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update/add scripts for SLNZ/SAutFn

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Marek Kaluba 2024-02-19 18:45:02 +01:00
parent f584df4c8d
commit 01ae87b4da
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3 changed files with 205 additions and 10 deletions

100
scripts/SAutFN_has_T.jl Normal file
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@ -0,0 +1,100 @@
using LinearAlgebra
BLAS.set_num_threads(4)
ENV["OMP_NUM_THREADS"] = 4
include(joinpath(@__DIR__, "../test/optimizers.jl"))
using SCS_MKL_jll
using Groups
import Groups.MatrixGroups
using PropertyT
import PropertyT.SW as SW
using PropertyT.PG
using PropertyT.SA
include(joinpath(@__DIR__, "argparse.jl"))
const N = parsed_args["N"]
const HALFRADIUS = parsed_args["halfradius"]
const UPPER_BOUND = parsed_args["upper_bound"]
G = SpecialAutomorphismGroup(FreeGroup(N))
@info "Running Δ² - λ·Δ sum of squares decomposition for " G
@info "computing group algebra structure"
RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
@info "computing WedderburnDecomposition"
wd = let RG = RG, N = N
G = StarAlgebras.object(RG)
P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
act = PropertyT.action_by_conjugation(G, Σ)
wdfl = @time SW.WedderburnDecomposition(
Float64,
Σ,
act,
basis(RG),
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
)
end
@info wd
Δ = RG(length(S)) - sum(RG(s) for s in S)
elt = Δ^2;
unit = Δ;
warm = nothing
@info "defining optimization problem"
@time model, varP = PropertyT.sos_problem_primal(
elt,
unit,
wd;
upper_bound = UPPER_BOUND,
augmented = true,
show_progress = true,
)
let status = JuMP.OPTIMIZE_NOT_CALLED, warm = warm, eps = 1e-10
certified, λ = false, 0.0
while status JuMP.OPTIMAL
@time status, warm = PropertyT.solve(
model,
scs_optimizer(;
linear_solver = SCS.MKLDirectSolver,
eps = eps,
max_iters = N * 10_000,
accel = 50,
alpha = 1.95,
),
warm,
)
@info "reconstructing the solution"
Q = @time let wd = wd, Ps = [JuMP.value.(P) for P in varP], eps = 1e-10
PropertyT.__droptol!.(Ps, 100eps)
Qs = real.(sqrt.(Ps))
PropertyT.__droptol!.(Qs, eps)
PropertyT.reconstruct(Qs, wd)
end
@info "certifying the solution"
certified, λ = PropertyT.certify_solution(
elt,
unit,
JuMP.objective_value(model),
Q;
halfradius = HALFRADIUS,
augmented = true,
)
end
if certified && λ > 0
Κ(λ, S) = round(sqrt(2λ / length(S)), Base.RoundDown; digits = 5)
@info "Certified result: $G has property (T):" N λ Κ(λ, S)
else
@info "Could NOT certify the result:" certified λ
end
end

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@ -1,18 +1,17 @@
using LinearAlgebra
using MKL_jll
BLAS.set_num_threads(4)
ENV["OMP_NUM_THREADS"] = 4
include(joinpath(@__DIR__, "../test/optimizers.jl"))
using SCS_MKL_jll
using Groups
import Groups.MatrixGroups
include(joinpath(@__DIR__, "../test/optimizers.jl"))
using PropertyT
using PropertyT.SymbolicWedderburn
using PropertyT.PermutationGroups
using PropertyT.StarAlgebras
import PropertyT.SW as SW
using PropertyT.PG
using PropertyT.SA
include(joinpath(@__DIR__, "argparse.jl"))
@ -33,7 +32,7 @@ wd = let RG = RG, N = N
Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
act = PropertyT.action_by_conjugation(G, Σ)
wdfl = @time SymbolicWedderburn.WedderburnDecomposition(
wdfl = @time SW.WedderburnDecomposition(
Float64,
Σ,
act,
@ -61,9 +60,9 @@ begin
model,
scs_optimizer(;
linear_solver = SCS.MKLDirectSolver,
eps = 1e-10,
max_iters = 20_000,
accel = 50,
eps = 1e-9,
max_iters = 30_000,
accel = -50,
alpha = 1.95,
),
warm,

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scripts/SLn_Adj.jl Normal file
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using LinearAlgebra
BLAS.set_num_threads(4)
ENV["OMP_NUM_THREADS"] = 4
include(joinpath(@__DIR__, "../test/optimizers.jl"))
using SCS_MKL_jll
using Groups
import Groups.MatrixGroups
using PropertyT
import PropertyT.SW as SW
using PropertyT.PG
using PropertyT.SA
include(joinpath(@__DIR__, "argparse.jl"))
const N = parsed_args["N"]
const HALFRADIUS = parsed_args["halfradius"]
const UPPER_BOUND = parsed_args["upper_bound"]
G = MatrixGroups.SpecialLinearGroup{N}(Int8)
@info "Running Adj - λ·Δ sum of squares decomposition for " G
@info "computing group algebra structure"
RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
@info "computing WedderburnDecomposition"
wd = let RG = RG, N = N
G = StarAlgebras.object(RG)
P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
act = PropertyT.action_by_conjugation(G, Σ)
wdfl = @time SW.WedderburnDecomposition(
Float64,
Σ,
act,
basis(RG),
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
)
end
@info wd
Δ = RG(length(S)) - sum(RG(s) for s in S)
Δs = let ψ = identity
PropertyT.laplacians(RG, S, x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])))
end
elt = PropertyT.Adj(Δs, :A₂)
unit = Δ
warm = nothing
@info "defining optimization problem"
@time model, varP = PropertyT.sos_problem_primal(
elt,
unit,
wd;
upper_bound = UPPER_BOUND,
augmented = true,
)
begin
@time status, warm = PropertyT.solve(
model,
scs_optimizer(;
eps = 1e-10,
max_iters = 20_000,
accel = 50,
alpha = 1.95,
),
warm,
)
@info "reconstructing the solution"
Q = let wd = wd, Ps = [JuMP.value.(P) for P in varP]
Qs = real.(sqrt.(Ps))
PropertyT.reconstruct(Qs, wd)
end
@info "certifying the solution"
@time certified, λ = PropertyT.certify_solution(
elt,
unit,
JuMP.objective_value(model),
Q;
halfradius = HALFRADIUS,
augmented = true,
)
end
if certified && λ > 0
Κ(λ, S) = round(sqrt(2λ / length(S)), Base.RoundDown; digits = 5)
@info "Certified result: $G has property (T):" N λ Κ(λ, S)
else
@info "Could NOT certify the result:" certified λ
end