transaction is characterized), the
|
|
||||||
> Corresponding Source conveyed under this section must be accompanied
|
|
||||||
> by the Installation Information. But this requirement does not apply
|
|
||||||
> if neither you nor any third party retains the ability to install
|
|
||||||
> modified object code on the User Product (for example, the work has
|
|
||||||
> been installed in ROM).
|
|
||||||
>
|
|
||||||
> The requirement to provide Installation Information does not include a
|
|
||||||
> requirement to continue to provide support service, warranty, or updates
|
|
||||||
> for a work that has been modified or installed by the recipient, or for
|
|
||||||
> the User Product in which it has been modified or installed. Access to a
|
|
||||||
> network may be denied when the modification itself materially and
|
|
||||||
> adversely affects the operation of the network or violates the rules and
|
|
||||||
> protocols for communication across the network.
|
|
||||||
>
|
|
||||||
> Corresponding Source conveyed, and Installation Information provided,
|
|
||||||
> in accord with this section must be in a format that is publicly
|
|
||||||
> documented (and with an implementation available to the public in
|
|
||||||
> source code form), and must require no special password or key for
|
|
||||||
> unpacking, reading or copying.
|
|
||||||
>
|
|
||||||
> 7. Additional Terms.
|
|
||||||
>
|
|
||||||
> "Additional permissions" are terms that supplement the terms of this
|
|
||||||
> License by making exceptions from one or more of its conditions.
|
|
||||||
> Additional permissions that are applicable to the entire Program shall
|
|
||||||
> be treated as though they were included in this License, to the extent
|
|
||||||
> that they are valid under applicable law. If additional permissions
|
|
||||||
> apply only to part of the Program, that part may be used separately
|
|
||||||
> under those permissions, but the entire Program remains governed by
|
|
||||||
> this License without regard to the additional permissions.
|
|
||||||
>
|
|
||||||
> When you convey a copy of a covered work, you may at your option
|
|
||||||
> remove any additional permissions from that copy, or from any part of
|
|
||||||
> it. (Additional permissions may be written to require their own
|
|
||||||
> removal in certain cases when you modify the work.) You may place
|
|
||||||
> additional permissions on material, added by you to a covered work,
|
|
||||||
> for which you have or can give appropriate copyright permission.
|
|
||||||
>
|
|
||||||
> Notwithstanding any other provision of this License, for material you
|
|
||||||
> add to a covered work, you may (if authorized by the copyright holders of
|
|
||||||
> that material) supplement the terms of this License with terms:
|
|
||||||
>
|
|
||||||
> a) Disclaiming warranty or limiting liability differently from the
|
|
||||||
> terms of sections 15 and 16 of this License; or
|
|
||||||
>
|
|
||||||
> b) Requiring preservation of specified reasonable legal notices or
|
|
||||||
> author attributions in that material or in the Appropriate Legal
|
|
||||||
> Notices displayed by works containing it; or
|
|
||||||
>
|
|
||||||
> c) Prohibiting misrepresentation of the origin of that material, or
|
|
||||||
> requiring that modified versions of such material be marked in
|
|
||||||
> reasonable ways as different from the original version; or
|
|
||||||
>
|
|
||||||
> d) Limiting the use for publicity purposes of names of licensors or
|
|
||||||
> authors of the material; or
|
|
||||||
>
|
|
||||||
> e) Declining to grant rights under trademark law for use of some
|
|
||||||
> trade names, trademarks, or service marks; or
|
|
||||||
>
|
|
||||||
> f) Requiring indemnification of licensors and authors of that
|
|
||||||
> material by anyone who conveys the material (or modified versions of
|
|
||||||
> it) with contractual assumptions of liability to the recipient, for
|
|
||||||
> any liability that these contractual assumptions directly impose on
|
|
||||||
> those licensors and authors.
|
|
||||||
>
|
|
||||||
> All other non-permissive additional terms are considered "further
|
|
||||||
> restrictions" within the meaning of section 10. If the Program as you
|
|
||||||
> received it, or any part of it, contains a notice stating that it is
|
|
||||||
> governed by this License along with a term that is a further
|
|
||||||
> restriction, you may remove that term. If a license document contains
|
|
||||||
> a further restriction but permits relicensing or conveying under this
|
|
||||||
> License, you may add to a covered work material governed by the terms
|
|
||||||
> of that license document, provided that the further restriction does
|
|
||||||
> not survive such relicensing or conveying.
|
|
||||||
>
|
|
||||||
> If you add terms to a covered work in accord with this section, you
|
|
||||||
> must place, in the relevant source files, a statement of the
|
|
||||||
> additional terms that apply to those files, or a notice indicating
|
|
||||||
> where to find the applicable terms.
|
|
||||||
>
|
|
||||||
> Additional terms, permissive or non-permissive, may be stated in the
|
|
||||||
> form of a separately written license, or stated as exceptions;
|
|
||||||
> the above requirements apply either way.
|
|
||||||
>
|
|
||||||
> 8. Termination.
|
|
||||||
>
|
|
||||||
> You may not propagate or modify a covered work except as expressly
|
|
||||||
> provided under this License. Any attempt otherwise to propagate or
|
|
||||||
> modify it is void, and will automatically terminate your rights under
|
|
||||||
> this License (including any patent licenses granted under the third
|
|
||||||
> paragraph of section 11).
|
|
||||||
>
|
|
||||||
> However, if you cease all violation of this License, then your
|
|
||||||
> license from a particular copyright holder is reinstated (a)
|
|
||||||
> provisionally, unless and until the copyright holder explicitly and
|
|
||||||
> finally terminates your license, and (b) permanently, if the copyright
|
|
||||||
> holder fails to notify you of the violation by some reasonable means
|
|
||||||
> prior to 60 days after the cessation.
|
|
||||||
>
|
|
||||||
> Moreover, your license from a particular copyright holder is
|
|
||||||
> reinstated permanently if the copyright holder notifies you of the
|
|
||||||
> violation by some reasonable means, this is the first time you have
|
|
||||||
> received notice of violation of this License (for any work) from that
|
|
||||||
> copyright holder, and you cure the violation prior to 30 days after
|
|
||||||
> your receipt of the notice.
|
|
||||||
>
|
|
||||||
> Termination of your rights under this section does not terminate the
|
|
||||||
> licenses of parties who have received copies or rights from you under
|
|
||||||
> this License. If your rights have been terminated and not permanently
|
|
||||||
> reinstated, you do not qualify to receive new licenses for the same
|
|
||||||
> material under section 10.
|
|
||||||
>
|
|
||||||
> 9. Acceptance Not Required for Having Copies.
|
|
||||||
>
|
|
||||||
> You are not required to accept this License in order to receive or
|
|
||||||
> run a copy of the Program. Ancillary propagation of a covered work
|
|
||||||
> occurring solely as a consequence of using peer-to-peer transmission
|
|
||||||
> to receive a copy likewise does not require acceptance. However,
|
|
||||||
> nothing other than this License grants you permission to propagate or
|
|
||||||
> modify any covered work. These actions infringe copyright if you do
|
|
||||||
> not accept this License. Therefore, by modifying or propagating a
|
|
||||||
> covered work, you indicate your acceptance of this License to do so.
|
|
||||||
>
|
|
||||||
> 10. Automatic Licensing of Downstream Recipients.
|
|
||||||
>
|
|
||||||
> Each time you convey a covered work, the recipient automatically
|
|
||||||
> receives a license from the original licensors, to run, modify and
|
|
||||||
> propagate that work, subject to this License. You are not responsible
|
|
||||||
> for enforcing compliance by third parties with this License.
|
|
||||||
>
|
|
||||||
> An "entity transaction" is a transaction transferring control of an
|
|
||||||
> organization, or substantially all assets of one, or subdividing an
|
|
||||||
> organization, or merging organizations. If propagation of a covered
|
|
||||||
> work results from an entity transaction, each party to that
|
|
||||||
> transaction who receives a copy of the work also receives whatever
|
|
||||||
> licenses to the work the party's predecessor in interest had or could
|
|
||||||
> give under the previous paragraph, plus a right to possession of the
|
|
||||||
> Corresponding Source of the work from the predecessor in interest, if
|
|
||||||
> the predecessor has it or can get it with reasonable efforts.
|
|
||||||
>
|
|
||||||
> You may not impose any further restrictions on the exercise of the
|
|
||||||
> rights granted or affirmed under this License. For example, you may
|
|
||||||
> not impose a license fee, royalty, or other charge for exercise of
|
|
||||||
> rights granted under this License, and you may not initiate litigation
|
|
||||||
> (including a cross-claim or counterclaim in a lawsuit) alleging that
|
|
||||||
> any patent claim is infringed by making, using, selling, offering for
|
|
||||||
> sale, or importing the Program or any portion of it.
|
|
||||||
>
|
|
||||||
> 11. Patents.
|
|
||||||
>
|
|
||||||
> A "contributor" is a copyright holder who authorizes use under this
|
|
||||||
> License of the Program or a work on which the Program is based. The
|
|
||||||
> work thus licensed is called the contributor's "contributor version".
|
|
||||||
>
|
|
||||||
> A contributor's "essential patent claims" are all patent claims
|
|
||||||
> owned or controlled by the contributor, whether already acquired or
|
|
||||||
> hereafter acquired, that would be infringed by some manner, permitted
|
|
||||||
> by this License, of making, using, or selling its contributor version,
|
|
||||||
> but do not include claims that would be infringed only as a
|
|
||||||
> consequence of further modification of the contributor version. For
|
|
||||||
> purposes of this definition, "control" includes the right to grant
|
|
||||||
> patent sublicenses in a manner consistent with the requirements of
|
|
||||||
> this License.
|
|
||||||
>
|
|
||||||
> Each contributor grants you a non-exclusive, worldwide, royalty-free
|
|
||||||
> patent license under the contributor's essential patent claims, to
|
|
||||||
> make, use, sell, offer for sale, import and otherwise run, modify and
|
|
||||||
> propagate the contents of its contributor version.
|
|
||||||
>
|
|
||||||
> In the following three paragraphs, a "patent license" is any express
|
|
||||||
> agreement or commitment, however denominated, not to enforce a patent
|
|
||||||
> (such as an express permission to practice a patent or covenant not to
|
|
||||||
> sue for patent infringement). To "grant" such a patent license to a
|
|
||||||
> party means to make such an agreement or commitment not to enforce a
|
|
||||||
> patent against the party.
|
|
||||||
>
|
|
||||||
> If you convey a covered work, knowingly relying on a patent license,
|
|
||||||
> and the Corresponding Source of the work is not available for anyone
|
|
||||||
> to copy, free of charge and under the terms of this License, through a
|
|
||||||
> publicly available network server or other readily accessible means,
|
|
||||||
> then you must either (1) cause the Corresponding Source to be so
|
|
||||||
> available, or (2) arrange to deprive yourself of the benefit of the
|
|
||||||
> patent license for this particular work, or (3) arrange, in a manner
|
|
||||||
> consistent with the requirements of this License, to extend the patent
|
|
||||||
> license to downstream recipients. "Knowingly relying" means you have
|
|
||||||
> actual knowledge that, but for the patent license, your conveying the
|
|
||||||
> covered work in a country, or your recipient's use of the covered work
|
|
||||||
> in a country, would infringe one or more identifiable patents in that
|
|
||||||
> country that you have reason to believe are valid.
|
|
||||||
>
|
|
||||||
> If, pursuant to or in connection with a single transaction or
|
|
||||||
> arrangement, you convey, or propagate by procuring conveyance of, a
|
|
||||||
> covered work, and grant a patent license to some of the parties
|
|
||||||
> receiving the covered work authorizing them to use, propagate, modify
|
|
||||||
> or convey a specific copy of the covered work, then the patent license
|
|
||||||
> you grant is automatically extended to all recipients of the covered
|
|
||||||
> work and works based on it.
|
|
||||||
>
|
|
||||||
> A patent license is "discriminatory" if it does not include within
|
|
||||||
> the scope of its coverage, prohibits the exercise of, or is
|
|
||||||
> conditioned on the non-exercise of one or more of the rights that are
|
|
||||||
> specifically granted under this License. You may not convey a covered
|
|
||||||
> work if you are a party to an arrangement with a third party that is
|
|
||||||
> in the business of distributing software, under which you make payment
|
|
||||||
> to the third party based on the extent of your activity of conveying
|
|
||||||
> the work, and under which the third party grants, to any of the
|
|
||||||
> parties who would receive the covered work from you, a discriminatory
|
|
||||||
> patent license (a) in connection with copies of the covered work
|
|
||||||
> conveyed by you (or copies made from those copies), or (b) primarily
|
|
||||||
> for and in connection with specific products or compilations that
|
|
||||||
> contain the covered work, unless you entered into that arrangement,
|
|
||||||
> or that patent license was granted, prior to 28 March 2007.
|
|
||||||
>
|
|
||||||
> Nothing in this License shall be construed as excluding or limiting
|
|
||||||
> any implied license or other defenses to infringement that may
|
|
||||||
> otherwise be available to you under applicable patent law.
|
|
||||||
>
|
|
||||||
> 12. No Surrender of Others' Freedom.
|
|
||||||
>
|
|
||||||
> If conditions are imposed on you (whether by court order, agreement or
|
|
||||||
> otherwise) that contradict the conditions of this License, they do not
|
|
||||||
> excuse you from the conditions of this License. If you cannot convey a
|
|
||||||
> covered work so as to satisfy simultaneously your obligations under this
|
|
||||||
> License and any other pertinent obligations, then as a consequence you may
|
|
||||||
> not convey it at all. For example, if you agree to terms that obligate you
|
|
||||||
> to collect a royalty for further conveying from those to whom you convey
|
|
||||||
> the Program, the only way you could satisfy both those terms and this
|
|
||||||
> License would be to refrain entirely from conveying the Program.
|
|
||||||
>
|
|
||||||
> 13. Use with the GNU Affero General Public License.
|
|
||||||
>
|
|
||||||
> Notwithstanding any other provision of this License, you have
|
|
||||||
> permission to link or combine any covered work with a work licensed
|
|
||||||
> under version 3 of the GNU Affero General Public License into a single
|
|
||||||
> combined work, and to convey the resulting work. The terms of this
|
|
||||||
> License will continue to apply to the part which is the covered work,
|
|
||||||
> but the special requirements of the GNU Affero General Public License,
|
|
||||||
> section 13, concerning interaction through a network will apply to the
|
|
||||||
> combination as such.
|
|
||||||
>
|
|
||||||
> 14. Revised Versions of this License.
|
|
||||||
>
|
|
||||||
> The Free Software Foundation may publish revised and/or new versions of
|
|
||||||
> the GNU General Public License from time to time. Such new versions will
|
|
||||||
> be similar in spirit to the present version, but may differ in detail to
|
|
||||||
> address new problems or concerns.
|
|
||||||
>
|
|
||||||
> Each version is given a distinguishing version number. If the
|
|
||||||
> Program specifies that a certain numbered version of the GNU General
|
|
||||||
> Public License "or any later version" applies to it, you have the
|
|
||||||
> option of following the terms and conditions either of that numbered
|
|
||||||
> version or of any later version published by the Free Software
|
|
||||||
> Foundation. If the Program does not specify a version number of the
|
|
||||||
> GNU General Public License, you may choose any version ever published
|
|
||||||
> by the Free Software Foundation.
|
|
||||||
>
|
|
||||||
> If the Program specifies that a proxy can decide which future
|
|
||||||
> versions of the GNU General Public License can be used, that proxy's
|
|
||||||
> public statement of acceptance of a version permanently authorizes you
|
|
||||||
> to choose that version for the Program.
|
|
||||||
>
|
|
||||||
> Later license versions may give you additional or different
|
|
||||||
> permissions. However, no additional obligations are imposed on any
|
|
||||||
> author or copyright holder as a result of your choosing to follow a
|
|
||||||
> later version.
|
|
||||||
>
|
|
||||||
> 15. Disclaimer of Warranty.
|
|
||||||
>
|
|
||||||
> THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
|
|
||||||
> APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
|
|
||||||
> HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
|
|
||||||
> OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
|
|
||||||
> THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
||||||
> PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
|
|
||||||
> IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
|
|
||||||
> ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
|
|
||||||
>
|
|
||||||
> 16. Limitation of Liability.
|
|
||||||
>
|
|
||||||
> IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
|
||||||
> WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
|
|
||||||
> THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
|
|
||||||
> GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
|
|
||||||
> USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
|
|
||||||
> DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
|
|
||||||
> PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
|
|
||||||
> EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
|
|
||||||
> SUCH DAMAGES.
|
|
||||||
>
|
|
||||||
> 17. Interpretation of Sections 15 and 16.
|
|
||||||
>
|
|
||||||
> If the disclaimer of warranty and limitation of liability provided
|
|
||||||
> above cannot be given local legal effect according to their terms,
|
|
||||||
> reviewing courts shall apply local law that most closely approximates
|
|
||||||
> an absolute waiver of all civil liability in connection with the
|
|
||||||
> Program, unless a warranty or assumption of liability accompanies a
|
|
||||||
> copy of the Program in return for a fee.
|
|
||||||
>
|
|
||||||
> END OF TERMS AND CONDITIONS
|
|
||||||
>
|
|
||||||
143
README.md
143
README.md
@ -1,143 +0,0 @@
|
|||||||
# DEPRECATED!
|
|
||||||
|
|
||||||
This repository has not been updated for a while!
|
|
||||||
If You are interested in replicating results for [1712.07167](https://arxiv.org/abs/1712.07167) please check [these instruction](https://kalmar.faculty.wmi.amu.edu.pl/post/1712.07176/)
|
|
||||||
Also [this notebook](https://nbviewer.jupyter.org/gist/kalmarek/03510181bc1e7c98615e86e1ec580b2a) could be of some help. If everything else fails the [zenodo dataset](https://zenodo.org/record/1133440) should contain the last-resort instructions.
|
|
||||||
|
|
||||||
This repository contains some legacy code for computations in [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680).
|
|
||||||
|
|
||||||
# Installing
|
|
||||||
To run the code You need `julia-v0.5` (should work on `v0.6`, but with warnings).
|
|
||||||
You also need to install julia packages: `Nemo-v0.6.3`, `ArgParse`. To do so in `julia`'s REPL run:
|
|
||||||
```julia
|
|
||||||
Pkg.update()
|
|
||||||
Pkg.add("Nemo")
|
|
||||||
Pkg.add("ArgParse")
|
|
||||||
```
|
|
||||||
Then clone the main repository of `Groups.jl`, `GroupRings.jl` and `PropertyT.jl`:
|
|
||||||
```julia
|
|
||||||
Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/Groups.jl.git")
|
|
||||||
Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/GroupRings.jl.git")
|
|
||||||
Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/PropertyT.jl.git")
|
|
||||||
Pkg.resolve()
|
|
||||||
```
|
|
||||||
This should resolve all dependencies (e.g. install `JuMP`, `SCS`, `IntervalArithmetic`, `JLD`, `Memento`). Exit julia and finally clone this repository:
|
|
||||||
```shell
|
|
||||||
git clone https://git.wmi.amu.edu.pl/kalmar/GroupsWithPropertyT.git
|
|
||||||
cd GroupswithPropertyT
|
|
||||||
```
|
|
||||||
|
|
||||||
# Running
|
|
||||||
|
|
||||||
## Naive implementation
|
|
||||||
|
|
||||||
To check that $\Delta^2-\lambda\Delta$ is not decomposable to a sum of hermitian squares of elements in the ball of radius $2$ in $SL(2,7)$ run
|
|
||||||
```shell
|
|
||||||
julia SL.jl -N 2 -p 7 --radius 2 --iterations 100000
|
|
||||||
```
|
|
||||||
(~30 seconds, depending on hardware). The monotonous decreasing $\lambda$ during the optimisation is in column `pri obj` (or `dua obj`) of `solver.log`.
|
|
||||||
|
|
||||||
Compare this to
|
|
||||||
```shell
|
|
||||||
julia SL.jl -N 2 -p 7 --radius 3 --iterations 100000
|
|
||||||
```
|
|
||||||
which finds $\lambda \geq 0.5857$ and decomposes $\Delta^2-\lambda\Delta$ into sum of $47$ hermitian squares in less than 20 seconds (including certification).
|
|
||||||
|
|
||||||
If You see in the output (or in `full.log`) that the upper end of the interval where $\lVert\Delta^2 - \lambda\Delta - \sum{\xi_i}^*\xi_i\rVert_1$ belongs to is too large (resulting in positive `Floating point distance`, but negative `The Augmentation-projected actual distance`), decrease the `--tol` parameter, e.g.
|
|
||||||
```
|
|
||||||
julia SL.jl -N 2 -p 7 --radius 3 --iterations 100000 --tol 1e-9
|
|
||||||
```
|
|
||||||
to achieve a better estimate (the residuals $\ell_1$-norm should be around $\|B_d(e))\|\cdot tol$)
|
|
||||||
|
|
||||||
## Symmetrization enhanced implementation
|
|
||||||
|
|
||||||
A newer version of the software uses orbit and Wedderburn decomposition to effecitively find a (much) smaller optimisation problem to compute the spectral gap $\lambda$. In particular the solution to the original (naive) optimisation problem can be reconstructed from the solution of the symmetrised one.
|
|
||||||
|
|
||||||
E.g. Run
|
|
||||||
```shell
|
|
||||||
julia SL_orbit.jl -N 4 --radius 2 --upper-bound 1.3
|
|
||||||
```
|
|
||||||
to find (and certify) the spectral gap for $SL(4, \mathbb{Z})$ is at least `1.2999...` in just under $2$ minutes time (for comparison this result requires over `5` hours in the old implementation on the same hardware).
|
|
||||||
|
|
||||||
To replicate the results of _$\operatorname{Aut}(\textbf{F}_5)$ has property (T)_ You neet to run (on a `4`-core CPU)
|
|
||||||
```shell
|
|
||||||
julia ../AutFN_orbit.jl -N 5 --upper-bound 1.2 --iterations 24000000 --cpus 4
|
|
||||||
```
|
|
||||||
|
|
||||||
Note that this computation took more than `12` days and required at least `32`GB of ram (and possible more).
|
|
||||||
|
|
||||||
# Help
|
|
||||||
|
|
||||||
```shell
|
|
||||||
julia SL.jl --help
|
|
||||||
usage: SL.jl [--tol TOL] [--iterations ITERATIONS]
|
|
||||||
[--upper-bound UPPER-BOUND] [--cpus CPUS] [-N N] [-p P]
|
|
||||||
[--radius RADIUS] [-h]
|
|
||||||
|
|
||||||
optional arguments:
|
|
||||||
--tol TOL set numerical tolerance for the SDP solver
|
|
||||||
(type: Float64, default: 1.0e-6)
|
|
||||||
--iterations ITERATIONS
|
|
||||||
set maximal number of iterations for the SDP
|
|
||||||
solver (default: 20000) (type: Int64, default:
|
|
||||||
50000)
|
|
||||||
--upper-bound UPPER-BOUND
|
|
||||||
Set an upper bound for the spectral gap (type:
|
|
||||||
Float64, default: Inf)
|
|
||||||
--cpus CPUS Set number of cpus used by solver (type:
|
|
||||||
Int64)
|
|
||||||
-N N Consider elementary matrices EL(N) (type:
|
|
||||||
Int64, default: 2)
|
|
||||||
-p P Matrices over field of p-elements (p=0 => over
|
|
||||||
ZZ) (type: Int64, default: 0)
|
|
||||||
--radius RADIUS Radius of ball B_r(e,S) to find solution over
|
|
||||||
(type: Int64, default: 2)
|
|
||||||
-h, --help show this help message and exit
|
|
||||||
```
|
|
||||||
|
|
||||||
# Specific version of [1703.09680](https://arxiv.org/abs/1703.09680)
|
|
||||||
|
|
||||||
To checkout the specific versions of packages used for [Certifying Numerical Estimates of Spectral Gaps](https://arxiv.org/abs/1703.09680) run (inside the cloned `GroupswithPropertyT`)
|
|
||||||
```shell
|
|
||||||
git checkout 1703.09680v1
|
|
||||||
```
|
|
||||||
|
|
||||||
Unfortunately: You need to link `~/.julia/v0.5/GroupRings` to `~/.julia/v0.5/GroupAlgebras` due to change in the name of the package. Then run in `julia`
|
|
||||||
```julia
|
|
||||||
Pkg.checkout("GroupRings", "1703.09680v1")
|
|
||||||
Pkg.checkout("PropertyT", "1703.09680v1")
|
|
||||||
Pkg.resolve()
|
|
||||||
```
|
|
||||||
|
|
||||||
# Specific version of [1712.07167](https://arxiv.org/abs/1712.07167)
|
|
||||||
|
|
||||||
You need to run `julia-0.6`.
|
|
||||||
|
|
||||||
Clone `https://git.wmi.amu.edu.pl/kalmar/GroupsWithPropertyT` and checkout the `1712.07167` branch:
|
|
||||||
```
|
|
||||||
git clone https://git.wmi.amu.edu.pl/kalmar/GroupsWithPropertyT.git
|
|
||||||
cd ./GroupsWithPropertyT
|
|
||||||
git checkout 1712.07167
|
|
||||||
```
|
|
||||||
|
|
||||||
In `julia`s REPL execute
|
|
||||||
```julia
|
|
||||||
Pkg.add("ArgParse")
|
|
||||||
Pkg.add("Nemo")
|
|
||||||
Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/Groups.jl.git")
|
|
||||||
Pkg.checkout("Groups", "1712.07167")
|
|
||||||
Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/GroupRings.jl.git")
|
|
||||||
Pkg.checkout("GroupRings", "1712.07167")
|
|
||||||
Pkg.clone("https://git.wmi.amu.edu.pl/kalmar/PropertyT.jl.git")
|
|
||||||
Pkg.checkout("PropertyT", "1712.07167")
|
|
||||||
Pkg.checkout("SCS")
|
|
||||||
Pkg.build("SCS")
|
|
||||||
```
|
|
||||||
|
|
||||||
This should resolve all the dependencies. Quit `julia` and place the `oSAutF5_r2` folder downloaded from [here](https://cloud.impan.pl/s/fGIpxvxdTYYkUxK) inside `GroupsWithPropertyT` folder. To verify the decomposition of $\Delta^2 - \lambda \Delta$ for the group run (if You have a `4`-core CPU at Your disposal)
|
|
||||||
```julia
|
|
||||||
julia AutFN_orbit.jl -N 5 --upper-bound=1.2 --cpus 4
|
|
||||||
```
|
|
||||||
If You want to generate `pm` and other files on Your own delete everything from the `oSAutF5_r2` folder but `1.2` folder and its contents and run the same command again.
|
|
||||||
|
|
||||||
Note: You need at least `32`GB of RAM and spare `24`h of Your CPU.
|
|
||||||
217
SL.jl
Normal file
217
SL.jl
Normal file
@ -0,0 +1,217 @@
|
|||||||
|
using ArgParse
|
||||||
|
using GroupAlgebras
|
||||||
|
using PropertyT
|
||||||
|
|
||||||
|
using Mods
|
||||||
|
import Primes: isprime
|
||||||
|
|
||||||
|
import SCS.SCSSolver
|
||||||
|
|
||||||
|
function SL_generatingset(n::Int)
|
||||||
|
|
||||||
|
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||||
|
|
||||||
|
S = [E(i,j,N=n) for (i,j) in indexing];
|
||||||
|
S = vcat(S, [convert(Array{Int,2},x') for x in S]);
|
||||||
|
S = vcat(S, [convert(Array{Int,2},inv(x)) for x in S]);
|
||||||
|
return unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
function E(i::Int, j::Int; val=1, N::Int=3, mod=Inf)
|
||||||
|
@assert i≠j
|
||||||
|
m = eye(Int, N)
|
||||||
|
m[i,j] = val
|
||||||
|
if mod == Inf
|
||||||
|
return m
|
||||||
|
else
|
||||||
|
return [Mod(x,mod) for x in m]
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function cofactor(i,j,M)
|
||||||
|
z1 = ones(Bool,size(M,1))
|
||||||
|
z1[i] = false
|
||||||
|
|
||||||
|
z2 = ones(Bool,size(M,2))
|
||||||
|
z2[j] = false
|
||||||
|
|
||||||
|
return M[z1,z2]
|
||||||
|
end
|
||||||
|
|
||||||
|
import Base.LinAlg.det
|
||||||
|
|
||||||
|
function det(M::Array{Mod,2})
|
||||||
|
if size(M,1) ≠ size(M,2)
|
||||||
|
d = Mod(0,M[1,1].mod)
|
||||||
|
elseif size(M,1) == 2
|
||||||
|
d = M[1,1]*M[2,2] - M[1,2]*M[2,1]
|
||||||
|
else
|
||||||
|
d = zero(eltype(M))
|
||||||
|
for i in 1:size(M,1)
|
||||||
|
d += (-1)^(i+1)*M[i,1]*det(cofactor(i,1,M))
|
||||||
|
end
|
||||||
|
end
|
||||||
|
# @show (M, d)
|
||||||
|
return d
|
||||||
|
end
|
||||||
|
|
||||||
|
function adjugate(M)
|
||||||
|
K = similar(M)
|
||||||
|
for i in 1:size(M,1), j in 1:size(M,2)
|
||||||
|
K[j,i] = (-1)^(i+j)*det(cofactor(i,j,M))
|
||||||
|
end
|
||||||
|
return K
|
||||||
|
end
|
||||||
|
|
||||||
|
import Base: inv, one, zero, *
|
||||||
|
|
||||||
|
one(::Type{Mod}) = 1
|
||||||
|
zero(::Type{Mod}) = 0
|
||||||
|
zero(x::Mod) = Mod(x.mod)
|
||||||
|
|
||||||
|
function inv(M::Array{Mod,2})
|
||||||
|
d = det(M)
|
||||||
|
d ≠ 0*d || thow(ArgumentError("Matrix is not invertible!"))
|
||||||
|
return inv(det(M))*adjugate(M)
|
||||||
|
return adjugate(M)
|
||||||
|
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!"))
|
||||||
|
isprime(p) || throw(ArgumentError("p should be a prime number!"))
|
||||||
|
|
||||||
|
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||||
|
S = [E(i,j, N=n, mod=p) for (i,j) in indexing]
|
||||||
|
S = vcat(S, [inv(s) for s in S])
|
||||||
|
S = vcat(S, [permutedims(x, [2,1]) for x in S]);
|
||||||
|
return unique(S)
|
||||||
|
end
|
||||||
|
|
||||||
|
function products{T}(U::AbstractVector{T}, V::AbstractVector{T})
|
||||||
|
result = Vector{T}()
|
||||||
|
for u in U
|
||||||
|
for v in V
|
||||||
|
push!(result, u*v)
|
||||||
|
end
|
||||||
|
end
|
||||||
|
return unique(result)
|
||||||
|
end
|
||||||
|
|
||||||
|
function ΔandSDPconstraints{T<:Number}(identity::Array{T,2}, S::Vector{Array{T,2}})
|
||||||
|
B₁ = vcat([identity], S)
|
||||||
|
B₂ = products(B₁, B₁);
|
||||||
|
B₃ = products(B₁, B₂);
|
||||||
|
B₄ = products(B₁, B₃);
|
||||||
|
@assert B₄[1:length(B₂)] == B₂
|
||||||
|
|
||||||
|
product_matrix = PropertyT.create_product_matrix(B₄,length(B₂));
|
||||||
|
sdp_constraints = PropertyT.constraints_from_pm(product_matrix, length(B₄))
|
||||||
|
L_coeff = PropertyT.splaplacian_coeff(S, B₂, length(B₄));
|
||||||
|
Δ = GroupAlgebraElement(L_coeff, product_matrix)
|
||||||
|
|
||||||
|
return Δ, sdp_constraints
|
||||||
|
end
|
||||||
|
|
||||||
|
ID(n::Int) = eye(Int, n)
|
||||||
|
|
||||||
|
function ID(n::Int, p::Int)
|
||||||
|
p==0 && return ID(n)
|
||||||
|
return [Mod(x,p) for x in eye(Int,N)]
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
#=
|
||||||
|
To use file property(T).jl (specifically: check_property_T function)
|
||||||
|
You need to define:
|
||||||
|
|
||||||
|
function ΔandSDPconstraints(identity, S):: (Δ, sdp_constraints)
|
||||||
|
|
||||||
|
=#
|
||||||
|
|
||||||
|
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()
|
||||||
|
s = ArgParseSettings()
|
||||||
|
|
||||||
|
@add_arg_table s begin
|
||||||
|
"--tol"
|
||||||
|
help = "set numerical tolerance for the SDP solver"
|
||||||
|
arg_type = Float64
|
||||||
|
default = 1e-9
|
||||||
|
"--iterations"
|
||||||
|
help = "set maximal number of iterations for the SDP solver"
|
||||||
|
arg_type = Int
|
||||||
|
default = 100000
|
||||||
|
"--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 matrices of size N"
|
||||||
|
arg_type = Int
|
||||||
|
default = 3
|
||||||
|
"-p"
|
||||||
|
help = "Matrices over filed of p-elements (0 = over ZZ)"
|
||||||
|
arg_type = Int
|
||||||
|
default = 0
|
||||||
|
end
|
||||||
|
|
||||||
|
return parse_args(s)
|
||||||
|
end
|
||||||
|
|
||||||
|
function main()
|
||||||
|
parsed_args = parse_commandline()
|
||||||
|
println("Parsed args:")
|
||||||
|
|
||||||
|
# SL(3,Z)
|
||||||
|
# upper_bound = 0.28-1e-5
|
||||||
|
# tol = 1e-12
|
||||||
|
# iterations = 500000
|
||||||
|
|
||||||
|
# SL(4,Z)
|
||||||
|
# upper_bound = 1.31
|
||||||
|
# tol = 3e-11
|
||||||
|
|
||||||
|
# upper_bound=0.738 # (N,p) = (3,7)
|
||||||
|
|
||||||
|
tol = parsed_args["tol"]
|
||||||
|
iterations = parsed_args["iterations"]
|
||||||
|
|
||||||
|
# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=false)
|
||||||
|
solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true)
|
||||||
|
|
||||||
|
N = parsed_args["N"]
|
||||||
|
upper_bound = parsed_args["upper-bound"]
|
||||||
|
p = parsed_args["p"]
|
||||||
|
if p == 0
|
||||||
|
name = "SL$(N)Z"
|
||||||
|
else
|
||||||
|
name = "SL$(N)_p"
|
||||||
|
end
|
||||||
|
|
||||||
|
S() = SL_generatingset(N, p)
|
||||||
|
|
||||||
|
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
|
||||||
|
@time PropertyT.check_property_T(name, ID(N,p), S, solver, upper_bound, tol)
|
||||||
|
end
|
||||||
|
|
||||||
|
main()
|
||||||
88
SemiDirectProduct.jl
Normal file
88
SemiDirectProduct.jl
Normal file
@ -0,0 +1,88 @@
|
|||||||
|
module SemiDirectProduct
|
||||||
|
|
||||||
|
import Base: convert, show, isequal, ==, size, inv
|
||||||
|
import Base: +, -, *, //
|
||||||
|
|
||||||
|
export SemiDirectProductElement, matrix_repr
|
||||||
|
|
||||||
|
"""
|
||||||
|
Implements elements of a semidirect product of groups H and N, where N is normal in the product. Usually written as H ⋉ N.
|
||||||
|
The multiplication inside semidirect product is defined as
|
||||||
|
(h₁, n₁) ⋅ (h₂, n₂) = (h₁h₂, n₁φ(h₁)(n₂)),
|
||||||
|
where φ:H → Aut(N) is a homomorphism.
|
||||||
|
|
||||||
|
In the case below we implement H = GL(n,K) and N = Kⁿ, the Affine Group (i.e. GL(n,K) ⋉ Kⁿ) where elements of GL(n,K) act on vectors in Kⁿ via matrix multiplication.
|
||||||
|
# Arguments:
|
||||||
|
* `h::Array{T,2}` : square invertible matrix (element of GL(n,K))
|
||||||
|
* `n::Vector{T,1}` : vector in Kⁿ
|
||||||
|
* `φ = φ(h,n) = φ(h)(n)` :2-argument function which defines the action of GL(n,K) on Kⁿ; matrix-vector multiplication by default.
|
||||||
|
"""
|
||||||
|
immutable SemiDirectProductElement{T<:Number}
|
||||||
|
h::Array{T,2}
|
||||||
|
n::Vector{T}
|
||||||
|
φ::Function
|
||||||
|
|
||||||
|
function SemiDirectProductElement(h::Array{T,2},n::Vector{T},φ::Function)
|
||||||
|
# size(h,1) == size(h,2)|| throw(ArgumentError("h has to be square matrix"))
|
||||||
|
det(h) ≠ 0 || throw(ArgumentError("h has to be invertible!"))
|
||||||
|
new(h,n,φ)
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
SemiDirectProductElement{T}(h::Array{T,2}, n::Vector{T}, φ) =
|
||||||
|
SemiDirectProductElement{T}(h,n,φ)
|
||||||
|
|
||||||
|
SemiDirectProductElement{T}(h::Array{T,2}, n::Vector{T}) =
|
||||||
|
SemiDirectProductElement(h,n,*)
|
||||||
|
|
||||||
|
SemiDirectProductElement{T}(h::Array{T,2}) =
|
||||||
|
SemiDirectProductElement(h,zeros(h[:,1]))
|
||||||
|
|
||||||
|
SemiDirectProductElement{T}(n::Vector{T}) =
|
||||||
|
SemiDirectProductElement(eye(eltype(n), n))
|
||||||
|
|
||||||
|
convert{T<:Number}(::Type{T}, X::SemiDirectProductElement) =
|
||||||
|
SemiDirectProductElement(convert(Array{T,2},X.h),
|
||||||
|
convert(Vector{T},X.n),
|
||||||
|
X.φ)
|
||||||
|
|
||||||
|
size(X::SemiDirectProductElement) = (size(X.h), size(X.n))
|
||||||
|
|
||||||
|
matrix_repr{T}(X::SemiDirectProductElement{T}) =
|
||||||
|
[X.h X.n; zeros(T, 1, size(X.h,2)) [1]]
|
||||||
|
|
||||||
|
show{T}(io::IO, X::SemiDirectProductElement{T}) = print(io,
|
||||||
|
"Element of SemiDirectProduct over $T of size $(size(X)):\n",
|
||||||
|
matrix_repr(X))
|
||||||
|
|
||||||
|
function isequal{T}(X::SemiDirectProductElement{T}, Y::SemiDirectProductElement{T})
|
||||||
|
X.h == Y.h || return false
|
||||||
|
X.n == Y.n || return false
|
||||||
|
X.φ == Y.φ || return false
|
||||||
|
return true
|
||||||
|
end
|
||||||
|
|
||||||
|
function isequal{T,S}(X::SemiDirectProductElement{T}, Y::SemiDirectProductElement{S})
|
||||||
|
W = promote_type(T,S)
|
||||||
|
warn("Comparing elements with different coefficients! trying to promoting to $W")
|
||||||
|
X = convert(W, X)
|
||||||
|
Y = convert(W, Y)
|
||||||
|
return isequal(X,Y)
|
||||||
|
end
|
||||||
|
|
||||||
|
(==)(X::SemiDirectProductElement, Y::SemiDirectProductElement) = isequal(X, Y)
|
||||||
|
|
||||||
|
function semidirect_multiplication{T}(X::SemiDirectProductElement{T},
|
||||||
|
Y::SemiDirectProductElement{T})
|
||||||
|
size(X) == size(Y) || throw(ArgumentError("trying to multiply elements from different groups!"))
|
||||||
|
return SemiDirectProductElement(X.h*Y.h, X.n + X.φ(X.h, Y.n))
|
||||||
|
end
|
||||||
|
|
||||||
|
(*){T}(X::SemiDirectProductElement{T}, Y::SemiDirectProductElement{T}) =
|
||||||
|
semidirect_multiplication(X,Y)
|
||||||
|
|
||||||
|
inv{T}(X::SemiDirectProductElement{T}) =
|
||||||
|
SemiDirectProductElement(inv(X.h), X.φ(inv(X.h), -X.n))
|
||||||
|
|
||||||
|
|
||||||
|
end
|
||||||
@ -1,56 +0,0 @@
|
|||||||
module PropertyTGroups
|
|
||||||
|
|
||||||
using PropertyT
|
|
||||||
using AbstractAlgebra
|
|
||||||
using Nemo
|
|
||||||
using Groups
|
|
||||||
using GroupRings
|
|
||||||
|
|
||||||
export PropertyTGroup, SymmetrizedGroup, GAPGroup,
|
|
||||||
SpecialLinearGroup,
|
|
||||||
SpecialAutomorphismGroup,
|
|
||||||
HigmanGroup,
|
|
||||||
CapraceGroup,
|
|
||||||
MappingClassGroup
|
|
||||||
|
|
||||||
export PropertyTGroup
|
|
||||||
|
|
||||||
abstract type PropertyTGroup end
|
|
||||||
|
|
||||||
abstract type SymmetrizedGroup <: PropertyTGroup end
|
|
||||||
|
|
||||||
abstract type GAPGroup <: PropertyTGroup end
|
|
||||||
|
|
||||||
function PropertyTGroup(args)
|
|
||||||
if haskey(args, "SL")
|
|
||||||
G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
elseif haskey(args, "SAut")
|
|
||||||
G = PropertyTGroups.SpecialAutomorphismGroup(args)
|
|
||||||
elseif haskey(args, "MCG")
|
|
||||||
G = PropertyTGroups.MappingClassGroup(args)
|
|
||||||
elseif haskey(args, "Higman")
|
|
||||||
G = PropertyTGroups.HigmanGroup(args)
|
|
||||||
elseif haskey(args, "Caprace")
|
|
||||||
G = PropertyTGroups.CapraceGroup(args)
|
|
||||||
else
|
|
||||||
throw("You must provide one of --SL, --SAut, --MCG, --Higman, --Caprace")
|
|
||||||
end
|
|
||||||
return G
|
|
||||||
end
|
|
||||||
|
|
||||||
include("autfreegroup.jl")
|
|
||||||
include("speciallinear.jl")
|
|
||||||
|
|
||||||
Comm(x,y) = x*y*x^-1*y^-1
|
|
||||||
|
|
||||||
function generatingset(G::GAPGroup)
|
|
||||||
S = gens(group(G))
|
|
||||||
return unique([S; inv.(S)])
|
|
||||||
end
|
|
||||||
|
|
||||||
include("mappingclassgroup.jl")
|
|
||||||
include("higman.jl")
|
|
||||||
include("caprace.jl")
|
|
||||||
include("actions.jl")
|
|
||||||
|
|
||||||
end # of module PropertyTGroups
|
|
||||||
@ -1,92 +0,0 @@
|
|||||||
function (p::perm)(A::GroupRingElem)
|
|
||||||
RG = parent(A)
|
|
||||||
result = zero(RG, eltype(A.coeffs))
|
|
||||||
|
|
||||||
for (idx, c) in enumerate(A.coeffs)
|
|
||||||
if c!= zero(eltype(A.coeffs))
|
|
||||||
result[p(RG.basis[idx])] = c
|
|
||||||
end
|
|
||||||
end
|
|
||||||
return result
|
|
||||||
end
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Action of WreathProductElems on Nemo.MatElem
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function matrix_emb(n::DirectProductGroupElem, p::perm)
|
|
||||||
Id = parent(n.elts[1])()
|
|
||||||
elt = diagm([(-1)^(el == Id ? 0 : 1) for el in n.elts])
|
|
||||||
return elt[:, p.d]
|
|
||||||
end
|
|
||||||
|
|
||||||
function (g::WreathProductElem)(A::MatElem)
|
|
||||||
g_inv = inv(g)
|
|
||||||
G = matrix_emb(g.n, g_inv.p)
|
|
||||||
G_inv = matrix_emb(g_inv.n, g.p)
|
|
||||||
M = parent(A)
|
|
||||||
return M(G)*A*M(G_inv)
|
|
||||||
end
|
|
||||||
|
|
||||||
import Base.*
|
|
||||||
|
|
||||||
doc"""
|
|
||||||
*(x::AbstractAlgebra.MatElem, P::Generic.perm)
|
|
||||||
> Apply the pemutation $P$ to the rows of the matrix $x$ and return the result.
|
|
||||||
"""
|
|
||||||
function *(x::AbstractAlgebra.MatElem, P::Generic.perm)
|
|
||||||
z = similar(x)
|
|
||||||
m = rows(x)
|
|
||||||
n = cols(x)
|
|
||||||
for i = 1:m
|
|
||||||
for j = 1:n
|
|
||||||
z[i, j] = x[i,P[j]]
|
|
||||||
end
|
|
||||||
end
|
|
||||||
return z
|
|
||||||
end
|
|
||||||
|
|
||||||
function (p::perm)(A::MatElem)
|
|
||||||
length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
|
|
||||||
return p*A*inv(p)
|
|
||||||
end
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Action of WreathProductElems on AutGroupElem
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function AutFG_emb(A::AutGroup, g::WreathProductElem)
|
|
||||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
|
||||||
parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
|
|
||||||
elt = A()
|
|
||||||
Id = parent(g.n.elts[1])()
|
|
||||||
flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
|
|
||||||
Groups.r_multiply!(elt, flips, reduced=false)
|
|
||||||
Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
function AutFG_emb(A::AutGroup, p::perm)
|
|
||||||
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
|
|
||||||
parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(p)) into $A")
|
|
||||||
return A(Groups.perm_autsymbol(p))
|
|
||||||
end
|
|
||||||
|
|
||||||
function (g::WreathProductElem)(a::Groups.Automorphism)
|
|
||||||
A = parent(a)
|
|
||||||
g = AutFG_emb(A,g)
|
|
||||||
res = A()
|
|
||||||
Groups.r_multiply!(res, g.symbols, reduced=false)
|
|
||||||
Groups.r_multiply!(res, a.symbols, reduced=false)
|
|
||||||
Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
|
|
||||||
return res
|
|
||||||
end
|
|
||||||
|
|
||||||
function (p::perm)(a::Groups.Automorphism)
|
|
||||||
g = AutFG_emb(parent(a),p)
|
|
||||||
return g*a*inv(g)
|
|
||||||
end
|
|
||||||
@ -1,21 +0,0 @@
|
|||||||
struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
|
|
||||||
group::AutGroup
|
|
||||||
end
|
|
||||||
|
|
||||||
function SpecialAutomorphismGroup(args::Dict)
|
|
||||||
N = args["SAut"]
|
|
||||||
return SpecialAutomorphismGroup{N}(AutGroup(FreeGroup(N), special=true))
|
|
||||||
end
|
|
||||||
|
|
||||||
name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"
|
|
||||||
|
|
||||||
group(G::SpecialAutomorphismGroup) = G.group
|
|
||||||
|
|
||||||
function generatingset(G::SpecialAutomorphismGroup)
|
|
||||||
S = gens(group(G));
|
|
||||||
return unique([S; inv.(S)])
|
|
||||||
end
|
|
||||||
|
|
||||||
function autS(G::SpecialAutomorphismGroup{N}) where N
|
|
||||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
|
||||||
end
|
|
||||||
@ -1,35 +0,0 @@
|
|||||||
struct CapraceGroup <: GAPGroup end
|
|
||||||
|
|
||||||
name(G::CapraceGroup) = "CapraceGroup"
|
|
||||||
|
|
||||||
function group(G::CapraceGroup)
|
|
||||||
|
|
||||||
caprace_group = Groups.FPGroup(["x","y","z","t","r"])
|
|
||||||
|
|
||||||
x,y,z,t,r = gens(caprace_group)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
x^7,
|
|
||||||
y^7,
|
|
||||||
t^2,
|
|
||||||
r^73,
|
|
||||||
t*r*t*r,
|
|
||||||
Comm(x,y)*z^-1,
|
|
||||||
Comm(x,z),
|
|
||||||
Comm(y,z),
|
|
||||||
Comm(x^2*y*z^-1, t),
|
|
||||||
Comm(x*y*z^3, t*r),
|
|
||||||
Comm(x^3*y*z^2, t*r^17),
|
|
||||||
Comm(x, t*r^-34),
|
|
||||||
Comm(y, t*r^-32),
|
|
||||||
Comm(z, t*r^-29),
|
|
||||||
Comm(x^-2*y*z, t*r^-25),
|
|
||||||
Comm(x^-1*y*z^-3, t*r^-19),
|
|
||||||
Comm(x^-3*y*z^-2, t*r^-11)
|
|
||||||
];
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
|
|
||||||
Groups.add_rels!(caprace_group, Dict(rel => caprace_group() for rel in relations))
|
|
||||||
return caprace_group
|
|
||||||
end
|
|
||||||
@ -1,22 +0,0 @@
|
|||||||
struct HigmanGroup <: GAPGroup end
|
|
||||||
|
|
||||||
name(G::HigmanGroup) = "HigmanGroup"
|
|
||||||
|
|
||||||
function group(G::HigmanGroup)
|
|
||||||
|
|
||||||
higman_group = Groups.FPGroup(["a","b","c","d"]);
|
|
||||||
|
|
||||||
a,b,c,d = gens(higman_group)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
b*Comm(b,a),
|
|
||||||
c*Comm(c,b),
|
|
||||||
d*Comm(d,c),
|
|
||||||
a*Comm(a,d)
|
|
||||||
];
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
|
|
||||||
Groups.add_rels!(higman_group, Dict(rel => higman_group() for rel in relations))
|
|
||||||
return higman_group
|
|
||||||
end
|
|
||||||
@ -1,83 +0,0 @@
|
|||||||
struct MappingClassGroup{N} <: GAPGroup end
|
|
||||||
|
|
||||||
MappingClassGroup(args::Dict) = MappingClassGroup{args["MCG"]}()
|
|
||||||
|
|
||||||
name(G::MappingClassGroup{N}) where N = "MCG(N)"
|
|
||||||
|
|
||||||
function group(G::MappingClassGroup{N}) where N
|
|
||||||
|
|
||||||
if N < 2
|
|
||||||
throw("Genus must be at least 2!")
|
|
||||||
elseif N == 2
|
|
||||||
MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
|
|
||||||
S = gens(MCGroup)
|
|
||||||
|
|
||||||
n = length(S)
|
|
||||||
A = prod(reverse(S))*prod(S)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
[Comm(S[i], S[j]) for i in 1:n for j in 1:n 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:G.n-1]...,
|
|
||||||
(S[1]*S[2]*S[3])^4*inv(S[5])^2,
|
|
||||||
Comm(A, S[1]),
|
|
||||||
A^2
|
|
||||||
]
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
|
|
||||||
return MCGroup
|
|
||||||
|
|
||||||
else
|
|
||||||
MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
|
|
||||||
S = gens(MCGroup)
|
|
||||||
|
|
||||||
a0 = S[1]
|
|
||||||
A = S[2:end]
|
|
||||||
k = length(A)
|
|
||||||
|
|
||||||
relations = [
|
|
||||||
[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
|
|
||||||
[Comm(a0, A[i]) for i in 1:k if i != 4]...,
|
|
||||||
[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
|
|
||||||
A[4]*a0*A[4]*inv(a0*A[4]*a0)
|
|
||||||
]
|
|
||||||
|
|
||||||
# 3-chain relation
|
|
||||||
c = prod(reverse(A[1:4]))*prod(A[1:4])
|
|
||||||
b0 = c*a0*inv(c)
|
|
||||||
push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
|
|
||||||
|
|
||||||
# Lantern relation
|
|
||||||
b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
|
|
||||||
b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
|
|
||||||
u = inv(A[6]*A[5])*b1*(A[6]*A[5])
|
|
||||||
x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
|
|
||||||
b3 = x*a0*inv(x)
|
|
||||||
push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
|
|
||||||
|
|
||||||
# Hyperelliptic relation
|
|
||||||
X = prod(reverse(A))*prod(A)
|
|
||||||
|
|
||||||
function n(i::Int, b=b0)
|
|
||||||
if i == 1
|
|
||||||
return A[1]
|
|
||||||
elseif i == 2
|
|
||||||
return b
|
|
||||||
else
|
|
||||||
return w(i-2)*n(i-2)*w(i-2)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function w(i::Int)
|
|
||||||
(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
|
|
||||||
(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
|
|
||||||
end
|
|
||||||
|
|
||||||
# push!(relations, X*n(N)*inv(n(N)*X))
|
|
||||||
|
|
||||||
relations = [relations; [inv(rel) for rel in relations]]
|
|
||||||
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
|
|
||||||
|
|
||||||
return MCGroup
|
|
||||||
end
|
|
||||||
end
|
|
||||||
@ -1,62 +0,0 @@
|
|||||||
struct SpecialLinearGroup{N} <: SymmetrizedGroup
|
|
||||||
group::AbstractAlgebra.Group
|
|
||||||
p::Int
|
|
||||||
X::Bool
|
|
||||||
end
|
|
||||||
|
|
||||||
function SpecialLinearGroup(args::Dict)
|
|
||||||
N = args["SL"]
|
|
||||||
p = args["p"]
|
|
||||||
X = args["X"]
|
|
||||||
|
|
||||||
if p == 0
|
|
||||||
G = MatrixSpace(Nemo.ZZ, N, N)
|
|
||||||
else
|
|
||||||
R = Nemo.NmodRing(UInt(p))
|
|
||||||
G = MatrixSpace(R, N, N)
|
|
||||||
end
|
|
||||||
return SpecialLinearGroup{N}(G, p, X)
|
|
||||||
end
|
|
||||||
|
|
||||||
function name(G::SpecialLinearGroup{N}) where N
|
|
||||||
if G.p == 0
|
|
||||||
R = (G.X ? "Z[x]" : "Z")
|
|
||||||
else
|
|
||||||
R = "F$(G.p)"
|
|
||||||
end
|
|
||||||
return SL($(G.N),$R)
|
|
||||||
end
|
|
||||||
|
|
||||||
group(G::SpecialLinearGroup) = G.group
|
|
||||||
|
|
||||||
function generatingset(G::SpecialLinearGroup{N}) where N
|
|
||||||
G.p > 0 && G.X && throw("SL(n, F_p[x]) not implemented")
|
|
||||||
SL = group(G)
|
|
||||||
return generatingset(SL, G.X)
|
|
||||||
end
|
|
||||||
|
|
||||||
# r is the injectivity radius of
|
|
||||||
# SL(n, Z[X]) -> SL(n, Z) induced by X -> 100
|
|
||||||
|
|
||||||
function generatingset(SL::MatSpace, X::Bool=false, r=5)
|
|
||||||
n = SL.cols
|
|
||||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
|
||||||
|
|
||||||
if !X
|
|
||||||
S = [E(idx[1],idx[2],SL) for idx in indexing]
|
|
||||||
else
|
|
||||||
S = [E(i,j,SL,v) for (i,j) in indexing for v in [1, 100*r]]
|
|
||||||
end
|
|
||||||
return unique([S; inv.(S)])
|
|
||||||
end
|
|
||||||
|
|
||||||
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 autS(G::SpecialLinearGroup{N}) where N
|
|
||||||
return WreathProduct(PermutationGroup(2), PermutationGroup(N))
|
|
||||||
end
|
|
||||||
58
logging.jl
58
logging.jl
@ -1,58 +0,0 @@
|
|||||||
using Memento
|
|
||||||
|
|
||||||
function setup_logging(filename::String, handlername::Symbol=:log)
|
|
||||||
isdir(dirname(filename)) || mkdir(dirname(filename))
|
|
||||||
logger = Memento.config!("info", fmt="{date}| {msg}")
|
|
||||||
handler = DefaultHandler(filename, DefaultFormatter("{date}| {msg}"))
|
|
||||||
logger.handlers[String(handlername)] = handler
|
|
||||||
return logger
|
|
||||||
end
|
|
||||||
|
|
||||||
macro logtime(logger, ex)
|
|
||||||
quote
|
|
||||||
local stats = Base.gc_num()
|
|
||||||
local elapsedtime = Base.time_ns()
|
|
||||||
local val = $(esc(ex))
|
|
||||||
elapsedtime = Base.time_ns() - elapsedtime
|
|
||||||
local diff = Base.GC_Diff(Base.gc_num(), stats)
|
|
||||||
local ts = time_string(elapsedtime,
|
|
||||||
diff.allocd,
|
|
||||||
diff.total_time,
|
|
||||||
Base.gc_alloc_count(diff)
|
|
||||||
)
|
|
||||||
$(esc(info))($(esc(logger)), ts)
|
|
||||||
val
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function time_string(elapsedtime, bytes, gctime, allocs)
|
|
||||||
str = @sprintf("%10.6f seconds", elapsedtime/1e9)
|
|
||||||
if bytes != 0 || allocs != 0
|
|
||||||
bytes, mb = Base.prettyprint_getunits(bytes, length(Base._mem_units), Int64(1024))
|
|
||||||
allocs, ma = Base.prettyprint_getunits(allocs, length(Base._cnt_units), Int64(1000))
|
|
||||||
if ma == 1
|
|
||||||
str*= @sprintf(" (%d%s allocation%s: ", allocs, Base._cnt_units[ma], allocs==1 ? "" : "s")
|
|
||||||
else
|
|
||||||
str*= @sprintf(" (%.2f%s allocations: ", allocs, Base._cnt_units[ma])
|
|
||||||
end
|
|
||||||
if mb == 1
|
|
||||||
str*= @sprintf("%d %s%s", bytes, Base._mem_units[mb], bytes==1 ? "" : "s")
|
|
||||||
else
|
|
||||||
str*= @sprintf("%.3f %s", bytes, Base._mem_units[mb])
|
|
||||||
end
|
|
||||||
if gctime > 0
|
|
||||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
|
||||||
end
|
|
||||||
str*=")"
|
|
||||||
elseif gctime > 0
|
|
||||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
|
||||||
end
|
|
||||||
return str
|
|
||||||
end
|
|
||||||
|
|
||||||
import Base: info, @time
|
|
||||||
|
|
||||||
Base.info(x) = info(getlogger(), x)
|
|
||||||
macro time(x)
|
|
||||||
return :(@logtime(getlogger(Main), $(esc(x))))
|
|
||||||
end
|
|
||||||
61
main.jl
61
main.jl
@ -1,61 +0,0 @@
|
|||||||
using PropertyT
|
|
||||||
|
|
||||||
include("FPGroups_GAP.jl")
|
|
||||||
|
|
||||||
include("groups/Allgroups.jl")
|
|
||||||
using PropertyTGroups
|
|
||||||
|
|
||||||
import PropertyT.Settings
|
|
||||||
|
|
||||||
function summarize(sett::PropertyT.Settings)
|
|
||||||
info("Threads: $(Threads.nthreads())")
|
|
||||||
info("Workers: $(workers())")
|
|
||||||
info("GroupDir: $(PropertyT.prepath(sett))")
|
|
||||||
info(string(sett.G))
|
|
||||||
info("with generating set of size $(length(sett.S))")
|
|
||||||
|
|
||||||
info("Radius: $(sett.radius)")
|
|
||||||
info("Precision: $(sett.tol)")
|
|
||||||
info("Upper bound: $(sett.upper_bound)")
|
|
||||||
info("Solver: $(sett.solver)")
|
|
||||||
end
|
|
||||||
|
|
||||||
function Settings(Gr::PropertyTGroup, args, solver)
|
|
||||||
r = get(args, "radius", 2)
|
|
||||||
gr_name = PropertyTGroups.name(Gr)*"_r$r"
|
|
||||||
G = PropertyTGroups.group(Gr)
|
|
||||||
S = PropertyTGroups.generatingset(Gr)
|
|
||||||
|
|
||||||
sol = solver
|
|
||||||
ub = get(args,"upper-bound", Inf)
|
|
||||||
tol = get(args,"tol", 1e-10)
|
|
||||||
ws = get(args, "warmstart", false)
|
|
||||||
|
|
||||||
if get(args, "nosymmetry", false)
|
|
||||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws)
|
|
||||||
else
|
|
||||||
autS = PropertyTGroups.autS(Gr)
|
|
||||||
return PropertyT.Settings(gr_name, G, S, r, sol, ub, tol, ws, autS)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function main(::PropertyTGroup, sett::PropertyT.Settings)
|
|
||||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
|
||||||
|
|
||||||
summarize(sett)
|
|
||||||
|
|
||||||
return PropertyT.check_property_T(sett)
|
|
||||||
end
|
|
||||||
|
|
||||||
function main(::GAPGroup, sett::PropertyT.Settings)
|
|
||||||
isdir(PropertyT.fullpath(sett)) || mkpath(PropertyT.fullpath(sett))
|
|
||||||
|
|
||||||
summarize(sett)
|
|
||||||
|
|
||||||
S = [s for s in sett.S if s.symbols[1].pow == 1]
|
|
||||||
relations = [k*inv(v) for (k,v) in sett.G.rels]
|
|
||||||
|
|
||||||
prepare_pm_delta(PropertyT.prepath(sett), GAP_groupcode(S, relations), sett.radius)
|
|
||||||
|
|
||||||
return PropertyT.check_property_T(sett)
|
|
||||||
end
|
|
||||||
@ -1,197 +0,0 @@
|
|||||||
using AbstractAlgebra
|
|
||||||
using Groups
|
|
||||||
using GroupRings
|
|
||||||
using PropertyT
|
|
||||||
|
|
||||||
using SCS
|
|
||||||
solver(tol, iterations) =
|
|
||||||
SCSSolver(linearsolver=SCS.Direct,
|
|
||||||
eps=tol, max_iters=iterations,
|
|
||||||
alpha=1.95, acceleration_lookback=1)
|
|
||||||
|
|
||||||
include("../main.jl")
|
|
||||||
|
|
||||||
using PropertyTGroups
|
|
||||||
|
|
||||||
args = Dict("SAut" => 5, "upper-bound" => 50.0, "radius" => 2, "nosymmetry"=>false, "tol"=>1e-12, "iterations" =>200000, "warmstart" => true)
|
|
||||||
|
|
||||||
Gr = PropertyTGroups.PropertyTGroup(args)
|
|
||||||
sett = PropertyT.Settings(Gr, args,
|
|
||||||
solver(args["tol"], args["iterations"]))
|
|
||||||
|
|
||||||
@show sett
|
|
||||||
|
|
||||||
fullpath = PropertyT.fullpath(sett)
|
|
||||||
isdir(fullpath) || mkpath(fullpath)
|
|
||||||
# setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
|
||||||
|
|
||||||
function small_generating_set(RG::GroupRing{AutGroup{N}}, n) where N
|
|
||||||
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
|
||||||
|
|
||||||
rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing]
|
|
||||||
lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing]
|
|
||||||
gen_set = RG.group.([rmuls; lmuls])
|
|
||||||
|
|
||||||
return [gen_set; inv.(gen_set)]
|
|
||||||
end
|
|
||||||
|
|
||||||
function computeX(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
Tn = small_generating_set(RG, N-1)
|
|
||||||
|
|
||||||
ℤ = Int64
|
|
||||||
Δn = length(Tn)*one(RG, ℤ) - RG(Tn, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
|
|
||||||
@time X = sum(σ(Δn)*sum(τ(Δn) for τ ∈ Alt_N if τ ≠ σ) for σ in Alt_N);
|
|
||||||
return X
|
|
||||||
end
|
|
||||||
|
|
||||||
function Sq(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
T2 = small_generating_set(RG, 2)
|
|
||||||
ℤ = Int64
|
|
||||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
elt = sum(σ(Δ₂)^2 for σ in Alt_N)
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
function Adj(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
T2 = small_generating_set(RG, 2)
|
|
||||||
|
|
||||||
ℤ = Int64
|
|
||||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
|
|
||||||
adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
|
|
||||||
adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 1]
|
|
||||||
|
|
||||||
@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
|
|
||||||
# return RG(elt.coeffs÷factorial(N-2)^2)
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
function Op(RG::GroupRing{AutGroup{N}}) where N
|
|
||||||
T2 = small_generating_set(RG, 2)
|
|
||||||
|
|
||||||
ℤ = Int64
|
|
||||||
Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ);
|
|
||||||
|
|
||||||
Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0]
|
|
||||||
|
|
||||||
adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]])
|
|
||||||
adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 0]
|
|
||||||
|
|
||||||
@time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N);
|
|
||||||
# return RG(elt.coeffs÷factorial(N-2)^2)
|
|
||||||
return elt
|
|
||||||
end
|
|
||||||
|
|
||||||
const ELT_FILE = joinpath(dirname(PropertyT.filename(sett, :Δ)), "SqAdjOp_coeffs.jld")
|
|
||||||
const WARMSTART_FILE = PropertyT.filename(sett, :warmstart)
|
|
||||||
|
|
||||||
if isfile(PropertyT.filename(sett,:Δ)) && isfile(ELT_FILE) &&
|
|
||||||
isfile(PropertyT.filename(sett, :OrbitData))
|
|
||||||
# cached
|
|
||||||
Δ = PropertyT.loadGRElem(PropertyT.filename(sett,:Δ), sett.G)
|
|
||||||
RG = parent(Δ)
|
|
||||||
orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
|
|
||||||
sq_c, adj_c, op_c = load(ELT_FILE, "Sq", "Adj", "Op")
|
|
||||||
# elt = ELT_FILE, sett.G)
|
|
||||||
sq = GroupRingElem(sq_c, RG)
|
|
||||||
adj = GroupRingElem(adj_c, RG)
|
|
||||||
op = GroupRingElem(op_c, RG);
|
|
||||||
else
|
|
||||||
info("Compute Laplacian")
|
|
||||||
Δ = PropertyT.Laplacian(sett.S, sett.radius)
|
|
||||||
RG = parent(Δ)
|
|
||||||
|
|
||||||
info("Compute Sq, Adj, Op")
|
|
||||||
@time sq, adj, op = Sq(RG), Adj(RG), Op(RG)
|
|
||||||
|
|
||||||
PropertyT.saveGRElem(PropertyT.filename(sett, :Δ), Δ)
|
|
||||||
save(ELT_FILE, "Sq", sq.coeffs, "Adj", adj.coeffs, "Op", op.coeffs)
|
|
||||||
|
|
||||||
info("Compute OrbitData")
|
|
||||||
if !isfile(PropertyT.filename(sett, :OrbitData))
|
|
||||||
orbit_data = PropertyT.OrbitData(parent(Y), sett.autS)
|
|
||||||
save(PropertyT.filename(sett, :OrbitData), "OrbitData", orbit_data)
|
|
||||||
else
|
|
||||||
orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData")
|
|
||||||
end
|
|
||||||
end;
|
|
||||||
|
|
||||||
orbit_data = PropertyT.decimate(orbit_data);
|
|
||||||
|
|
||||||
elt = adj+2op;
|
|
||||||
|
|
||||||
const SOLUTION_FILE = PropertyT.filename(sett, :solution)
|
|
||||||
|
|
||||||
if !isfile(SOLUTION_FILE)
|
|
||||||
|
|
||||||
SDP_problem, varλ, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=sett.upper_bound)
|
|
||||||
|
|
||||||
begin
|
|
||||||
using SCS
|
|
||||||
scs_solver = SCS.SCSSolver(linearsolver=SCS.Direct,
|
|
||||||
eps=sett.tol,
|
|
||||||
max_iters=args["iterations"],
|
|
||||||
alpha=1.95,
|
|
||||||
acceleration_lookback=1)
|
|
||||||
|
|
||||||
JuMP.setsolver(SDP_problem, scs_solver)
|
|
||||||
end
|
|
||||||
|
|
||||||
λ = Ps = nothing
|
|
||||||
ws = PropertyT.warmstart(sett)
|
|
||||||
|
|
||||||
# using ProgressMeter
|
|
||||||
|
|
||||||
# @showprogress "Running SDP optimization step... " for i in 1:args["repetitions"]
|
|
||||||
while true
|
|
||||||
λ, Ps, ws = PropertyT.solve(PropertyT.filename(sett, :solverlog),
|
|
||||||
SDP_problem, varλ, varP, ws);
|
|
||||||
|
|
||||||
if all((!isnan).(ws[1]))
|
|
||||||
save(WARMSTART_FILE, "warmstart", ws, "λ", λ, "Ps", Ps)
|
|
||||||
save(WARMSTART_FILE[1:end-4]*"_$(now()).jld", "warmstart", ws, "λ", λ, "Ps", Ps)
|
|
||||||
else
|
|
||||||
warn("No valid solution was saved!")
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
info("Reconstructing P...")
|
|
||||||
@time P = PropertyT.reconstruct(Ps, orbit_data);
|
|
||||||
save(SOLUTION_FILE, "λ", λ, "P", P)
|
|
||||||
end
|
|
||||||
|
|
||||||
P, λ = load(SOLUTION_FILE, "P", "λ")
|
|
||||||
@show λ;
|
|
||||||
|
|
||||||
@time const Q = real(sqrtm(P));
|
|
||||||
|
|
||||||
function SOS_residual(eoi::GroupRingElem, Q::Matrix)
|
|
||||||
RG = parent(eoi)
|
|
||||||
@time sos = PropertyT.compute_SOS(RG, Q);
|
|
||||||
return eoi - sos
|
|
||||||
end
|
|
||||||
|
|
||||||
info("Floating Point arithmetic:")
|
|
||||||
EOI = elt - λ*Δ
|
|
||||||
b = SOS_residual(EOI, Q)
|
|
||||||
@show norm(b, 1);
|
|
||||||
|
|
||||||
info("Interval arithmetic:")
|
|
||||||
using IntervalArithmetic
|
|
||||||
Qint = PropertyT.augIdproj(Q);
|
|
||||||
@assert all([zero(eltype(Q)) in sum(view(Qint, :, i)) for i in 1:size(Qint, 2)])
|
|
||||||
|
|
||||||
EOI_int = elt - @interval(λ)*Δ;
|
|
||||||
Q_int = PropertyT.augIdproj(Q);
|
|
||||||
@assert all([zero(eltype(Q)) in sum(view(Q_int, :, i)) for i in 1:size(Q_int, 2)])
|
|
||||||
b_int = SOS_residual(EOI_int, Q_int)
|
|
||||||
@show norm(b_int, 1);
|
|
||||||
|
|
||||||
info("λ is certified to be > ", (@interval(λ) - 2^2*norm(b_int,1)).lo)
|
|
||||||
108
run.jl
108
run.jl
@ -1,108 +0,0 @@
|
|||||||
using ArgParse
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Parsing command line
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
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"
|
|
||||||
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
|
|
||||||
"--radius"
|
|
||||||
help = "Radius of ball B_r(e,S) to find solution over"
|
|
||||||
arg_type = Int
|
|
||||||
default = 2
|
|
||||||
"--warmstart"
|
|
||||||
help = "Use warmstart.jld as the initial guess for SCS"
|
|
||||||
action = :store_true
|
|
||||||
"--nosymmetry"
|
|
||||||
help = "Don't use symmetries of the Laplacian"
|
|
||||||
action = :store_true
|
|
||||||
|
|
||||||
"--SL "
|
|
||||||
help = "GROUP: the group generated by elementary matrices of size n by n"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
"-p"
|
|
||||||
help = "Matrices over field of p-elements (p=0 => over ZZ) [only with --SL]"
|
|
||||||
arg_type = Int
|
|
||||||
default = 0
|
|
||||||
"-X"
|
|
||||||
help = "Consider EL(N, ZZ⟨X⟩) [only with --SL]"
|
|
||||||
action = :store_true
|
|
||||||
|
|
||||||
"--SAut"
|
|
||||||
help = "GROUP: the automorphisms group of the free group on N generators"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
|
|
||||||
"--MCG"
|
|
||||||
help = "GROUP: mapping class group of surface of genus N"
|
|
||||||
arg_type = Int
|
|
||||||
required = false
|
|
||||||
|
|
||||||
"--Higman"
|
|
||||||
help = "GROUP: the Higman Group"
|
|
||||||
action = :store_true
|
|
||||||
|
|
||||||
"--Caprace"
|
|
||||||
help = "GROUP: for Caprace Group"
|
|
||||||
action = :store_true
|
|
||||||
end
|
|
||||||
return parse_args(settings)
|
|
||||||
end
|
|
||||||
|
|
||||||
const PARSEDARGS = parse_commandline()
|
|
||||||
|
|
||||||
set_parallel_mthread(PARSEDARGS, workers=false)
|
|
||||||
|
|
||||||
include("CPUselect.jl")
|
|
||||||
include("logging.jl")
|
|
||||||
include("main.jl")
|
|
||||||
|
|
||||||
using SCS.SCSSolver
|
|
||||||
# using Mosek
|
|
||||||
# using CSDP
|
|
||||||
# using SDPA
|
|
||||||
|
|
||||||
solver(tol, iterations) =
|
|
||||||
SCSSolver(linearsolver=SCS.Direct,
|
|
||||||
eps=tol, max_iters=iterations,
|
|
||||||
alpha=1.95, acceleration_lookback=1)
|
|
||||||
|
|
||||||
# Mosek.MosekSolver(
|
|
||||||
# MSK_DPAR_INTPNT_CO_TOL_REL_GAP=tol,
|
|
||||||
# MSK_IPAR_INTPNT_MAX_ITERATIONS=iterations,
|
|
||||||
# QUIET=false)
|
|
||||||
|
|
||||||
# CSDP.CSDPSolver(axtol=tol, atytol=tol, objtol=tol, minstepp=tol*10.0^-1, minstepd=tol*10.0^-1)
|
|
||||||
|
|
||||||
# SDPA.SDPASolver(epsilonStar=tol, epsilonDash=tol)
|
|
||||||
|
|
||||||
const Gr = PropertyTGroups.PropertyTGroup(PARSEDARGS)
|
|
||||||
const sett = PropertyT.Settings(Gr, PARSEDARGS,
|
|
||||||
solver(PARSEDARGS["tol"], PARSEDARGS["iterations"]))
|
|
||||||
|
|
||||||
fullpath = PropertyT.fullpath(sett)
|
|
||||||
isdir(fullpath) || mkpath(fullpath)
|
|
||||||
setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog)
|
|
||||||
|
|
||||||
main(Gr, sett)
|
|
||||||
222
runtests.jl
222
runtests.jl
@ -1,222 +0,0 @@
|
|||||||
using Base.Test
|
|
||||||
|
|
||||||
include("main.jl")
|
|
||||||
|
|
||||||
testdir = "tests_"*string(now())
|
|
||||||
mkdir(testdir)
|
|
||||||
include("logging.jl")
|
|
||||||
logger=setup_logging(joinpath(testdir, "tests.log"))
|
|
||||||
info(testdir)
|
|
||||||
|
|
||||||
cd(testdir)
|
|
||||||
|
|
||||||
# groupname = name(G)
|
|
||||||
# ub = PARSEDARGS["upper-bound"]
|
|
||||||
#
|
|
||||||
# fullpath = joinpath(groupname, string(ub))
|
|
||||||
# isdir(fullpath) || mkpath(fullpath)
|
|
||||||
|
|
||||||
separator(n=60) = info("\n"*("\n"*"="^n*"\n"^3)*"\n")
|
|
||||||
|
|
||||||
|
|
||||||
function SL_tests(args)
|
|
||||||
|
|
||||||
|
|
||||||
args["SL"] = 2
|
|
||||||
args["p"] = 3
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == true
|
|
||||||
separator()
|
|
||||||
|
|
||||||
let args = args
|
|
||||||
args["SL"] = 2
|
|
||||||
args["p"] = 5
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["warmstart"] = true
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["upper-bound"] = 0.1
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == true
|
|
||||||
separator()
|
|
||||||
end
|
|
||||||
|
|
||||||
args["SL"] = 2
|
|
||||||
args["p"] = 7
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["SL"] = 3
|
|
||||||
args["p"] = 7
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == true
|
|
||||||
separator()
|
|
||||||
|
|
||||||
# begin
|
|
||||||
# args["iterations"] = 25000
|
|
||||||
# args["N"] = 3
|
|
||||||
# args["p"] = 0
|
|
||||||
# args["upper-bound"] = Inf
|
|
||||||
#
|
|
||||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
# @test main(G) == false
|
|
||||||
# separator()
|
|
||||||
#
|
|
||||||
# args["warmstart"] = false
|
|
||||||
# args["upper-bound"] = 0.27
|
|
||||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
# @test main(G) == false
|
|
||||||
# separator()
|
|
||||||
#
|
|
||||||
# args["warmstart"] = true
|
|
||||||
# G = PropertyTGroups.SpecialLinearGroup(args)
|
|
||||||
# @test main(G) == true
|
|
||||||
# separator()
|
|
||||||
# end
|
|
||||||
|
|
||||||
return 0
|
|
||||||
end
|
|
||||||
|
|
||||||
function SAut_tests(args)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["warmstart"] = true
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
args["upper-bound"] = 0.1
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
separator()
|
|
||||||
|
|
||||||
return 0
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "Groups with(out) (T)" begin
|
|
||||||
|
|
||||||
@testset "GAPGroups" begin
|
|
||||||
args = Dict(
|
|
||||||
"Higman" => true,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"Caprace" => true,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"MCG" => 3,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
G = PropertyTGroup(args)
|
|
||||||
@test main(G) == false
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "SLn's" begin
|
|
||||||
@testset "Non-Symmetrized" begin
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"SL" => 2,
|
|
||||||
"p" => 3,
|
|
||||||
"X" => false,
|
|
||||||
"iterations"=>50000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
|
|
||||||
SL_tests(args)
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "Symmetrized" begin
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"SL" => 2,
|
|
||||||
"p" => 3,
|
|
||||||
"X" => false,
|
|
||||||
"iterations"=>20000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>false,
|
|
||||||
)
|
|
||||||
|
|
||||||
SL_tests(args)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "SAutF_n's" begin
|
|
||||||
|
|
||||||
@testset "Non-Symmetrized" begin
|
|
||||||
|
|
||||||
args = Dict(
|
|
||||||
"SAut" => 2,
|
|
||||||
"iterations"=>5000,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>true,
|
|
||||||
)
|
|
||||||
SAut_tests(args)
|
|
||||||
end
|
|
||||||
|
|
||||||
@testset "Symmetrized" begin
|
|
||||||
args = Dict(
|
|
||||||
"SAut" => 3,
|
|
||||||
"iterations"=>500,
|
|
||||||
"tol"=>1e-7,
|
|
||||||
"upper-bound"=>Inf,
|
|
||||||
"cpus"=>2,
|
|
||||||
"radius"=>2,
|
|
||||||
"warmstart"=>false,
|
|
||||||
"nosymmetry"=>false,
|
|
||||||
)
|
|
||||||
SAut_tests(args)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
|
|
||||||
end
|
|
||||||
Loading…
Reference in New Issue
Block a user